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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Principles" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Principles"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Principles</span> </div> </a> <button aria-controls="toc-Principles-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Principles subsection</span> </button> <ul id="toc-Principles-sublist" class="vector-toc-list"> <li id="toc-Ideal_transformer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ideal_transformer"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Ideal transformer</span> </div> </a> <ul id="toc-Ideal_transformer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Real_transformer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Real_transformer"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Real transformer</span> </div> </a> <ul id="toc-Real_transformer-sublist" class="vector-toc-list"> <li id="toc-Deviations_from_ideal_transformer" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Deviations_from_ideal_transformer"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Deviations from ideal transformer</span> </div> </a> <ul id="toc-Deviations_from_ideal_transformer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Leakage_flux" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Leakage_flux"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Leakage flux</span> </div> </a> <ul id="toc-Leakage_flux-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equivalent_circuit" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Equivalent_circuit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.3</span> <span>Equivalent circuit</span> </div> </a> <ul id="toc-Equivalent_circuit-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Transformer_EMF_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transformer_EMF_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Transformer EMF equation</span> </div> </a> <ul id="toc-Transformer_EMF_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polarity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polarity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Polarity</span> </div> </a> <ul id="toc-Polarity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effect_of_frequency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effect_of_frequency"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Effect of frequency</span> </div> </a> <ul id="toc-Effect_of_frequency-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energy_losses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_losses"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Energy losses</span> </div> </a> <ul id="toc-Energy_losses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Construction" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Construction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Construction</span> </div> </a> <button aria-controls="toc-Construction-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Construction subsection</span> </button> <ul id="toc-Construction-sublist" class="vector-toc-list"> <li id="toc-Cores" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cores"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Cores</span> </div> </a> <ul id="toc-Cores-sublist" class="vector-toc-list"> <li id="toc-Laminated_steel_cores" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Laminated_steel_cores"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Laminated steel cores</span> </div> </a> <ul id="toc-Laminated_steel_cores-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solid_cores" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solid_cores"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Solid cores</span> </div> </a> <ul id="toc-Solid_cores-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Toroidal_cores" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Toroidal_cores"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3</span> <span>Toroidal cores</span> </div> </a> <ul id="toc-Toroidal_cores-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Air_cores" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Air_cores"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.4</span> <span>Air cores</span> </div> </a> <ul id="toc-Air_cores-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Windings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Windings"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Windings</span> </div> </a> <ul id="toc-Windings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cooling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cooling"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Cooling</span> </div> </a> <ul id="toc-Cooling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Insulation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Insulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Insulation</span> </div> </a> <ul id="toc-Insulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bushings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bushings"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Bushings</span> </div> </a> <ul id="toc-Bushings-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Classification_parameters" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Classification_parameters"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Classification parameters</span> </div> </a> <ul id="toc-Classification_parameters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Discovery_of_induction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discovery_of_induction"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Discovery of induction</span> </div> </a> <ul id="toc-Discovery_of_induction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Induction_coils" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Induction_coils"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Induction coils</span> </div> </a> <ul id="toc-Induction_coils-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-First_alternating_current_transformers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#First_alternating_current_transformers"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>First alternating current transformers</span> </div> </a> <ul id="toc-First_alternating_current_transformers-sublist" class="vector-toc-list"> <li id="toc-Early_series_circuit_transformer_distribution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Early_series_circuit_transformer_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.1</span> <span>Early series circuit transformer distribution</span> </div> </a> <ul id="toc-Early_series_circuit_transformer_distribution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Closed-core_transformers_and_parallel_power_distribution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Closed-core_transformers_and_parallel_power_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Closed-core transformers and parallel power distribution</span> </div> </a> <ul id="toc-Closed-core_transformers_and_parallel_power_distribution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Westinghouse_improvements" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Westinghouse_improvements"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Westinghouse improvements</span> </div> </a> <ul id="toc-Westinghouse_improvements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_early_transformer_designs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_early_transformer_designs"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Other early transformer designs</span> </div> </a> <ul id="toc-Other_early_transformer_designs-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Transformer</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 110 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-110" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">110 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Transformator" title="Transformator – Afrikaans" lang="af" hreflang="af" data-title="Transformator" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Transformator" title="Transformator – Alemannic" lang="gsw" hreflang="gsw" data-title="Transformator" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D9%88%D9%84" title="محول – Arabic" lang="ar" hreflang="ar" data-title="محول" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Transformador" title="Transformador – Aragonese" lang="an" hreflang="an" data-title="Transformador" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Tresformador" title="Tresformador – Asturian" lang="ast" hreflang="ast" data-title="Tresformador" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Transformator" title="Transformator – Azerbaijani" lang="az" hreflang="az" data-title="Transformator" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AA%D8%B1%D8%A7%D9%86%D8%B3%D9%81%D9%88%D8%B1%D9%85%D8%A7%D8%AA%D9%88%D8%B1" title="ترانسفورماتور – South Azerbaijani" lang="azb" hreflang="azb" data-title="ترانسفورماتور" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A7%82%E0%A6%AA%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0%E0%A6%95" title="রূপান্তরক – Bangla" lang="bn" hreflang="bn" data-title="রূপান্তরক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Pi%C3%A0n-ap-kh%C3%AC" title="Piàn-ap-khì – Minnan" lang="nan" hreflang="nan" data-title="Piàn-ap-khì" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Bashkir" lang="ba" hreflang="ba" data-title="Трансформатор" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%B0%D1%80%D0%BC%D0%B0%D1%82%D0%B0%D1%80" title="Трансфарматар – Belarusian" lang="be" hreflang="be" data-title="Трансфарматар" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%B0%D1%80%D0%BC%D0%B0%D1%82%D0%B0%D1%80" title="Трансфарматар – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Трансфарматар" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Bulgarian" lang="bg" hreflang="bg" data-title="Трансформатор" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Traunsfoamatoa" title="Traunsfoamatoa – Bavarian" lang="bar" hreflang="bar" data-title="Traunsfoamatoa" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Transformator" title="Transformator – Bosnian" lang="bs" hreflang="bs" data-title="Transformator" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Transformador" title="Transformador – Catalan" lang="ca" hreflang="ca" data-title="Transformador" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Transform%C3%A1tor" title="Transformátor – Czech" lang="cs" hreflang="cs" data-title="Transformátor" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Trasfurmadore" title="Trasfurmadore – Corsican" lang="co" hreflang="co" data-title="Trasfurmadore" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Newidydd" title="Newidydd – Welsh" lang="cy" hreflang="cy" data-title="Newidydd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Transformator" title="Transformator – Danish" lang="da" hreflang="da" data-title="Transformator" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://de.wikipedia.org/wiki/Transformator" title="Transformator – German" lang="de" hreflang="de" data-title="Transformator" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Transformaator" title="Transformaator – Estonian" lang="et" hreflang="et" data-title="Transformaator" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B5%CF%84%CE%B1%CF%83%CF%87%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CF%83%CF%84%CE%AE%CF%82" title="Μετασχηματιστής – Greek" lang="el" hreflang="el" data-title="Μετασχηματιστής" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Transformador" title="Transformador – Spanish" lang="es" hreflang="es" data-title="Transformador" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Transformatoro" title="Transformatoro – Esperanto" lang="eo" hreflang="eo" data-title="Transformatoro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Transformadore" title="Transformadore – Basque" lang="eu" hreflang="eu" data-title="Transformadore" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B1%D8%A7%D9%86%D8%B3%D9%81%D9%88%D8%B1%D9%85%D8%A7%D8%AA%D9%88%D8%B1" title="ترانسفورماتور – Persian" lang="fa" hreflang="fa" data-title="ترانسفورماتور" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Transformer" title="Transformer – Fiji Hindi" lang="hif" hreflang="hif" data-title="Transformer" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Transformateur_%C3%A9lectrique" title="Transformateur électrique – French" lang="fr" hreflang="fr" data-title="Transformateur électrique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Trasfhoirmeoir" title="Trasfhoirmeoir – Irish" lang="ga" hreflang="ga" data-title="Trasfhoirmeoir" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Transformador" title="Transformador – Galician" lang="gl" hreflang="gl" data-title="Transformador" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%80%EC%95%95%EA%B8%B0" title="변압기 – Korean" lang="ko" hreflang="ko" data-title="변압기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D6%80%D5%A1%D5%B6%D5%BD%D6%86%D5%B8%D6%80%D5%B4%D5%A1%D5%BF%D5%B8%D6%80" title="Տրանսֆորմատոր – Armenian" lang="hy" hreflang="hy" data-title="Տրանսֆորմատոր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%81%E0%A4%B8%E0%A4%AB%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%AE%E0%A4%B0" title="ट्राँसफार्मर – Hindi" lang="hi" hreflang="hi" data-title="ट्राँसफार्मर" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Transformator" title="Transformator – Croatian" lang="hr" hreflang="hr" data-title="Transformator" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Transformatoro" title="Transformatoro – Ido" lang="io" hreflang="io" data-title="Transformatoro" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Transformator" title="Transformator – Indonesian" lang="id" hreflang="id" data-title="Transformator" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Transformator" title="Transformator – Interlingua" lang="ia" hreflang="ia" data-title="Transformator" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/I-transformer" title="I-transformer – Zulu" lang="zu" hreflang="zu" data-title="I-transformer" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Spennubreytir" title="Spennubreytir – Icelandic" lang="is" hreflang="is" data-title="Spennubreytir" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Trasformatore" title="Trasformatore – Italian" lang="it" hreflang="it" data-title="Trasformatore" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%A0%D7%90%D7%99" title="שנאי – Hebrew" lang="he" hreflang="he" data-title="שנאי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Transformator" title="Transformator – Javanese" lang="jv" hreflang="jv" data-title="Transformator" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%A6%E0%B3%8D%E0%B2%AF%E0%B3%81%E0%B2%A4%E0%B3%8D_%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%B5%E0%B2%B0%E0%B3%8D%E0%B2%A4%E0%B2%95" title="ವಿದ್ಯುತ್ ಪರಿವರ್ತಕ – Kannada" lang="kn" hreflang="kn" data-title="ವಿದ್ಯುತ್ ಪರಿವರ್ತಕ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%90%E1%83%9C%E1%83%A1%E1%83%A4%E1%83%9D%E1%83%A0%E1%83%9B%E1%83%90%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98" title="ტრანსფორმატორი – Georgian" lang="ka" hreflang="ka" data-title="ტრანსფორმატორი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Kazakh" lang="kk" hreflang="kk" data-title="Трансформатор" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Transfoma" title="Transfoma – Swahili" lang="sw" hreflang="sw" data-title="Transfoma" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Transf%C3%B2mat%C3%A8_elektrik" title="Transfòmatè elektrik – Haitian Creole" lang="ht" hreflang="ht" data-title="Transfòmatè elektrik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Kyrgyz" lang="ky" hreflang="ky" data-title="Трансформатор" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Transformatrum" title="Transformatrum – Latin" lang="la" hreflang="la" data-title="Transformatrum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Transformators" title="Transformators – Latvian" lang="lv" hreflang="lv" data-title="Transformators" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Transformatorius" title="Transformatorius – Lithuanian" lang="lt" hreflang="lt" data-title="Transformatorius" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Trasformator" title="Trasformator – Lombard" lang="lmo" hreflang="lmo" data-title="Trasformator" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Transzform%C3%A1tor" title="Transzformátor – Hungarian" lang="hu" hreflang="hu" data-title="Transzformátor" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Macedonian" lang="mk" hreflang="mk" data-title="Трансформатор" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Mpanova_(haikoriam-boanaratra)" title="Mpanova (haikoriam-boanaratra) – Malagasy" lang="mg" hreflang="mg" data-title="Mpanova (haikoriam-boanaratra)" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9F%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B5%BB%E0%B4%B8%E0%B5%8D%E0%B4%AB%E0%B5%8B%E0%B5%BC%E0%B4%AE%E0%B5%BC" title="ട്രാൻസ്ഫോർമർ – Malayalam" lang="ml" hreflang="ml" data-title="ട്രാൻസ്ഫോർമർ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%B0%E0%A5%8B%E0%A4%B9%E0%A4%BF%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="विद्युत रोहित्र – Marathi" lang="mr" hreflang="mr" data-title="विद्युत रोहित्र" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Alatubah" title="Alatubah – Malay" lang="ms" hreflang="ms" data-title="Alatubah" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Mongolian" lang="mn" hreflang="mn" data-title="Трансформатор" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9C%E1%80%BB%E1%80%BE%E1%80%95%E1%80%BA%E1%80%90%E1%80%AC%E1%80%95%E1%80%BC%E1%80%B1%E1%80%AC%E1%80%84%E1%80%BA%E1%80%B8" title="လျှပ်တာပြောင်း – Burmese" lang="my" hreflang="my" data-title="လျှပ်တာပြောင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Transformator" title="Transformator – Dutch" lang="nl" hreflang="nl" data-title="Transformator" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%B8%E0%A4%AB%E0%A4%B0%E0%A5%8D%E0%A4%AE%E0%A4%B0" title="ट्रान्सफर्मर – Nepali" lang="ne" hreflang="ne" data-title="ट्रान्सफर्मर" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%B8%E0%A4%AB%E0%A4%B0%E0%A5%8D%E0%A4%AE%E0%A4%B0" title="त्रान्सफर्मर – Newari" lang="new" hreflang="new" data-title="त्रान्सफर्मर" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%89%E5%9C%A7%E5%99%A8" title="変圧器 – Japanese" lang="ja" hreflang="ja" data-title="変圧器" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Chechen" lang="ce" hreflang="ce" data-title="Трансформатор" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Transformaator" title="Transformaator – Northern Frisian" lang="frr" hreflang="frr" data-title="Transformaator" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://no.wikipedia.org/wiki/Transformator" title="Transformator – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Transformator" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Transformator" title="Transformator – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Transformator" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Transformador" title="Transformador – Occitan" lang="oc" hreflang="oc" data-title="Transformador" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%9F%E0%AD%8D%E0%AC%B0%E0%AC%BE%E0%AC%A8%E0%AD%8D%E0%AC%B8%E0%AC%AB%E0%AC%B0%E0%AD%8D%E0%AC%AE%E0%AC%B0" title="ଟ୍ରାନ୍ସଫର୍ମର – Odia" lang="or" hreflang="or" data-title="ଟ୍ରାନ୍ସଫର୍ମର" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Transformator" title="Transformator – Uzbek" lang="uz" hreflang="uz" data-title="Transformator" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9F%E0%A8%B0%E0%A8%BE%E0%A8%82%E0%A8%B8%E0%A8%AB%E0%A8%BE%E0%A8%B0%E0%A8%AE%E0%A8%B0" title="ਟਰਾਂਸਫਾਰਮਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਟਰਾਂਸਫਾਰਮਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%B9%D8%B1%D8%A7%D9%86%D8%B3%D9%81%D8%A7%D8%B1%D9%85%D8%B1" title="ٹرانسفارمر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ٹرانسفارمر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Transformator" title="Transformator – Polish" lang="pl" hreflang="pl" data-title="Transformator" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Transformador" title="Transformador – Portuguese" lang="pt" hreflang="pt" data-title="Transformador" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Transformator" title="Transformator – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Transformator" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Transformator" title="Transformator – Romanian" lang="ro" hreflang="ro" data-title="Transformator" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Rusyn" lang="rue" hreflang="rue" data-title="Трансформатор" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Russian" lang="ru" hreflang="ru" data-title="Трансформатор" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Transformer" title="Transformer – Scots" lang="sco" hreflang="sco" data-title="Transformer" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Transformator" title="Transformator – Saterland Frisian" lang="stq" hreflang="stq" data-title="Transformator" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Transformator%C3%ABt" title="Transformatorët – Albanian" lang="sq" hreflang="sq" data-title="Transformatorët" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Transformer" title="Transformer – Simple English" lang="en-simple" hreflang="en-simple" data-title="Transformer" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%BD%D8%B1%D8%A7%D9%86%D8%B3%D9%81%D8%A7%D8%B1%D9%85%D8%B1" title="ٽرانسفارمر – Sindhi" lang="sd" hreflang="sd" data-title="ٽرانسفارمر" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Transform%C3%A1tor" title="Transformátor – Slovak" lang="sk" hreflang="sk" data-title="Transformátor" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Transformator" title="Transformator – Slovenian" lang="sl" hreflang="sl" data-title="Transformator" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%D8%B1%D8%A7%D9%86%D8%B3%D9%81%DB%86%D8%B1%D9%85%DB%95%D8%B1" title="ترانسفۆرمەر – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ترانسفۆرمەر" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Serbian" lang="sr" hreflang="sr" data-title="Трансформатор" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Transformator" title="Transformator – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Transformator" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Trafo" title="Trafo – Sundanese" lang="su" hreflang="su" data-title="Trafo" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Muuntaja" title="Muuntaja – Finnish" lang="fi" hreflang="fi" data-title="Muuntaja" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Transformator" title="Transformator – Swedish" lang="sv" hreflang="sv" data-title="Transformator" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Transpormador" title="Transpormador – Tagalog" lang="tl" hreflang="tl" data-title="Transpormador" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%BF" title="மின்மாற்றி – Tamil" lang="ta" hreflang="ta" data-title="மின்மாற்றி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Tatar" lang="tt" hreflang="tt" data-title="Трансформатор" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%9F%E0%B1%8D%E0%B0%B0%E0%B0%BE%E0%B0%A8%E0%B1%8D%E0%B0%B8%E0%B1%8D%E2%80%8C%E0%B0%AB%E0%B0%BE%E0%B0%B0%E0%B1%8D%E0%B0%AE%E0%B0%B0%E0%B1%8D" title="ట్రాన్స్‌ఫార్మర్ – Telugu" lang="te" hreflang="te" data-title="ట్రాన్స్‌ఫార్మర్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AB%E0%B8%A1%E0%B9%89%E0%B8%AD%E0%B9%81%E0%B8%9B%E0%B8%A5%E0%B8%87%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="หม้อแปลงไฟฟ้า – Thai" lang="th" hreflang="th" data-title="หม้อแปลงไฟฟ้า" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Tajik" lang="tg" hreflang="tg" data-title="Трансформатор" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Transformat%C3%B6r" title="Transformatör – Turkish" lang="tr" hreflang="tr" data-title="Transformatör" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Transformator" title="Transformator – Turkmen" lang="tk" hreflang="tk" data-title="Transformator" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%BE%D1%80" title="Трансформатор – Ukrainian" lang="uk" hreflang="uk" data-title="Трансформатор" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%A8%D8%AF%D9%91%D9%84" title="مبدّل – Urdu" lang="ur" hreflang="ur" data-title="مبدّل" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Bi%E1%BA%BFn_%C3%A1p" title="Biến áp – Vietnamese" lang="vi" hreflang="vi" data-title="Biến áp" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Transpormer" title="Transpormer – Waray" lang="war" hreflang="war" data-title="Transpormer" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Soppalikaay" title="Soppalikaay – Wolof" lang="wo" hreflang="wo" data-title="Soppalikaay" data-language-autonym="Wolof" data-language-local-name="Wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8F%98%E5%8E%8B%E5%99%A8" title="变压器 – Wu" lang="wuu" hreflang="wuu" data-title="变压器" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%98%D7%A8%D7%90%D7%A0%D7%A1%D7%A4%D7%90%D7%A8%D7%9E%D7%90%D7%98%D7%90%D7%A8" title="טראנספארמאטאר – Yiddish" lang="yi" hreflang="yi" data-title="טראנספארמאטאר" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%81%AB%E7%89%9B" title="火牛 – Cantonese" lang="yue" hreflang="yue" data-title="火牛" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%98%E5%8E%8B%E5%99%A8" title="变压器 – Chinese" lang="zh" hreflang="zh" data-title="变压器" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Device to couple energy between circuits</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the electrical device. For other uses, see <a href="/wiki/Transformer_(disambiguation)" class="mw-disambig" title="Transformer (disambiguation)">Transformer (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Philips_N4422_-_power_supply_transformer-2098.