CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Frequency multiplier - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"3fe4c539-e889-429b-978a-038ddd83d23d","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Frequency_multiplier","wgTitle":"Frequency multiplier","wgCurRevisionId":1251570211,"wgRevisionId":1251570211,"wgArticleId":1199421,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description is different from Wikidata","Articles needing additional references from July 2011","All articles needing additional references","Articles needing cleanup from July 2011","All pages needing cleanup","Cleanup tagged articles without a reason field from July 2011","Wikipedia pages needing cleanup from July 2011","Articles with multiple maintenance issues","Articles to be expanded from May 2019", "All articles to be expanded","All articles with failed verification","Articles with failed verification from February 2017","All articles with unsourced statements","Articles with unsourced statements from August 2012","Communication circuits"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Frequency_multiplier","wgRelevantArticleId":1199421,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000, "wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1074289","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready", "ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Frequency multiplier - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Frequency_multiplier"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Frequency_multiplier&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Frequency_multiplier"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Frequency_multiplier rootpage-Frequency_multiplier skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Frequency+multiplier" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Frequency+multiplier" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Frequency+multiplier" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Frequency+multiplier" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Theory</span> </div> </a> <ul id="toc-Theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circuits" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Circuits</span> </div> </a> <button aria-controls="toc-Circuits-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Circuits subsection</span> </button> <ul id="toc-Circuits-sublist" class="vector-toc-list"> <li id="toc-Diode" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diode"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Diode</span> </div> </a> <ul id="toc-Diode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Class_C_amplifier_and_multiplier" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Class_C_amplifier_and_multiplier"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Class C amplifier and multiplier</span> </div> </a> <ul id="toc-Class_C_amplifier_and_multiplier-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Step_recovery_diode" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Step_recovery_diode"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Step recovery diode</span> </div> </a> <ul id="toc-Step_recovery_diode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Varactor_diode" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Varactor_diode"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Varactor diode</span> </div> </a> <ul id="toc-Varactor_diode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Previous_uses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Previous_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Previous uses</span> </div> </a> <ul id="toc-Previous_uses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Microelectromechanical_(MEMS)_frequency_doubler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Microelectromechanical_(MEMS)_frequency_doubler"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Microelectromechanical (MEMS) frequency doubler</span> </div> </a> <ul id="toc-Microelectromechanical_(MEMS)_frequency_doubler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Graphene_based_frequency_multipliers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Graphene_based_frequency_multipliers"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Graphene based frequency multipliers</span> </div> </a> <ul id="toc-Graphene_based_frequency_multipliers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Phase-locked_loops_with_frequency_dividers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Phase-locked_loops_with_frequency_dividers"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Phase-locked loops with frequency dividers</span> </div> </a> <button aria-controls="toc-Phase-locked_loops_with_frequency_dividers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Phase-locked loops with frequency dividers subsection</span> </button> <ul id="toc-Phase-locked_loops_with_frequency_dividers-sublist" class="vector-toc-list"> <li id="toc-Fractional-N_synthesizer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fractional-N_synthesizer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Fractional-N