Modulatie (radio) - Wikipedia

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class="vector-toc-numb">1</span> <span>Redenen</span> </div> </a> <ul id="toc-Redenen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Draaggolf" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Draaggolf"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Draaggolf</span> </div> </a> <button aria-controls="toc-Draaggolf-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>Draaggolf-subkopje inklappen</span> </button> <ul id="toc-Draaggolf-sublist" class="vector-toc-list"> <li id="toc-Vermogen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vermogen"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Vermogen</span> </div> </a> <ul id="toc-Vermogen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Amplitudemodulatie_(AM)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Amplitudemodulatie_(AM)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Amplitudemodulatie (AM)</span> </div> </a> <button aria-controls="toc-Amplitudemodulatie_(AM)-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>Amplitudemodulatie (AM)-subkopje inklappen</span> </button> <ul id="toc-Amplitudemodulatie_(AM)-sublist" class="vector-toc-list"> <li id="toc-Karakteristieken" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Karakteristieken"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Karakteristieken</span> </div> </a> <ul id="toc-Karakteristieken-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-AM-zijbanden" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#AM-zijbanden"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>AM-zijbanden</span> </div> </a> <ul id="toc-AM-zijbanden-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-AM-vermogen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#AM-vermogen"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>AM-vermogen</span> </div> </a> <ul id="toc-AM-vermogen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Frequentiemodulatie_(FM)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Frequentiemodulatie_(FM)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Frequentiemodulatie (FM)</span> </div> </a> <button aria-controls="toc-Frequentiemodulatie_(FM)-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>Frequentiemodulatie (FM)-subkopje inklappen</span> </button> <ul id="toc-Frequentiemodulatie_(FM)-sublist" class="vector-toc-list"> <li id="toc-FM-zijbanden" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#FM-zijbanden"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>FM-zijbanden</span> </div> </a> <ul id="toc-FM-zijbanden-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-FM-vermogen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#FM-vermogen"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>FM-vermogen</span> </div> </a> <ul id="toc-FM-vermogen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Andere_vormen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Andere_vormen"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Andere vormen</span> </div> </a> <ul id="toc-Andere_vormen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modulatie_van_digitale_signalen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modulatie_van_digitale_signalen"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Modulatie van digitale signalen</span> </div> </a> <ul id="toc-Modulatie_van_digitale_signalen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aanverwante_vormen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aanverwante_vormen"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Aanverwante vormen</span> </div> </a> <button aria-controls="toc-Aanverwante_vormen-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>Aanverwante vormen-subkopje inklappen</span> </button> <ul id="toc-Aanverwante_vormen-sublist" class="vector-toc-list"> <li id="toc-Choppen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Choppen"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Choppen</span> </div> </a> <ul id="toc-Choppen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mengen" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mengen"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Mengen</span> </div> </a> <ul id="toc-Mengen-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zie_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zie_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Zie ook</span> </div> </a> <ul id="toc-Zie_ook-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Modulatie (radio)</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="Ga naar een artikel in een andere taal. Beschikbaar in 61 talen" > <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-61" 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">61 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B6%D9%85%D9%8A%D9%86_(%D8%A5%D9%84%D9%83%D8%AA%D8%B1%D9%88%D9%86%D9%8A%D8%A7%D8%AA)" title="تضمين (إلكترونيات) – Arabisch" lang="ar" hreflang="ar" data-title="تضمين (إلكترونيات)" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D1%8B%D1%8F" title="Мадуляцыя – Belarussisch" lang="be" hreflang="be" data-title="Мадуляцыя" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%9C%D0%B0%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D1%8B%D1%8F" title="Мадуляцыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Мадуляцыя" 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%9C%D0%BE%D0%B4%D1%83%D0%BB%D0%B0%D1%86%D0%B8%D1%8F_(%D1%82%D0%B5%D1%85%D0%BD%D0%B8%D0%BA%D0%B0)" title="Модулация (техника) – Bulgaars" lang="bg" hreflang="bg" data-title="Модулация (техника)" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A6%A1%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%B2%E0%A7%87%E0%A6%B6%E0%A6%A8" title="মড্যুলেশন – Bengaals" lang="bn" hreflang="bn" data-title="মড্যুলেশন" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Modulaci%C3%B3_(telecomunicacions)" title="Modulació (telecomunicacions) – Catalaans" lang="ca" hreflang="ca" data-title="Modulació (telecomunicacions)" data-language-autonym="Català" data-language-local-name="Catalaans" 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/Modulace" title="Modulace – Tsjechisch" lang="cs" hreflang="cs" data-title="Modulace" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Modulation" title="Modulation – Deens" lang="da" hreflang="da" data-title="Modulation" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Modulation_(Technik)" title="Modulation (Technik) – Duits" lang="de" hreflang="de" data-title="Modulation (Technik)" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CE%BC%CF%8C%CF%81%CF%86%CF%89%CF%83%CE%B7_%CF%83%CE%AE%CE%BC%CE%B1%CF%84%CE%BF%CF%82" title="Διαμόρφωση σήματος – Grieks" lang="el" hreflang="el" data-title="Διαμόρφωση σήματος" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Modulation" title="Modulation – Engels" lang="en" hreflang="en" data-title="Modulation" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Modulado_(tekniko)" title="Modulado (tekniko) – Esperanto" lang="eo" hreflang="eo" data-title="Modulado (tekniko)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Modulaci%C3%B3n_(telecomunicaci%C3%B3n)" title="Modulación (telecomunicación) – Spaans" lang="es" hreflang="es" data-title="Modulación (telecomunicación)" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Modulatsioon_(%C3%BClekandetehnika)" title="Modulatsioon (ülekandetehnika) – Estisch" lang="et" hreflang="et" data-title="Modulatsioon (ülekandetehnika)" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Modulazio" title="Modulazio – Baskisch" lang="eu" hreflang="eu" data-title="Modulazio" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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/%D9%85%D8%AF%D9%88%D9%84%D9%87%E2%80%8C%D8%B3%D8%A7%D8%B2%DB%8C" title="مدوله‌سازی – Perzisch" lang="fa" hreflang="fa" data-title="مدوله‌سازی" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Modulaatio_(elektroniikka)" title="Modulaatio (elektroniikka) – Fins" lang="fi" hreflang="fi" data-title="Modulaatio (elektroniikka)" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Modulation_du_signal" title="Modulation du signal – Frans" lang="fr" hreflang="fr" data-title="Modulation du signal" data-language-autonym="Français" data-language-local-name="Frans" 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/Modhn%C3%BA" title="Modhnú – Iers" lang="ga" hreflang="ga" data-title="Modhnú" data-language-autonym="Gaeilge" data-language-local-name="Iers" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%A0%D7%95%D7%9F" title="אפנון – Hebreeuws" lang="he" hreflang="he" data-title="אפנון" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A5%89%E0%A4%A1%E0%A5%81%E0%A4%B2%E0%A4%A8" title="मॉडुलन – Hindi" lang="hi" hreflang="hi" data-title="मॉडुलन" 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/Modulacija" title="Modulacija – Kroatisch" lang="hr" hreflang="hr" data-title="Modulacija" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Modul%C3%A1ci%C3%B3_(fizika)" title="Moduláció (fizika) – Hongaars" lang="hu" hreflang="hu" data-title="Moduláció (fizika)" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%B8%D5%A4%D5%B8%D6%82%D5%AC%D5%B8%D6%82%D5%B4" title="Մոդուլում – Armeens" lang="hy" hreflang="hy" data-title="Մոդուլում" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Modulasi" title="Modulasi – Indonesisch" lang="id" hreflang="id" data-title="Modulasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Modulazione" title="Modulazione – Italiaans" lang="it" hreflang="it" data-title="Modulazione" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%89%E8%AA%BF%E6%96%B9%E5%BC%8F" title="変調方式 – Japans" lang="ja" hreflang="ja" data-title="変調方式" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Модуляция – Kazachs" lang="kk" hreflang="kk" data-title="Модуляция" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%80%EC%A1%B0" title="변조 – Koreaans" lang="ko" hreflang="ko" data-title="변조" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Модуляция – Kirgizisch" lang="ky" hreflang="ky" data-title="Модуляция" data-language-autonym="Кыргызча" data-language-local-name="Kirgizisch" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Moduliacija" title="Moduliacija – Litouws" lang="lt" hreflang="lt" data-title="Moduliacija" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Modul%C4%81cija" title="Modulācija – Lets" lang="lv" hreflang="lv" data-title="Modulācija" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Fifanaraham-peo" title="Fifanaraham-peo – Malagassisch" lang="mg" hreflang="mg" data-title="Fifanaraham-peo" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Модулација – Macedonisch" lang="mk" hreflang="mk" data-title="Модулација" data-language-autonym="Македонски" data-language-local-name="Macedonisch" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B5%8B%E0%B4%A1%E0%B5%81%E0%B4%B2%E0%B4%A8%E0%B4%82" title="മോഡുലനം – Malayalam" lang="ml" hreflang="ml" data-title="മോഡുലനം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pemodulatan" title="Pemodulatan – Maleis" lang="ms" hreflang="ms" data-title="Pemodulatan" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%99%E1%80%B1%E1%80%AC%E1%80%BA%E1%80%92%E1%80%BB%E1%80%B0%E1%80%9C%E1%80%B1%E1%80%B8%E1%80%9B%E1%80%BE%E1%80%84%E1%80%BA%E1%80%B8" title="မော်ဒျူလေးရှင်း – Birmaans" lang="my" hreflang="my" data-title="မော်ဒျူလေးရှင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Modulasjon" title="Modulasjon – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Modulasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Modulasjon" title="Modulasjon – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Modulasjon" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Modulacja" title="Modulacja – Pools" lang="pl" hreflang="pl" data-title="Modulacja" data-language-autonym="Polski" data-language-local-name="Pools" 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/Modula%C3%A7%C3%A3o" title="Modulação – Portugees" lang="pt" hreflang="pt" data-title="Modulação" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modula%C8%9Bie" title="Modulație – Roemeens" lang="ro" hreflang="ro" data-title="Modulație" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Модуляция – Russisch" lang="ru" hreflang="ru" data-title="Модуляция" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Modulacija" title="Modulacija – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Modulacija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B8%E0%B7%96%E0%B6%BB%E0%B7%8A%E0%B6%A2%E0%B6%B1%E0%B6%BA" title="මූර්ජනය – Singalees" lang="si" hreflang="si" data-title="මූර්ජනය" data-language-autonym="සිංහල" data-language-local-name="Singalees" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Modul%C3%A1cia_(elektronika)" title="Modulácia (elektronika) – Slowaaks" lang="sk" hreflang="sk" data-title="Modulácia (elektronika)" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Modulacija" title="Modulacija – Sloveens" lang="sl" hreflang="sl" data-title="Modulacija" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Модулација – Servisch" lang="sr" hreflang="sr" data-title="Модулација" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Modulasi" title="Modulasi – Soendanees" lang="su" hreflang="su" data-title="Modulasi" data-language-autonym="Sunda" data-language-local-name="Soendanees" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Modulation" title="Modulation – Zweeds" lang="sv" hreflang="sv" data-title="Modulation" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%A3%E0%AF%8D%E0%AE%AA%E0%AF%87%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="பண்பேற்றம் – Tamil" lang="ta" hreflang="ta" data-title="பண்பேற்றம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%81%E0%B8%A5%E0%B9%89%E0%B8%B3%E0%B8%AA%E0%B8%B1%E0%B8%8D%E0%B8%8D%E0%B8%B2%E0%B8%93" title="การกล้ำสัญญาณ – Thai" lang="th" hreflang="th" data-title="การกล้ำสัญญาณ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mod%C3%BClasyon" title="Modülasyon – Turks" lang="tr" hreflang="tr" data-title="Modülasyon" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D1%96%D1%8F" title="Модуляція – Oekraïens" lang="uk" hreflang="uk" data-title="Модуляція" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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/%D8%AA%D8%AD%D9%88%DB%8C%D8%B1" title="تحویر – Urdu" lang="ur" hreflang="ur" data-title="تحویر" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Signal_modulyatsiya" title="Signal modulyatsiya – Oezbeeks" lang="uz" hreflang="uz" data-title="Signal modulyatsiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%81u_ch%E1%BA%BF_t%C3%ADn_hi%E1%BB%87u" title="Điều chế tín hiệu – Vietnamees" lang="vi" hreflang="vi" data-title="Điều chế tín hiệu" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B0%83%E5%88%B6" title="调制 – Wuyu" lang="wuu" hreflang="wuu" data-title="调制" data-language-autonym="吴语" data-language-local-name="Wuyu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%AA%BF%E8%AE%8A" title="調變 – Chinees" lang="zh" hreflang="zh" data-title="調變" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</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-ti%C4%81u_(ti%C4%81n-s%C3%ACn)" title="Piàn-tiāu (tiān-sìn) – Minnanyu" lang="nan" hreflang="nan" data-title="Piàn-tiāu (tiān-sìn)" 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verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><p><b>Modulatie</b> is het combineren van een laagfrequent informatiesignaal met een <a href="/wiki/Draaggolf" title="Draaggolf">draaggolf</a> met een hogere frequentie, zodat een signaal ontstaat met een frequentieband rondom de frequentie van de draaggolf. </p><p>Stel dat een <a href="/wiki/Radio" title="Radio">radio</a>- of <a href="/wiki/Televisie" title="Televisie">televisiesignaal</a> direct zonder draaggolf draadloos wordt uitgezonden. Het audiosignaal dat door een <a href="/wiki/Microfoon" title="Microfoon">microfoon</a> wordt opgewekt, en <a href="/wiki/Frequentie" title="Frequentie">frequenties</a> onder 20 kHz bevat, zou dus dan met die frequenties worden uitgezonden. Er zou dan maar één zender tegelijk in bedrijf kunnen zijn, maar het grootste probleem is dat dergelijke frequenties zich niet goed voortplanten door de <a href="/wiki/Aardatmosfeer" title="Aardatmosfeer">atmosfeer</a>. </p><p>Dit probleem wordt opgelost door het bronsignaal met een draaggolf met een veel hogere frequentie over te brengen. Met een modulator wordt het signaal <a href="/wiki/Superpositie_(natuurkunde)#Radio_en_televisie" title="Superpositie (natuurkunde)">gesuperponeerd</a> op een sinusvormige draaggolf, waaruit later door <a href="/wiki/Demodulatie_(transmissie)" title="Demodulatie (transmissie)">demodulatie</a> het oorspronkelijke signaal weer kan worden teruggewonnen. Door gebruikmaking van draaggolven van verschillende frequenties kunnen verschillende <a href="/wiki/Zender" title="Zender">zenders</a> uitzenden zonder elkaar te storen en worden ze door de <a href="/w/index.php?title=Selectiviteit_(radio)&action=edit&redlink=1" class="new" title="Selectiviteit (radio) (de pagina bestaat niet)">selectiviteit</a> van de <a href="/wiki/Ontvanger_(elektronica)" title="Ontvanger (elektronica)">ontvanger</a> uit elkaar gehouden. Door een hoogfrequente draaggolf te gebruiken krijgt het signaal de transmissiekwaliteiten om draadloos te worden uitgezonden, maar uiteraard kan het nog steeds door een draad- of glasvezelverbinding worden getransporteerd zoals bij kabeltelevisie. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Redenen">Redenen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=1" title="Bewerk dit kopje: Redenen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=1" title="De broncode bewerken van de sectie: Redenen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Laagfrequente signalen hebben voor sommigen toepassingen grote nadelen waarvoor modulatie een oplossing kan bieden. </p> <ul><li>De gebruikte spectra van verschillende bronnen overlappen elkaar. Verschillende <a href="/wiki/Zender" title="Zender">zenders</a> kunnen door modulatie draaggolven van verschillende frequenties uitzenden en zodoende uit elkaars 'vaarwater' blijven, de signalen worden door de <a href="/w/index.php?title=Selectiviteit_(radio)&action=edit&redlink=1" class="new" title="Selectiviteit (radio) (de pagina bestaat niet)">selectiviteit</a> van de <a href="/wiki/Ontvanger_(elektronica)" title="Ontvanger (elektronica)">ontvanger</a> uit elkaar gehouden. (Zie ook <a href="/w/index.php?title=FDM&action=edit&redlink=1" class="new" title="FDM (de pagina bestaat niet)">FDM</a>).</li> <li>Zeer laagfrequente signalen of langzaam variërende gelijkspanningen, zoals meetsignalen van sensoren, laten zich lastig accuraat versterken en overzenden. Ook hiervoor is modulatie een oplossing.</li> <li>Voor het verkrijgen van een goede selectiviteit worden in de <a href="/wiki/Superheterodyne" title="Superheterodyne">superheterodyne</a> alle signalen omgezet naar eenzelfde frequentie.</li></ul> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Draaggolf">Draaggolf</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=2" title="Bewerk dit kopje: Draaggolf" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=2" title="De broncode bewerken van de sectie: Draaggolf"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De draaggolf <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 c(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e77d04462d26c4fdbfe8f988b182babd15059df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.656ex; height:2.843ex;" alt="{\displaystyle c(t)}"></span> is een zuiver <a href="/wiki/Sinus_en_cosinus" title="Sinus en cosinus">sinusvormig</a> signaal, met een frequentie <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>, veel hoger dan de hoogste in het bronsignaal <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 x(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d54c275db3a1e620737b58e143b0818107fa5f5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle x(t)}"></span> voorkomende frequentie. Voor de draaggolf geldt: </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 c(t)=A\cos(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c(t)=A\cos(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/387dddd2d5ab2ed6feb9ebbf8efa679c4c775338" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.451ex; height:2.843ex;" alt="{\displaystyle c(t)=A\cos(\omega t+\varphi )}"></span>,</dd></dl> <p>waarin <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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> de amplitude is van de draaggolf, <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 \omega =2\pi f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =2\pi f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a1bf35d395c2d52391265e4bbda0aed14f52579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.317ex; height:2.509ex;" alt="{\displaystyle \omega =2\pi f}"></span> de <a href="/wiki/Hoekfrequentie" title="Hoekfrequentie">hoekfrequentie</a> en <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> de <a href="/wiki/Fase_(golf)" title="Fase (golf)">fasehoek</a>. </p><p>In beginsel ontstaan de mogelijkheden voor modulatie door het variëren van een van de parameters. Bij variatie van de amplitude <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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> spreekt men van <a href="/wiki/Amplitudemodulatie" title="Amplitudemodulatie">amplitudemodulatie</a>, bij variatie van de frequentie <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> van <a href="/wiki/Frequentiemodulatie" title="Frequentiemodulatie">frequentiemodulatie</a> en bij variatie van de fasehoek <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> van <a href="/wiki/Fasemodulatie" title="Fasemodulatie">fasemodulatie</a>. Daarbij zorgt men er in de praktijk voor dat de variaties niet te groot zijn, zodat de gunstige draaggolfeigenschappen behouden blijven. Het gevolg is dat de gemoduleerde signalen lokaal, dat wil zeggen gedurende enkele perioden van de draaggolf op een harmonisch signaal lijken met de bij de modulatievorm behorende amplitude en frequentie. </p> <div class="mw-heading mw-heading3"><h3 id="Vermogen">Vermogen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=3" title="Bewerk dit kopje: Vermogen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=3" title="De broncode bewerken van de sectie: Vermogen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Voor een sinusvormige draaggolf met een topspanning <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 {\hat {u}}_{hf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {u}}_{hf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87c36ad48003dce7cd6c6aab8106e268ded5ec06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.413ex; height:2.843ex;" alt="{\displaystyle {\hat {u}}_{hf}}"></span> geldt: </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 u_{c}(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{c}(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6bdaf062db590fb86c8940dad8719aceef38a94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.11ex; height:3.009ex;" alt="{\displaystyle u_{c}(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)}"></span>,</dd></dl> <p>Het draaggolfvermogen volgt uit de effectieve waarde van de (sinusvormige) draaggolf, en de weerstand <i>R</i> waarin het vermogen wordt gedissipeerd. De effectieve waarde van de spanning is: </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 u_{c}={\frac {{\hat {u}}_{hf}}{\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{c}={\frac {{\hat {u}}_{hf}}{\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/729e8835b182aee1235ba181e01c5d29bebd26e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:9.621ex; height:6.676ex;" alt="{\displaystyle u_{c}={\frac {{\hat {u}}_{hf}}{\sqrt {2}}}}"></span></dd></dl> <p>en het draaggolfvermogen bedraagt dus: </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 P_{c}=\left({\frac {{\hat {u}}_{hf}}{\sqrt {2}}}\right)^{2}{\frac {1}{R}}={{\hat {u}}_{hf}^{2} \over 2R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{c}=\left({\frac {{\hat {u}}_{hf}}{\sqrt {2}}}\right)^{2}{\frac {1}{R}}={{\hat {u}}_{hf}^{2} \over 2R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bdbe1cf6568fbfaceaab1530782728c9a37b329" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:24.207ex; height:7.343ex;" alt="{\displaystyle P_{c}=\left({\frac {{\hat {u}}_{hf}}{\sqrt {2}}}\right)^{2}{\frac {1}{R}}={{\hat {u}}_{hf}^{2} \over 2R}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Amplitudemodulatie_(AM)"><span id="Amplitudemodulatie_.28AM.29"></span>Amplitudemodulatie (AM)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=4" title="Bewerk dit kopje: Amplitudemodulatie (AM)" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=4" title="De broncode bewerken van de sectie: Amplitudemodulatie (AM)"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Modulatie_am_tijd.