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Philips_N4422_-_power_supply_transformer-2098.jpg/220px-Philips_N4422_-_power_supply_transformer-2098.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Philips_N4422_-_power_supply_transformer-2098.jpg/330px-Philips_N4422_-_power_supply_transformer-2098.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Philips_N4422_-_power_supply_transformer-2098.jpg/440px-Philips_N4422_-_power_supply_transformer-2098.jpg 2x" data-file-width="3178" data-file-height="3178" /></a><figcaption>An O-core transformer consisting of two coils of copper wire wrapped around a magnetic core</figcaption></figure> <p>In <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, a <b>transformer</b> is a <a href="/wiki/Passive_component" class="mw-redirect" title="Passive component">passive component</a> that transfers <a href="/wiki/Electrical_energy" title="Electrical energy">electrical energy</a> from one electrical circuit to another circuit, or multiple <a href="/wiki/Electrical_network" title="Electrical network">circuits</a>. A varying current in any coil of the transformer produces a varying <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> in the transformer's core, which induces a varying <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force (EMF)</a> across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits. <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a>, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil. </p><p>Transformers are used to change <a href="/wiki/Alternating_current" title="Alternating current">AC</a> voltage levels, such transformers being termed step-up or step-down type to increase or decrease voltage level, respectively. Transformers can also be used to provide <a href="/wiki/Galvanic_isolation" title="Galvanic isolation">galvanic isolation</a> between circuits as well as to couple stages of signal-processing circuits. Since the invention of the first <a href="/wiki/Constant-potential_transformer" class="mw-redirect" title="Constant-potential transformer">constant-potential transformer</a> in 1885, transformers have become essential for the <a href="/wiki/Electric_power_transmission" title="Electric power transmission">transmission</a>, <a href="/wiki/Electric_power_distribution" title="Electric power distribution">distribution</a>, and utilization of alternating current electric power.<sup id="cite_ref-Bedell_(1942)_1-0" class="reference"><a href="#cite_note-Bedell_(1942)-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from <a href="/wiki/Radio_Frequency" class="mw-redirect" title="Radio Frequency">RF</a> transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the <a href="/wiki/Power_grid" class="mw-redirect" title="Power grid">power grid</a>. </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Principles">Principles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=1" title="Edit section: Principles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right" style="width:30%"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-text plainlist"><span class="anchor" id="Ideal_transformer_equations"></span> <p><b>Ideal transformer equations</b> </p><p>By Faraday's law of induction: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{P}}=-N_{\text{P}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{P}}=-N_{\text{P}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/135194b2c053dd060ad99e0fb7e27c6a9a513d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.638ex; height:5.509ex;" alt="{\displaystyle V_{\text{P}}=-N_{\text{P}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._1" class="reference nourlexpansion" style="font-weight:bold;">Eq. 1</span><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>)</b></td></tr></tbody></table> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{S}}=-N_{\text{S}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{S}}=-N_{\text{S}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a8a9d92b4d32d3dfd5b06f558676c775c52ba11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.227ex; height:5.509ex;" alt="{\displaystyle V_{\text{S}}=-N_{\text{S}}{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._2" class="reference nourlexpansion" style="font-weight:bold;">Eq. 2</span>)</b></td></tr></tbody></table> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> is the <a href="/wiki/Derivative" title="Derivative">instantaneous</a> <a href="/wiki/Voltage" title="Voltage">voltage</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> is the <a href="/wiki/Number_of_turns" class="mw-redirect" title="Number of turns">number of turns</a> in a winding, dΦ/dt is the <a href="/wiki/Derivative" title="Derivative">derivative</a> of the magnetic flux Φ through one turn of the winding over time (<i><b>t</b></i>), and subscripts <sub><b>P</b></sub> and <sub><b>S</b></sub> denotes primary and secondary. </p><p>Combining the ratio of eq. 1 & eq. 2: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap">Turns ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e921299a274685b5e565f13287137fbfed2d5a5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.477ex; height:5.676ex;" alt="{\displaystyle ={\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}=a}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._3" class="reference nourlexpansion" style="font-weight:bold;">Eq. 3</span>)</b></td></tr></tbody></table> <p>where for a step-up transformer <i>a</i> < 1 and for a step-down transformer <i>a</i> > 1.<sup id="cite_ref-Brenner18-6_4-0" class="reference"><a href="#cite_note-Brenner18-6-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>By the law of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>, <a href="/wiki/Apparent_power" class="mw-redirect" title="Apparent power">apparent</a>, <a href="/wiki/Real_power" class="mw-redirect" title="Real power">real</a> and <a href="/wiki/Reactive_power" class="mw-redirect" title="Reactive power">reactive</a> power are each conserved in the input and output: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=I_{\text{P}}V_{\text{P}}=I_{\text{S}}V_{\text{S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=I_{\text{P}}V_{\text{P}}=I_{\text{S}}V_{\text{S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b70234b0d498fae984ca635eb24af0bd17eab0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.448ex; height:2.509ex;" alt="{\displaystyle S=I_{\text{P}}V_{\text{P}}=I_{\text{S}}V_{\text{S}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._4" class="reference nourlexpansion" style="font-weight:bold;">Eq. 4</span>)</b></td></tr></tbody></table> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> is apparent power and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> is <a href="/wiki/Electric_current" title="Electric current">current</a>. </p><p>Combining Eq. 3 & Eq. 4 with this endnote<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Brenner18-1_6-0" class="reference"><a href="#cite_note-Brenner18-1-6"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> gives the ideal transformer <a href="/wiki/Identity_function" title="Identity function">identity</a>: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {I_{\text{S}}}{I_{\text{P}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}={\sqrt {\frac {L_{\text{P}}}{L_{\text{S}}}}}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </msqrt> </mrow> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {I_{\text{S}}}{I_{\text{P}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}={\sqrt {\frac {L_{\text{P}}}{L_{\text{S}}}}}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9de7f0a73010b63861cec8ed60356c3c9cfb8738" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:30.525ex; height:7.509ex;" alt="{\displaystyle {\frac {V_{\text{P}}}{V_{\text{S}}}}={\frac {I_{\text{S}}}{I_{\text{P}}}}={\frac {N_{\text{P}}}{N_{\text{S}}}}={\sqrt {\frac {L_{\text{P}}}{L_{\text{S}}}}}=a}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._5" class="reference nourlexpansion" style="font-weight:bold;">Eq. 5</span>)</b></td></tr></tbody></table> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> is winding self-inductance. </p><p>By <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a> and ideal transformer identity: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{\text{L}}={\frac {V_{\text{S}}}{I_{\text{S}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\text{L}}={\frac {V_{\text{S}}}{I_{\text{S}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16150625df72684abb8bc7bbf02f3d1355caa19c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.283ex; height:5.843ex;" alt="{\displaystyle Z_{\text{L}}={\frac {V_{\text{S}}}{I_{\text{S}}}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._6" class="reference nourlexpansion" style="font-weight:bold;">Eq. 6</span>)</b></td></tr></tbody></table> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z'_{\text{L}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {aV_{\text{S}}}{I_{\text{S}}/a}}=a^{2}{\frac {V_{\text{S}}}{I_{\text{S}}}}=a^{2}{Z_{\text{L}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z'_{\text{L}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {aV_{\text{S}}}{I_{\text{S}}/a}}=a^{2}{\frac {V_{\text{S}}}{I_{\text{S}}}}=a^{2}{Z_{\text{L}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c362c5fb9b56a597fa0bac4121719b4ddc4560ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:34.934ex; height:6.176ex;" alt="{\displaystyle Z'_{\text{L}}={\frac {V_{\text{P}}}{I_{\text{P}}}}={\frac {aV_{\text{S}}}{I_{\text{S}}/a}}=a^{2}{\frac {V_{\text{S}}}{I_{\text{S}}}}=a^{2}{Z_{\text{L}}}}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_Eq._7" class="reference nourlexpansion" style="font-weight:bold;">Eq. 7</span>)</b></td></tr></tbody></table> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{\text{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\text{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8382cd55a813e173bbff84e196e60dfdf8b79db0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.847ex; height:2.509ex;" alt="{\displaystyle Z_{\text{L}}}"></span> is the load impedance of the secondary circuit & <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z'_{\text{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z'_{\text{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4019d2a9881006092dbe9f71e0a8ac1dac32a46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.847ex; height:2.843ex;" alt="{\displaystyle Z'_{\text{L}}}"></span> is the apparent load or driving point impedance of the primary circuit, the superscript <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/761bf83727fb142497cfbee036fd61b368d4fbf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:0.685ex; height:2.343ex;" alt="{\displaystyle '}"></span> denoting referred to the primary.</div></div> </div> <div class="mw-heading mw-heading3"><h3 id="Ideal_transformer">Ideal transformer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=2" title="Edit section: Ideal transformer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An ideal transformer is <a href="/wiki/Linearity" title="Linearity">linear</a>, lossless and perfectly <a href="/wiki/Inductive_coupling" title="Inductive coupling">coupled</a>. Perfect coupling implies infinitely high core <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">magnetic permeability</a> and winding <a href="/wiki/Inductance" title="Inductance">inductance</a> and zero net <a href="/wiki/Magnetomotive_force" title="Magnetomotive force">magnetomotive force</a> (i.e. <i>i</i><sub><i>p</i></sub><i>n</i><sub><i>p</i></sub> − <i>i</i><sub><i>s</i></sub><i>n</i><sub><i>s</i></sub> = 0).<sup id="cite_ref-Brenner18-6_4-1" class="reference"><a href="#cite_note-Brenner18-6-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Ideal_transformer.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Ideal_transformer.svg/440px-Ideal_transformer.svg.png" decoding="async" width="440" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Ideal_transformer.svg/660px-Ideal_transformer.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Ideal_transformer.svg/880px-Ideal_transformer.svg.png 2x" data-file-width="408" data-file-height="250" /></a><figcaption>Ideal transformer connected with source <i>V</i><sub><i>P</i></sub> on primary and load impedance <i>Z</i><sub><i>L</i></sub> on secondary, where 0 < <i>Z</i><sub><i>L</i></sub> < ∞.</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer3d_col3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Transformer3d_col3.svg/440px-Transformer3d_col3.svg.png" decoding="async" width="440" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Transformer3d_col3.svg/660px-Transformer3d_col3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Transformer3d_col3.svg/880px-Transformer3d_col3.svg.png 2x" data-file-width="763" data-file-height="573" /></a><figcaption>Ideal transformer and induction law<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup></figcaption></figure> <div style="clear:both;" class=""></div> <p>A varying current in the transformer's primary winding creates a varying magnetic flux in the transformer core, which is also encircled by the secondary winding. This varying flux at the secondary winding induces a varying <a href="/wiki/Electromotive_force" title="Electromotive force"> electromotive force or voltage</a> in the secondary winding. This electromagnetic induction phenomenon is the basis of transformer action and, in accordance with <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, the secondary current so produced creates a flux equal and opposite to that produced by the primary winding. </p><p>The windings are wound around a core of infinitely high magnetic permeability so that all of the magnetic flux passes through both the primary and secondary windings. With a <a href="/wiki/Voltage_source" title="Voltage source">voltage source</a> connected to the primary winding and a load connected to the secondary winding, the transformer currents flow in the indicated directions and the core magnetomotive force cancels to zero. </p><p>According to <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law</a>, since the same magnetic flux passes through both the primary and secondary windings in an ideal transformer, a voltage is induced in each winding proportional to its number of turns. The transformer winding voltage ratio is equal to the winding turns ratio.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>An ideal transformer is a reasonable approximation for a typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to the corresponding current ratio. </p><p>The load impedance <i>referred</i> to the primary circuit is equal to the turns ratio squared times the secondary circuit load impedance.<sup id="cite_ref-Flanagan1993-1_11-0" class="reference"><a href="#cite_note-Flanagan1993-1-11"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Real_transformer">Real transformer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=3" title="Edit section: Real transformer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Transformer_Flux.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Transformer_Flux.svg/300px-Transformer_Flux.svg.png" decoding="async" width="300" height="224" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Transformer_Flux.svg/450px-Transformer_Flux.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Transformer_Flux.svg/600px-Transformer_Flux.svg.png 2x" data-file-width="670" data-file-height="500" /></a><figcaption>Leakage flux of a transformer</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Deviations_from_ideal_transformer">Deviations from ideal transformer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=4" title="Edit section: Deviations from ideal transformer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ideal transformer model neglects many basic linear aspects of real transformers, including unavoidable losses and inefficiencies.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>(a) Core losses, collectively called magnetizing current losses, consisting of<sup id="cite_ref-Say1983_13-0" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Magnetic_hysteresis" title="Magnetic hysteresis">Hysteresis</a> losses due to nonlinear magnetic effects in the transformer core, and</li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a> losses due to joule heating in the core that are proportional to the square of the transformer's applied voltage.</li></ul> <p>(b) Unlike the ideal model, the windings in a real transformer have non-zero resistances and inductances associated with: </p> <ul><li><a href="/wiki/Joule_heating" title="Joule heating">Joule losses</a> due to resistance in the primary and secondary windings<sup id="cite_ref-Say1983_13-1" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance.</li></ul> <p>(c) similar to an <a href="/wiki/Inductor" title="Inductor">inductor</a>, parasitic capacitance and self-resonance phenomenon due to the electric field distribution. Three kinds of parasitic capacitance are usually considered and the closed-loop equations are provided<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Capacitance between adjacent turns in any one layer;</li> <li>Capacitance between adjacent layers;</li> <li>Capacitance between the core and the layer(s) adjacent to the core;</li></ul> <p>Inclusion of capacitance into the transformer model is complicated, and is rarely attempted; the <a href="#Real_transformer_equivalent_circuit_figure">'real' transformer model's equivalent circuit shown below</a> does not include parasitic capacitance. However, the capacitance effect can be measured by comparing open-circuit inductance, i.e. the inductance of a primary winding when the secondary circuit is open, to a short-circuit inductance when the secondary winding is shorted. </p> <div class="mw-heading mw-heading4"><h4 id="Leakage_flux">Leakage flux</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=5" title="Edit section: Leakage flux"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Leakage_inductance" title="Leakage inductance">Leakage inductance</a></div> <p>The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings.<sup id="cite_ref-McLaren1984-68_15-0" class="reference"><a href="#cite_note-McLaren1984-68-15"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Such flux is termed <i>leakage flux</i>, and results in <a href="/wiki/Leakage_inductance" title="Leakage inductance">leakage inductance</a> in <a href="/wiki/Series_and_parallel_circuits" title="Series and parallel circuits">series</a> with the mutually coupled transformer windings.<sup id="cite_ref-calvert2001_16-0" class="reference"><a href="#cite_note-calvert2001-16"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. It is not directly a power loss, but results in inferior <a href="/wiki/Voltage_regulation" title="Voltage regulation">voltage regulation</a>, causing the secondary voltage not to be directly proportional to the primary voltage, particularly under heavy load.<sup id="cite_ref-McLaren1984-68_15-1" class="reference"><a href="#cite_note-McLaren1984-68-15"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Transformers are therefore normally designed to have very low leakage inductance. </p><p>In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may deliberately be introduced in a transformer design to limit the <a href="/wiki/Short_circuit" title="Short circuit">short-circuit</a> current it will supply.<sup id="cite_ref-calvert2001_16-1" class="reference"><a href="#cite_note-calvert2001-16"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Leaky transformers may be used to supply loads that exhibit <a href="/wiki/Negative_resistance" title="Negative resistance">negative resistance</a>, such as <a href="/wiki/Electric_arc" title="Electric arc">electric arcs</a>, <a href="/wiki/Mercury-vapor_lamp" title="Mercury-vapor lamp">mercury-</a> and <a href="/wiki/Sodium-vapor_lamp" title="Sodium-vapor lamp">sodium-</a> vapor lamps and <a href="/wiki/Neon_sign" title="Neon sign">neon signs</a> or for safely handling loads that become periodically short-circuited such as <a href="/wiki/Arc_welding" title="Arc welding">electric arc welders</a>.<sup id="cite_ref-Say1983_13-2" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 485">: 485 </span></sup> </p><p><a href="/wiki/Air_gap_(magnetic)" title="Air gap (magnetic)">Air gaps</a> are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a DC component flowing in the windings.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> A <a href="/wiki/Saturable_reactor" title="Saturable reactor">saturable reactor</a> exploits saturation of the core to control alternating current. </p><p>Knowledge of leakage inductance is also useful when transformers are operated in parallel. It can be shown that if the <a href="/wiki/Per-unit_system" title="Per-unit system">percent impedance</a><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup> and associated winding leakage reactance-to-resistance (<i>X</i>/<i>R</i>) ratio of two transformers were the same, the transformers would share the load power in proportion to their respective ratings. However, the impedance tolerances of commercial transformers are significant. Also, the impedance and X/R ratio of different capacity transformers tends to vary.<sup id="cite_ref-Knowlton6-97_20-0" class="reference"><a href="#cite_note-Knowlton6-97-20"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading4"><h4 id="Equivalent_circuit">Equivalent circuit</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=6" title="Edit section: Equivalent circuit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Induction_motor#Steinmetz_equivalent_circuit" title="Induction motor">Steinmetz equivalent circuit</a></div> <p>Referring to the diagram, a practical transformer's physical behavior may be represented by an <a href="/wiki/Equivalent_circuit" title="Equivalent circuit">equivalent circuit</a> model, which can incorporate an ideal transformer.<sup id="cite_ref-daniels1985-47_21-0" class="reference"><a href="#cite_note-daniels1985-47-21"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Winding joule losses and leakage reactance are represented by the following series loop impedances of the model: </p> <ul><li>Primary winding: <i>R</i><sub>P</sub>, <i>X</i><sub>P</sub></li> <li>Secondary winding: <i>R</i><sub>S</sub>, <i>X</i><sub>S</sub>.</li></ul> <p>In normal course of circuit equivalence transformation, <i>R</i><sub>S</sub> and <i>X</i><sub>S</sub> are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (<i>N</i><sub>P</sub>/<i>N</i><sub>S</sub>)<sup> 2</sup> = a<sup>2</sup>. </p><p><span class="anchor" id="Real_transformer_equivalent_circuit_figure"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer_equivalent_circuit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Transformer_equivalent_circuit.svg/440px-Transformer_equivalent_circuit.svg.png" decoding="async" width="440" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Transformer_equivalent_circuit.svg/660px-Transformer_equivalent_circuit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Transformer_equivalent_circuit.svg/880px-Transformer_equivalent_circuit.svg.png 2x" data-file-width="750" data-file-height="275" /></a><figcaption>Real transformer equivalent circuit</figcaption></figure> <p>Core loss and reactance is represented by the following shunt leg impedances of the model: </p> <ul><li>Core or iron losses: <i>R</i><sub>C</sub></li> <li>Magnetizing reactance: <i>X</i><sub>M</sub>.</li></ul> <p><i>R</i><sub>C</sub> and <i>X</i><sub>M</sub> are collectively termed the <i>magnetizing branch</i> of the model. </p><p>Core losses are caused mostly by hysteresis and eddy current effects in the core and are proportional to the square of the core flux for operation at a given frequency.<sup id="cite_ref-Say1983_13-3" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 142–143">: 142–143 </span></sup> The finite permeability core requires a magnetizing current <i>I</i><sub>M</sub> to maintain mutual flux in the core. Magnetizing current is in phase with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits.<sup id="cite_ref-Say1983_13-4" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 142">: 142 </span></sup> With <a href="/wiki/Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current <i>I</i><sub>0</sub> equals transformer no-load current.<sup id="cite_ref-daniels1985-47_21-1" class="reference"><a href="#cite_note-daniels1985-47-21"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Instrument_Transformer_LV_terminals.