synthesizer</span> </div> </a> <ul id="toc-Fractional-N_synthesizer-sublist" class="vector-toc-list"> <li id="toc-Delta_sigma_synthesizer" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Delta_sigma_synthesizer"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Delta sigma synthesizer</span> </div> </a> <ul id="toc-Delta_sigma_synthesizer-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-PLL_References" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#PLL_References"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>PLL References</span> </div> </a> <ul id="toc-PLL_References-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Frequency multiplier</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 7 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-7" 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">7 languages</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/%D9%85%D8%B6%D8%A7%D8%B9%D9%81_%D8%A7%D9%84%D8%AA%D8%B1%D8%AF%D8%AF" title="مضاعف التردد – Arabic" lang="ar" hreflang="ar" data-title="مضاعف التردد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BF%CE%BB%CE%BB%CE%B1%CF%80%CE%BB%CE%B1%CF%83%CE%B9%CE%B1%CF%83%CF%84%CE%AE%CF%82_%CF%83%CF%85%CF%87%CE%BD%CF%8C%CF%84%CE%B7%CF%84%CE%B1%CF%82" title="Πολλαπλασιαστής συχνότητας – Greek" lang="el" hreflang="el" data-title="Πολλαπλασιαστής συχνότητας" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Multiplicateur_de_fr%C3%A9quence" title="Multiplicateur de fréquence – French" lang="fr" hreflang="fr" data-title="Multiplicateur de fréquence" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A3%BC%ED%8C%8C%EC%88%98_%EC%B2%B4%EB%B0%B0%EA%B8%B0" title="주파수 체배기 – Korean" lang="ko" hreflang="ko" data-title="주파수 체배기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Powielacz_cz%C4%99stotliwo%C5%9Bci" title="Powielacz częstotliwości – Polish" lang="pl" hreflang="pl" data-title="Powielacz częstotliwości" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D1%82%D0%B5%D0%BB%D1%8C_%D1%87%D0%B0%D1%81%D1%82%D0%BE%D1%82%D1%8B" title="Умножитель частоты – Russian" lang="ru" hreflang="ru" data-title="Умножитель частоты" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%80%8D%E9%A0%BB%E5%99%A8" title="倍頻器 – Chinese" lang="zh" hreflang="zh" data-title="倍頻器" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1074289#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Frequency_multiplier" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Frequency_multiplier" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Frequency_multiplier"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Frequency_multiplier"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Frequency_multiplier" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Frequency_multiplier" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&oldid=1251570211" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Frequency_multiplier&id=1251570211&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FFrequency_multiplier"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FFrequency_multiplier"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Frequency_multiplier&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Frequency_multiplier&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Frequency_multipliers" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1074289" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</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">From Wikipedia, the free encyclopedia</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="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Electronic circuit</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1248332772">.mw-parser-output .multiple-issues-text{width:95%;margin:0.2em 0}.mw-parser-output .multiple-issues-text>.mw-collapsible-content{margin-top:0.3em}.mw-parser-output .compact-ambox .ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This article has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Frequency_multiplier" title="Special:EditPage/Frequency multiplier">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Frequency_multiplier" title="Talk:Frequency multiplier">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Frequency_multiplier" title="Special:EditPage/Frequency multiplier">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Frequency+multiplier%22">"Frequency multiplier"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Frequency+multiplier%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Frequency+multiplier%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Frequency+multiplier%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Frequency+multiplier%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Frequency+multiplier%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">July 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Cleanup plainlinks metadata ambox ambox-style ambox-Cleanup" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article may <b>require <a href="/wiki/Wikipedia:Cleanup" title="Wikipedia:Cleanup">cleanup</a></b> to meet Wikipedia's <a href="/wiki/Wikipedia:Manual_of_Style" title="Wikipedia:Manual of Style">quality standards</a>.