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Modulatie_am_tijd.png/600px-Modulatie_am_tijd.png" decoding="async" width="600" height="375" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/32/Modulatie_am_tijd.png 1.5x" data-file-width="800" data-file-height="500" /></a><figcaption>afbeelding 1: Amplitudegemoduleerd signaal<div style="display: flex;"><span style="display: inline-block; min-width: 1.2em; height: 1.2em; line-height: 1.1; margin: 2px 0 0; border-radius: 2px; box-sizing: border-box; color-adjust: exact;background-color: green; color: transparent;border: 1px solid gray;">■</span> <span style="margin:0;">Oorspronkelijk signaal</span></div><div style="display: flex;"><span style="display: inline-block; min-width: 1.2em; height: 1.2em; line-height: 1.1; margin: 2px 0 0; border-radius: 2px; box-sizing: border-box; color-adjust: exact;background-color: grey; color: transparent;border: 1px solid gray;">■</span> <span style="margin:0;">gemoduleerde draaggolf</span></div><div style="display: flex;"><span style="display: inline-block; min-width: 1.2em; height: 1.2em; line-height: 1.1; margin: 2px 0 0; border-radius: 2px; box-sizing: border-box; color-adjust: exact;background-color: red; color: transparent;border: 1px solid gray;">■</span> <span style="margin:0;">fictieve omhullende van draaggolf</span></div></figcaption></figure> <p><a href="/wiki/Amplitudemodulatie" title="Amplitudemodulatie">Amplitudemodulatie</a> (AM) is de oudste vorm van modulatie, de detectie is namelijk zeer eenvoudig uit te voeren. </p><p>In de simpelste vorm bestaat AM uit het herhaaldelijk in- en uitschakelen van de zender. Door de schakeltijden te variëren kunnen codes als <a href="/wiki/Morse" title="Morse">morse</a> worden verstuurd. Deze mode duidt men over het algemeen aan met <a href="/w/index.php?title=Continuous_wave&action=edit&redlink=1" class="new" title="Continuous wave (de pagina bestaat niet)">CW</a> wat staat voor continuous wave. Overdracht van geluid door middel van AM gebeurt door de amplitude van de draaggolf geleidelijk te veranderen, gestuurd door de amplitude van het LF-signaal. </p> <div class="mw-heading mw-heading3"><h3 id="Karakteristieken">Karakteristieken</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=5" title="Bewerk dit kopje: Karakteristieken" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=5" title="De broncode bewerken van de sectie: Karakteristieken"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een amplitudegemoduleerd signaal <i>v(t)</i> is van de vorm: </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 v(t)=A(t)\cos(\omega t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A(t)\cos(\omega t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95e83116b66bb94668256abb1017b25b2afbb301" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.86ex; height:2.843ex;" alt="{\displaystyle v(t)=A(t)\cos(\omega t)}"></span>,</dd></dl> <p>met <i>A(t)</i> een <a href="/wiki/Lineair" class="mw-redirect" title="Lineair">lineaire</a> <a href="/wiki/Functie_(wiskunde)" title="Functie (wiskunde)">functie</a> van het bronsignaal, dus </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 A(t)=a+bx(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(t)=a+bx(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8eb83317acf48a52755b8cc3678b8f6e7184b3f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.537ex; height:2.843ex;" alt="{\displaystyle A(t)=a+bx(t)}"></span>.</dd></dl> <p>In afbeelding 1 is zichtbaar dat het signaal (lichtgrijs) lokaal rond elke <i>t</i> een sinus lijkt met frequentie <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 2\pi \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/121bd4297be2033827f783ed7857484b24f85af2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.94ex; height:2.176ex;" alt="{\displaystyle 2\pi \omega }"></span> en amplitude <i>A(t)</i>. </p> <div class="mw-heading mw-heading3"><h3 id="AM-zijbanden">AM-zijbanden</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=6" title="Bewerk dit kopje: AM-zijbanden" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=6" title="De broncode bewerken van de sectie: AM-zijbanden"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Er ontstaan bij het moduleren signaalcomponenten met nieuwe frequenties. </p><p>Uit de goniometrische 'standaard' betrekkingen </p> <ul><li><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 \cos(\alpha +\beta )=\cos(\alpha )\cos(\beta )-\sin(\alpha )\sin(\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(\alpha +\beta )=\cos(\alpha )\cos(\beta )-\sin(\alpha )\sin(\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70c0a7c8142b8713d27cd787216f5249a4230922" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.103ex; height:2.843ex;" alt="{\displaystyle \cos(\alpha +\beta )=\cos(\alpha )\cos(\beta )-\sin(\alpha )\sin(\beta )}"></span></li> <li><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 \cos(\alpha -\beta )=\cos(\alpha )\cos(\beta )+\sin(\alpha )\sin(\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(\alpha -\beta )=\cos(\alpha )\cos(\beta )+\sin(\alpha )\sin(\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198ea36bf9dda5c52b893c23ffb34ac1f4582b08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.103ex; height:2.843ex;" alt="{\displaystyle \cos(\alpha -\beta )=\cos(\alpha )\cos(\beta )+\sin(\alpha )\sin(\beta )}"></span></li></ul> <p>kan door optellen worden afgeleid dat: </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 \cos(\alpha )\cos(\beta )={\frac {1}{2}}\cos(\alpha -\beta )+{\frac {1}{2}}\cos(\alpha +\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(\alpha )\cos(\beta )={\frac {1}{2}}\cos(\alpha -\beta )+{\frac {1}{2}}\cos(\alpha +\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/400dce710fb2bf712ba2358e88307feea691e8c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:44.919ex; height:5.176ex;" alt="{\displaystyle \cos(\alpha )\cos(\beta )={\frac {1}{2}}\cos(\alpha -\beta )+{\frac {1}{2}}\cos(\alpha +\beta )}"></span></dd></dl> <p>Door nu voor A(t) een cosinusvorm te kiezen kan het resulterende signaal worden geschreven als: <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(t)={{{\hat {u}}_{lf}{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}-\omega _{lf})t)+\cos((\omega _{hf}+\omega _{lf})t)\rbrace }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo fence="false" stretchy="false">{</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)={{{\hat {u}}_{lf}{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}-\omega _{lf})t)+\cos((\omega _{hf}+\omega _{lf})t)\rbrace }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17de7830b2878b82be8411351bf6a66d9068607f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:53.268ex; height:5.676ex;" alt="{\displaystyle v(t)={{{\hat {u}}_{lf}{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}-\omega _{lf})t)+\cos((\omega _{hf}+\omega _{lf})t)\rbrace }"></span> </p><p>Hierin zijn <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 {\hat {u}}_{hf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {u}}_{hf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87c36ad48003dce7cd6c6aab8106e268ded5ec06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.413ex; height:2.843ex;" alt="{\displaystyle {\hat {u}}_{hf}}"></span> en <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 {\hat {u}}_{lf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {u}}_{lf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aa7347cbc4a3bf87323009d740499f885523d5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.956ex; height:2.843ex;" alt="{\displaystyle {\hat {u}}_{lf}}"></span> de respectievelijke topwaarden van de draaggolf en het LF-signaal, en <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 \omega _{hf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{hf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f22b6f073f1060026461cacedbc804d613317d90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.529ex; height:2.343ex;" alt="{\displaystyle \omega _{hf}}"></span> en <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 \omega _{lf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{lf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5556e1b8e7087d384b02d6aadac316ac1b660c2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.072ex; height:2.343ex;" alt="{\displaystyle \omega _{lf}}"></span> de respectievelijke hoekfrequenties. </p><p>Door de <i>vermenigvuldiging</i> van de drager en het signaal ontstaan som- en verschilfrequenties. De uitkomst representeert een zogenaamd dubbelzijbandsignaal, het bestaat uit alleen de zijbanden (rood in afbeelding 2). Merk op dat de draaggolf en het laagfrequent signaal niet als zodanig in deze uitkomst voorkomen, en dat het vermogen van de draaggolf en het LF-signaal volledig in de zijbanden is opgegaan. Alle informatie uit het LF-signaal is aanwezig in <i>elke</i> zijband. Om vermogen te besparen wordt daarom soms slechts één zijband uitgezonden, men spreekt dan van <a href="/wiki/Enkelzijbandmodulatie" title="Enkelzijbandmodulatie">enkelzijbandmodulatie</a> (EZB) of single sideband (SSB) er wordt dan nader gespecificeerd of het gaat om de lage (LSB) of de hoge (USB) zijband. </p><p>In de afbeelding is te zien dat de onderste zijband is gespiegeld, het geluidsspectrum is in deze zijband omgedraaid. Wanneer met een USB-ontvanger naar een LSB-signaal wordt geluisterd lijken mensen dan ook een vreemde taal te spreken. </p><p>Een 'normale' AM-zender zendt naast de genoemde zijbanden ook de draaggolf zelf uit. Dit type signaal (een 'echt' AM-signaal) wordt voorgesteld door: </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 v(t)=(1+m){\hat {u}}_{hf}\cos(\omega _{hf}t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>m</mi> <mo stretchy="false">)</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=(1+m){\hat {u}}_{hf}\cos(\omega _{hf}t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc83ca3f1748aa9147a73f07a0ef8058621bd5f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.816ex; height:3.009ex;" alt="{\displaystyle v(t)=(1+m){\hat {u}}_{hf}\cos(\omega _{hf}t)}"></span></dd></dl> <p>Hierin is m de modulatiediepte: </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 m={{\hat {u}}_{lf} \over {\hat {u}}_{hf}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={{\hat {u}}_{lf} \over {\hat {u}}_{hf}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/212b1fc0bf41f93826d73e26c857aac33b578fff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:9.388ex; height:6.509ex;" alt="{\displaystyle m={{\hat {u}}_{lf} \over {\hat {u}}_{hf}}}"></span></dd></dl> <p>ze stelt de verhouding tussen de amplituden van de draaggolf en het laagfrequent signaal voor. De waarde van m loopt van nul (de draaggolf is ongemoduleerd) tot maximaal 1 (de draaggolf is volledig gemoduleerd). </p><p>Door invullen van m kan het AM-signaal daarmee worden geschreven als: </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 v(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)+{{m{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}+\omega _{lf})t)+\cos((\omega _{hf}-\omega _{lf})t)\rbrace }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo fence="false" stretchy="false">{</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)+{{m{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}+\omega _{lf})t)+\cos((\omega _{hf}-\omega _{lf})t)\rbrace }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0279443799698458569238f8fbf7326d7041ce18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:68.281ex; height:5.676ex;" alt="{\displaystyle v(t)={\hat {u}}_{hf}\cos(\omega _{hf}t)+{{m{\hat {u}}_{hf}} \over 2}\lbrace \cos((\omega _{hf}+\omega _{lf})t)+\cos((\omega _{hf}-\omega _{lf})t)\rbrace }"></span></dd></dl> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Modulatie_am_freq.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Modulatie_am_freq.png/600px-Modulatie_am_freq.png" decoding="async" width="600" height="375" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/bc/Modulatie_am_freq.png 1.5x" data-file-width="800" data-file-height="500" /></a><figcaption>afbeelding 2: Frequentiespectrum van amplitudemodulatie</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="AM-vermogen">AM-vermogen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=7" title="Bewerk dit kopje: AM-vermogen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=7" title="De broncode bewerken van de sectie: AM-vermogen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het vermogen in de AM-draaggolf wordt beschreven door: </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 P_{c}={{\hat {u}}_{hf}^{2} \over 2R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{c}={{\hat {u}}_{hf}^{2} \over 2R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51292f9427de6d607cca5b952950f46c34a192b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.784ex; height:6.509ex;" alt="{\displaystyle P_{c}={{\hat {u}}_{hf}^{2} \over 2R}}"></span></dd></dl> <p>De effectieve waarde van het zijbandsignaal is -bij een sinusvormig modulerend signaal- dus </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 u_{z}={{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{z}={{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52a5f76f05e4dba1cb24e2a31485f07aeb7f425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:11.719ex; height:6.676ex;" alt="{\displaystyle u_{z}={{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}}}"></span></dd></dl> <p>En het in een weerstand R ontwikkelde vermogen is </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 P_{z}={({{{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}})^{2}} \over R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mrow> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{z}={({{{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}})^{2}} \over R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6262ba40eec72c4073173b6d4905d27fa112b401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.184ex; height:8.343ex;" alt="{\displaystyle P_{z}={({{{m{\hat {u}}_{hf}} \over {2{\sqrt {2}}}})^{2}} \over R}}"></span></dd></dl> <p>of </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 P_{z}={{({m{\hat {u}}_{hf}})^{2}} \over 8R}={{m^{2} \over 4}{{\hat {u}}_{hf}^{2} \over 2R}}={{m^{2} \over 4}P_{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>R</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>4</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>4</mn> </mfrac> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{z}={{({m{\hat {u}}_{hf}})^{2}} \over 8R}={{m^{2} \over 4}{{\hat {u}}_{hf}^{2} \over 2R}}={{m^{2} \over 4}P_{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b386f88ec5bc5367be6246284ad1f0e9a14d0f18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:35.489ex; height:6.509ex;" alt="{\displaystyle P_{z}={{({m{\hat {u}}_{hf}})^{2}} \over 8R}={{m^{2} \over 4}{{\hat {u}}_{hf}^{2} \over 2R}}={{m^{2} \over 4}P_{c}}}"></span></dd></dl> <p>Zodat voor het totale vermogen van een AM-signaal (met sinusvormig modulatiesignaal) geldt: </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 P_{am}=\left(1+{m^{2} \over 2}\right)P_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{am}=\left(1+{m^{2} \over 2}\right)P_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7165dc0a8a9fed16e23f0b69ac48562cdb334136" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.314ex; height:6.343ex;" alt="{\displaystyle P_{am}=\left(1+{m^{2} \over 2}\right)P_{c}}"></span></dd></dl> <p>Omdat het relatief gemakkelijk is om de topwaarde van een HF-signaal te bepalen -in tegenstelling tot bijvoorbeeld de effectieve waarde- is het gebruikelijk om met name het vermogen uit te drukken in die topspanning. Dit in tegenstelling met de 'gewone' elektronica waar men het liefst in termen van U<sub>eff</sub> rekent. </p><p>In de praktijk wordt vaak een andere maat voor het AM-vermogen gebruikt: het <a href="/wiki/Zendvermogen" title="Zendvermogen">PEP</a>-vermogen (Eng. Peak Envelope Power). Hierbij wordt de topwaarde van het gemoduleerde signaal -ook wel de omhullende (envelope)- als spanning genomen in de 'gewone' vermogensberekening, die eigenlijk berust op de effectieve waarde. Het feitelijke vermogen is dus lager dan het PEP-vermogen. In afbeelding 1 is een AM-signaal te zien, het modulerend signaal is groen en de rode lijnen vormen de omhullende (Eng. Envelope). Het PEP-vermogen van de zender is dus gebaseerd op de extreme waarden van de rode lijnen. </p> <div class="mw-heading mw-heading2"><h2 id="Frequentiemodulatie_(FM)"><span id="Frequentiemodulatie_.28FM.29"></span>Frequentiemodulatie (FM)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=8" title="Bewerk dit kopje: Frequentiemodulatie (FM)" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=8" title="De broncode bewerken van de sectie: Frequentiemodulatie (FM)"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bij FM wordt de momentane hoekfrequentie van de draaggolf veranderd in relatie met de amplitude van het laagfrequent signaal. Over het algemeen gebruikte FM-signalen zijn echter feitelijk een vorm van hoekmodulatie. </p><p>Bij hoekmodulatie heeft het gemoduleerde signaal <i>v(t)</i> de vorm: </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 v(t)=A\cos(h(t))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A\cos(h(t))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9dd73ea1d0fa676171238798aa01f1c38912f8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.913ex; height:2.843ex;" alt="{\displaystyle v(t)=A\cos(h(t))}"></span>,</dd></dl> <p>waarin h(t) zo gekozen wordt dat </p> <ul><li>de draaggolfeigenschappen bewaard blijven</li> <li>er een relatie is met het bronsignaal</li></ul> <p>Bij deze modulatievorm worden zowel de frequentie als de fase van het signaal beïnvloed, aangezien </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 \omega _{mom}={{d\phi } \over {dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>ϕ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{mom}={{d\phi } \over {dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/970d60859a0f64726dbe85732523161c7587f099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.897ex; height:5.509ex;" alt="{\displaystyle \omega _{mom}={{d\phi } \over {dt}}}"></span></dd></dl> <p>Men spreekt traditioneel echter van <a href="/wiki/Frequentiemodulatie" title="Frequentiemodulatie">frequentiemodulatie</a> (FM) als de <a href="/w/index.php?title=Momentane_hoekfrequentie&action=edit&redlink=1" class="new" title="Momentane hoekfrequentie (de pagina bestaat niet)">momentane hoekfrequentie</a> (de afgeleide van <i>h(t)</i>) een lineaire functie is van het bronsignaal. Dus als: </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 h'(t)=a+bx(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h'(t)=a+bx(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/418e9035f004287923a72030e99053017eb76cec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.817ex; height:3.009ex;" alt="{\displaystyle h'(t)=a+bx(t)}"></span>.