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Instrument_Transformer_LV_terminals.jpg/220px-Instrument_Transformer_LV_terminals.jpg" decoding="async" width="220" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Instrument_Transformer_LV_terminals.jpg/330px-Instrument_Transformer_LV_terminals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Instrument_Transformer_LV_terminals.jpg/440px-Instrument_Transformer_LV_terminals.jpg 2x" data-file-width="1685" data-file-height="1813" /></a><figcaption>Instrument transformer, with <a href="/wiki/Polarity_(mutual_inductance)" title="Polarity (mutual inductance)">polarity dot</a> and X1 markings on low-voltage ("LV") side terminal</figcaption></figure> <p>The resulting model, though sometimes termed 'exact' equivalent circuit based on <a href="/wiki/Linearity" title="Linearity">linearity</a> assumptions, retains a number of approximations.<sup id="cite_ref-daniels1985-47_21-2" class="reference"><a href="#cite_note-daniels1985-47-21"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Analysis may be simplified by assuming that magnetizing branch impedance is relatively high and relocating the branch to the left of the primary impedances. This introduces error but allows combination of primary and referred secondary resistances and reactance by simple summation as two series impedances. </p><p>Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: <a href="/wiki/Open-circuit_test" title="Open-circuit test">open-circuit test</a>, <a href="/wiki/Short-circuit_test" title="Short-circuit test">short-circuit test</a>, winding resistance test, and transformer ratio test. </p> <div class="mw-heading mw-heading3"><h3 id="Transformer_EMF_equation">Transformer EMF equation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=7" title="Edit section: Transformer EMF equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Transformer_universal_EMF_equation"></span> If the flux in the core is purely <a href="/wiki/Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a>, the relationship for either winding between its <b><a href="/wiki/Root_mean_square" title="Root mean square">rms</a> voltage</b> <i>E</i><sub>rms</sub> of the winding, and the supply frequency <i>f</i>, number of turns <i>N</i>, core cross-sectional area <i>A</i> in m<sup>2</sup> and peak magnetic flux density <i>B</i><sub>peak</sub> in Wb/m<sup>2</sup> or T (tesla) is given by the universal EMF equation:<sup id="cite_ref-Say1983_13-5" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{rms}}={\frac {2\pi fNAB_{\text{peak}}}{\sqrt {2}}}\approx 4.44fNAB_{\text{peak}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>rms</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>N</mi> <mi>A</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>peak</mtext> </mrow> </msub> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>≈</mo> <mn>4.44</mn> <mi>f</mi> <mi>N</mi> <mi>A</mi> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>peak</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{rms}}={\frac {2\pi fNAB_{\text{peak}}}{\sqrt {2}}}\approx 4.44fNAB_{\text{peak}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3df89cef335d32120fba69d797aa9e7a830269a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:39.102ex; height:6.676ex;" alt="{\displaystyle E_{\text{rms}}={\frac {2\pi fNAB_{\text{peak}}}{\sqrt {2}}}\approx 4.44fNAB_{\text{peak}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Polarity">Polarity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=8" title="Edit section: Polarity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Dot_convention" class="mw-redirect" title="Dot convention">dot convention</a> is often used in transformer circuit diagrams, nameplates or terminal markings to define the relative polarity of transformer windings. Positively increasing instantaneous current entering the primary winding's 'dot' end induces positive polarity voltage exiting the secondary winding's 'dot' end. Three-phase transformers used in electric power systems will have a nameplate that indicate the phase relationships between their terminals. This may be in the form of a <a href="/wiki/Phasor" title="Phasor">phasor</a> diagram, or using an alpha-numeric code to show the type of internal connection (wye or delta) for each winding. </p> <div class="mw-heading mw-heading3"><h3 id="Effect_of_frequency">Effect of frequency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=9" title="Edit section: Effect of frequency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The EMF of a transformer at a given flux increases with frequency.<sup id="cite_ref-Say1983_13-6" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation and fewer turns are needed to achieve the same impedance. However, properties such as core loss and conductor <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> also increase with frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Conversely, frequencies used for some <a href="/wiki/Railway_electrification_system" class="mw-redirect" title="Railway electrification system">railway electrification systems</a> were much lower (e.g. 16.7 Hz and 25 Hz) than normal utility frequencies (50–60 Hz) for historical reasons concerned mainly with the limitations of early <a href="/wiki/Traction_motor" title="Traction motor">electric traction motors</a>. Consequently, the transformers used to step-down the high overhead line voltages were much larger and heavier for the same power rating than those required for the higher frequencies. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Power_Transformer_Over-Excitation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Power_Transformer_Over-Excitation.gif/220px-Power_Transformer_Over-Excitation.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Power_Transformer_Over-Excitation.gif/330px-Power_Transformer_Over-Excitation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Power_Transformer_Over-Excitation.gif/440px-Power_Transformer_Over-Excitation.gif 2x" data-file-width="450" data-file-height="450" /></a><figcaption>Power transformer overexcitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).</figcaption></figure> <p>Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current. At a lower frequency, the magnetizing current will increase. Operation of a large transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. Transformers may require <a href="/wiki/Protective_relay" title="Protective relay">protective relays</a> to protect the transformer from overvoltage at higher than rated frequency. </p><p>One example is in traction transformers used for <a href="/wiki/Electric_multiple_unit" title="Electric multiple unit">electric multiple unit</a> and <a href="/wiki/High-speed_rail" title="High-speed rail">high-speed</a> train service operating across regions with different electrical standards. The converter equipment and traction transformers have to accommodate different input frequencies and voltage (ranging from as high as 50 Hz down to 16.7 Hz and rated up to 25 kV). </p><p>At much higher frequencies the transformer core size required drops dramatically: a physically small transformer can handle power levels that would require a massive iron core at mains frequency. The development of switching power semiconductor devices made <a href="/wiki/Switch_mode_power_supply" class="mw-redirect" title="Switch mode power supply">switch-mode power supplies</a> viable, to generate a high frequency, then change the voltage level with a small transformer. </p><p>Transformers for higher frequency applications such as <a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">SMPS</a> typically use core materials with much lower hysteresis and eddy-current losses than those for 50/60 Hz. Primary examples are iron-powder and ferrite cores. The lower frequency-dependant losses of these cores often is at the expense of flux density at saturation. For instance, <a href="/wiki/Ferrite_core" title="Ferrite core">ferrite</a> saturation occurs at a substantially lower flux density than laminated iron. </p><p>Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning. </p> <div class="mw-heading mw-heading3"><h3 id="Energy_losses">Energy losses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=10" title="Edit section: Energy losses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity.<sup id="cite_ref-De_Keulenaer2001_23-0" class="reference"><a href="#cite_note-De_Keulenaer2001-23"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The efficiency of typical distribution transformers is between about 98 and 99 percent.<sup id="cite_ref-De_Keulenaer2001_23-1" class="reference"><a href="#cite_note-De_Keulenaer2001-23"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>As transformer losses vary with load, it is often useful to tabulate <a href="/wiki/No-load_loss" title="No-load loss">no-load loss</a>, full-load loss, half-load loss, and so on. Hysteresis and <a href="/wiki/Eddy_current" title="Eddy current">eddy current</a> losses are constant at all load levels and dominate at no load, while winding loss increases as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply. Designing <a href="/wiki/Energy_efficient_transformer" title="Energy efficient transformer">energy efficient transformers</a> for lower loss requires a larger core, good-quality <a href="/wiki/Electrical_steel" title="Electrical steel">silicon steel</a>, or even <a href="/wiki/Electrical_steel#Amorphous_steel" title="Electrical steel">amorphous steel</a> for the core and thicker wire, increasing initial cost. The choice of construction represents a <a href="/wiki/Trade-off" title="Trade-off">trade-off</a> between initial cost and operating cost.<sup id="cite_ref-Heathcote1998-41_25-0" class="reference"><a href="#cite_note-Heathcote1998-41-25"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Transformer losses arise from: </p> <dl><dt>Winding joule losses</dt> <dd>Current flowing through a winding's conductor causes <a href="/wiki/Joule_heating" title="Joule heating">joule heating</a> due to the <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> of the wire. As frequency increases, skin effect and <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a> causes the winding's resistance and, hence, losses to increase.</dd> <dt><a href="/wiki/Magnetic_core#Core_loss" title="Magnetic core">Core losses</a></dt> <dd> <dl><dt>Hysteresis losses</dt> <dd>Each time the magnetic field is reversed, a small amount of energy is lost due to <a href="/wiki/Magnetic_hysteresis" title="Magnetic hysteresis">hysteresis</a> within the core, caused by motion of the <a href="/wiki/Magnetic_domain" title="Magnetic domain">magnetic domains</a> within the steel. According to Steinmetz's formula, the heat energy due to hysteresis is given by <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{\text{h}}\approx \eta \beta _{\text{max}}^{1.6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>h</mtext> </mrow> </msub> <mo>≈</mo> <mi>η</mi> <msubsup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1.6</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{\text{h}}\approx \eta \beta _{\text{max}}^{1.6}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69fd6bd3dc634a1547879341549aa8dd5451ada0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.215ex; height:3.009ex;" alt="{\displaystyle W_{\text{h}}\approx \eta \beta _{\text{max}}^{1.6}}"></span> and,</dd></dl></dd> <dd>hysteresis loss is thus given by <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{h}}\approx {W}_{\text{h}}f\approx \eta {f}\beta _{\text{max}}^{1.6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>h</mtext> </mrow> </msub> <mo>≈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>h</mtext> </mrow> </msub> <mi>f</mi> <mo>≈</mo> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <msubsup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1.6</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{h}}\approx {W}_{\text{h}}f\approx \eta {f}\beta _{\text{max}}^{1.6}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e9a7da8f6b875b9590113a49c9cfc6d63f4074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.509ex; height:3.009ex;" alt="{\displaystyle P_{\text{h}}\approx {W}_{\text{h}}f\approx \eta {f}\beta _{\text{max}}^{1.6}}"></span></dd></dl></dd> <dd>where, <i>f</i> is the frequency, <i>η</i> is the hysteresis coefficient and <i>β</i><sub>max</sub> is the maximum flux density, the empirical exponent of which varies from about 1.4 to 1.8 but is often given as 1.6 for iron.<sup id="cite_ref-Heathcote1998-41_25-1" class="reference"><a href="#cite_note-Heathcote1998-41-25"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> For more detailed analysis, see <a href="/wiki/Magnetic_core#Core_losses" title="Magnetic core">Magnetic core</a> and <a href="/wiki/Steinmetz%27s_equation" title="Steinmetz's equation">Steinmetz's equation</a>.</dd> <dt>Eddy current losses</dt> <dd><a href="/wiki/Eddy_current" title="Eddy current">Eddy currents</a> are induced in the conductive metal transformer core by the changing magnetic field, and this current flowing through the resistance of the iron dissipates energy as heat in the core. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.<sup id="cite_ref-Heathcote1998-41_25-2" class="reference"><a href="#cite_note-Heathcote1998-41-25"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Eddy current losses can be reduced by making the core of a stack of laminations (thin plates) electrically insulated from each other, rather than a solid block; all transformers operating at low frequencies use laminated or similar cores.</dd></dl></dd></dl> <dl><dt>Magnetostriction related transformer hum</dt> <dd>Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known as <a href="/wiki/Magnetostriction" title="Magnetostriction">magnetostriction</a>, the frictional energy of which produces an audible noise known as <a href="/wiki/Mains_hum" title="Mains hum">mains hum</a> or "transformer hum".<sup id="cite_ref-PF_(nd)_26-0" class="reference"><a href="#cite_note-PF_(nd)-26"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This transformer hum is especially objectionable in transformers supplied at <a href="/wiki/Utility_frequency" title="Utility frequency">power frequencies</a> and in <a href="/wiki/High-frequency" class="mw-redirect" title="High-frequency">high-frequency</a> <a href="/wiki/Flyback_transformer" title="Flyback transformer">flyback transformers</a> associated with television <a href="/wiki/Cathode-ray_tube" title="Cathode-ray tube">CRTs</a>.</dd> <dt><span class="anchor" id="stray"></span> Stray losses</dt> <dd>Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer's support structure will give rise to eddy currents and be converted to heat.<sup id="cite_ref-nailen_27-0" class="reference"><a href="#cite_note-nailen-27"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></dd> <dt>Radiative</dt> <dd>There are also radiative losses due to the oscillating magnetic field but these are usually small.</dd> <dt>Mechanical vibration and audible noise transmission</dt> <dd>In addition to magnetostriction, the alternating magnetic field causes fluctuating forces between the primary and secondary windings. This energy incites vibration transmission in interconnected metalwork, thus amplifying audible transformer hum.<sup id="cite_ref-Pansini1999-23_28-0" class="reference"><a href="#cite_note-Pansini1999-23-28"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Construction">Construction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=11" title="Edit section: Construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Cores">Cores</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=12" title="Edit section: Cores"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer_winding_formats.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Transformer_winding_formats.jpg/220px-Transformer_winding_formats.jpg" decoding="async" width="220" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Transformer_winding_formats.jpg/330px-Transformer_winding_formats.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Transformer_winding_formats.jpg/440px-Transformer_winding_formats.jpg 2x" data-file-width="960" data-file-height="877" /></a><figcaption>Core form = core type; shell form = shell type</figcaption></figure></dt></dl> <p>Closed-core transformers are constructed in 'core form' or 'shell form'. When windings surround the core, the transformer is core form; when windings are surrounded by the core, the transformer is shell form.<sup id="cite_ref-Del_Vecchio2002-10_29-0" class="reference"><a href="#cite_note-Del_Vecchio2002-10-29"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Shell form design may be more prevalent than core form design for distribution transformer applications due to the relative ease in stacking the core around winding coils.<sup id="cite_ref-Del_Vecchio2002-10_29-1" class="reference"><a href="#cite_note-Del_Vecchio2002-10-29"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Core form design tends to, as a general rule, be more economical, and therefore more prevalent, than shell form design for high voltage power transformer applications at the lower end of their voltage and power rating ranges (less than or equal to, nominally, 230 kV or 75 MVA). At higher voltage and power ratings, shell form transformers tend to be more prevalent.<sup id="cite_ref-Del_Vecchio2002-10_29-2" class="reference"><a href="#cite_note-Del_Vecchio2002-10-29"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-HRTSG_(2005)_30-0" class="reference"><a href="#cite_note-HRTSG_(2005)-30"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-US_Army_Corps_of_Engineers1994_31-0" class="reference"><a href="#cite_note-US_Army_Corps_of_Engineers1994-31"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Shell form design tends to be preferred for extra-high voltage and higher MVA applications because, though more labor-intensive to manufacture, shell form transformers are characterized as having inherently better kVA-to-weight ratio, better short-circuit strength characteristics and higher immunity to transit damage.<sup id="cite_ref-US_Army_Corps_of_Engineers1994_31-1" class="reference"><a href="#cite_note-US_Army_Corps_of_Engineers1994-31"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Laminated_steel_cores">Laminated steel cores</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=13" title="Edit section: Laminated steel cores"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer.filament.agr.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Transformer.filament.agr.jpg/220px-Transformer.filament.agr.jpg" decoding="async" width="220" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Transformer.filament.agr.jpg/330px-Transformer.filament.agr.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Transformer.filament.agr.jpg/440px-Transformer.filament.agr.jpg 2x" data-file-width="769" data-file-height="550" /></a><figcaption>Shell type transformer with laminated core showing edges of laminations at the top of the photo</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:EI-transformer_core_interleaved_with_flux_paths.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/220px-EI-transformer_core_interleaved_with_flux_paths.png" decoding="async" width="220" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/330px-EI-transformer_core_interleaved_with_flux_paths.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/EI-transformer_core_interleaved_with_flux_paths.png/440px-EI-transformer_core_interleaved_with_flux_paths.png 2x" data-file-width="8656" data-file-height="3200" /></a><figcaption>Interleaved E-I transformer laminations showing air gap and flux paths</figcaption></figure> <p>Transformers for use at power or audio frequencies typically have cores made of high permeability <a href="/wiki/Silicon_steel" class="mw-redirect" title="Silicon steel">silicon steel</a>.<sup id="cite_ref-Hindmarsh1977-29_32-0" class="reference"><a href="#cite_note-Hindmarsh1977-29-32"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> The steel has a permeability many times that of <a href="/wiki/Free_space" class="mw-redirect" title="Free space">free space</a> and the core thus serves to greatly reduce the magnetizing current and confine the flux to a path which closely couples the windings.<sup id="cite_ref-Gottlieb_33-0" class="reference"><a href="#cite_note-Gottlieb-33"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Early transformer developers soon realized that cores constructed from solid iron resulted in prohibitive eddy current losses, and their designs mitigated this effect with cores consisting of bundles of insulated iron wires.<sup id="cite_ref-allan_34-0" class="reference"><a href="#cite_note-allan-34"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Later designs constructed the core by stacking layers of thin steel laminations, a principle that has remained in use. Each lamination is insulated from its neighbors by a thin non-conducting layer of insulation.<sup id="cite_ref-Kulkarni2004-36_35-0" class="reference"><a href="#cite_note-Kulkarni2004-36-35"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> The <a href="#Transformer_universal_EMF_equation">transformer universal EMF equation</a> can be used to calculate the core cross-sectional area for a preferred level of magnetic flux.<sup id="cite_ref-Say1983_13-7" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The effect of laminations is to confine <a href="/wiki/Eddy_current" title="Eddy current">eddy currents</a> to highly elliptical paths that enclose little flux, and so reduce their magnitude. Thinner laminations reduce losses,<sup id="cite_ref-Hindmarsh1977-29_32-1" class="reference"><a href="#cite_note-Hindmarsh1977-29-32"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> but are more laborious and expensive to construct.<sup id="cite_ref-McLyman2004-3-9_36-0" class="reference"><a href="#cite_note-McLyman2004-3-9-36"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Thin laminations are generally used on high-frequency transformers, with some of very thin steel laminations able to operate up to 10 kHz. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Laminering_av_k%C3%A4rna.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Laminering_av_k%C3%A4rna.svg/170px-Laminering_av_k%C3%A4rna.svg.png" decoding="async" width="170" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Laminering_av_k%C3%A4rna.svg/255px-Laminering_av_k%C3%A4rna.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Laminering_av_k%C3%A4rna.svg/340px-Laminering_av_k%C3%A4rna.svg.png 2x" data-file-width="445" data-file-height="546" /></a><figcaption>Laminating the core greatly reduces eddy-current losses</figcaption></figure> <p>One common design of laminated core is made from interleaved stacks of <a href="/wiki/E-shaped" class="mw-redirect" title="E-shaped">E-shaped</a> steel sheets capped with <a href="/wiki/I-shaped" class="mw-redirect" title="I-shaped">I-shaped</a> pieces, leading to its name of <b>E-I transformer</b>.<sup id="cite_ref-McLyman2004-3-9_36-1" class="reference"><a href="#cite_note-McLyman2004-3-9-36"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Such a design tends to exhibit more losses, but is very economical to manufacture. The cut-core or C-core type is made by winding a steel strip around a rectangular form and then bonding the layers together. It is then cut in two, forming two C shapes, and the core assembled by binding the two C halves together with a steel strap.<sup id="cite_ref-McLyman2004-3-9_36-2" class="reference"><a href="#cite_note-McLyman2004-3-9-36"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> They have the advantage that the flux is always oriented parallel to the metal grains, reducing reluctance. </p><p>A steel core's <a href="/wiki/Remanence" title="Remanence">remanence</a> means that it retains a static magnetic field when power is removed. When power is then reapplied, the residual field will cause a high <a href="/wiki/Inrush_current" title="Inrush current">inrush current</a> until the effect of the remaining magnetism is reduced, usually after a few cycles of the applied AC waveform.<sup id="cite_ref-Harlow2004-2_37-0" class="reference"><a href="#cite_note-Harlow2004-2-37"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Overcurrent protection devices such as <a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">fuses</a> must be selected to allow this harmless inrush to pass. </p><p>On transformers connected to long, overhead power transmission lines, induced currents due to <a href="/wiki/Geomagnetically_induced_current" title="Geomagnetically induced current">geomagnetic disturbances</a> during <a href="/wiki/Geomagnetic_storm" title="Geomagnetic storm">solar storms</a> can cause <a href="/wiki/Saturation_(magnetic)" title="Saturation (magnetic)">saturation of the core</a> and operation of transformer protection devices.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>Distribution transformers can achieve low no-load losses by using cores made with low-loss high-permeability silicon steel or <a href="/wiki/Amorphous#Metallic_glass" class="mw-redirect" title="Amorphous">amorphous (non-crystalline) metal alloy</a>. The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Solid_cores">Solid cores</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=14" title="Edit section: Solid cores"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Powdered iron cores are used in circuits such as switch-mode power supplies that operate above mains frequencies and up to a few tens of kilohertz. These materials combine high magnetic permeability with high bulk electrical <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a>. For frequencies extending beyond the <a href="/wiki/Very_high_frequency" title="Very high frequency">VHF band</a>, cores made from non-conductive magnetic <a href="/wiki/Ceramic" title="Ceramic">ceramic</a> materials called <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrites</a> are common.