<span class="hide-when-compact"> No <a href="/wiki/Template:Cleanup/doc" title="Template:Cleanup/doc">cleanup reason</a> has been specified. Please help <a href="/wiki/Special:EditPage/Frequency_multiplier" title="Special:EditPage/Frequency multiplier">improve this article</a> if you can.</span> <span class="date-container"><i>(<span class="date">July 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Electronics" title="Electronics">electronics</a>, a <b>frequency multiplier</b> is an <a href="/wiki/Electronic_circuit" title="Electronic circuit">electronic circuit</a> that generates an output <a href="/wiki/Signal_(electronics)" class="mw-redirect" title="Signal (electronics)">signal</a> and that output <a href="/wiki/Frequency" title="Frequency">frequency</a> is a <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> (multiple) of its input frequency. Frequency multipliers consist of a <a href="/wiki/Linear_circuit" title="Linear circuit">nonlinear</a> circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent <a href="/wiki/Bandpass_filter" class="mw-redirect" title="Bandpass filter">bandpass filter</a> selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output. </p><p>Frequency multipliers are often used in <a href="/wiki/Frequency_synthesizer" title="Frequency synthesizer">frequency synthesizers</a> and <a href="/wiki/Communications" class="mw-redirect" title="Communications">communications</a> circuits. It can be more economical to develop a lower frequency signal with lower power and less expensive devices, and then use a frequency multiplier chain to generate an output frequency in the <a href="/wiki/Microwave" title="Microwave">microwave</a> or <a href="/wiki/Millimeter_wave" class="mw-redirect" title="Millimeter wave">millimeter wave</a> range. Some modulation schemes, such as <a href="/wiki/Frequency_modulation" title="Frequency modulation">frequency modulation</a>, survive the nonlinear distortion without ill effect (but schemes such as <a href="/wiki/Amplitude_modulation" title="Amplitude modulation">amplitude modulation</a> do not). </p><p>Frequency multiplication is also used in <a href="/wiki/Nonlinear_optics" title="Nonlinear optics">nonlinear optics</a>. The nonlinear distortion in crystals can be used to generate harmonics of laser light. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=1" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A pure <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a> has a single frequency <i>f</i> </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 x(t)=A\sin(2\pi ft)\,}"> <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> <mo>=</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=A\sin(2\pi ft)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddcd1b20cf7dd89c69e8b91bb1b1bf301f2cfb7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.872ex; height:2.843ex;" alt="{\displaystyle x(t)=A\sin(2\pi ft)\,}"></span></dd></dl> <p>If the sine wave is applied to a <a href="/wiki/Linear_circuit" title="Linear circuit">linear circuit</a>, such as a non–distortion <a href="/wiki/Amplifier" title="Amplifier">amplifier</a>, the output is still a sine wave (but may acquire a phase shift). However, if the sine wave is applied to a <a href="/wiki/Nonlinear_circuit" class="mw-redirect" title="Nonlinear circuit">nonlinear circuit</a>, the resulting distortion creates <a href="/wiki/Harmonic" title="Harmonic">harmonics</a>; frequency components at integer multiples <i>nf</i> of the fundamental frequency <i>f</i>. The distorted signal can be described by a <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a> in <i>f</i>. </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 x(t)=\sum _{k=-\infty }^{\infty }c_{k}e^{j2\pi kft}.}"> <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> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>2</mn> <mi>π</mi> <mi>k</mi> <mi>f</mi> <mi>t</mi> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=\sum _{k=-\infty }^{\infty }c_{k}e^{j2\pi kft}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12585e0827bbdaa956042be118987e3b22ba4610" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.375ex; height:7.009ex;" alt="{\displaystyle x(t)=\sum _{k=-\infty }^{\infty }c_{k}e^{j2\pi kft}.}"></span></dd></dl> <p>The nonzero <i>c<sub>k</sub></i> represent the generated harmonics. The Fourier coefficients are given by integrating over the fundamental period <i>T</i>: </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_{k}={\frac {1}{2\pi }}\int _{0}^{T}x(t)\,e^{-j2\pi kt/T}\,dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msubsup> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>2</mn> <mi>π</mi> <mi>k</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{k}={\frac {1}{2\pi }}\int _{0}^{T}x(t)\,e^{-j2\pi kt/T}\,dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2738bede3208800927764ee78f9a6861fa4f2a36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.425ex; height:6.176ex;" alt="{\displaystyle c_{k}={\frac {1}{2\pi }}\int _{0}^{T}x(t)\,e^{-j2\pi kt/T}\,dt}"></span></dd></dl> <p>So a frequency multiplier can be built from a nonlinear electronic