</dd></dl> <p>Men kiest meestal voor <i>a</i> de hoekfrequentie van de draaggolf, zodat: </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 h(t)=\omega t+b\int x(t)dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>b</mi> <mo>∫</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=\omega t+b\int x(t)dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ac089e246b5321937347f149589e6628efaecb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.212ex; height:5.676ex;" alt="{\displaystyle h(t)=\omega t+b\int x(t)dt}"></span></dd></dl> <p>en </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 v(t)=A\cos \left(\omega t+b\int x(t)dt\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>b</mi> <mo>∫</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A\cos \left(\omega t+b\int x(t)dt\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0679f411de1a1eaae6ea1bd4d80e74cba2a4a880" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.663ex; height:6.176ex;" alt="{\displaystyle v(t)=A\cos \left(\omega t+b\int x(t)dt\right)}"></span>.</dd></dl> <p>Strikt genomen wordt hier de fase van de draaggolf gemoduleerd en zou men dus van fasemodulatie (PM) moeten spreken. Het signaal is wel genoteerd met behulp van een cosinus, maar is geen cosinus in de tijd. Door de condities echter die men bij modulatie hanteert, is de variatie in frequentie relatief gering, waardoor het signaal lokaal rond t een (co)sinus lijkt met vaste amplitude <i>A</i> en <a href="/w/index.php?title=Momentane_hoekfrequentie&action=edit&redlink=1" class="new" title="Momentane hoekfrequentie (de pagina bestaat niet)">momentane hoekfrequentie</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 \omega +bx(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega +bx(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0054d2af92f6e5b1cdaceb7d0c5256c2907c3b0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.262ex; height:2.843ex;" alt="{\displaystyle \omega +bx(t)}"></span>. </p><p>Voor "echte" FM zou men de hoekfrequentie moeten variëren, dus: </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 h(t)=w(t)t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>w</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=w(t)t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1433f4eacdd5156edc30d1fb137d16e2403d3ca8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.239ex; height:2.843ex;" alt="{\displaystyle h(t)=w(t)t}"></span></dd></dl> <p>moeten kiezen, met voor <i>w(t)</i> een voor de hand liggende keuze: </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 w(t)=w+qx(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>w</mi> <mo>+</mo> <mi>q</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w(t)=w+qx(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21cef5be2483c28c91541903d2f5e7785313fb18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.964ex; height:2.843ex;" alt="{\displaystyle w(t)=w+qx(t)}"></span> of <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(t)=w(1+qx(t))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>w</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>q</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w(t)=w(1+qx(t))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c82b4ac25f86324122b376ac2fe3c56db9e92063" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.936ex; height:2.843ex;" alt="{\displaystyle w(t)=w(1+qx(t))}"></span>.</dd></dl> <p>Dit houdt echter in dat de momentane hoekfrequentie afhangt van zowel het bronsignaal zelf als van de <a href="/wiki/Afgeleide" title="Afgeleide">afgeleide</a> daarvan, zodat demodulatie moeilijk is. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Modulatie_fm_tijd.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modulatie_fm_tijd.png/600px-Modulatie_fm_tijd.png" decoding="async" width="600" height="375" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/2c/Modulatie_fm_tijd.png 1.5x" data-file-width="800" data-file-height="500" /></a><figcaption>afbeelding 3: Frequentiegemoduleerd signaal (blauw) en hoekgemoduleerd signaal (rood) in het tijddomein</figcaption></figure> <p>In afbeelding 3 is het verschil tussen hoekmodulatie (rood) en frequentiemodulatie (blauw) duidelijk te zien. De praktische uitvoering van FM geschiedt over het algemeen door de oscillator van de draaggolf te beïnvloeden, zodat de opgewekte frequentie op de gewenste manier varieert met het bronsignaal (groen). </p> <div class="mw-heading mw-heading3"><h3 id="FM-zijbanden">FM-zijbanden</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=9" title="Bewerk dit kopje: FM-zijbanden" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=9" title="De broncode bewerken van de sectie: FM-zijbanden"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Bessels.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Bessels.png/300px-Bessels.png" decoding="async" width="300" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Bessels.png/450px-Bessels.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Bessels.png/600px-Bessels.png 2x" data-file-width="800" data-file-height="499" /></a><figcaption>afbeelding 4: Besselse functies</figcaption></figure> <p>Ook bij FM ontstaan zijbanden. Wanneer we voor de frequentiezwaai van het signaal <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 \Delta \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b32f8e32a72fd8afb871214c670c130ea3e7e325" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.382ex; height:2.176ex;" alt="{\displaystyle \Delta \omega }"></span> schrijven, kan bij hoekmodulatie met een cosinusvormig signaal het argument worden geschreven als: </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 h(t)=\int _{0}^{t}{\omega _{hf}+\Delta \omega _{hf}\cos(\omega _{lf}t)dt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=\int _{0}^{t}{\omega _{hf}+\Delta \omega _{hf}\cos(\omega _{lf}t)dt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/689dcae9f1547be19e2b08554c7cf6865b27825e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.873ex; height:6.176ex;" alt="{\displaystyle h(t)=\int _{0}^{t}{\omega _{hf}+\Delta \omega _{hf}\cos(\omega _{lf}t)dt}}"></span></dd></dl> <p>en dus ook als: </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 h(t)=\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}}t)+h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mrow> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}}t)+h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e326ada21b27368e0213ebe87729018b6c9ce364" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.794ex; height:6.343ex;" alt="{\displaystyle h(t)=\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}}t)+h_{0}}"></span></dd></dl> <p>De gemoduleerde draaggolf (met amplitude A) kan dus behoudens de integratieconstante <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 h_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08c1c908b03c3f63383c7199465c7fd0b105030f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.509ex;" alt="{\displaystyle h_{0}}"></span> geschreven worden als: </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 v(t)=A\sin \left(\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}})\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A\sin \left(\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}})\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d738ccb95a1be94d601304d551c4abee78899167" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.916ex; height:6.343ex;" alt="{\displaystyle v(t)=A\sin \left(\omega _{hf}t+{{{\Delta \omega _{hf}} \over \omega _{lf}}\sin(\omega _{lf}})\right)}"></span></dd></dl> <p>De verhouding tussen de frequentiezwaai van het FM-signaal en de <a href="/wiki/Hoeksnelheid" title="Hoeksnelheid">hoeksnelheid</a> van het modulerende signaal noemt men de modulatieindex. </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 m'={{\Delta \omega _{hf}} \over \omega _{lf}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> </mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m'={{\Delta \omega _{hf}} \over \omega _{lf}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57dfcc9870e9defb04105e820fa828574004dc34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:12.125ex; height:6.343ex;" alt="{\displaystyle m'={{\Delta \omega _{hf}} \over \omega _{lf}}}"></span></dd></dl> <p>Met deze modulatieindex (m') kan voor het signaal worden geschreven: </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 v(t)=A\sin(\omega _{hf}t+{{m'}\sin(\omega _{lf}}))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A\sin(\omega _{hf}t+{{m'}\sin(\omega _{lf}}))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45797a6f9aee8d625c126b26eec4483c5c078fa3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:31.729ex; height:3.176ex;" alt="{\displaystyle v(t)=A\sin(\omega _{hf}t+{{m'}\sin(\omega _{lf}}))}"></span></dd></dl> <p>Na omwerken tot </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 v(t)=A\left\lbrace \sin(\omega _{hf}t)\cos({m'}\sin(\omega _{lf}t))+\cos(\omega _{hf}t)\sin({m'}\sin(\omega _{lf}t))\right\rbrace }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mrow> <mo>{</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=A\left\lbrace \sin(\omega _{hf}t)\cos({m'}\sin(\omega _{lf}t))+\cos(\omega _{hf}t)\sin({m'}\sin(\omega _{lf}t))\right\rbrace }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53b735f2ef7394c74c14b8fd9ec0d00cfa73e1ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:66.231ex; height:3.176ex;" alt="{\displaystyle v(t)=A\left\lbrace \sin(\omega _{hf}t)\cos({m'}\sin(\omega _{lf}t))+\cos(\omega _{hf}t)\sin({m'}\sin(\omega _{lf}t))\right\rbrace }"></span></dd></dl> <p>en substitutie van </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 \cos({m'}\sin(\omega _{lf}t))=J_{0}(m')+2\sum _{n=0}^{\inf }{J_{2n}(m')\cos(2n\omega _{lf}t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">inf</mo> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos({m'}\sin(\omega _{lf}t))=J_{0}(m')+2\sum _{n=0}^{\inf }{J_{2n}(m')\cos(2n\omega _{lf}t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feb5478d4454a28330b8a409d263f41abbc191e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:54.361ex; height:7.343ex;" alt="{\displaystyle \cos({m'}\sin(\omega _{lf}t))=J_{0}(m')+2\sum _{n=0}^{\inf }{J_{2n}(m')\cos(2n\omega _{lf}t)}}"></span></dd></dl> <p>en </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 \sin({m'}\sin(\omega _{lf}t))=2\sum _{n=0}^{\inf }{J_{2n+1}(m')\sin((2n+1)\omega _{lf}t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">inf</mo> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin({m'}\sin(\omega _{lf}t))=2\sum _{n=0}^{\inf }{J_{2n+1}(m')\sin((2n+1)\omega _{lf}t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/269f06d386ece051d42f21091a130440133727bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:52.043ex; height:7.343ex;" alt="{\displaystyle \sin({m'}\sin(\omega _{lf}t))=2\sum _{n=0}^{\inf }{J_{2n+1}(m')\sin((2n+1)\omega _{lf}t)}}"></span></dd></dl> <p>ontstaat de volgende vorm voor het signaal: </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 {\begin{matrix}v(t)=\\AJ_{0}(m')+\\AJ_{1}(m')\left[\sin((\omega _{hf}+\omega _{lf})t)-\sin((\omega _{hf}-\omega _{lf})t)\right]+\\AJ_{2}(m')\left[\sin((\omega _{hf}+2\omega _{lf})t)-\sin((\omega _{hf}-2\omega _{lf})t)\right]+\\AJ_{3}(m')\left[\sin((\omega _{hf}+3\omega _{lf})t)-\sin((\omega _{hf}-3\omega _{lf})t)\right]+\\AJ_{4}(m')\left[\sin((\omega _{hf}+4\omega _{lf})t)-\sin((\omega _{hf}-4\omega _{lf})t)\right]+\\\dots +\\AJ_{n}(m')\left[\sin((\omega _{hf}+n\omega _{lf})t)-\sin((\omega _{hf}-n\omega _{lf})t)\right]\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <mn>2</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mn>3</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <mn>3</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mn>4</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <mn>4</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>⋯</mo> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>+</mo> <mi>n</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>f</mi> </mrow> </msub> <mo>−</mo> <mi>n</mi> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}v(t)=\\AJ_{0}(m')+\\AJ_{1}(m')\left[\sin((\omega _{hf}+\omega _{lf})t)-\sin((\omega _{hf}-\omega _{lf})t)\right]+\\AJ_{2}(m')\left[\sin((\omega _{hf}+2\omega _{lf})t)-\sin((\omega _{hf}-2\omega _{lf})t)\right]+\\AJ_{3}(m')\left[\sin((\omega _{hf}+3\omega _{lf})t)-\sin((\omega _{hf}-3\omega _{lf})t)\right]+\\AJ_{4}(m')\left[\sin((\omega _{hf}+4\omega _{lf})t)-\sin((\omega _{hf}-4\omega _{lf})t)\right]+\\\dots +\\AJ_{n}(m')\left[\sin((\omega _{hf}+n\omega _{lf})t)-\sin((\omega _{hf}-n\omega _{lf})t)\right]\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/590a0fe1c6d9f6f117fb1a2ea2e0d2bae84631d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.838ex; width:51.926ex; height:26.843ex;" alt="{\displaystyle {\begin{matrix}v(t)=\\AJ_{0}(m')+\\AJ_{1}(m')\left[\sin((\omega _{hf}+\omega _{lf})t)-\sin((\omega _{hf}-\omega _{lf})t)\right]+\\AJ_{2}(m')\left[\sin((\omega _{hf}+2\omega _{lf})t)-\sin((\omega _{hf}-2\omega _{lf})t)\right]+\\AJ_{3}(m')\left[\sin((\omega _{hf}+3\omega _{lf})t)-\sin((\omega _{hf}-3\omega _{lf})t)\right]+\\AJ_{4}(m')\left[\sin((\omega _{hf}+4\omega _{lf})t)-\sin((\omega _{hf}-4\omega _{lf})t)\right]+\\\dots +\\AJ_{n}(m')\left[\sin((\omega _{hf}+n\omega _{lf})t)-\sin((\omega _{hf}-n\omega _{lf})t)\right]\end{matrix}}}"></span></dd></dl> <p>Hierin is <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 J_{n}(m')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{n}(m')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc81db08461fd1bf860279025c1f1983088a53fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.043ex; height:3.009ex;" alt="{\displaystyle J_{n}(m')}"></span> de Besselse functie van de eerste soort en orde n. De interpretatie hiervan is dat de zijbanden van een FM-signaal zich oneindig ver uitstrekken om de draaggolf heen, en dat ze samen met de draaggolf een amplitude hebben die wordt bepaald door de <a href="/wiki/Besselse_functies" class="mw-redirect" title="Besselse functies">Besselse functies</a> van het eerste soort. Het domein van de Besselse functie is in deze de modulatie-index, in afbeelding 4 zijn de respectievelijke functies afgebeeld, de functiewaarden voor m'=2 zijn gemarkeerd. </p><p>Afbeelding 5 laat het bij m'=2 horende frequentiespectrum zien. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Modulatie_fm_freq.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Modulatie_fm_freq.png/600px-Modulatie_fm_freq.png" decoding="async" width="600" height="375" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/73/Modulatie_fm_freq.png 1.5x" data-file-width="800" data-file-height="500" /></a><figcaption>afbeelding 5: Frequentiespectrum van frequentiemodulatie</figcaption></figure> <p>We zien hier dat de amplitude van de component op de draaggolffrequentie inderdaad gelijk is aan ongeveer 0,11 (J<sub>0</sub>(2) * draaggolfamplitude). </p><p>Voor de <a href="/wiki/Bandbreedte" title="Bandbreedte">bandbreedte</a> van een FM-signaal kan worden opgemerkt dat de modulatieindex een graadmeter blijkt te zijn voor de breedte van gemiddelde signalen. <i>"Het aantal benodigde zijbanden is gelijk aan m'+1"</i> is een vaak gebruikte vuistregel. </p> <div class="mw-heading mw-heading3"><h3 id="FM-vermogen">FM-vermogen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=10" title="Bewerk dit kopje: FM-vermogen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=10" title="De broncode bewerken van de sectie: FM-vermogen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het blijkt in de praktijk dat voor normale waarden van m' het vermogen van de draaggolf niet verandert door de frequentie te moduleren. Dit is aannemelijk omdat voor elke momentane frequentie de uitdrukking voor het vermogen hetzelfde blijft. Het vermogen wordt wel verspreid over een bepaalde bandbreedte, waardoor in sommige situaties het gemeten vermogen wel verandert. </p> <div class="mw-heading mw-heading2"><h2 id="Andere_vormen">Andere vormen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=11" title="Bewerk dit kopje: Andere vormen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=11" title="De broncode bewerken van de sectie: Andere vormen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De meeste andere vormen van modulatie zijn in essentie speciale vormen van AM of FM, dan wel een combinatie van beide. Dit geldt niet voor <a href="/wiki/Pulsbreedtemodulatie" title="Pulsbreedtemodulatie">pulsbreedtemodulatie</a> en <a href="/wiki/Pulspositiemodulatie" title="Pulspositiemodulatie">pulspositiemodulatie</a>. </p><p>Naast