<sup id="cite_ref-McLyman2004-3-9_36-3" class="reference"><a href="#cite_note-McLyman2004-3-9-36"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Some radio-frequency transformers also have movable cores (sometimes called 'slugs') which allow adjustment of the <a href="/wiki/Coupling_coefficient_(inductors)" class="mw-redirect" title="Coupling coefficient (inductors)">coupling coefficient</a> (and <a href="/wiki/Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>) of tuned radio-frequency circuits. </p> <div class="mw-heading mw-heading4"><h4 id="Toroidal_cores">Toroidal cores</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=15" title="Edit section: Toroidal cores"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Small_toroidal_transformer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Small_toroidal_transformer.jpg/220px-Small_toroidal_transformer.jpg" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Small_toroidal_transformer.jpg/330px-Small_toroidal_transformer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Small_toroidal_transformer.jpg/440px-Small_toroidal_transformer.jpg 2x" data-file-width="710" data-file-height="618" /></a><figcaption>Small toroidal core transformer</figcaption></figure> <p>Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of <a href="/wiki/Silicon_steel" class="mw-redirect" title="Silicon steel">silicon steel</a> or <a href="/wiki/Permalloy" title="Permalloy">permalloy</a> wound into a coil, powdered iron, or <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrite</a>.<sup id="cite_ref-McLyman2004-3-1_40-0" class="reference"><a href="#cite_note-McLyman2004-3-1-40"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> A strip construction ensures that the <a href="/wiki/Grain_boundary" title="Grain boundary">grain boundaries</a> are optimally aligned, improving the transformer's efficiency by reducing the core's <a href="/wiki/Reluctance" class="mw-redirect" title="Reluctance">reluctance</a>. The closed ring shape eliminates air gaps inherent in the construction of an E-I core.<sup id="cite_ref-Say1983_13-8" class="reference"><a href="#cite_note-Say1983-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <sup class="reference nowrap"><span title="Page / location: 485">: 485 </span></sup> The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimizes the length of wire needed and provides screening to minimize the core's magnetic field from generating <a href="/wiki/Electromagnetic_interference" title="Electromagnetic interference">electromagnetic interference</a>. </p><p>Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level. Other advantages compared to E-I types, include smaller size (about half), lower weight (about half), less mechanical hum (making them superior in audio amplifiers), lower exterior magnetic field (about one tenth), low off-load losses (making them more efficient in standby circuits), single-bolt mounting, and greater choice of shapes. The main disadvantages are higher cost and limited power capacity (see <a href="#Classification_parameters">Classification parameters</a> below). Because of the lack of a residual gap in the magnetic path, toroidal transformers also tend to exhibit higher inrush current, compared to laminated E-I types. </p><p>Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of inductive components. A drawback of toroidal transformer construction is the higher labor cost of winding. This is because it is necessary to pass the entire length of a coil winding through the core aperture each time a single turn is added to the coil. As a consequence, toroidal transformers rated more than a few kVA are uncommon. Relatively few toroids are offered with power ratings above 10 kVA, and practically none above 25 kVA. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Air_cores">Air cores</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=16" title="Edit section: Air cores"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A transformer can be produced by placing the windings near each other, an arrangement termed an "air-core" transformer. An air-core transformer eliminates loss due to hysteresis in the core material.<sup id="cite_ref-calvert2001_16-2" class="reference"><a href="#cite_note-calvert2001-16"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The magnetizing inductance is drastically reduced by the lack of a magnetic core, resulting in large magnetizing currents and losses if used at low frequencies. Air-core transformers are unsuitable for use in power distribution,<sup id="cite_ref-calvert2001_16-3" class="reference"><a href="#cite_note-calvert2001-16"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> but are frequently employed in radio-frequency applications.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Air cores are also used for <a href="/wiki/Transformer_types#Resonant_transformer" title="Transformer types">resonant transformers</a> such as Tesla coils, where they can achieve reasonably low loss despite the low magnetizing inductance. </p> <div class="mw-heading mw-heading3"><h3 id="Windings">Windings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=17" title="Edit section: Windings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer-hightolow_smaller.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Transformer-hightolow_smaller.jpg/220px-Transformer-hightolow_smaller.jpg" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Transformer-hightolow_smaller.jpg/330px-Transformer-hightolow_smaller.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Transformer-hightolow_smaller.jpg/440px-Transformer-hightolow_smaller.jpg 2x" data-file-width="1099" data-file-height="995" /></a><figcaption>Windings are usually arranged concentrically to minimize flux leakage.</figcaption></figure> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer_min_stray_field_geometry.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Transformer_min_stray_field_geometry.svg/220px-Transformer_min_stray_field_geometry.svg.png" decoding="async" width="220" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Transformer_min_stray_field_geometry.svg/330px-Transformer_min_stray_field_geometry.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Transformer_min_stray_field_geometry.svg/440px-Transformer_min_stray_field_geometry.svg.png 2x" data-file-width="1949" data-file-height="1772" /></a><figcaption>Cut view through transformer windings. Legend: <br /> <b>White</b>: Air, liquid or other insulating medium <br /> <b>Green spiral</b>: <a href="/wiki/Electrical_steel" title="Electrical steel">Grain oriented silicon steel</a><br /> <b>Black</b>: Primary winding <br /> <b>Red</b>: Secondary winding </figcaption></figure> <p>The electrical conductor used for the windings depends upon the application, but in all cases the individual turns must be electrically insulated from each other to ensure that the current travels throughout every turn. For small transformers, in which currents are low and the potential difference between adjacent turns is small, the coils are often wound from <a href="/wiki/Enameled_wire" class="mw-redirect" title="Enameled wire">enamelled magnet wire</a>. Larger power transformers may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of <a href="/wiki/Transformerboard" class="mw-redirect" title="Transformerboard">pressboard</a>.<sup id="cite_ref-CEGB1982_43-0" class="reference"><a href="#cite_note-CEGB1982-43"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided <a href="/wiki/Litz_wire" title="Litz wire">Litz wire</a> to minimize the <a href="/wiki/Skin_effect" title="Skin effect">skin-effect</a> and proximity effect losses.<sup id="cite_ref-dixon_44-0" class="reference"><a href="#cite_note-dixon-44"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> Large power transformers use multiple-stranded conductors as well, since even at low power frequencies non-uniform distribution of current would otherwise exist in high-current windings.<sup id="cite_ref-CEGB1982_43-1" class="reference"><a href="#cite_note-CEGB1982-43"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Each strand is individually insulated, and the strands are arranged so that at certain points in the winding, or throughout the whole winding, each portion occupies different relative positions in the complete conductor. The transposition equalizes the current flowing in each strand of the conductor, and reduces eddy current losses in the winding itself. The stranded conductor is also more flexible than a solid conductor of similar size, aiding manufacture.<sup id="cite_ref-CEGB1982_43-2" class="reference"><a href="#cite_note-CEGB1982-43"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>The windings of signal transformers minimize leakage inductance and stray capacitance to improve high-frequency response. Coils are split into sections, and those sections interleaved between the sections of the other winding. </p><p>Power-frequency transformers may have <i>taps</i> at intermediate points on the winding, usually on the higher voltage winding side, for voltage adjustment. Taps may be manually reconnected, or a manual or automatic switch may be provided for changing taps. Automatic on-load <a href="/wiki/Tap_changer" title="Tap changer">tap changers</a> are used in electric power transmission or distribution, on equipment such as <a href="/wiki/Arc_furnace" class="mw-redirect" title="Arc furnace">arc furnace</a> transformers, or for automatic voltage regulators for sensitive loads. Audio-frequency transformers, used for the distribution of audio to public address loudspeakers, have taps to allow adjustment of impedance to each speaker. A <a href="/wiki/Center_tap" title="Center tap">center-tapped transformer</a> is often used in the output stage of an audio power <a href="/wiki/Amplifier" title="Amplifier">amplifier</a> in a <a href="/wiki/Push-pull_converter" class="mw-redirect" title="Push-pull converter">push-pull circuit</a>. Modulation transformers in <a href="/wiki/Amplitude_modulation" title="Amplitude modulation">AM</a> transmitters are very similar. </p> <div class="mw-heading mw-heading3"><h3 id="Cooling">Cooling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=18" title="Edit section: Cooling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Drehstromtransformater_im_Schnitt_Hochspannung.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Drehstromtransformater_im_Schnitt_Hochspannung.jpg/170px-Drehstromtransformater_im_Schnitt_Hochspannung.jpg" decoding="async" width="170" height="291" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Drehstromtransformater_im_Schnitt_Hochspannung.jpg/255px-Drehstromtransformater_im_Schnitt_Hochspannung.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Drehstromtransformater_im_Schnitt_Hochspannung.jpg/340px-Drehstromtransformater_im_Schnitt_Hochspannung.jpg 2x" data-file-width="640" data-file-height="1095" /></a><figcaption>Cutaway view of liquid-immersed transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation.</figcaption></figure> <p>It is a rule of thumb that the life expectancy of electrical insulation is halved for about every 7 °C to 10 °C increase in <a href="/wiki/Operating_temperature" title="Operating temperature">operating temperature</a> (an instance of the application of the <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a>).<sup id="cite_ref-Harlow2004-3_45-0" class="reference"><a href="#cite_note-Harlow2004-3-45"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>Small dry-type and liquid-immersed transformers are often self-cooled by natural convection and <a href="/wiki/Radiation" title="Radiation">radiation</a> heat dissipation. As power ratings increase, transformers are often cooled by forced-air cooling, forced-oil cooling, water-cooling, or combinations of these.<sup id="cite_ref-Pansini1999-32_46-0" class="reference"><a href="#cite_note-Pansini1999-32-46"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Large transformers are filled with <a href="/wiki/Transformer_oil" title="Transformer oil">transformer oil</a> that both cools and insulates the windings.<sup id="cite_ref-willis2004_47-0" class="reference"><a href="#cite_note-willis2004-47"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> Transformer oil is often a highly refined <a href="/wiki/Mineral_oil" title="Mineral oil">mineral oil</a> that cools the windings and insulation by circulating within the transformer tank. The mineral oil and <a href="/wiki/Electrical_insulation_paper" title="Electrical insulation paper">paper</a> insulation system has been extensively studied and used for more than 100 years. It is estimated that 50% of power transformers will survive 50 years of use, that the average age of failure of power transformers is about 10 to 15 years, and that about 30% of power transformer failures are due to insulation and overloading failures.<sup id="cite_ref-Hartley_(2003)_48-0" class="reference"><a href="#cite_note-Hartley_(2003)-48"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hartley_(~2011)_49-0" class="reference"><a href="#cite_note-Hartley_(~2011)-49"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Prolonged operation at elevated temperature degrades insulating properties of winding insulation and dielectric coolant, which not only shortens transformer life but can ultimately lead to catastrophic transformer failure.<sup id="cite_ref-Harlow2004-3_45-1" class="reference"><a href="#cite_note-Harlow2004-3-45"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> With a great body of empirical study as a guide, <a href="/wiki/Transformer_oil_testing" title="Transformer oil testing">transformer oil testing</a> including <a href="/wiki/Dissolved_gas_analysis" title="Dissolved gas analysis">dissolved gas analysis</a> provides valuable maintenance information. </p><p>Building regulations in many jurisdictions require indoor liquid-filled transformers to either use dielectric fluids that are less flammable than oil, or be installed in fire-resistant rooms.<sup id="cite_ref-De_Keulenaer2001_23-2" class="reference"><a href="#cite_note-De_Keulenaer2001-23"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Air-cooled dry transformers can be more economical where they eliminate the cost of a fire-resistant transformer room. </p><p>The tank of liquid-filled transformers often has radiators through which the liquid coolant circulates by natural convection or fins. Some large transformers employ electric fans for forced-air cooling, pumps for forced-liquid cooling, or have <a href="/wiki/Heat_exchangers" class="mw-redirect" title="Heat exchangers">heat exchangers</a> for water-cooling.<sup id="cite_ref-willis2004_47-1" class="reference"><a href="#cite_note-willis2004-47"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> An oil-immersed transformer may be equipped with a <a href="/wiki/Buchholz_relay" title="Buchholz relay">Buchholz relay</a>, which, depending on severity of gas accumulation due to internal arcing, is used to either trigger an alarm or de-energize the transformer.<sup id="cite_ref-Harlow2004-2_37-1" class="reference"><a href="#cite_note-Harlow2004-2-37"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Oil-immersed transformer installations usually include fire protection measures such as walls, oil containment, and fire-suppression sprinkler systems. </p><p><a href="/wiki/Polychlorinated_biphenyl" title="Polychlorinated biphenyl">Polychlorinated biphenyls</a> (PCBs) have properties that once favored their use as a <a href="/wiki/Coolant" title="Coolant">dielectric coolant</a>, though concerns over their <a href="/wiki/Persistent_organic_pollutant" title="Persistent organic pollutant">environmental persistence</a> led to a widespread ban on their use.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Today, non-toxic, stable <a href="/wiki/Silicone" title="Silicone">silicone</a>-based oils, or <a href="/wiki/Fluorocarbon" title="Fluorocarbon">fluorinated hydrocarbons</a> may be used where the expense of a fire-resistant liquid offsets additional building cost for a transformer vault.<sup id="cite_ref-De_Keulenaer2001_23-3" class="reference"><a href="#cite_note-De_Keulenaer2001-23"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kulkarni2004-2_51-0" class="reference"><a href="#cite_note-Kulkarni2004-2-51"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> However, the long life span of transformers can mean that the potential for exposure can be high long after banning.<sup id="cite_ref-:0_52-0" class="reference"><a href="#cite_note-:0-52"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Some transformers are gas-insulated. Their windings are enclosed in sealed, pressurized tanks and often cooled by <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a> or <a href="/wiki/Sulfur_hexafluoride" title="Sulfur hexafluoride">sulfur hexafluoride</a> gas.<sup id="cite_ref-Kulkarni2004-2_51-1" class="reference"><a href="#cite_note-Kulkarni2004-2-51"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>Experimental power transformers in the 500–1,000 kVA range have been built with <a href="/wiki/Liquid_nitrogen" title="Liquid nitrogen">liquid nitrogen</a> or <a href="/wiki/Liquid_helium" title="Liquid helium">helium</a> cooled <a href="/wiki/Superconductivity" title="Superconductivity">superconducting</a> windings, which eliminates winding losses without affecting core losses.<sup id="cite_ref-Mehta_(1997)_53-0" class="reference"><a href="#cite_note-Mehta_(1997)-53"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pansini1999-66_54-0" class="reference"><a href="#cite_note-Pansini1999-66-54"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Insulation">Insulation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=19" title="Edit section: Insulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Substation_transfomer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Substation_transfomer.jpg/220px-Substation_transfomer.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Substation_transfomer.jpg/330px-Substation_transfomer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Substation_transfomer.jpg/440px-Substation_transfomer.jpg 2x" data-file-width="2976" data-file-height="3968" /></a><figcaption>Substation transformer undergoing testing.</figcaption></figure> <p>Insulation must be provided between the individual turns of the windings, between the windings, between windings and core, and at the terminals of the winding. </p><p>Inter-turn insulation of small transformers may be a layer of insulating varnish on the wire. Layer of paper or polymer films may be inserted between layers of windings, and between primary and secondary windings. A transformer may be coated or dipped in a polymer resin to improve the strength of windings and protect them from moisture or corrosion. The resin may be impregnated into the winding insulation using combinations of vacuum and pressure during the coating process, eliminating all air voids in the winding. In the limit, the entire coil may be placed in a mold, and resin cast around it as a solid block, encapsulating the windings.<sup id="cite_ref-Lane_(2007)_55-0" class="reference"><a href="#cite_note-Lane_(2007)-55"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p>Large oil-filled power transformers use windings wrapped with insulating paper, which is impregnated with oil during assembly of the transformer. Oil-filled transformers use highly refined mineral oil to insulate and cool the windings and core. Construction of oil-filled transformers requires that the insulation covering the windings be thoroughly dried of residual moisture before the oil is introduced. Drying may be done by circulating hot air around the core, by circulating externally heated transformer oil, or by vapor-phase drying (VPD) where an evaporated solvent transfers heat by condensation on the coil and core. For small transformers, resistance heating by injection of current into the windings is used. </p> <div class="mw-heading mw-heading3"><h3 id="Bushings">Bushings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=20" title="Edit section: Bushings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Larger transformers are provided with high-voltage insulated <a href="/wiki/Bushing_(electrical)" title="Bushing (electrical)">bushings</a> made of polymers or porcelain. A large bushing can be a complex structure since it must provide careful control of the <a href="/wiki/Electric_field_gradient" title="Electric field gradient">electric field gradient</a> without letting the transformer leak oil.<sup id="cite_ref-Ryan2004-416_56-0" class="reference"><a href="#cite_note-Ryan2004-416-56"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Classification_parameters">Classification parameters</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=21" title="Edit section: Classification parameters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Melbourne_Terminal_Station.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Melbourne_Terminal_Station.JPG/220px-Melbourne_Terminal_Station.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Melbourne_Terminal_Station.JPG/330px-Melbourne_Terminal_Station.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Melbourne_Terminal_Station.JPG/440px-Melbourne_Terminal_Station.JPG 2x" data-file-width="4000" data-file-height="3000" /></a><figcaption>An <a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">electrical substation</a> in <a href="/wiki/Melbourne" title="Melbourne">Melbourne</a>, <a href="/wiki/Australia" title="Australia">Australia</a> showing three of five 220 kV – 66 kV transformers, each with a capacity of 150 MVA</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Camoflaged_Transformer_Langley_City.jpg" class="mw-file-description"><img alt="Camouflaged transformer in Langley City" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Camoflaged_Transformer_Langley_City.jpg/220px-Camoflaged_Transformer_Langley_City.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Camoflaged_Transformer_Langley_City.jpg/330px-Camoflaged_Transformer_Langley_City.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Camoflaged_Transformer_Langley_City.jpg/440px-Camoflaged_Transformer_Langley_City.jpg 2x" data-file-width="3264" data-file-height="2448" /></a><figcaption><a href="/wiki/Camouflage" title="Camouflage">Camouflaged</a> transformer in <a href="/wiki/Langley_City" class="mw-redirect" title="Langley City">Langley City</a>, <a href="/wiki/Canada" title="Canada">Canada</a></figcaption></figure> <p>Transformers can be classified in many ways, such as the following: </p> <ul><li><i><a href="/wiki/Power_rating" title="Power rating">Power rating</a></i>: From a fraction of a volt-ampere (VA) to over a thousand MVA.</li> <li><i>Duty of a transformer</i>: Continuous, short-time, intermittent, periodic, varying.</li> <li><i>Frequency range</i>: <a href="/wiki/Utility_frequency" title="Utility frequency">Power-frequency</a>, <a href="/wiki/Audio_frequency" title="Audio frequency">audio-frequency</a>, or <a href="/wiki/Radio_frequency" title="Radio frequency">radio-frequency</a>.</li> <li><i>Voltage class</i>: From a few volts to hundreds of kilovolts.</li> <li><i>Cooling type</i>: Dry or liquid-immersed; self-cooled, forced air-cooled;forced oil-cooled, water-cooled.</li> <li><i>Application</i>: power supply, impedance matching, output voltage and current stabilizer, <a href="/wiki/Pulse_transformer" class="mw-redirect" title="Pulse transformer">pulse</a>, circuit isolation, <a href="/wiki/Electricity_distribution" class="mw-redirect" title="Electricity distribution">power distribution</a>, <a href="/wiki/Rectifier" title="Rectifier">rectifier</a>, <a href="/wiki/Arc_furnace" class="mw-redirect" title="Arc furnace">arc furnace</a>, amplifier output, etc..</li> <li><i>Basic magnetic form</i>: Core form, shell form, concentric, sandwich.</li> <li><i>Constant-potential transformer descriptor</i>: Step-up, step-down, <a href="/wiki/Isolation_transformer" title="Isolation transformer">isolation</a>.</li> <li><i>General winding configuration</i>: By <a href="/wiki/Vector_group" title="Vector group">IEC vector group</a>, two-winding combinations of the phase designations delta, wye or star, and <a href="/wiki/Zigzag_transformer" title="Zigzag transformer">zigzag</a>; <a href="/wiki/Autotransformer" title="Autotransformer">autotransformer</a>, <a href="/wiki/Scott-T_transformer" title="Scott-T transformer">Scott-T</a></li> <li><i>Rectifier phase-shift winding configuration</i>: 2-winding, 6-pulse; 3-winding, 12-pulse; . . ., <span class="nowrap"><i>n</i>-winding</span>, [<i>n</i> − 1]·6-pulse; polygon; etc..</li></ul> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=22" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Transformer-Limestone-Generating-Station.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Transformer-Limestone-Generating-Station.JPG/220px-Transformer-Limestone-Generating-Station.JPG" decoding="async" width="220" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Transformer-Limestone-Generating-Station.JPG/330px-Transformer-Limestone-Generating-Station.