component which generates a series of harmonics, followed by a <a href="/wiki/Bandpass_filter" class="mw-redirect" title="Bandpass filter">bandpass filter</a> which passes one of the harmonics to the output and blocks the others. </p><p>From a conversion efficiency standpoint, the nonlinear circuit should maximize the coefficient for the desired harmonic and minimize the others. Consequently, the transcribing function is often specially chosen. Easy choices are to use an even function to generate even harmonics or an odd function for odd harmonics. See <a href="/wiki/Even_and_odd_functions#Harmonics" title="Even and odd functions">Even and odd functions#Harmonics</a>. A full wave rectifier, for example, is good for making a doubler. To produce a times-3 multiplier, the original signal may be input to an amplifier that is over driven to produce nearly a square wave. This signal is high in 3rd order harmonics and can be filtered to produce the desired x3 outcome. </p><p>YIG multipliers often want to select an arbitrary harmonic, so they use a stateful distortion circuit that converts the input sine wave into an approximate <a href="/wiki/Dirac_comb" title="Dirac comb">impulse train</a>. The ideal (but impractical) impulse train generates an infinite number of (weak) harmonics. In practice, an impulse train generated by a monostable circuit will have many usable harmonics. YIG multipliers using step recovery diodes may, for example, take an input frequency of 1 to 2 GHz and produce outputs up to 18 GHz.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Sometimes the frequency multiplier circuit will adjust the width of the impulses to improve conversion efficiency for a specific harmonic. </p> <div class="mw-heading mw-heading2"><h2 id="Circuits">Circuits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=2" title="Edit section: Circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Frequency_multiplier&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">May 2019</span>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Diode">Diode</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=3" title="Edit section: Diode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Clipping circuits. Full wave bridge doubler. </p> <div class="mw-heading mw-heading3"><h3 id="Class_C_amplifier_and_multiplier">Class C amplifier and multiplier</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=4" title="Edit section: Class C amplifier and multiplier"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Efficiently generating power becomes more important at high power levels. Linear Class A amplifiers are at best 25 percent efficient. Push-pull Class B amplifiers are at best 50 percent efficient. The basic problem is the amplifying element is dissipating power. Switching Class C amplifiers are nonlinear, but they can be better than 50 percent efficient because an ideal switch does not dissipate any power. </p><p>A clever design can use the nonlinear Class C amplifier for both gain and as a frequency multiplier. </p> <div class="mw-heading mw-heading3"><h3 id="Step_recovery_diode">Step recovery diode</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=5" title="Edit section: Step recovery diode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Generating a large number of useful harmonics requires a fast nonlinear device, such as a <a href="/wiki/Step_recovery_diode" title="Step recovery diode">step recovery diode</a>. </p><p>Microwave generators may use a step recovery diode impulse generator followed by a tunable <a href="/wiki/YIG_filter" class="mw-redirect" title="YIG filter">YIG filter</a>. The YIG filter has a <a href="/wiki/YIG_sphere" title="YIG sphere">yttrium iron garnet sphere</a> that is tuned with a magnetic field. The step recovery diode impulse generator is driven at a subharmonic of the desired output frequency. An electromagnet then tunes the YIG filter to select the desired harmonic.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Varactor_diode">Varactor diode</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=6" title="Edit section: Varactor diode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Resistive loaded <a href="/wiki/Varicap" title="Varicap">varactors</a>. Regenerative varactors. Penfield. </p><p>Frequency multipliers have much in common with <a href="/wiki/Frequency_mixer" title="Frequency mixer">frequency mixers</a>, and some of the same nonlinear devices are used for both: <a href="/wiki/Transistor" title="Transistor">transistors</a> operated in <a href="/wiki/Electronic_amplifier#Class_C" class="mw-redirect" title="Electronic amplifier">Class C</a> and <a href="/wiki/Diode" title="Diode">diodes</a>. In transmitting circuits many of the amplifying devices (<a href="/wiki/Vacuum_tubes" class="mw-redirect" title="Vacuum tubes">vacuum tubes</a> or transistors) operate nonlinearly and create harmonics, so an amplifier stage can be made a multiplier by tuning the <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuit</a> at the output to a multiple of the input frequency. Usually the power (<a href="/wiki/Gain_(electronics)" title="Gain (electronics)">gain</a>) produced