AM en FM onderscheidt men nog: </p> <ul><li><i><a href="/wiki/Single-sideband_modulation" class="mw-redirect" title="Single-sideband modulation">Single-sideband modulation</a></i> (SSB)</li> <li><i><a href="/wiki/Vestigial-sideband_modulation" title="Vestigial-sideband modulation">Vestigial-sideband modulation</a></i> (VSB, or VSB-AM)</li> <li><i><a href="/wiki/QAM" class="mw-redirect" title="QAM">Quadrature amplitude modulation</a></i> (QAM)</li> <li><i><a href="/wiki/Orthogonal_frequency_division_modulation" class="mw-redirect" title="Orthogonal frequency division modulation">Orthogonal frequency division modulation</a></i> (OFDM), dat ook wel bekendstaat als <i><a href="/wiki/Discrete_multitone_modulation" class="mw-redirect" title="Discrete multitone modulation">Discrete multitone modulation</a></i> (DMT)</li> <li><a href="/wiki/Ingrid_Daubechies" title="Ingrid Daubechies">Wavelet modulatie</a></li> <li><a href="/wiki/Ringmodulatie" title="Ringmodulatie">Ringmodulatie</a></li></ul> <p>Als OFDM wordt gebruikt in combinatie met <a href="/wiki/Kanaalcodering" title="Kanaalcodering">kanaalcodeertechnieken</a>, wordt het omschreven als <a href="/w/index.php?title=Coded_orthogonal_frequency_division_modulation&action=edit&redlink=1" class="new" title="Coded orthogonal frequency division modulation (de pagina bestaat niet)">Coded orthogonal frequency division modulation</a> (COFDM). </p><p>Pulsmodulatietechnieken zijn onder andere: </p> <ul><li><a href="/wiki/Pulscodemodulatie" title="Pulscodemodulatie">Pulscodemodulatie</a> (PCM)</li> <li><a href="/wiki/Pulsbreedtemodulatie" title="Pulsbreedtemodulatie">Pulsbreedtemodulatie</a> (PWM)</li> <li><a href="/w/index.php?title=Pulsamplitudemodulatie&action=edit&redlink=1" class="new" title="Pulsamplitudemodulatie (de pagina bestaat niet)">Pulsamplitudemodulatie</a> (PAM)</li> <li><a href="/wiki/Pulspositiemodulatie" title="Pulspositiemodulatie">Pulspositiemodulatie</a> (PPM)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Modulatie_van_digitale_signalen">Modulatie van digitale signalen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=12" title="Bewerk dit kopje: Modulatie van digitale signalen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=12" title="De broncode bewerken van de sectie: Modulatie van digitale signalen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Als een signaal een eenvoudige, langzame aan/uit indicatie heeft zoals in <a href="/wiki/Morsecode" class="mw-redirect" title="Morsecode">morsecode</a> of in <a href="/wiki/Radioteletype" title="Radioteletype">radioteletype</a> (<a href="/wiki/RTTY" class="mw-redirect" title="RTTY">RTTY</a>), wordt modulatie ook wel aangeduid met het Engelse <i>keying</i> zoals in de volgende termen: </p> <ul><li>Amplitude-shift keying (<a href="/w/index.php?title=ASK&action=edit&redlink=1" class="new" title="ASK (de pagina bestaat niet)">ASK</a>)</li> <li>Frequency-shift keying (<a href="/wiki/FSK" class="mw-redirect" title="FSK">FSK</a>), zie ook <a href="/wiki/Frequentiemodulatie" title="Frequentiemodulatie">Frequentiemodulatie</a></li> <li>Phase-shift keying (PSK), zie <a href="/wiki/Fasemodulatie" title="Fasemodulatie">Fasemodulatie</a></li></ul> <p>RTTY kan ook gezien worden als een simpele vorm van pulscodemodulatie. </p> <div class="mw-heading mw-heading2"><h2 id="Aanverwante_vormen">Aanverwante vormen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=13" title="Bewerk dit kopje: Aanverwante vormen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=13" title="De broncode bewerken van de sectie: Aanverwante vormen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Choppen">Choppen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=14" title="Bewerk dit kopje: Choppen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=14" title="De broncode bewerken van de sectie: Choppen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een veelgebruikte techniek die een AM-signaal maakt van een LF-spanning is het zogenaamde choppen. Een simpele <a href="/w/index.php?title=Chopper_(meettechniek)&action=edit&redlink=1" class="new" title="Chopper (meettechniek) (de pagina bestaat niet)">chopper</a> verbindt periodiek zijn uitgang beurtelings met nul, en het te meten signaal. Het resultaat is een pulstrein, met als frequentie de schakelfrequentie, en als topwaarde de te meten spanning. Na verwijdering van de gelijkspanningscomponent is de gemeten waarde dus beschikbaar als de amplitude van een -min of meer- <a href="/wiki/Hoogfrequent" title="Hoogfrequent">hoogfrequent</a> signaal. Dit signaal is veel eenvoudiger accuraat te versterken en bewerken dan een gelijkspanningssignaal. </p> <div class="mw-heading mw-heading3"><h3 id="Mengen">Mengen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=15" title="Bewerk dit kopje: Mengen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=15" title="De broncode bewerken van de sectie: Mengen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een aan AM gerelateerde signaalbehandeling, is het mengen (Eng. mixing). Bij het mengen worden twee sinusvormige sigalen met elkaar <a href="/wiki/Mixer_(frequentie)" title="Mixer (frequentie)">vermenigvuldigd</a>, en komen de draaggolf en het ingangssignaal dus - in het ideale geval - niet in het uitgangssignaal voor. Een dergelijke vermenigvuldiger noemt men een <a href="/wiki/Mixer_(frequentie)" title="Mixer (frequentie)">mixer</a>. Een ideale mixer geeft als uitgangssignaal: </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 v(t)={{AB} \over 2}\cos(\alpha -\beta )+{{AB} \over 2}\cos(\alpha +\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)={{AB} \over 2}\cos(\alpha -\beta )+{{AB} \over 2}\cos(\alpha +\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b971e3ec25353673240feb9ab4569e5858bc0d67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.337ex; height:5.343ex;" alt="{\displaystyle v(t)={{AB} \over 2}\cos(\alpha -\beta )+{{AB} \over 2}\cos(\alpha +\beta )}"></span></dd></dl> <p>Met A en B de respectievelijke amplituden van de ingangssignalen en <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> <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 \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> hun respectievelijke argumenten. Mixers vinden hun toepassing in hoogfrequentapparatuur als televisies, radio's en telefoons. </p> <div class="mw-heading mw-heading2"><h2 id="Zie_ook">Zie ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Modulatie_(radio)&veaction=edit&section=16" title="Bewerk dit kopje: Zie ook" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Modulatie_(radio)&action=edit&section=16" title="De broncode bewerken van de sectie: Zie ook"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Spiegelfrequentie" title="Spiegelfrequentie">Spiegelfrequentie</a></li> <li><a href="/wiki/Frequentiemodulatie" title="Frequentiemodulatie">Frequentiemodulatie</a></li> <li><a href="/wiki/Amplitudemodulatie" title="Amplitudemodulatie">Amplitudemodulatie</a></li> <li><a href="/wiki/Zijband" title="Zijband">Zijband</a></li> <li><a href="/wiki/HF-modulator" title="HF-modulator">HF-modulator</a></li></ul> <div class="interProject commons mw-list-item" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Modulatie_(radio)#mw-subcategories" class="extiw" title="commons:Category:Modulatie (radio)">Mediabestanden</a></div> <div class="interProjectTemplate interProject-groot toccolours" style="display:flex; gap:1em; align-items:center; clear:both; margin:1em 0 -0.5em 0;"> <div style="min-width:max-content;"><span class="noviewer noresize" typeof="mw:File"><a href="/wiki/Bestand:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/25px-Commons-logo.svg.png" decoding="async" width="25" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/38px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div>Zie de categorie <i><b><a href="https://commons.wikimedia.org/wiki/Category:Modulation#mw-subcategories" class="extiw" title="commons:Category:Modulation">Modulation</a></b></i> van <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> voor mediabestanden over dit onderwerp.</div> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Modulatie_(radio)&oldid=68230442">https://nl.wikipedia.org/w/index.php?title=Modulatie_(radio)&oldid=68230442</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorie</a>: <ul><li><a href="/wiki/Categorie:Radiotechniek" title="Categorie:Radiotechniek">Radiotechniek</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor het laatst bewerkt op 10 okt 2024 om 13:43.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. 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Modulatie (radio) - Wikipedia