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Transformer-Limestone-Generating-Station.JPG/440px-Transformer-Limestone-Generating-Station.JPG 2x" data-file-width="2108" data-file-height="1888" /></a><figcaption>Transformer at the <a href="/wiki/Limestone_Generating_Station" title="Limestone Generating Station">Limestone Generating Station</a> in <a href="/wiki/Manitoba" title="Manitoba">Manitoba</a>, Canada</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Transformer_types" title="Transformer types">Transformer types</a></div> <p>Various specific electrical application designs require a variety of <a href="/wiki/Transformer_types" title="Transformer types">transformer types</a>. Although they all share the basic characteristic transformer principles, they are customized in construction or electrical properties for certain installation requirements or circuit conditions. </p><p>In <a href="/wiki/Electric_power_transmission" title="Electric power transmission">electric power transmission</a>, transformers allow transmission of electric power at high voltages, which reduces the loss due to heating of the wires. This allows generating plants to be located economically at a distance from electrical consumers.<sup id="cite_ref-Heathcote1998-1_57-0" class="reference"><a href="#cite_note-Heathcote1998-1-57"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> All but a tiny fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer.<sup id="cite_ref-nailen_27-1" class="reference"><a href="#cite_note-nailen-27"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>In many electronic devices, a transformer is used to convert voltage from the distribution wiring to convenient values for the circuit requirements, either directly at the power line frequency or through a <a href="/wiki/Switch_mode_power_supply" class="mw-redirect" title="Switch mode power supply">switch mode power supply</a>. </p><p>Signal and audio transformers are used to couple stages of <a href="/wiki/Amplifier" title="Amplifier">amplifiers</a> and to match devices such as <a href="/wiki/Microphone" title="Microphone">microphones</a> and <a href="/wiki/Record_player" class="mw-redirect" title="Record player">record players</a> to the input of amplifiers. Audio transformers allowed <a href="/wiki/Telephone" title="Telephone">telephone</a> circuits to carry on a <a href="/wiki/Hybrid_coil" class="mw-redirect" title="Hybrid coil">two-way conversation</a> over a single pair of wires. A <a href="/wiki/Balun" title="Balun">balun</a> transformer converts a signal that is referenced to ground to a signal that has <a href="/wiki/Balanced_line" title="Balanced line">balanced voltages to ground</a>, such as between external cables and internal circuits. Isolation transformers prevent leakage of current into the secondary circuit and are used in medical equipment and at construction sites. Resonant transformers are used for coupling between stages of radio receivers, or in high-voltage Tesla coils. </p> <div style="clear:both;" class=""></div> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Vermogentransformator_1.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Vermogentransformator_1.GIF/440px-Vermogentransformator_1.GIF" decoding="async" width="440" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Vermogentransformator_1.GIF/660px-Vermogentransformator_1.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Vermogentransformator_1.GIF/880px-Vermogentransformator_1.GIF 2x" data-file-width="1479" data-file-height="942" /></a><figcaption>Schematic of a large oil-filled power transformer 1. Tank 2. Lid 3. Conservator tank 4. Oil level indicator 5. Buchholz relay for detecting gas bubbles after an internal fault 6. Piping 7. Tap changer 8. Drive motor for tap changer 9. Drive shaft for tap changer 10. High voltage (HV) bushing 11. High voltage bushing current transformers 12. Low voltage (LV) bushing 13. Low voltage current transformers 14. Bushing voltage-transformer for metering 15. Core 16. Yoke of the core 17. Limbs connect the yokes and hold them up 18. Coils 19. Internal wiring between coils and tapchanger 20. Oil release valve 21. Vacuum valve</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=23" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Discovery_of_induction">Discovery of induction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=24" title="Edit section: Discovery of induction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Induction_experiment.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Induction_experiment.png/220px-Induction_experiment.png" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Induction_experiment.png/330px-Induction_experiment.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Induction_experiment.png/440px-Induction_experiment.png 2x" data-file-width="826" data-file-height="625" /></a><figcaption>Faraday's experiment with induction between coils of wire<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a>, the principle of the operation of the transformer, was discovered independently by <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> in 1831 and <a href="/wiki/Joseph_Henry" title="Joseph Henry">Joseph Henry</a> in 1832.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-MacPhersonRC_61-0" class="reference"><a href="#cite_note-MacPhersonRC-61"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Guarnieri2013-56_62-0" class="reference"><a href="#cite_note-Guarnieri2013-56-62"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Only Faraday furthered his experiments to the point of working out the equation describing the relationship between EMF and magnetic flux now known as <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\mathcal {E}}|=\left|{{\mathrm {d} \Phi _{\text{B}}} \over \mathrm {d} t}\right|,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\mathcal {E}}|=\left|{{\mathrm {d} \Phi _{\text{B}}} \over \mathrm {d} t}\right|,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24e04118a284bef7188cdc6a890ec18796b1daec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.233ex; height:5.843ex;" alt="{\displaystyle |{\mathcal {E}}|=\left|{{\mathrm {d} \Phi _{\text{B}}} \over \mathrm {d} t}\right|,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\mathcal {E}}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\mathcal {E}}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f77a1c5f85a871b24dae1a6ae22703ac58b7050c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.605ex; height:2.843ex;" alt="{\displaystyle |{\mathcal {E}}|}"></span> is the magnitude of the EMF in volts and Φ<sub>B</sub> is the magnetic flux through the circuit in <a href="/wiki/Weber_(unit)" title="Weber (unit)">webers</a>.<sup id="cite_ref-Chow171_63-0" class="reference"><a href="#cite_note-Chow171-63"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p><p>Faraday performed early experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first <a href="/wiki/Toroid_(geometry)" class="mw-redirect" title="Toroid (geometry)">toroidal</a> closed-core transformer.<sup id="cite_ref-Guarnieri2013-56_62-1" class="reference"><a href="#cite_note-Guarnieri2013-56-62"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> However he only applied individual pulses of current to his transformer, and never discovered the relation between the turns ratio and EMF in the windings. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Induktionsapparat_hg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Induktionsapparat_hg.jpg/220px-Induktionsapparat_hg.jpg" decoding="async" width="220" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Induktionsapparat_hg.jpg/330px-Induktionsapparat_hg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Induktionsapparat_hg.jpg/440px-Induktionsapparat_hg.jpg 2x" data-file-width="2460" data-file-height="1770" /></a><figcaption>Induction coil, 1900, Bremerhaven, Germany</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Induction_coils">Induction coils</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=25" title="Edit section: Induction coils"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Induction_coil" title="Induction coil">Induction coil</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Faradays_transformer.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Faradays_transformer.png/220px-Faradays_transformer.png" decoding="async" width="220" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Faradays_transformer.png/330px-Faradays_transformer.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Faradays_transformer.png/440px-Faradays_transformer.png 2x" data-file-width="1484" data-file-height="1568" /></a><figcaption>Faraday's ring transformer</figcaption></figure> <p>The first type of transformer to see wide use was the <a href="/wiki/Induction_coil" title="Induction coil">induction coil</a>, invented by Irish-Catholic Rev. <a href="/wiki/Nicholas_Callan" title="Nicholas Callan">Nicholas Callan</a> of <a href="/wiki/Maynooth_College" class="mw-redirect" title="Maynooth College">Maynooth College</a>, Ireland in 1836.<sup id="cite_ref-Guarnieri2013-56_62-2" class="reference"><a href="#cite_note-Guarnieri2013-56-62"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> He was one of the first researchers to realize the more turns the secondary winding has in relation to the primary winding, the larger the induced secondary EMF will be. Induction coils evolved from scientists' and inventors' efforts to get higher voltages from batteries. Since batteries produce <a href="/wiki/Direct_current" title="Direct current">direct current (DC)</a> rather than AC, induction coils relied upon vibrating <a href="/wiki/Electrical_contact" title="Electrical contact">electrical contacts</a> that regularly interrupted the current in the primary to create the flux changes necessary for induction. Between the 1830s and the 1870s, efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformers. </p> <div class="mw-heading mw-heading3"><h3 id="First_alternating_current_transformers">First alternating current transformers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=26" title="Edit section: First alternating current transformers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>By the 1870s, efficient <a href="/wiki/Electric_generator" title="Electric generator">generators</a> producing <a href="/wiki/Alternating_current" title="Alternating current">alternating current (AC)</a> were available, and it was found AC could power an induction coil directly, without an <a href="/wiki/Interrupter" title="Interrupter">interrupter</a>. </p><p>In 1876, Russian engineer <a href="/wiki/Pavel_Yablochkov" title="Pavel Yablochkov">Pavel Yablochkov</a> invented a lighting system based on a set of induction coils where the primary windings were connected to a source of AC. The secondary windings could be connected to several <a href="/wiki/Yablochkov_candle" title="Yablochkov candle">'electric candles'</a> (arc lamps) of his own design. The coils Yablochkov employed functioned essentially as transformers.<sup id="cite_ref-maglab_65-0" class="reference"><a href="#cite_note-maglab-65"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p>In 1878, the <a href="/wiki/Ganz_Works" title="Ganz Works">Ganz factory</a>, Budapest, Hungary, began producing equipment for electric lighting and, by 1883, had installed over fifty systems in Austria-Hungary. Their AC systems used arc and incandescent lamps, generators, and other equipment.<sup id="cite_ref-Guarnieri2013-56_62-3" class="reference"><a href="#cite_note-Guarnieri2013-56-62"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hughes1993-95_66-0" class="reference"><a href="#cite_note-Hughes1993-95-66"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>In 1882, <a href="/wiki/Lucien_Gaulard" title="Lucien Gaulard">Lucien Gaulard</a> and <a href="/wiki/John_Dixon_Gibbs" title="John Dixon Gibbs">John Dixon Gibbs</a> first exhibited a device with an initially widely criticized laminated plate open iron core called a 'secondary generator' in London, then sold the idea to the <a href="/wiki/Westinghouse_Electric_Corporation" title="Westinghouse Electric Corporation">Westinghouse</a> company in the United States in 1886.<sup id="cite_ref-allan_34-1" class="reference"><a href="#cite_note-allan-34"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> They also exhibited the invention in Turin, Italy in 1884, where it was highly successful and adopted for an electric lighting system.<sup id="cite_ref-Uppenborn1889_67-0" class="reference"><a href="#cite_note-Uppenborn1889-67"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> Their open-core device used a fixed 1:1 ratio to supply a series circuit for the utilization load (lamps). The voltage was controlled by moving the iron core in or out.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Early_series_circuit_transformer_distribution">Early series circuit transformer distribution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=27" title="Edit section: Early series circuit transformer distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Induction coils with open magnetic circuits are inefficient at transferring power to <a href="/wiki/Electrical_load" title="Electrical load">loads</a>. Until about 1880, the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit. Open-core transformers with a ratio near 1:1 were connected with their primaries in series to allow use of a high voltage for transmission while presenting a low voltage to the lamps. The inherent flaw in this method was that turning off a single lamp (or other electric device) affected the voltage supplied to all others on the same circuit. Many adjustable transformer designs were introduced to compensate for this problematic characteristic of the series circuit, including those employing methods of adjusting the core or bypassing the magnetic flux around part of a coil.<sup id="cite_ref-Uppenborn1889_67-1" class="reference"><a href="#cite_note-Uppenborn1889-67"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> Efficient, practical transformer designs did not appear until the 1880s, but within a decade, the transformer would be instrumental in the <a href="/wiki/War_of_the_currents" title="War of the currents">war of the currents</a>, and in seeing AC distribution systems triumph over their DC counterparts, a position in which they have remained dominant ever since.<sup id="cite_ref-Coltman1988_69-0" class="reference"><a href="#cite_note-Coltman1988-69"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Trafo1885.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Trafo1885.jpg/220px-Trafo1885.jpg" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Trafo1885.jpg/330px-Trafo1885.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Trafo1885.jpg/440px-Trafo1885.jpg 2x" data-file-width="996" data-file-height="886" /></a><figcaption>Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles.<sup id="cite_ref-Uppenborn1889_67-2" class="reference"><a href="#cite_note-Uppenborn1889-67"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:DBZ_trafo.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/DBZ_trafo.jpg/220px-DBZ_trafo.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/DBZ_trafo.jpg/330px-DBZ_trafo.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/DBZ_trafo.jpg/440px-DBZ_trafo.jpg 2x" data-file-width="1712" data-file-height="1368" /></a><figcaption>Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:ZBD_team.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/ZBD_team.jpg/220px-ZBD_team.jpg" decoding="async" width="220" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/ZBD_team.jpg/330px-ZBD_team.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/ZBD_team.jpg/440px-ZBD_team.jpg 2x" data-file-width="800" data-file-height="491" /></a><figcaption>The ZBD team consisted of <a href="/wiki/K%C3%A1roly_Zipernowsky" title="Károly Zipernowsky">Károly Zipernowsky</a>, <a href="/wiki/Ott%C3%B3_Bl%C3%A1thy" title="Ottó Bláthy">Ottó Bláthy</a> and <a href="/wiki/Miksa_D%C3%A9ri" title="Miksa Déri">Miksa Déri</a></figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:StanleyTransformer.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/StanleyTransformer.png/220px-StanleyTransformer.png" decoding="async" width="220" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/c1/StanleyTransformer.png 1.5x" data-file-width="268" data-file-height="219" /></a><figcaption>Stanley's 1886 design for adjustable gap open-core induction coils</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Closed-core_transformers_and_parallel_power_distribution">Closed-core transformers and parallel power distribution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=28" title="Edit section: Closed-core transformers and parallel power distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the autumn of 1884, <a href="/wiki/K%C3%A1roly_Zipernowsky" title="Károly Zipernowsky">Károly Zipernowsky</a>, <a href="/wiki/Ott%C3%B3_Bl%C3%A1thy" title="Ottó Bláthy">Ottó Bláthy</a> and <a href="/wiki/Miksa_D%C3%A9ri" title="Miksa Déri">Miksa Déri</a> (ZBD), three Hungarian engineers associated with the <a href="/wiki/Ganz_Works" title="Ganz Works">Ganz Works</a>, had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage.<sup id="cite_ref-Hughes1993-95_66-1" class="reference"><a href="#cite_note-Hughes1993-95-66"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> The Ganz factory had also in the autumn of 1884 made delivery of the world's first five high-efficiency AC transformers, the first of these units having been shipped on September 16, 1884.<sup id="cite_ref-Halacsy1961_70-0" class="reference"><a href="#cite_note-Halacsy1961-70"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.<sup id="cite_ref-Halacsy1961_70-1" class="reference"><a href="#cite_note-Halacsy1961-70"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around an iron wire ring core or surrounded by an iron wire core.<sup id="cite_ref-Uppenborn1889_67-3" class="reference"><a href="#cite_note-Uppenborn1889-67"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> The two designs were the first application of the two basic transformer constructions in common use to this day, termed "core form" or "shell form" .<sup id="cite_ref-Lucas_(2000)_71-0" class="reference"><a href="#cite_note-Lucas_(2000)-71"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </p><p>In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see <a href="#Toroidal_cores">Toroidal cores</a> below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs.<sup id="cite_ref-Jeszenszky_72-0" class="reference"><a href="#cite_note-Jeszenszky-72"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1,400 to 2,000 V) than the voltage of utilization loads (100 V initially preferred).<sup id="cite_ref-Ideal_(2008)_73-0" class="reference"><a href="#cite_note-Ideal_(2008)-73"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-BUTE-OMIKK-BlathyOtto_74-0" class="reference"><a href="#cite_note-BUTE-OMIKK-BlathyOtto-74"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of <a href="/wiki/Shunt_(electrical)" title="Shunt (electrical)">parallel shunt connections</a>, and Déri had performed the experiments;<sup id="cite_ref-Smil_75-0" class="reference"><a href="#cite_note-Smil-75"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> In early 1885, the three engineers also eliminated the problem of <a href="/wiki/Eddy_current" title="Eddy current">eddy current</a> losses with the invention of the lamination of electromagnetic cores.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p><p>Transformers today are designed on the principles discovered by the three engineers. They also popularized the word 'transformer' to describe a device for altering the EMF of an electric current<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> although the term had already been in use by 1882.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> In 1886, the ZBD engineers designed, and the Ganz factory supplied electrical equipment for, the world's first <a href="/wiki/Power_station" title="Power station">power station</a> that used AC generators to power a parallel connected common electrical network, the steam-powered Rome-Cerchi power plant.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Westinghouse_improvements">Westinghouse improvements</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=29" title="Edit section: Westinghouse improvements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Blachy_transformatorowe.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Blachy_transformatorowe.jpg/220px-Blachy_transformatorowe.jpg" decoding="async" width="220" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Blachy_transformatorowe.jpg/330px-Blachy_transformatorowe.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Blachy_transformatorowe.jpg/440px-Blachy_transformatorowe.jpg 2x" data-file-width="1668" data-file-height="840" /></a><figcaption>E-shaped plates for transformer cores developed by Westinghouse</figcaption></figure> <p>Building on the advancement of AC technology in Europe,<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> <a href="/wiki/George_Westinghouse" title="George Westinghouse">George Westinghouse</a> founded the <a href="/wiki/Westinghouse_Electric_Corporation" title="Westinghouse Electric Corporation">Westinghouse Electric</a> in Pittsburgh, Pennsylvania, on January 8, 1886.<sup id="cite_ref-Tinicum_Township_82-0" class="reference"><a href="#cite_note-Tinicum_Township-82"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> The new firm became active in developing alternating current (AC) electric infrastructure throughout the United States. The <a href="/wiki/Edison_Electric_Light_Company" class="mw-redirect" title="Edison Electric Light Company">Edison Electric Light Company</a> held an option on the US rights for the ZBD transformers, requiring Westinghouse to pursue alternative designs on the same principles. George Westinghouse had bought Gaulard and Gibbs' patents for $50,000 in February 1886.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> He assigned to <a href="/wiki/William_Stanley,_Jr." class="mw-redirect" title="William Stanley, Jr.">William Stanley</a> the task of redesign the Gaulard and Gibbs transformer for commercial use in United States.<sup id="cite_ref-Skrabec_84-0" class="reference"><a href="#cite_note-Skrabec-84"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> Stanley's first patented design was for induction coils with single cores of soft iron and adjustable gaps to regulate the EMF present in the secondary winding (see image). This design<sup id="cite_ref-Coltman2002_85-0" class="reference"><a href="#cite_note-Coltman2002-85"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> was first used commercially in the US in 1886<sup id="cite_ref-IEC_History_86-0" class="reference"><a href="#cite_note-IEC_History-86"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> but Westinghouse was intent on improving the Stanley design to make it (unlike the ZBD type) easy and cheap to produce.<sup id="cite_ref-Coltman2002_85-1" class="reference"><a href="#cite_note-Coltman2002-85"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p><p>Westinghouse, Stanley and associates soon developed a core that was easier to manufacture, consisting of a stack of thin 'E‑shaped' iron plates insulated by thin sheets of paper or other insulating material. Pre-wound copper coils could then be slid into place, and straight iron plates laid in to create a closed magnetic circuit. Westinghouse obtained a patent for the new low-cost design in 1887.<sup id="cite_ref-Smil_75-1" class="reference"><a href="#cite_note-Smil-75"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_early_transformer_designs">Other early transformer designs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=30" title="Edit section: Other early transformer designs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1889, Russian-born engineer <a href="/wiki/Mikhail_Dolivo-Dobrovolsky" title="Mikhail Dolivo-Dobrovolsky">Mikhail Dolivo-Dobrovolsky</a> developed the first <a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">three-phase</a> transformer at the <a href="/wiki/Allgemeine_Elektricit%C3%A4ts-Gesellschaft" class="mw-redirect" title="Allgemeine Elektricitäts-Gesellschaft">Allgemeine Elektricitäts-Gesellschaft</a> ('General Electricity Company') in Germany.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> </p><p>In 1891, <a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Nikola Tesla</a> invented the <a href="/wiki/Tesla_coil" title="Tesla coil">Tesla coil</a>, an air-cored, dual-tuned resonant transformer for producing very <a href="/wiki/High_voltage" title="High voltage">high voltages</a> at high frequency.<sup id="cite_ref-PBS_88-0" class="reference"><a href="#cite_note-PBS-88"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Audio_frequency" title="Audio frequency">Audio frequency</a> transformers ("<a href="/wiki/Repeating_coil" title="Repeating coil">repeating coils</a>") were used by early experimenters in the development of the <a href="/wiki/Telephone" title="Telephone">telephone</a>.