by the nonlinear device drops off rapidly at the higher harmonics, so most frequency multipliers just double or triple the frequency, and multiplication by higher factors is accomplished by cascading doubler and tripler stages. </p> <div class="mw-heading mw-heading3"><h3 id="Previous_uses">Previous uses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=7" title="Edit section: Previous uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Frequency multipliers use circuits tuned to a harmonic of the input frequency. Non-linear elements such as diodes may be added to enhance the production of harmonic frequencies. Since the power in the harmonics declines rapidly, usually a frequency multiplier is tuned to only a small multiple (twice, three times, or five times) of the input frequency. Usually <a href="/wiki/Amplifier" title="Amplifier">amplifiers</a> are inserted in a chain of frequency multipliers to ensure adequate signal level at the final frequency. </p><p>Since the tuned circuits have a limited bandwidth, if the base frequency is changed significantly (more than one percent or so), the multiplier stages may have to be adjusted; this can take significant time if there are many stages. </p> <div class="mw-heading mw-heading3"><h3 id="Microelectromechanical_(MEMS)_frequency_doubler"><span id="Microelectromechanical_.28MEMS.29_frequency_doubler"></span>Microelectromechanical (MEMS) frequency doubler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=8" title="Edit section: Microelectromechanical (MEMS) frequency doubler"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An electric-field driven <a href="/wiki/Microelectromechanical_systems" class="mw-redirect" title="Microelectromechanical systems">micromechanical</a> <a href="/wiki/Cantilever" title="Cantilever">cantilever</a> <a href="/wiki/Resonator" title="Resonator">resonator</a> is one of the most fundamental and widely studied structures in <a href="/wiki/Microelectromechanical_systems" class="mw-redirect" title="Microelectromechanical systems">MEMS</a>, which can provide a high Q and narrow bandpass filtering function. The inherent square-law nonlinearity of the voltage-to-force transfer function of a cantilever resonator's capacitive transducer can be employed for the realization of frequency doubling effect.<sup id="cite_ref-MEMS_freq_doubler_3-0" class="reference"><a href="#cite_note-MEMS_freq_doubler-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Due to the low-loss attribute (or equivalently, a high Q) offered by MEMS devices, improved circuit performance can be expected from a micromechanical frequency doubler than semiconductor devices utilized for the same task.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Graphene_based_frequency_multipliers">Graphene based frequency multipliers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=9" title="Edit section: Graphene based frequency multipliers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Graphene" title="Graphene">Graphene</a> based FETs have also been employed for frequency doubling with more than 90% converting efficiency.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In fact, all <a href="/wiki/Ambipolar_transistor" class="mw-redirect" title="Ambipolar transistor">ambipolar transistors</a> can be used for designing frequency multiplier circuits.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Graphene can work over a large frequency range due to its unique characteristics.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Phase-locked_loops_with_frequency_dividers">Phase-locked loops with frequency dividers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=10" title="Edit section: Phase-locked loops with frequency dividers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Phase-locked_loop" title="Phase-locked loop">phase-locked loop</a> (PLL) uses a reference frequency to generate a multiple of that frequency. A <a href="/wiki/Voltage_controlled_oscillator" class="mw-redirect" title="Voltage controlled oscillator">voltage controlled oscillator</a> (VCO) is initially tuned roughly to the range of the desired frequency multiple. The signal from the VCO is divided down using <a href="/wiki/Frequency_divider" title="Frequency divider">frequency dividers</a> by the multiplication factor. The divided signal and the reference frequency are fed into a phase comparator. The output of the phase comparator is a voltage that is proportional to the phase difference. After passing through a low pass filter and being converted to the proper voltage range, this voltage is fed to the VCO to adjust the frequency. This adjustment increases the frequency as the phase of the VCO's signal lags that of the reference signal and decreases the frequency as the lag decreases (or lead increases). The VCO will stabilize at the desired frequency multiple. This type of PLL is a type of <a href="/wiki/Frequency_synthesizer" title="Frequency synthesizer">frequency synthesizer</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Fractional-N_synthesizer">Fractional-N synthesizer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=11" title="Edit section: Fractional-N synthesizer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In some PLLs the reference frequency may also be divided by an integer multiple before being input to the phase comparator. This allows the synthesis of frequencies that are N/M times the reference frequency. </p><p>This can be accomplished in a different manner by periodically changing the integer value of an integer-N <a href="/wiki/Frequency_divider" title="Frequency divider">frequency divider</a>, effectively resulting in a multiplier with both whole number and fractional component. Such a multiplier is called a fractional-N synthesizer after its fractional component.