<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=31" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 23em;"> <ul><li><a href="/wiki/High-voltage_transformer_fire_barriers" title="High-voltage transformer fire barriers">High-voltage transformer fire barriers</a></li> <li><a href="/wiki/Inductive_coupling" title="Inductive coupling">Inductive coupling</a></li> <li><a href="/wiki/Load_profile" title="Load profile">Load profile</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Parametric_transformer" title="Parametric transformer">Parametric transformer</a></li> <li><a href="/wiki/Polyphase_system" title="Polyphase system">Polyphase system</a></li> <li><a href="/wiki/Power_inverter" title="Power inverter">Power inverter</a></li> <li><a href="/wiki/Rectiformer" title="Rectiformer">Rectiformer</a></li> <li><a href="/wiki/Voltage_converter" title="Voltage converter">Voltage converter</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=32" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">With turns of the winding oriented perpendicularly to the magnetic field lines, the flux is the product of the <a href="/wiki/Magnetic_flux_density" class="mw-redirect" title="Magnetic flux density">magnetic flux density</a> and the core area, the magnetic field varying with time according to the excitation of the primary. The expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi /\mathrm {d} t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi /\mathrm {d} t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6599990b1b8733541ea2deb6d716cff49d3170a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.265ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} \Phi /\mathrm {d} t}"></span>, defined as the derivative of magnetic flux <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> with time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, provides a measure of rate of magnetic flux in the core and hence of EMF induced in the respective winding. The negative sign in eq. 1 & eq. 2 is consistent with Lenz's law and Faraday's law in that by convention EMF "induced by an <i>increase</i> of magnetic flux linkages is <i>opposite</i> to the direction that would be given by the <a href="/wiki/Right-hand_rule" title="Right-hand rule">right-hand rule</a>."</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Although ideal transformer's winding inductances are each infinitely high, the square root of winding inductances' ratio is equal to the turns ratio.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">This also implies the following: The net core flux is zero, the input impedance is infinite when secondary is open and zero when secondary is shorted; there is zero phase-shift through an ideal transformer; input and output power and reactive volt-ampere are each conserved; these three statements apply for any frequency above zero and periodic waveforms are conserved.<sup id="cite_ref-Crosby1958-145_7-0" class="reference"><a href="#cite_note-Crosby1958-145-7"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Direction of transformer currents is according to <a href="/wiki/Right-hand_rule#Rotations" title="Right-hand rule">the Right-Hand Rule.</a></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Percent impedance is the ratio of the voltage drop in the secondary from no load to full load.<sup id="cite_ref-Heathcote1998-4_18-0" class="reference"><a href="#cite_note-Heathcote1998-4-18"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=33" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Bedell_(1942)-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bedell_(1942)_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBedell1942" class="citation journal cs1">Bedell, Frederick (1942). "History of A-C Wave Form, Its Determination and Standardization". <i>Transactions of the American Institute of Electrical Engineers</i>. <b>61</b> (12): 864. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FT-AIEE.1942.5058456">10.1109/T-AIEE.1942.5058456</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51658522">51658522</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+American+Institute+of+Electrical+Engineers&rft.atitle=History+of+A-C+Wave+Form%2C+Its+Determination+and+Standardization&rft.volume=61&rft.issue=12&rft.pages=864&rft.date=1942&rft_id=info%3Adoi%2F10.1109%2FT-AIEE.1942.5058456&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51658522%23id-name%3DS2CID&rft.aulast=Bedell&rft.aufirst=Frederick&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkilling1962" class="citation book cs1">Skilling, Hugh Hildreth (1962). <i>Electromechanics</i>. John Wiley & Sons, Inc.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromechanics&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=1962&rft.aulast=Skilling&rft.aufirst=Hugh+Hildreth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span> p. 39</span> </li> <li id="cite_note-Brenner18-6-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Brenner18-6_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Brenner18-6_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFBrennerJavid1959">Brenner & Javid 1959</a>, §18-6 The Ideal Transformer, pp. 598–600</span> </li> <li id="cite_note-Brenner18-1-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brenner18-1_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBrennerJavid1959">Brenner & Javid 1959</a>, §18-1 Symbols and Polarity of Mutual Inductance, pp.=589–590</span> </li> <li id="cite_note-Crosby1958-145-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Crosby1958-145_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCrosby1958">Crosby 1958</a>, p. 145</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Paul A. Tipler, <i>Physics</i>, Worth Publishers, Inc., 1976 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87901-041-X" title="Special:BookSources/0-87901-041-X">0-87901-041-X</a>, pp. 937-940</span> </li> <li id="cite_note-Flanagan1993-1-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Flanagan1993-1_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFlanagan1993" class="citation book cs1">Flanagan, William M. (1993). <a rel="nofollow" class="external text" href="https://archive.org/details/FlagananHandbookOfTransformerDesignApplications"><i>Handbook of Transformer Design & Applications</i></a> (2nd ed.). McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-021291-6" title="Special:BookSources/978-0-07-021291-6"><bdi>978-0-07-021291-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Transformer+Design+%26+Applications&rft.edition=2nd&rft.pub=McGraw-Hill&rft.date=1993&rft.isbn=978-0-07-021291-6&rft.aulast=Flanagan&rft.aufirst=William+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FFlagananHandbookOfTransformerDesignApplications&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span> pp. 2-1, 2-2</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Electrical Engineering: An Introduction</i>. Saunders College Publishing. 1984. p. 610. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-03-061758-8" title="Special:BookSources/0-03-061758-8"><bdi>0-03-061758-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Engineering%3A+An+Introduction&rft.pages=610&rft.pub=Saunders+College+Publishing&rft.date=1984&rft.isbn=0-03-061758-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-Say1983-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Say1983_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Say1983_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Say1983_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Say1983_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Say1983_13-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Say1983_13-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Say1983_13-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-Say1983_13-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-Say1983_13-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSay1983" class="citation book cs1">Say, M. G. (1983). <i>Alternating Current Machines</i> (5th ed.). London: Pitman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-273-01969-5" title="Special:BookSources/978-0-273-01969-5"><bdi>978-0-273-01969-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Alternating+Current+Machines&rft.place=London&rft.edition=5th&rft.pub=Pitman&rft.date=1983&rft.isbn=978-0-273-01969-5&rft.aulast=Say&rft.aufirst=M.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">L. Dalessandro, F. d. S. Cavalcante, and J. W. Kolar, "Self-Capacitance of High-Voltage Transformers," IEEE Transactions on Power Electronics, vol. 22, no. 5, pp. 2081–2092, 2007.</span> </li> <li id="cite_note-McLaren1984-68-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-McLaren1984-68_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McLaren1984-68_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMcLaren1984">McLaren 1984</a>, pp. 68–74</span> </li> <li id="cite_note-calvert2001-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-calvert2001_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-calvert2001_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-calvert2001_16-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-calvert2001_16-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCalvert2001" class="citation web cs1">Calvert, James (2001). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070509111407/http://www.du.edu/~jcalvert/tech/transfor.htm">"Inside Transformers"</a>. University of Denver. Archived from <a rel="nofollow" class="external text" href="http://www.du.edu/~jcalvert/tech/transfor.htm">the original</a> on May 9, 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">May 19,</span> 2007</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Inside+Transformers&rft.pub=University+of+Denver&rft.date=2001&rft.aulast=Calvert&rft.aufirst=James&rft_id=http%3A%2F%2Fwww.du.edu%2F~jcalvert%2Ftech%2Ftransfor.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTerman1955" class="citation book cs1">Terman, Frederick E. (1955). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/electronicradioe00term"><i>Electronic and Radio Engineering</i></a></span> (4th ed.). New York: McGraw-Hill. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/electronicradioe00term/page/15">15</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electronic+and+Radio+Engineering&rft.place=New+York&rft.pages=15&rft.edition=4th&rft.pub=McGraw-Hill&rft.date=1955&rft.aulast=Terman&rft.aufirst=Frederick+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectronicradioe00term&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-Heathcote1998-4-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Heathcote1998-4_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHeathcote1998">Heathcote 1998</a>, p. 4</span> </li> <li id="cite_note-Knowlton6-97-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Knowlton6-97_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnowlton1949" class="citation book cs1">Knowlton, A.E., ed. (1949). <i>Standard Handbook for Electrical Engineers</i> (8th ed.). McGraw-Hill. p. see esp. Section 6 Transformers, etc, pp. 547–644.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Standard+Handbook+for+Electrical+Engineers&rft.pages=see+esp.+Section+6+Transformers%2C+etc%2C+pp.+547-644&rft.edition=8th&rft.pub=McGraw-Hill&rft.date=1949&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span> Nomenclature for Parallel Operation, pp. 585–586</span> </li> <li id="cite_note-daniels1985-47-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-daniels1985-47_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-daniels1985-47_21-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-daniels1985-47_21-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFDaniels1985">Daniels 1985</a>, pp. 47–49</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.aerospaceweb.org/question/electronics/q0219.shtml">"400 Hz Electrical Systems"</a>. <i>Aerospaceweb.org</i><span class="reference-accessdate">. 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Algora Publishing. p. 102. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87586-508-9" title="Special:BookSources/978-0-87586-508-9"><bdi>978-0-87586-508-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=George+Westinghouse%3A+Gentle+Genius&rft.pages=102&rft.pub=Algora+Publishing&rft.date=2007&rft.isbn=978-0-87586-508-9&rft.aulast=Skrabec&rft.aufirst=Quentin+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DC3GYdiFM41oC%26pg%3DPA102&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-Coltman2002-85"><span class="mw-cite-backlink">^ <a href="#cite_ref-Coltman2002_85-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Coltman2002_85-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFColtman2002">Coltman 2002</a></span> </li> <li id="cite_note-IEC_History-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-IEC_History_86-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFInternational_Electrotechnical_Commission" class="citation book cs1"><a href="/wiki/International_Electrotechnical_Commission" title="International Electrotechnical Commission">International Electrotechnical Commission</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101206042832/http://www.iec.ch/cgi-bin/tl_to_htm.pl?section=technology&item=144"><i>Otto Blathy, Miksa Déri, Károly Zipernowsky</i></a>. Archived from <a rel="nofollow" class="external text" href="http://www.iec.ch/cgi-bin/tl_to_htm.pl?section=technology&item=144">the original</a> on December 6, 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">May 17,</span> 2007</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Otto+Blathy%2C+Miksa+D%C3%A9ri%2C+K%C3%A1roly+Zipernowsky&rft.au=International+Electrotechnical+Commission&rft_id=http%3A%2F%2Fwww.iec.ch%2Fcgi-bin%2Ftl_to_htm.pl%3Fsection%3Dtechnology%26item%3D144&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|work=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-87"><span class="mw-cite-backlink"><b><a href="#cite_ref-87">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeidhöfer2008" class="citation book cs1 cs1-prop-foreign-lang-source">Neidhöfer, Gerhard (2008). <a rel="nofollow" class="external text" href="http://d-nb.info/990964361"><i>Michael von Dolivo-Dobrowolsky and Three-Phase: The Beginnings of Modern e Technology and Power Supply</i></a> (in German). In collaboration with VDE "History of Electrical Engineering" Committee (2nd ed.). Berlin: VDE-Verl. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-8007-3115-2" title="Special:BookSources/978-3-8007-3115-2"><bdi>978-3-8007-3115-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Michael+von+Dolivo-Dobrowolsky+and+Three-Phase%3A+The+Beginnings+of+Modern+e+Technology+and+Power+Supply&rft.place=Berlin&rft.edition=2nd&rft.pub=VDE-Verl.&rft.date=2008&rft.isbn=978-3-8007-3115-2&rft.aulast=Neidh%C3%B6fer&rft.aufirst=Gerhard&rft_id=http%3A%2F%2Fd-nb.info%2F990964361&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-PBS-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-PBS_88-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUth2000" class="citation web cs1">Uth, Robert (Dec 12, 2000). <a rel="nofollow" class="external text" href="https://www.pbs.org/tesla/ins/lab_tescoil.html">"Tesla Coil"</a>. <i>Tesla: Master of Lightning</i>. PBS.org<span class="reference-accessdate">. Retrieved <span class="nowrap">May 20,</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Tesla%3A+Master+of+Lightning&rft.atitle=Tesla+Coil&rft.date=2000-12-12&rft.aulast=Uth&rft.aufirst=Robert&rft_id=https%3A%2F%2Fwww.pbs.org%2Ftesla%2Fins%2Flab_tescoil.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> <li id="cite_note-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-89">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/technology/telephone">"telephone | History, Definition, Invention, Uses, & Facts | Britannica"</a>. <i>www.britannica.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-07-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.britannica.com&rft.atitle=telephone+%7C+History%2C+Definition%2C+Invention%2C+Uses%2C+%26+Facts+%7C+Britannica&rft_id=https%3A%2F%2Fwww.britannica.com%2Ftechnology%2Ftelephone&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=34" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeeman1955" class="citation book cs1">Beeman, Donald, ed. (1955). <i>Industrial Power Systems Handbook</i>. McGraw-Hill.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Industrial+Power+Systems+Handbook&rft.pub=McGraw-Hill&rft.date=1955&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCalvert2001" class="citation web cs1">Calvert, James (2001). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070509111407/http://www.du.edu/~jcalvert/tech/transfor.htm">"Inside Transformers"</a>. University of Denver. Archived from <a rel="nofollow" class="external text" href="http://www.du.edu/~jcalvert/tech/transfor.htm">the original</a> on May 9, 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">May 19,</span> 2007</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Inside+Transformers&rft.pub=University+of+Denver&rft.date=2001&rft.aulast=Calvert&rft.aufirst=James&rft_id=http%3A%2F%2Fwww.du.edu%2F~jcalvert%2Ftech%2Ftransfor.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColtman1988" class="citation journal cs1">Coltman, J. W. (Jan 1988). "The Transformer". <i>Scientific American</i>. <b>258</b> (1): 86–95. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988SciAm.258a..86C">1988SciAm.258a..86C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fscientificamerican0188-86">10.1038/scientificamerican0188-86</a>. <a href="/wiki/OSTI_(identifier)" class="mw-redirect" title="OSTI (identifier)">OSTI</a> <a rel="nofollow" class="external text" href="https://www.osti.gov/biblio/6851152">6851152</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=The+Transformer&rft.volume=258&rft.issue=1&rft.pages=86-95&rft.date=1988-01&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0188-86&rft_id=https%3A%2F%2Fwww.osti.gov%2Fbiblio%2F6851152%23id-name%3DOSTI&rft_id=info%3Abibcode%2F1988SciAm.258a..86C&rft.aulast=Coltman&rft.aufirst=J.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColtman2002" class="citation journal cs1">Coltman, J. W. (Jan–Feb 2002). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/974352">"The Transformer [Historical Overview]"</a>. <i>IEEE Industry Applications Magazine</i>. <b>8</b> (1): 8–15. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F2943.974352">10.1109/2943.974352</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18160717">18160717</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Industry+Applications+Magazine&rft.atitle=The+Transformer+%5BHistorical+Overview%5D&rft.volume=8&rft.issue=1&rft.pages=8-15&rft.date=2002-01%2F2002-02&rft_id=info%3Adoi%2F10.1109%2F2943.974352&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18160717%23id-name%3DS2CID&rft.aulast=Coltman&rft.aufirst=J.+W.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F974352&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrennerJavid1959" class="citation conference cs1">Brenner, Egon; Javid, Mansour (1959). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V4FrAAAAMAAJ">"Chapter 18–Circuits with Magnetic Coupling"</a>. <i>Analysis of Electric Circuits</i>. McGraw-Hill. pp. 586–622.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Chapter+18%E2%80%93Circuits+with+Magnetic+Coupling&rft.btitle=Analysis+of+Electric+Circuits&rft.pages=586-622&rft.pub=McGraw-Hill&rft.date=1959&rft.aulast=Brenner&rft.aufirst=Egon&rft.au=Javid%2C+Mansour&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DV4FrAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCEGB1982" class="citation book cs1">CEGB, (Central Electricity Generating Board) (1982). <i>Modern Power Station Practice</i>. Pergamon. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-016436-6" title="Special:BookSources/978-0-08-016436-6"><bdi>978-0-08-016436-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Power+Station+Practice&rft.pub=Pergamon&rft.date=1982&rft.isbn=978-0-08-016436-6&rft.aulast=CEGB&rft.aufirst=%28Central+Electricity+Generating+Board%29&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCrosby1958" class="citation journal cs1">Crosby, D. (1958). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/1086447">"The Ideal Transformer"</a>. <i>IRE Transactions on Circuit Theory</i>. <b>5</b> (2): 145. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTCT.1958.1086447">10.1109/TCT.1958.1086447</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IRE+Transactions+on+Circuit+Theory&rft.atitle=The+Ideal+Transformer&rft.volume=5&rft.issue=2&rft.pages=145&rft.date=1958&rft_id=info%3Adoi%2F10.1109%2FTCT.1958.1086447&rft.aulast=Crosby&rft.aufirst=D.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F1086447&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaniels1985" class="citation book cs1">Daniels, A. R. (1985). <i>Introduction to Electrical Machines</i>. Macmillan. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-333-19627-4" title="Special:BookSources/978-0-333-19627-4"><bdi>978-0-333-19627-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Electrical+Machines&rft.pub=Macmillan&rft.date=1985&rft.isbn=978-0-333-19627-4&rft.aulast=Daniels&rft.aufirst=A.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDe_KeulenaerChapmanFassbinderMcDermott2001" class="citation conference cs1">De Keulenaer, Hans; Chapman, David; Fassbinder, Stefan; McDermott, Mike (2001). <a rel="nofollow" class="external text" href="http://www.cired.net/publications/cired2001/4_27.pdf"><i>The Scope for Energy Saving in the EU through the Use of Energy-Efficient Electricity Distribution Transformers</i></a> <span class="cs1-format">(PDF)</span>. 16th International Conference and Exhibition on Electricity Distribution (CIRED 2001). Institution of Engineering and Technology. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1049%2Fcp%3A20010853">10.1049/cp:20010853</a><span class="reference-accessdate">. Retrieved <span class="nowrap">10 July</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=The+Scope+for+Energy+Saving+in+the+EU+through+the+Use+of+Energy-Efficient+Electricity+Distribution+Transformers&rft.pub=Institution+of+Engineering+and+Technology&rft.date=2001&rft_id=info%3Adoi%2F10.1049%2Fcp%3A20010853&rft.aulast=De+Keulenaer&rft.aufirst=Hans&rft.au=Chapman%2C+David&rft.au=Fassbinder%2C+Stefan&rft.au=McDermott%2C+Mike&rft_id=http%3A%2F%2Fwww.cired.net%2Fpublications%2Fcired2001%2F4_27.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDel_VecchioPoulinFeghaliShah2002" class="citation book cs1">Del Vecchio, Robert M.; Poulin, Bertrand; Feghali, Pierre T.M.; Shah, Dilipkumar; Ahuja, Rajendra (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Lzjs0LNHhVYC"><i>Transformer Design Principles: With Applications to Core-Form Power Transformers</i></a>. Boca Raton: CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-5699-703-8" title="Special:BookSources/978-90-5699-703-8"><bdi>978-90-5699-703-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transformer+Design+Principles%3A+With+Applications+to+Core-Form+Power+Transformers&rft.place=Boca+Raton&rft.pub=CRC+Press&rft.date=2002&rft.isbn=978-90-5699-703-8&rft.aulast=Del+Vecchio&rft.aufirst=Robert+M.&rft.au=Poulin%2C+Bertrand&rft.au=Feghali%2C+Pierre+T.M.&rft.au=Shah%2C+Dilipkumar&rft.au=Ahuja%2C+Rajendra&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLzjs0LNHhVYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFinkBeatty1978" class="citation book cs1">Fink, Donald G.; Beatty, H. Wayne, eds. (1978). <i>Standard Handbook for Electrical Engineers</i> (11th ed.). McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-020974-9" title="Special:BookSources/978-0-07-020974-9"><bdi>978-0-07-020974-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Standard+Handbook+for+Electrical+Engineers&rft.edition=11th&rft.pub=McGraw+Hill&rft.date=1978&rft.isbn=978-0-07-020974-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGottlieb1998" class="citation book cs1">Gottlieb, Irving (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HFFo2TNIu88C"><i>Practical Transformer Handbook: for Electronics, Radio and Communications Engineers</i></a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-3992-7" title="Special:BookSources/978-0-7506-3992-7"><bdi>978-0-7506-3992-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Practical+Transformer+Handbook%3A+for+Electronics%2C+Radio+and+Communications+Engineers&rft.pub=Elsevier&rft.date=1998&rft.isbn=978-0-7506-3992-7&rft.aulast=Gottlieb&rft.aufirst=Irving&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHFFo2TNIu88C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuarnieri2013" class="citation journal cs1">Guarnieri, M. (2013). "Who Invented the Transformer?". <i>IEEE Industrial Electronics Magazine</i>. <b>7</b> (4): 56–59. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMIE.2013.2283834">10.1109/MIE.2013.2283834</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:27936000">27936000</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Industrial+Electronics+Magazine&rft.atitle=Who+Invented+the+Transformer%3F&rft.volume=7&rft.issue=4&rft.pages=56-59&rft.date=2013&rft_id=info%3Adoi%2F10.1109%2FMIE.2013.2283834&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A27936000%23id-name%3DS2CID&rft.aulast=Guarnieri&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHalacsyVon_Fuchs1961" class="citation journal cs1">Halacsy, A. A.; Von Fuchs, G. H. (April 1961). "Transformer Invented 75 Years Ago". <i>IEEE Transactions of the American Institute of Electrical Engineers</i>. <b>80</b> (3): 121–125. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FAIEEPAS.1961.4500994">10.1109/AIEEPAS.1961.4500994</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51632693">51632693</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+of+the+American+Institute+of+Electrical+Engineers&rft.atitle=Transformer+Invented+75+Years+Ago&rft.volume=80&rft.issue=3&rft.pages=121-125&rft.date=1961-04&rft_id=info%3Adoi%2F10.1109%2FAIEEPAS.1961.4500994&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51632693%23id-name%3DS2CID&rft.aulast=Halacsy&rft.aufirst=A.+A.&rft.au=Von+Fuchs%2C+G.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHameyer2004" class="citation book cs1">Hameyer, Kay (2004). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130210003139/http://materialy.itc.pw.edu.pl/zpnis/electric_machines_I/ForStudents/Script_EMIHanneberger.pdf"><i>Electrical Machines I: Basics, Design, Function, Operation</i></a> <span class="cs1-format">(PDF)</span>. RWTH Aachen University Institute of Electrical Machines. Archived from <a rel="nofollow" class="external text" href="http://materialy.itc.pw.edu.pl/zpnis/electric_machines_I/ForStudents/Script_EMIHanneberger.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2013-02-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Machines+I%3A+Basics%2C+Design%2C+Function%2C+Operation&rft.pub=RWTH+Aachen+University+Institute+of+Electrical+Machines&rft.date=2004&rft.aulast=Hameyer&rft.aufirst=Kay&rft_id=http%3A%2F%2Fmaterialy.itc.pw.edu.pl%2Fzpnis%2Felectric_machines_I%2FForStudents%2FScript_EMIHanneberger.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHammond1941" class="citation book cs1">Hammond, John Winthrop (1941). <a rel="nofollow" class="external text" href="https://archive.org/details/menandvoltsstory00hammrich"><i>Men and Volts: The Story of General Electric</i></a>. J. B. Lippincott Company. pp. see esp. 106–107, 178, 238.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Men+and+Volts%3A+The+Story+of+General+Electric&rft.pages=see+esp.+106-107%2C+178%2C+238&rft.pub=J.+B.+Lippincott+Company&rft.date=1941&rft.aulast=Hammond&rft.aufirst=John+Winthrop&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmenandvoltsstory00hammrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarlow2004" class="citation conference cs1">Harlow, James (2004). <a rel="nofollow" class="external text" href="ftp://180.211.120.110/02%20Electrical%20Engineering%20Department/E%20Books/Electric%20Power%20Transformer%20Engineering.pdf"><i>Electric Power Transformer Engineering</i></a> <span class="cs1-format">(PDF)</span>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-1704-5" title="Special:BookSources/0-8493-1704-5"><bdi>0-8493-1704-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Electric+Power+Transformer+Engineering&rft.pub=CRC+Press&rft.date=2004&rft.isbn=0-8493-1704-5&rft.aulast=Harlow&rft.aufirst=James&rft_id=ftp%3A%2F%2F180.211.120.110%2F02%2520Electrical%2520Engineering%2520Department%2FE%2520Books%2FElectric%2520Power%2520Transformer%2520Engineering.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged December 2021">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHughes1993" class="citation book cs1">Hughes, Thomas P. (1993). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=g07Q9M4agp4C&pg=PA96"><i>Networks of Power: Electrification in Western Society, 1880-1930</i></a>. Baltimore: The Johns Hopkins University Press. p. 96. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8018-2873-7" title="Special:BookSources/978-0-8018-2873-7"><bdi>978-0-8018-2873-7</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">Sep 9,</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Networks+of+Power%3A+Electrification+in+Western+Society%2C+1880-1930&rft.place=Baltimore&rft.pages=96&rft.pub=The+Johns+Hopkins+University+Press&rft.date=1993&rft.isbn=978-0-8018-2873-7&rft.aulast=Hughes&rft.aufirst=Thomas+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dg07Q9M4agp4C%26pg%3DPA96&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeathcote1998" class="citation book cs1">Heathcote, Martin (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=paPKsOXn5FMC"><i>J & P Transformer Book</i></a> (12th ed.). Newnes. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-1158-9" title="Special:BookSources/978-0-7506-1158-9"><bdi>978-0-7506-1158-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=J+%26+P+Transformer+Book&rft.edition=12th&rft.pub=Newnes&rft.date=1998&rft.isbn=978-0-7506-1158-9&rft.aulast=Heathcote&rft.aufirst=Martin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DpaPKsOXn5FMC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHindmarsh1977" class="citation book cs1">Hindmarsh, John (1977). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/electricalmachin0000hind"><i>Electrical Machines and Their Applications</i></a></span> (4th ed.). Exeter: Pergamon. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-030573-8" title="Special:BookSources/978-0-08-030573-8"><bdi>978-0-08-030573-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Machines+and+Their+Applications&rft.place=Exeter&rft.edition=4th&rft.pub=Pergamon&rft.date=1977&rft.isbn=978-0-08-030573-8&rft.aulast=Hindmarsh&rft.aufirst=John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectricalmachin0000hind&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKothariNagrath2010" class="citation book cs1">Kothari, D.P.; Nagrath, I.J. (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fR1rNJhBbmcC&pg=PA73"><i>Electric Machines</i></a> (4th ed.). Tata McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-069967-0" title="Special:BookSources/978-0-07-069967-0"><bdi>978-0-07-069967-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+Machines&rft.edition=4th&rft.pub=Tata+McGraw-Hill&rft.date=2010&rft.isbn=978-0-07-069967-0&rft.aulast=Kothari&rft.aufirst=D.P.&rft.au=Nagrath%2C+I.J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfR1rNJhBbmcC%26pg%3DPA73&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKulkarniKhaparde2004" class="citation book cs1">Kulkarni, S. V.; Khaparde, S. A. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qy4QT0BlV0MC"><i>Transformer Engineering: Design and Practice</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8247-5653-6" title="Special:BookSources/978-0-8247-5653-6"><bdi>978-0-8247-5653-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transformer+Engineering%3A+Design+and+Practice&rft.pub=CRC+Press&rft.date=2004&rft.isbn=978-0-8247-5653-6&rft.aulast=Kulkarni&rft.aufirst=S.+V.&rft.au=Khaparde%2C+S.+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dqy4QT0BlV0MC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcLaren1984" class="citation book cs1">McLaren, Peter (1984). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/elementaryelectr0000mcla"><i>Elementary Electric Power and Machines</i></a></span>. Ellis Horwood. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-20057-5" title="Special:BookSources/978-0-470-20057-5"><bdi>978-0-470-20057-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Electric+Power+and+Machines&rft.pub=Ellis+Horwood&rft.date=1984&rft.isbn=978-0-470-20057-5&rft.aulast=McLaren&rft.aufirst=Peter&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felementaryelectr0000mcla&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcLyman2004" class="citation conference cs1">McLyman, Colonel William (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=s_iMztIS8y4C">"Chapter 3"</a>. <i>Transformer and Inductor Design Handbook</i>. CRC. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-5393-3" title="Special:BookSources/0-8247-5393-3"><bdi>0-8247-5393-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Chapter+3&rft.btitle=Transformer+and+Inductor+Design+Handbook&rft.pub=CRC&rft.date=2004&rft.isbn=0-8247-5393-3&rft.aulast=McLyman&rft.aufirst=Colonel+William&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Ds_iMztIS8y4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPansini1999" class="citation book cs1">Pansini, Anthony (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=f77zWwA3oS4C"><i>Electrical Transformers and Power Equipment</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88173-311-2" title="Special:BookSources/978-0-88173-311-2"><bdi>978-0-88173-311-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Transformers+and+Power+Equipment&rft.pub=CRC+Press&rft.date=1999&rft.isbn=978-0-88173-311-2&rft.aulast=Pansini&rft.aufirst=Anthony&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Df77zWwA3oS4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParkerUlaWebb2005" class="citation conference cs1">Parker, M. R; Ula, S.; Webb, W. E. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=FdSQSAC3_EwC&pg=PA1017">"§2.5.5 'Transformers' & §10.1.3 'The Ideal Transformer'<span class="cs1-kern-right"></span>"</a>. In Whitaker, Jerry C. (ed.). <i>The Electronics Handbook</i> (2nd ed.). Taylor & Francis. pp. 172, 1017. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-1889-0" title="Special:BookSources/0-8493-1889-0"><bdi>0-8493-1889-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=%C2%A72.5.5+%27Transformers%27+%26+%C2%A710.1.3+%27The+Ideal+Transformer%27&rft.btitle=The+Electronics+Handbook&rft.pages=172%2C+1017&rft.edition=2nd&rft.pub=Taylor+%26+Francis&rft.date=2005&rft.isbn=0-8493-1889-0&rft.aulast=Parker&rft.aufirst=M.+R&rft.au=Ula%2C+S.&rft.au=Webb%2C+W.+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DFdSQSAC3_EwC%26pg%3DPA1017&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRyan2004" class="citation book cs1">Ryan, H. M. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Jg1xA65n56oC&q=High+Voltage+Engineering+and+Testing&pg=PA7"><i>High Voltage Engineering and Testing</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85296-775-1" title="Special:BookSources/978-0-85296-775-1"><bdi>978-0-85296-775-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=High+Voltage+Engineering+and+Testing&rft.pub=CRC+Press&rft.date=2004&rft.isbn=978-0-85296-775-1&rft.aulast=Ryan&rft.aufirst=H.+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJg1xA65n56oC%26q%3DHigh%2BVoltage%2BEngineering%2Band%2BTesting%26pg%3DPA7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATransformer" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transformer&action=edit&section=35" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Transformers" class="extiw" title="commons:Category:Transformers">Transformers</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="side-box-text plainlist">The Wikibook <i><a href="https://en.wikibooks.org/wiki/School_Science" class="extiw" title="wikibooks:School Science">School Science</a></i> has a page on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/School_Science/How_to_make_a_transformer" class="extiw" title="wikibooks:School Science/How to make a transformer">How to make a transformer</a></b></i></div></div> </div> <p><b>General links</b>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col"> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=XRb1RKbv0LM">(Video) Power transformer inrush current (animation)</a></li></ul> <p><br /> </p> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul 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.navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Transformer_topics" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini 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title="Special:EditPage/Template:Electric transformers"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Transformer_topics" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Transformer</a> topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Balun" title="Balun">Balun</a></li> <li><a href="/wiki/Buchholz_relay" title="Buchholz relay">Buchholz relay</a></li> <li><a href="/wiki/Bushing_(electrical)" title="Bushing (electrical)">Bushing</a></li> <li><a href="/wiki/Center_tap" title="Center tap">Center tap</a></li> <li><a href="/wiki/Circle_diagram" title="Circle diagram">Circle diagram</a></li> <li><a href="/wiki/Condition_monitoring_of_transformers" title="Condition monitoring of transformers">Condition monitoring of transformers</a></li> <li><a href="/wiki/Electrical_insulation_paper" title="Electrical insulation paper">Electrical insulation paper</a></li> <li><a href="/wiki/Growler_(electrical_device)" title="Growler (electrical device)">Growler</a></li> <li><a href="/wiki/High-leg_delta" title="High-leg delta">High-leg delta</a></li> <li><a href="/wiki/Induction_regulator" title="Induction regulator">Induction regulator</a></li> <li><a href="/wiki/Leakage_inductance" title="Leakage inductance">Leakage inductance</a></li> <li><a href="/wiki/Magnet_wire" title="Magnet wire">Magnet wire</a></li> <li><a href="/wiki/Metadyne" title="Metadyne">Metadyne</a></li> <li><a href="/wiki/Open-circuit_test" title="Open-circuit test">Open-circuit test</a></li> <li><a href="/wiki/Polarity_(mutual_inductance)" title="Polarity (mutual inductance)">Polarity</a></li> <li><a href="/wiki/Pressure_relief_valve" class="mw-redirect" title="Pressure relief valve">Pressure relief valve</a></li> <li><a href="/wiki/Quadrature_booster" title="Quadrature booster">Quadrature booster</a></li> <li><a href="/wiki/Resolver_(electrical)" title="Resolver (electrical)">Resolver</a></li> <li><a href="/wiki/Resonant_inductive_coupling" title="Resonant inductive coupling">Resonant inductive coupling</a></li> <li><a href="/wiki/Severity_factor" title="Severity factor">Severity factor</a></li> <li><a href="/wiki/Short-circuit_test" title="Short-circuit test">Short-circuit test</a></li> <li><a href="/wiki/Stacking_factor" title="Stacking factor">Stacking factor</a></li> <li><a href="/wiki/Synchro" title="Synchro">Synchro</a></li> <li><a href="/wiki/Tap_changer" title="Tap changer">Tap changer</a></li> <li><a href="/wiki/Toroidal_inductors_and_transformers" title="Toroidal inductors and transformers">Toroidal inductors and transformers</a></li> <li><a href="/wiki/Transformer_oil" title="Transformer oil">Transformer oil</a> <ul><li><a href="/wiki/Dissolved_gas_analysis" title="Dissolved gas analysis">Dissolved gas analysis</a></li> <li><a href="/wiki/Transformer_oil_testing" title="Transformer oil testing">Transformer oil testing</a></li></ul></li> <li><a href="/wiki/Transformer_utilization_factor" title="Transformer utilization factor">Transformer utilization factor</a></li> <li><a href="/wiki/Vector_group" title="Vector group">Vector group</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Transformer_Step-up_Iron_Core.svg" class="mw-file-description" title="Transformers"><img alt="Transformers" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Transformer_Step-up_Iron_Core.svg/80px-Transformer_Step-up_Iron_Core.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Transformer_Step-up_Iron_Core.svg/120px-Transformer_Step-up_Iron_Core.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Transformer_Step-up_Iron_Core.svg/160px-Transformer_Step-up_Iron_Core.svg.png 2x" data-file-width="50" data-file-height="50" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Transformer_types" title="Transformer types">Types</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autotransformer" title="Autotransformer">Autotransformer</a></li> <li><a href="/wiki/Buck%E2%80%93boost_transformer" title="Buck–boost transformer">Buck–boost transformer</a></li> <li><a href="/wiki/Distribution_transformer" title="Distribution transformer">Distribution transformer</a> <ul><li><a href="/wiki/Pad-mounted_transformer" title="Pad-mounted transformer">Pad-mounted transformer</a></li></ul></li> <li><a href="/wiki/Delta-wye_transformer" title="Delta-wye transformer">Delta-wye transformer</a></li> <li><a href="/wiki/Energy_efficient_transformer" title="Energy efficient transformer">Energy efficient transformer</a> <ul><li><a href="/wiki/Amorphous_metal_transformer" title="Amorphous metal transformer">Amorphous metal transformer</a></li></ul></li> <li><a href="/wiki/Flyback_transformer" title="Flyback transformer">Flyback transformer</a></li> <li><a href="/wiki/Grounding_transformer" title="Grounding transformer">Grounding transformer</a></li> <li><a href="/wiki/Instrument_transformer" title="Instrument transformer">Instrument transformer</a> <ul><li><a href="/wiki/Current_transformer" title="Current transformer">Current transformer</a></li> <li><a href="/wiki/Voltage_transformer" title="Voltage transformer">Voltage transformer</a></li></ul></li> <li><a href="/wiki/Isolation_transformer" title="Isolation transformer">Isolation transformer</a> <ul><li><a href="/wiki/Austin_transformer" title="Austin transformer">Austin transformer</a></li></ul></li> <li><a href="/wiki/Linear_variable_differential_transformer" title="Linear variable differential transformer">Linear variable differential transformer</a></li> <li><a href="/wiki/Parametric_transformer" title="Parametric transformer">Parametric transformer</a></li> <li><a href="/wiki/Planar_transformer" title="Planar transformer">Planar transformer</a></li> <li><a href="/wiki/Rotary_transformer" title="Rotary transformer">Rotary transformer</a></li> <li><a href="/wiki/Rotary_variable_differential_transformer" title="Rotary variable differential transformer">Rotary variable differential transformer</a></li> <li><a href="/wiki/Scott-T_transformer" title="Scott-T transformer">Scott-T transformer</a></li> <li><a href="/wiki/Solid-state_transformer" title="Solid-state transformer">Solid-state transformer</a></li> <li><a href="/wiki/Trigger_transformer" title="Trigger transformer">Trigger transformer</a></li> <li><a href="/wiki/Variable-frequency_transformer" title="Variable-frequency transformer">Variable-frequency transformer</a></li> <li><a href="/wiki/Zigzag_transformer" title="Zigzag transformer">Zigzag transformer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Coils</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hybrid_coil" class="mw-redirect" title="Hybrid coil">Hybrid coil</a></li> <li><a href="/wiki/Induction_coil" title="Induction coil">Induction coil</a></li> <li><a href="/wiki/Oudin_coil" title="Oudin coil">Oudin coil</a></li> <li><a href="/wiki/Polyphase_coil" title="Polyphase coil">Polyphase coil</a></li> <li><a href="/wiki/Repeating_coil" title="Repeating coil">Repeating coil</a></li> <li><a href="/wiki/Tesla_coil" title="Tesla coil">Tesla coil</a></li> <li><a href="/wiki/Trembler_coil" title="Trembler coil">Trembler coil</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Manufacturers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ABB" title="ABB">ABB</a></li> <li><a href="/wiki/General_Electric" title="General Electric">General Electric</a></li> <li><a href="/wiki/Mitsubishi_Electric" title="Mitsubishi Electric">Mitsubishi Electric</a></li> <li><a href="/wiki/ProlecGE" title="ProlecGE">ProlecGE</a></li> <li><a href="/wiki/Schneider_Electric" title="Schneider Electric">Schneider Electric</a></li> <li><a href="/wiki/Siemens" title="Siemens">Siemens</a></li> <li><a href="/wiki/TBEA" title="TBEA">TBEA</a></li> <li><a href="/wiki/WEG_Industries" title="WEG Industries">WEG</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Electricity_delivery" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electricity_delivery" title="Template:Electricity delivery"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electricity_delivery" title="Template talk:Electricity delivery"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electricity_delivery" title="Special:EditPage/Template:Electricity delivery"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Electricity_delivery" style="font-size:114%;margin:0 4em"><a href="/wiki/Electricity_delivery" title="Electricity delivery">Electricity delivery</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Automatic_generation_control" title="Automatic generation control">Automatic generation control</a></li> <li><a href="/wiki/Backfeeding" title="Backfeeding">Backfeeding</a></li> <li><a href="/wiki/Base_load" title="Base load">Base load</a></li> <li><a href="/wiki/Demand_factor" title="Demand factor">Demand factor</a></li> <li><a href="/wiki/Droop_speed_control" title="Droop speed control">Droop speed control</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electric_power_quality" title="Electric power quality">Electric power quality</a></li> <li><a href="/wiki/Electrical_fault" title="Electrical fault">Electrical fault</a></li> <li><a href="/wiki/Energy_demand_management" title="Energy demand management">Energy demand management</a></li> <li><a href="/wiki/Energy_return_on_investment" title="Energy return on investment">Energy return on investment</a></li> <li><a href="/wiki/Grid_code" title="Grid code">Grid code</a></li> <li><a href="/wiki/Grid_energy_storage" title="Grid energy storage">Grid energy storage</a></li> <li><a href="/wiki/Grid_strength" class="mw-redirect" title="Grid strength">Grid strength</a></li> <li><a href="/wiki/Home_energy_storage" title="Home energy storage">Home energy storage</a></li> <li><a href="/wiki/Load-following_power_plant" title="Load-following power plant">Load-following</a></li> <li><a href="/wiki/Merit_order" title="Merit order">Merit order</a></li> <li><a href="/wiki/Nameplate_capacity" title="Nameplate capacity">Nameplate capacity</a></li> <li><a href="/wiki/Peak_demand" title="Peak demand">Peak demand</a></li> <li><a href="/wiki/Power_factor" title="Power factor">Power factor</a></li> <li><a href="/wiki/Power-flow_study" title="Power-flow study">Power-flow study</a></li> <li><a href="/wiki/Repowering" title="Repowering">Repowering</a></li> <li><a href="/wiki/Utility_frequency" title="Utility frequency">Utility frequency</a></li> <li><a href="/wiki/Variable_renewable_energy" title="Variable renewable energy">Variability</a></li> <li><a href="/wiki/Vehicle-to-grid" title="Vehicle-to-grid">Vehicle-to-grid</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Abspannportal.jpg" class="mw-file-description" title="Portal pylons of Kriftel substation near Frankfurt"><img alt="Portal pylons of Kriftel substation near Frankfurt" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/120px-Abspannportal.jpg" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/180px-Abspannportal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/240px-Abspannportal.jpg 2x" data-file-width="2048" data-file-height="1536" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sources</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7em"><a href="/wiki/Non-renewable_resource" title="Non-renewable resource">Non-renewable</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fossil_fuel_power_station" title="Fossil fuel power station">Fossil fuel power station</a> <ul><li><a href="/wiki/Coal" title="Coal">Coal</a></li> <li><a href="/wiki/Natural_gas" title="Natural gas">Natural gas</a></li> <li><a href="/wiki/Oil_shale" title="Oil shale">Oil shale</a></li> <li><a href="/wiki/Petroleum" title="Petroleum">Petroleum</a></li></ul></li> <li><a href="/wiki/Nuclear_power" title="Nuclear power">Nuclear</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7em"><a href="/wiki/Renewable_energy" title="Renewable energy">Renewable</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biofuel" title="Biofuel">Biofuel</a></li> <li><a href="/wiki/Biogas" title="Biogas">Biogas</a></li> <li><a href="/wiki/Biomass" title="Biomass">Biomass</a></li> <li><a href="/wiki/Geothermal_power" title="Geothermal power">Geothermal</a></li> <li><a href="/wiki/Hydroelectricity" title="Hydroelectricity">Hydro</a></li> <li><a href="/wiki/Marine_energy" title="Marine energy">Marine</a> <ul><li><a href="/wiki/Marine_current_power" title="Marine current power">Current</a></li> <li><a href="/wiki/Osmotic_power" title="Osmotic power">Osmotic</a></li> <li><a href="/wiki/Ocean_thermal_energy_conversion" title="Ocean thermal energy conversion">Thermal</a></li> <li><a href="/wiki/Tidal_power" title="Tidal power">Tidal</a></li> <li><a href="/wiki/Wave_power" title="Wave power">Wave</a></li></ul></li> <li><a href="/wiki/Solar_power" title="Solar power">Solar</a></li> <li><a href="/wiki/Sustainable_biofuel" title="Sustainable biofuel">Sustainable biofuel</a></li> <li><a href="/wiki/Wind_power" title="Wind power">Wind</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Power_station_technology" title="Category:Power station technology">Generation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AC_power" title="AC power">AC power</a></li> <li><a href="/wiki/Cogeneration" title="Cogeneration">Cogeneration</a></li> <li><a href="/wiki/Combined_cycle_power_plant" title="Combined cycle power plant">Combined cycle</a></li> <li><a href="/wiki/Cooling_tower" title="Cooling tower">Cooling tower</a></li> <li><a href="/wiki/Induction_generator" title="Induction generator">Induction generator</a></li> <li><a href="/wiki/Micro_combined_heat_and_power" title="Micro combined heat and power">Micro CHP</a></li> <li><a href="/wiki/Microgeneration" title="Microgeneration">Microgeneration</a></li> <li><a href="/wiki/Rankine_cycle" title="Rankine cycle">Rankine cycle</a></li> <li><a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">Three-phase electric power</a></li> <li><a href="/wiki/Virtual_power_plant" title="Virtual power plant">Virtual power plant</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Electric_power_transmission" title="Electric power transmission">Transmission</a><br />and <a href="/wiki/Electric_power_distribution" title="Electric power distribution">distribution</a></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Demand_response" title="Demand response">Demand response</a></li> <li><a href="/wiki/Distributed_generation" title="Distributed generation">Distributed generation</a></li> <li><a href="/wiki/Dynamic_demand_(electric_power)" title="Dynamic demand (electric power)">Dynamic demand</a></li> <li><a href="/wiki/Electric_power_distribution" title="Electric power distribution">Electric power distribution</a></li> <li><a href="/wiki/Electric_power_system" title="Electric power system">Electric power system</a></li> <li><a href="/wiki/Electric_power_transmission" title="Electric power transmission">Electric power transmission</a></li> <li><a href="/wiki/Electrical_busbar_system" title="Electrical busbar system">Electrical busbar system</a></li> <li><a href="/wiki/Electrical_grid" title="Electrical grid">Electrical grid</a></li> <li><a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">Electrical substation</a></li> <li><a href="/wiki/Electricity_retailing" title="Electricity retailing">Electricity retailing</a></li> <li><a href="/wiki/High-voltage_direct_current" title="High-voltage direct current">High-voltage direct current</a></li> <li><a href="/wiki/High-voltage_shore_connection" title="High-voltage shore connection">High-voltage shore connection</a></li> <li><a href="/wiki/Interconnector" title="Interconnector">Interconnector</a></li> <li><a href="/wiki/Load_management" title="Load management">Load management</a></li> <li><a href="/wiki/Mains_electricity_by_country" title="Mains electricity by country">Mains electricity by country</a></li> <li><a href="/wiki/Overhead_power_line" title="Overhead power line">Overhead power line</a></li> <li><a href="/wiki/Power_station" title="Power station">Power station</a></li> <li><a href="/wiki/Pumped-storage_hydroelectricity" title="Pumped-storage hydroelectricity">Pumped hydro</a></li> <li><a href="/wiki/Single-wire_earth_return" title="Single-wire earth return">Single-wire earth return</a></li> <li><a href="/wiki/Smart_grid" title="Smart grid">Smart grid</a></li> <li><a href="/wiki/Super_grid" title="Super grid">Super grid</a></li> <li><a class="mw-selflink selflink">Transformer</a></li> <li><a href="/wiki/Transmission_system_operator" title="Transmission system operator">Transmission system operator</a> (TSO)</li> <li><a href="/wiki/Transmission_tower" title="Transmission tower">Transmission tower</a></li> <li><a href="/wiki/Utility_pole" title="Utility pole">Utility pole</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Failure modes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_start" title="Black start">Black start</a></li> <li><a href="/wiki/Brownout_(electricity)" title="Brownout (electricity)">Brownout</a></li> <li><a href="/wiki/Cascading_failure" title="Cascading failure">Cascading failure</a></li> <li><a href="/wiki/Power_outage" title="Power outage">Power outage</a> <ul><li><a href="/wiki/Rolling_blackout" title="Rolling blackout">Rolling blackout</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Protective<br />devices</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arc-fault_circuit_interrupter" title="Arc-fault circuit interrupter">Arc-fault circuit interrupter</a></li> <li><a href="/wiki/Circuit_breaker" title="Circuit breaker">Circuit breaker</a> <ul><li><a href="/wiki/Earth-leakage_circuit_breaker" title="Earth-leakage circuit breaker">Earth-leakage</a></li> <li><a href="/wiki/Sulfur_hexafluoride_circuit_breaker" title="Sulfur hexafluoride circuit breaker">Sulfur hexafluoride</a></li></ul></li> <li><a href="/wiki/Generator_interlock_kit" title="Generator interlock kit">Generator interlock kit</a></li> <li><a href="/wiki/Numerical_relay" title="Numerical relay">Numerical relay</a></li> <li><a href="/wiki/Power_system_protection" title="Power system protection">Power system protection</a></li> <li><a href="/wiki/Protective_relay" title="Protective relay">Protective relay</a></li> <li><a href="/wiki/Residual-current_device" title="Residual-current device">Residual-current device</a> (GFI)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Economics<br />and policies</div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Availability_factor" title="Availability factor">Availability factor</a></li> <li><a href="/wiki/Capacity_factor" title="Capacity factor">Capacity factor</a></li> <li><a href="/wiki/Carbon_offsets_and_credits" title="Carbon offsets and credits">Carbon offsets and credits</a></li> <li><a href="/wiki/Cost_of_electricity_by_source" title="Cost of electricity by source">Cost of electricity by source</a></li> <li><a href="/wiki/Energy_subsidy" title="Energy subsidy">Energy subsidies</a></li> <li><a href="/wiki/Environmental_tax" title="Environmental tax">Environmental tax</a></li> <li><a href="/wiki/Feed-in_tariff" title="Feed-in tariff">Feed-in tariff</a></li> <li><a href="/wiki/Fossil_fuel_phase-out" title="Fossil fuel phase-out">Fossil fuel phase-out</a></li> <li><a href="/wiki/Load_factor_(electrical)" title="Load factor (electrical)">Load factor</a></li> <li><a href="/wiki/Net_metering" title="Net metering">Net metering</a></li> <li><a href="/wiki/Pigouvian_tax" title="Pigouvian tax">Pigouvian tax</a></li> <li><a href="/wiki/Renewable_Energy_Certificate_(United_States)" title="Renewable Energy Certificate (United States)">Renewable Energy Certificates</a></li> <li><a href="/wiki/Renewable_energy_commercialization" title="Renewable energy commercialization">Renewable energy commercialization</a></li> <li><a href="/wiki/Renewable_Energy_Payments" title="Renewable Energy Payments">Renewable Energy Payments</a></li> <li><a href="/wiki/Spark_spread" title="Spark spread">Spark/Dark/Quark/Bark spread</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Statistics and<br />production</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electric_energy_consumption" title="Electric energy consumption">Electric energy consumption</a></li> <li><a href="/wiki/List_of_electricity_sectors" title="List of electricity sectors">List of electricity sectors</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Electric_power_distribution" title="Category:Electric power distribution">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Electronic_components" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electronic_components" title="Template:Electronic components"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electronic_components" title="Template talk:Electronic components"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electronic_components" title="Special:EditPage/Template:Electronic components"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Electronic_components" style="font-size:114%;margin:0 4em"><a href="/wiki/Electronic_component" title="Electronic component">Electronic components</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductor<br />devices</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/MOSFET" title="MOSFET">MOS <br />transistors</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/NMOS_logic" title="NMOS logic">NMOS</a></li> <li><a href="/wiki/PMOS_logic" title="PMOS logic">PMOS</a></li> <li><a href="/wiki/BiCMOS" title="BiCMOS">BiCMOS</a></li> <li><a href="/wiki/Bio-FET" title="Bio-FET">BioFET</a></li> <li><a href="/wiki/Chemical_field-effect_transistor" title="Chemical field-effect transistor">Chemical field-effect transistor</a> (ChemFET)</li> <li><a href="/wiki/CMOS" title="CMOS">Complementary MOS</a> (CMOS)</li> <li><a href="/wiki/Depletion-load_NMOS_logic" title="Depletion-load NMOS logic">Depletion-load NMOS</a></li> <li><a href="/wiki/FinFET" class="mw-redirect" title="FinFET">Fin field-effect transistor</a> (FinFET)</li> <li><a href="/wiki/Floating-gate_MOSFET" title="Floating-gate MOSFET">Floating-gate MOSFET</a> (FGMOS)</li> <li><a href="/wiki/Insulated-gate_bipolar_transistor" title="Insulated-gate bipolar transistor">Insulated-gate bipolar transistor</a> (IGBT)</li> <li><a href="/wiki/ISFET" title="ISFET">ISFET</a></li> <li><a href="/wiki/LDMOS" title="LDMOS">LDMOS</a></li> <li><a href="/wiki/MOSFET" title="MOSFET">MOS field-effect transistor</a> (MOSFET)</li> <li><a href="/wiki/Multigate_device" title="Multigate device">Multi-gate field-effect transistor</a> (MuGFET)</li> <li><a href="/wiki/Power_MOSFET" title="Power MOSFET">Power MOSFET</a></li> <li><a href="/wiki/Thin-film_transistor" title="Thin-film transistor">Thin-film transistor</a> (TFT)</li> <li><a href="/wiki/VMOS" title="VMOS">VMOS</a></li> <li><a href="/wiki/Power_MOSFET#UMOS" title="Power MOSFET">UMOS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Transistor" title="Transistor">Other <br />transistors</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bipolar_junction_transistor" title="Bipolar junction transistor">Bipolar junction transistor</a> (BJT)</li> <li><a href="/wiki/Darlington_transistor" title="Darlington transistor">Darlington transistor</a></li> <li><a href="/wiki/Diffused_junction_transistor" title="Diffused junction transistor">Diffused junction transistor</a></li> <li><a href="/wiki/Field-effect_transistor" title="Field-effect transistor">Field-effect transistor</a> (FET) <ul><li><a href="/wiki/JFET" title="JFET">Junction Gate FET (JFET)</a></li> <li><a href="/wiki/Organic_field-effect_transistor" title="Organic field-effect transistor">Organic FET (OFET)</a></li></ul></li> <li><a href="/wiki/Light-emitting_transistor" title="Light-emitting transistor">Light-emitting transistor</a> (LET) <ul><li><a href="/wiki/Organic_light-emitting_transistor" title="Organic light-emitting transistor">Organic LET (OLET)</a></li></ul></li> <li><a href="/wiki/Pentode_transistor" title="Pentode transistor">Pentode transistor</a></li> <li><a href="/wiki/Point-contact_transistor" title="Point-contact transistor">Point-contact transistor</a></li> <li><a href="/wiki/Programmable_unijunction_transistor" title="Programmable unijunction transistor">Programmable unijunction transistor</a> (PUT)</li> <li><a href="/wiki/Static_induction_transistor" title="Static induction transistor">Static induction transistor</a> (SIT)</li> <li><a href="/wiki/Tetrode_transistor" title="Tetrode transistor">Tetrode transistor</a></li> <li><a href="/wiki/Unijunction_transistor" title="Unijunction transistor">Unijunction transistor</a> (UJT)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Diode" title="Diode">Diodes</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Avalanche_diode" title="Avalanche diode">Avalanche diode</a></li> <li><a href="/wiki/Constant-current_diode" title="Constant-current diode">Constant-current diode</a> (CLD, CRD)</li> <li><a href="/wiki/Gunn_diode" title="Gunn diode">Gunn diode</a></li> <li><a href="/wiki/Laser_diode" title="Laser diode">Laser diode</a> (LD)</li> <li><a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diode</a> (LED)</li> <li><a href="/wiki/OLED" title="OLED">Organic light-emitting diode</a> (OLED)</li> <li><a href="/wiki/Photodiode" title="Photodiode">Photodiode</a></li> <li><a href="/wiki/PIN_diode" title="PIN diode">PIN diode</a></li> <li><a href="/wiki/Schottky_diode" title="Schottky diode">Schottky diode</a></li> <li><a href="/wiki/Step_recovery_diode" title="Step recovery diode">Step recovery diode</a></li> <li><a href="/wiki/Zener_diode" title="Zener diode">Zener diode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <br />devices</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Printed_electronics" title="Printed electronics">Printed electronics</a></li> <li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/DIAC" title="DIAC">DIAC</a></li> <li><a href="/wiki/Heterostructure_barrier_varactor" title="Heterostructure barrier varactor">Heterostructure barrier varactor</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li> <li><a href="/wiki/Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a></li> <li><a href="/wiki/Light_emitting_capacitor" class="mw-redirect" title="Light emitting capacitor">Light emitting capacitor</a> (LEC)</li> <li><a href="/wiki/Memistor" title="Memistor">Memistor</a></li> <li><a href="/wiki/Memristor" title="Memristor">Memristor</a></li> <li><a href="/wiki/Memtransistor" title="Memtransistor">Memtransistor</a></li> <li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Metal-oxide_varistor" class="mw-redirect" title="Metal-oxide varistor">Metal-oxide varistor</a> (MOV)</li> <li><a href="/wiki/Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li> <li><a href="/wiki/MOS_integrated_circuit" class="mw-redirect" title="MOS integrated circuit">MOS integrated circuit</a> (MOS IC)</li> <li><a href="/wiki/Organic_semiconductor" title="Organic semiconductor">Organic semiconductor</a></li> <li><a href="/wiki/Photodetector" title="Photodetector">Photodetector</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/RF_CMOS" title="RF CMOS">RF CMOS</a></li> <li><a href="/wiki/Silicon_controlled_rectifier" title="Silicon controlled rectifier">Silicon controlled rectifier</a> (SCR)</li> <li><a href="/wiki/Solaristor" title="Solaristor">Solaristor</a></li> <li><a href="/wiki/Static_induction_thyristor" title="Static induction thyristor">Static induction thyristor</a> (SITh)</li> <li><a href="/wiki/Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li> <li><a href="/wiki/Thyristor" title="Thyristor">Thyristor</a></li> <li><a href="/wiki/Trancitor" title="Trancitor">Trancitor</a></li> <li><a href="/wiki/TRIAC" title="TRIAC">TRIAC</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Voltage_regulator" title="Voltage regulator">Voltage regulators</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Linear_regulator" title="Linear regulator">Linear regulator</a></li> <li><a href="/wiki/Low-dropout_regulator" title="Low-dropout regulator">Low-dropout regulator</a></li> <li><a href="/wiki/Switching_regulator" class="mw-redirect" title="Switching regulator">Switching regulator</a></li> <li><a href="/wiki/Buck_converter" title="Buck converter">Buck</a></li> <li><a href="/wiki/Boost_converter" title="Boost converter">Boost</a></li> <li><a href="/wiki/Buck%E2%80%93boost_converter" title="Buck–boost converter">Buck–boost</a></li> <li><a href="/wiki/Split-pi_topology" title="Split-pi topology">Split-pi</a></li> <li><a href="/wiki/%C4%86uk_converter" title="Ćuk converter">Ćuk</a></li> <li><a href="/wiki/Single-ended_primary-inductor_converter" title="Single-ended primary-inductor converter">SEPIC</a></li> <li><a href="/wiki/Charge_pump" title="Charge pump">Charge pump</a></li> <li><a href="/wiki/Switched_capacitor" title="Switched capacitor">Switched capacitor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acorn_tube" title="Acorn tube">Acorn tube</a></li> <li><a href="/wiki/Audion" title="Audion">Audion</a></li> <li><a href="/wiki/Beam_tetrode" title="Beam tetrode">Beam tetrode</a></li> <li><a href="/wiki/Hot-wire_barretter" title="Hot-wire barretter">Barretter</a></li> <li><a href="/wiki/Compactron" title="Compactron">Compactron</a></li> <li><a href="/wiki/Vacuum_diode" class="mw-redirect" title="Vacuum diode">Diode</a></li> <li><a href="/wiki/Fleming_valve" title="Fleming valve">Fleming valve</a></li> <li><a href="/wiki/Neutron_generator" title="Neutron generator">Neutron tube</a></li> <li><a href="/wiki/Nonode" title="Nonode">Nonode</a></li> <li><a href="/wiki/Nuvistor" title="Nuvistor">Nuvistor</a></li> <li><a href="/wiki/Pentagrid_converter" title="Pentagrid converter">Pentagrid</a> (Hexode, Heptode, Octode)</li> <li><a href="/wiki/Pentode" title="Pentode">Pentode</a></li> <li><a href="/wiki/Photomultiplier_tube" title="Photomultiplier tube">Photomultiplier</a></li> <li><a href="/wiki/Phototube" title="Phototube">Phototube</a></li> <li><a href="/wiki/Tetrode" title="Tetrode">Tetrode</a></li> <li><a href="/wiki/Triode" title="Triode">Triode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a> (<a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">RF</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Backward-wave_oscillator" title="Backward-wave oscillator">Backward-wave oscillator</a> (BWO)</li> <li><a href="/wiki/Cavity_magnetron" title="Cavity magnetron">Cavity magnetron</a></li> <li><a href="/wiki/Crossed-field_amplifier" title="Crossed-field amplifier">Crossed-field amplifier</a> (CFA)</li> <li><a href="/wiki/Gyrotron" title="Gyrotron">Gyrotron</a></li> <li><a href="/wiki/Inductive_output_tube" title="Inductive output tube">Inductive output tube</a> (IOT)</li> <li><a href="/wiki/Klystron" title="Klystron">Klystron</a></li> <li><a href="/wiki/Maser" title="Maser">Maser</a></li> <li><a href="/wiki/Sutton_tube" title="Sutton tube">Sutton tube</a></li> <li><a href="/wiki/Traveling-wave_tube" title="Traveling-wave tube">Traveling-wave tube</a> (TWT)</li> <li><a href="/wiki/X-ray_tube" title="X-ray tube">X-ray tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Cathode-ray_tube" title="Cathode-ray tube">Cathode-ray tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Beam_deflection_tube" title="Beam deflection tube">Beam deflection tube</a></li> <li><a href="/wiki/Charactron" title="Charactron">Charactron</a></li> <li><a href="/wiki/Iconoscope" title="Iconoscope">Iconoscope</a></li> <li><a href="/wiki/Magic_eye_tube" title="Magic eye tube">Magic eye tube</a></li> <li><a href="/wiki/Monoscope" title="Monoscope">Monoscope</a></li> <li><a href="/wiki/Selectron_tube" title="Selectron tube">Selectron tube</a></li> <li><a href="/wiki/Storage_tube" title="Storage tube">Storage tube</a></li> <li><a href="/wiki/Trochotron" class="mw-redirect" title="Trochotron">Trochotron</a></li> <li><a href="/wiki/Video_camera_tube" title="Video camera tube">Video camera tube</a></li> <li><a href="/wiki/Williams_tube" title="Williams tube">Williams tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Gas-filled_tube" title="Gas-filled tube">Gas-filled tubes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cold_cathode" title="Cold cathode">Cold cathode</a></li> <li><a href="/wiki/Crossatron" title="Crossatron">Crossatron</a></li> <li><a href="/wiki/Dekatron" title="Dekatron">Dekatron</a></li> <li><a href="/wiki/Ignitron" title="Ignitron">Ignitron</a></li> <li><a href="/wiki/Krytron" title="Krytron">Krytron</a></li> <li><a href="/wiki/Mercury-arc_valve" title="Mercury-arc valve">Mercury-arc valve</a></li> <li><a href="/wiki/Neon_lamp" title="Neon lamp">Neon lamp</a></li> <li><a href="/wiki/Nixie_tube" title="Nixie tube">Nixie tube</a></li> <li><a href="/wiki/Thyratron" title="Thyratron">Thyratron</a></li> <li><a href="/wiki/Trigatron" title="Trigatron">Trigatron</a></li> <li><a href="/wiki/Voltage-regulator_tube" title="Voltage-regulator tube">Voltage-regulator tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Adjustable</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Potentiometer" title="Potentiometer">Potentiometer</a> <ul><li><a href="/wiki/Digital_potentiometer" title="Digital potentiometer">digital</a></li></ul></li> <li><a href="/wiki/Variable_capacitor" title="Variable capacitor">Variable capacitor</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Passive</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Connector <ul><li><a href="/wiki/Audio_and_video_interfaces_and_connectors" title="Audio and video interfaces and connectors">audio and video</a></li> <li><a href="/wiki/AC_power_plugs_and_sockets" title="AC power plugs and sockets">electrical power</a></li> <li><a href="/wiki/RF_connector" title="RF connector">RF</a></li></ul></li> <li><a href="/wiki/Electrolytic_detector" title="Electrolytic detector">Electrolytic detector</a></li> <li><a href="/wiki/Ferrite_core" title="Ferrite core">Ferrite</a></li> <li><a href="/wiki/Antifuse" title="Antifuse">Antifuse</a></li> <li><a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">Fuse</a> <ul><li><a href="/wiki/Resettable_fuse" title="Resettable fuse">resettable</a></li> <li><a href="/wiki/EFUSE" class="mw-redirect" title="EFUSE">eFUSE</a></li></ul></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Switch" title="Switch">Switch</a></li> <li><a href="/wiki/Thermistor" title="Thermistor">Thermistor</a></li> <li><a class="mw-selflink selflink">Transformer</a></li> <li><a href="/wiki/Varistor" title="Varistor">Varistor</a></li> <li><a href="/wiki/Wire" title="Wire">Wire</a> <ul><li><a href="/wiki/Wollaston_wire" title="Wollaston wire">Wollaston wire</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electrical_reactance" title="Electrical reactance">Reactive</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Capacitor" title="Capacitor">Capacitor</a> <ul><li><a href="/wiki/Capacitor_types" title="Capacitor types">types</a></li></ul></li> <li><a href="/wiki/Ceramic_resonator" title="Ceramic resonator">Ceramic resonator</a></li> <li><a href="/wiki/Crystal_oscillator" title="Crystal oscillator">Crystal oscillator</a></li> <li><a href="/wiki/Inductor" title="Inductor">Inductor</a></li> <li><a href="/wiki/Parametron" title="Parametron">Parametron</a></li> <li><a href="/wiki/Relay" title="Relay">Relay</a> <ul><li><a href="/wiki/Reed_relay" title="Reed relay">reed relay</a></li> <li><a href="/wiki/Mercury_relay" title="Mercury relay">mercury relay</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" 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83.151 1 Template:Electric_transformers"," 6.67% 77.074 28 Template:Harvnb"," 6.53% 75.514 21 Template:Cite_web"," 5.96% 68.902 1 Template:Short_description"]},"scribunto":{"limitreport-timeusage":{"value":"0.685","limit":"10.000"},"limitreport-memusage":{"value":8095656,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREFAllan1991\"] = 1,\n [\"CITEREFBedell1942\"] = 1,\n [\"CITEREFBeeman1955\"] = 1,\n [\"CITEREFBotelerPirjolaNevanlinna1998\"] = 1,\n [\"CITEREFBrennerJavid1959\"] = 1,\n [\"CITEREFBrussoAllerhand2021\"] = 1,\n [\"CITEREFCEGB1982\"] = 1,\n [\"CITEREFCalvert2001\"] = 2,\n [\"CITEREFChow2006\"] = 1,\n [\"CITEREFColtman1988\"] = 1,\n [\"CITEREFColtman2002\"] = 1,\n [\"CITEREFCrosby1958\"] = 1,\n [\"CITEREFDaniels1985\"] = 1,\n [\"CITEREFDe_KeulenaerChapmanFassbinderMcDermott2001\"] = 1,\n [\"CITEREFDel_VecchioPoulinFeghaliShah2002\"] = 1,\n [\"CITEREFDixon2001\"] = 1,\n [\"CITEREFElectrical_Society_of_Cornell_University1896\"] = 1,\n [\"CITEREFFaraday1834\"] = 1,\n [\"CITEREFFinkBeatty1978\"] = 1,\n [\"CITEREFFlanagan1993\"] = 1,\n [\"CITEREFGottlieb1998\"] = 1,\n [\"CITEREFGuarnieri2013\"] = 1,\n [\"CITEREFHalacsyFuchs1961\"] = 1,\n [\"CITEREFHalacsyVon_Fuchs1961\"] = 1,\n [\"CITEREFHameyer2004\"] = 1,\n [\"CITEREFHammond1941\"] = 1,\n [\"CITEREFHarlow2004\"] = 1,\n [\"CITEREFHartley\"] = 2,\n [\"CITEREFHasegawa2000\"] = 1,\n [\"CITEREFHeathcote1998\"] = 1,\n [\"CITEREFHindmarsh1977\"] = 1,\n [\"CITEREFHospitalier1882\"] = 1,\n [\"CITEREFHughes1993\"] = 1,\n [\"CITEREFHydroelectric_Research_and_Technical_Services_Group\"] = 1,\n [\"CITEREFInternational_Electrotechnical_Commission\"] = 1,\n [\"CITEREFJeszenszky\"] = 1,\n [\"CITEREFKnowlton1949\"] = 1,\n [\"CITEREFKothariNagrath2010\"] = 1,\n [\"CITEREFKuboSachsNadel2001\"] = 1,\n [\"CITEREFKulkarniKhaparde2004\"] = 1,\n [\"CITEREFLane2007\"] = 1,\n [\"CITEREFLee\"] = 1,\n [\"CITEREFLucas\"] = 1,\n [\"CITEREFMacPherson,_Ph.D.\"] = 1,\n [\"CITEREFMcLaren1984\"] = 1,\n [\"CITEREFMcLyman2004\"] = 1,\n [\"CITEREFMehtaAversa,_N.Walker,_M.S.1997\"] = 1,\n [\"CITEREFNagy1996\"] = 1,\n [\"CITEREFNailen2005\"] = 1,\n [\"CITEREFNeidhöfer2008\"] = 1,\n [\"CITEREFPansini1999\"] = 1,\n [\"CITEREFParkerUlaWebb2005\"] = 1,\n [\"CITEREFPoyser1892\"] = 1,\n [\"CITEREFRyan2004\"] = 1,\n [\"CITEREFSay1983\"] = 1,\n [\"CITEREFSkilling1962\"] = 1,\n [\"CITEREFSkrabec2007\"] = 1,\n [\"CITEREFSmil2005\"] = 1,\n [\"CITEREFTerman1955\"] = 1,\n [\"CITEREFUS_Army_Corps_of_Engineers1994\"] = 1,\n [\"CITEREFUppenborn1889\"] = 1,\n [\"CITEREFUth2000\"] = 1,\n [\"CITEREFWilliam_R._Huber2022\"] = 1,\n [\"Ideal_transformer_equations\"] = 1,\n [\"Real_transformer_equivalent_circuit_figure\"] = 1,\n [\"Transformer_universal_EMF_equation\"] = 1,\n [\"stray\"] = 1,\n}\ntemplate_list = table#1 {\n [\"!\"] = 3,\n [\"About\"] = 1,\n [\"Anchor\"] = 4,\n [\"Authority control\"] = 1,\n [\"Cite book\"] = 36,\n [\"Cite conference\"] = 8,\n [\"Cite encyclopedia\"] = 1,\n [\"Cite journal\"] = 14,\n [\"Cite web\"] = 21,\n [\"Clear\"] = 6,\n [\"Col div\"] = 1,\n [\"Col div end\"] = 1,\n [\"Colbegin\"] = 1,\n [\"Colend\"] = 1,\n [\"Commons category\"] = 1,\n [\"Dead link\"] = 1,\n [\"Efn\"] = 5,\n [\"Electric transformers\"] = 1,\n [\"Electricity delivery\"] = 1,\n [\"Electronic component\"] = 1,\n [\"EquationRef\"] = 7,\n [\"Harvnb\"] = 28,\n [\"ISBN\"] = 2,\n [\"Main\"] = 3,\n [\"Notelist\"] = 1,\n [\"Nowrap\"] = 1,\n [\"NumBlk\"] = 7,\n [\"Reflist\"] = 1,\n [\"Rp\"] = 4,\n [\"See also\"] = 1,\n [\"Short description\"] = 1,\n [\"Side box\"] = 1,\n [\"TOC limit\"] = 1,\n [\"Wikibooks\"] = 1,\n [\"\\\\mathrm{d\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n"},"cachereport":{"origin":"mw-web.codfw.main-f69cdc8f6-lnt6z","timestamp":"20241122140734","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Transformer","url":"https:\/\/en.wikipedia.org\/wiki\/Transformer","sameAs":"http:\/\/www.wikidata.org\/entity\/Q11658","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q11658","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2001-10-12T17:25:38Z","dateModified":"2024-11-19T15:09:35Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/f\/f4\/Philips_N4422_-_power_supply_transformer-2098.jpg","headline":"electrical device that transfers energy through electromagnetic induction from one circuit to another circuit"}</script> </body> </html>