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="Fractional-N is more than variable modulus; phase error is also modified (February 2017)">failed verification</span></a></i>]</sup> Fractional-N synthesizers provide an effective means of achieving fine frequency resolution with lower values of N, allowing loop architectures with tens of thousands of times less phase noise than alternative designs with lower reference frequencies and higher integer N values. They also allow a faster settling time because of their higher reference frequencies, allowing wider closed and open loop bandwidths.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2012)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading4"><h4 id="Delta_sigma_synthesizer">Delta sigma synthesizer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=12" title="Edit section: Delta sigma synthesizer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A delta sigma synthesizer adds a randomization to programmable-N <a href="/wiki/Frequency_divider" title="Frequency divider">frequency divider</a> of the fractional-N synthesizer. This is done to shrink sidebands created by periodic changes of an integer-N <a href="/wiki/Frequency_divider#Fractional-n_dividers" title="Frequency divider">frequency divider</a>. </p> <div class="mw-heading mw-heading3"><h3 id="PLL_References">PLL References</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=13" title="Edit section: PLL References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Egan, William F. 2000. <i>Frequency Synthesis by Phase-lock</i>, 2nd Ed., John Wiley & Sons, <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-32104-4" title="Special:BookSources/0-471-32104-4">0-471-32104-4</a></li> <li><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US4686488">Fractional N frequency synthesizer with modulation compensation</a> U.S. Patent 4,686,488, Attenborough, C. (1987, August 11)</li> <li><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US5224132">Programmable fractional-N frequency synthesizer</a> U.S. Patent 5,224,132, Bar-Giora Goldberg, (1993, June 29)</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Heterostructure_barrier_varactor" title="Heterostructure barrier varactor">Heterostructure barrier varactor</a></li> <li><a href="/wiki/CPU_multiplier" title="CPU multiplier">CPU multiplier</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Frequency_multiplier&action=edit&section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">For example, the old Hewlett Packard 83590A.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120223205016/http://www.microlambdawireless.com/apppdfs/ytodefinitions2.pdf"><i>Technology Description: YIG Tuned Oscillators</i></a> <span class="cs1-format">(PDF)</span>, Fremont, CA: Micro Lambda Wireless, archived from <a rel="nofollow" class="external text" href="http://www.microlambdawireless.com/apppdfs/ytodefinitions2.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 23 February 2012<span class="reference-accessdate">, retrieved <span class="nowrap">18 May</span> 2012</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Technology+Description%3A+YIG+Tuned+Oscillators&rft.place=Fremont%2C+CA&rft.pub=Micro+Lambda+Wireless&rft_id=http%3A%2F%2Fwww.microlambdawireless.com%2Fapppdfs%2Fytodefinitions2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-MEMS_freq_doubler-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-MEMS_freq_doubler_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBasuBhattacharyya2013" class="citation journal cs1">Basu, Joydeep; Bhattacharyya, Tarun K. (2013). "Microelectromechanical system cantilever-based frequency doublers". <i>Journal of Intelligent Material Systems and Structures</i>. <b>24</b> (2): 240–246. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1210.3491">1210.3491</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1045389X12461695">10.1177/1045389X12461695</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1266952">1266952</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Intelligent+Material+Systems+and+Structures&rft.atitle=Microelectromechanical+system+cantilever-based+frequency+doublers&rft.volume=24&rft.issue=2&rft.pages=240-246&rft.date=2013&rft_id=info%3Aarxiv%2F1210.3491&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1266952%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1177%2F1045389X12461695&rft.aulast=Basu&rft.aufirst=Joydeep&rft.au=Bhattacharyya%2C+Tarun+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJing_WangRenNguyen2004" class="citation journal cs1">Jing Wang; Ren, Z.; Nguyen, C.T.-C. (2004). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/1386679">"1.156-GHz self-aligned vibrating micromechanical disk resonator"</a>. <i>IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control</i>. <b>51</b> (12): 1607–1628. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTUFFC.2004.1386679">10.1109/TUFFC.2004.1386679</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15690722">15690722</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9498440">9498440</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Ultrasonics%2C+Ferroelectrics+and+Frequency+Control&rft.atitle=1.156-GHz+self-aligned+vibrating+micromechanical+disk+resonator&rft.volume=51&rft.issue=12&rft.pages=1607-1628&rft.date=2004&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9498440%23id-name%3DS2CID&rft_id=info%3Apmid%2F15690722&rft_id=info%3Adoi%2F10.1109%2FTUFFC.2004.1386679&rft.au=Jing+Wang&rft.au=Ren%2C+Z.&rft.au=Nguyen%2C+C.T.-C.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F1386679&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangNezichKongPalacios2009" class="citation journal cs1">Wang, Han; Nezich, D.; Kong, Jing; Palacios, T. (2009). <a rel="nofollow" class="external text" href="https://dspace.mit.edu/bitstream/1721.1/54736/2/Wang-2009-Graphene%20Frequency%20M.pdf">"Graphene Frequency Multipliers"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Electron Device Letters</i>. <b>30</b> (5): 547–549. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009IEDL...30..547H">2009IEDL...30..547H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FLED.2009.2016443">10.1109/LED.2009.2016443</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F54736">1721.1/54736</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9317247">9317247</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Electron+Device+Letters&rft.atitle=Graphene+Frequency+Multipliers&rft.volume=30&rft.issue=5&rft.pages=547-549&rft.date=2009&rft_id=info%3Ahdl%2F1721.1%2F54736&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9317247%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FLED.2009.2016443&rft_id=info%3Abibcode%2F2009IEDL...30..547H&rft.aulast=Wang&rft.aufirst=Han&rft.au=Nezich%2C+D.&rft.au=Kong%2C+Jing&rft.au=Palacios%2C+T.&rft_id=https%3A%2F%2Fdspace.mit.edu%2Fbitstream%2F1721.1%2F54736%2F2%2FWang-2009-Graphene%2520Frequency%2520M.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangZhangXuDing2010" class="citation journal cs1">Wang, Zhenxing; Zhang, Zhiyong; Xu, Huilong; Ding, Li; Wang, Sheng; Peng, Lian-Mao (2010). "A high-performance top-gate graphene field-effect transistor based frequency doubler". <i>Applied Physics Letters</i>. <b>96</b> (17): 173104. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010ApPhL..96q3104W">2010ApPhL..96q3104W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3413959">10.1063/1.3413959</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Physics+Letters&rft.atitle=A+high-performance+top-gate+graphene+field-effect+transistor+based+frequency+doubler&rft.volume=96&rft.issue=17&rft.pages=173104&rft.date=2010&rft_id=info%3Adoi%2F10.1063%2F1.3413959&rft_id=info%3Abibcode%2F2010ApPhL..96q3104W&rft.aulast=Wang&rft.aufirst=Zhenxing&rft.au=Zhang%2C+Zhiyong&rft.au=Xu%2C+Huilong&rft.au=Ding%2C+Li&rft.au=Wang%2C+Sheng&rft.au=Peng%2C+Lian-Mao&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangLiangZhangLiu2014" class="citation journal cs1">Wang, Zhenxing; Liang, Shibo; Zhang, Zhiyong; Liu, Honggang; Zhong, Hua; Ye, Lin-Hui; Wang, Sheng; Zhou, Weiwei; Liu, Jie; Chen, Yabin; Zhang, Jin; Peng, Lian-Mao (2014). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201302793">"Scalable Fabrication of Ambipolar Transistors and Radio-Frequency Circuits Using Aligned Carbon Nanotube Arrays"</a>. <i>Advanced Materials</i>. <b>26</b> (4): 645–652. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014AdM....26..645W">2014AdM....26..645W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fadma.201302793">10.1002/adma.201302793</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24458579">24458579</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:20376132">20376132</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advanced+Materials&rft.atitle=Scalable+Fabrication+of+Ambipolar+Transistors+and+Radio-Frequency+Circuits+Using+Aligned+Carbon+Nanotube+Arrays&rft.volume=26&rft.issue=4&rft.pages=645-652&rft.date=2014&rft_id=info%3Adoi%2F10.1002%2Fadma.201302793&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A20376132%23id-name%3DS2CID&rft_id=info%3Apmid%2F24458579&rft_id=info%3Abibcode%2F2014AdM....26..645W&rft.aulast=Wang&rft.aufirst=Zhenxing&rft.au=Liang%2C+Shibo&rft.au=Zhang%2C+Zhiyong&rft.au=Liu%2C+Honggang&rft.au=Zhong%2C+Hua&rft.au=Ye%2C+Lin-Hui&rft.au=Wang%2C+Sheng&rft.au=Zhou%2C+Weiwei&rft.au=Liu%2C+Jie&rft.au=Chen%2C+Yabin&rft.au=Zhang%2C+Jin&rft.au=Peng%2C+Lian-Mao&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2Ffull%2F10.1002%2Fadma.201302793&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKabirSalahuddin2017" class="citation journal cs1">Kabir, Hussain Mohammed Dipu; Salahuddin, S.M. (2017). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/S0026269216307832">"A frequency multiplier using three ambipolar graphene transistors"</a>. <i>Microelectronics Journal</i>. <b>70</b>: 12–15. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.mejo.2017.10.002">10.1016/j.mejo.2017.10.002</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31657795">31657795</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Microelectronics+Journal&rft.atitle=A+frequency+multiplier+using+three+ambipolar+graphene+transistors&rft.volume=70&rft.pages=12-15&rft.date=2017&rft_id=info%3Adoi%2F10.1016%2Fj.mejo.2017.10.002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A31657795%23id-name%3DS2CID&rft.aulast=Kabir&rft.aufirst=Hussain+Mohammed+Dipu&rft.au=Salahuddin%2C+S.M.&rft_id=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0026269216307832&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFrequency+multiplier" class="Z3988"></span></span> </li> </ol></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="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Frequency_multiplier&oldid=1251570211">https://en.wikipedia.org/w/index.php?title=Frequency_multiplier&oldid=1251570211</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Communication_circuits" title="Category:Communication circuits">Communication circuits</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_July_2011" title="Category:Articles needing additional references from July 2011">Articles needing additional references from July 2011</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:Articles_needing_cleanup_from_July_2011" title="Category:Articles needing cleanup from July 2011">Articles needing cleanup from July 2011</a></li><li><a href="/wiki/Category:All_pages_needing_cleanup" title="Category:All pages needing cleanup">All pages needing cleanup</a></li><li><a href="/wiki/Category:Cleanup_tagged_articles_without_a_reason_field_from_July_2011" title="Category:Cleanup tagged articles without a reason field from July 2011">Cleanup tagged articles without a reason field from July 2011</a></li><li><a href="/wiki/Category:Wikipedia_pages_needing_cleanup_from_July_2011" title="Category:Wikipedia pages needing cleanup from July 2011">Wikipedia pages needing cleanup from July 2011</a></li><li><a href="/wiki/Category:Articles_with_multiple_maintenance_issues" title="Category:Articles with multiple maintenance issues">Articles with multiple maintenance issues</a></li><li><a href="/wiki/Category:Articles_to_be_expanded_from_May_2019" title="Category:Articles to be expanded from May 2019">Articles to be expanded from May 2019</a></li><li><a href="/wiki/Category:All_articles_to_be_expanded" title="Category:All articles to be expanded">All articles to be expanded</a></li><li><a href="/wiki/Category:All_articles_with_failed_verification" title="Category:All articles with failed verification">All articles with failed verification</a></li><li><a href="/wiki/Category:Articles_with_failed_verification_from_February_2017" title="Category:Articles with failed verification from February 2017">Articles with failed verification from February 2017</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_August_2012" title="Category:Articles with unsourced statements from August 2012">Articles with unsourced statements from August 2012</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"> This page was last edited on 16 October 2024, at 21:01<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Frequency_multiplier&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-694cf4987f-cz85g","wgBackendResponseTime":189,"wgPageParseReport":{"limitreport":{"cputime":"0.323","walltime":"0.720","ppvisitednodes":{"value":1811,"limit":1000000},"postexpandincludesize":{"value":63964,"limit":2097152},"templateargumentsize":{"value":11710,"limit":2097152},"expansiondepth":{"value":20,"limit":100},"expensivefunctioncount":{"value":9,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":39498,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 588.527 1 -total"," 36.61% 215.445 1 Template:Multiple_issues"," 30.13% 177.313 1 Template:Reflist"," 19.31% 113.654 1 Template:More_citations_needed"," 19.07% 112.246 3 Template:Ambox"," 17.89% 105.269 1 Template:Citation"," 15.14% 89.082 1 Template:Short_description"," 10.77% 63.362 1 Template:Cleanup"," 9.59% 56.433 1 Template:ISBN"," 9.28% 54.589 4 Template:Category_handler"]},"scribunto":{"limitreport-timeusage":{"value":"0.180","limit":"10.000"},"limitreport-memusage":{"value":5622738,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-5dc468848-kspxv","timestamp":"20241122143529","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Frequency multiplier","url":"https:\/\/en.wikipedia.org\/wiki\/Frequency_multiplier","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1074289","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1074289","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-11-23T00:32:10Z","dateModified":"2024-10-16T21:01:41Z","headline":"electronic circuit that generates an output signal whose output frequency is a harmonic of its input frequency"}</script> </body> </html>