<!DOCTYPE html>
<html class="client-nojs" lang="en" dir="ltr">
<head>
<meta charset="UTF-8"/>
<title>Pulse-width modulation - Wikipedia</title>
<script>document.documentElement.className="client-js";RLCONF={"wgBreakFrames":!1,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"6cd38cf5-080d-4447-a3ff-655268211a0c","wgCSPNonce":!1,"wgCanonicalNamespace":"","wgCanonicalSpecialPageName":!1,"wgNamespaceNumber":0,"wgPageName":"Pulse-width_modulation","wgTitle":"Pulse-width modulation","wgCurRevisionId":1003507942,"wgRevisionId":1003507942,"wgArticleId":81242,"wgIsArticle":!0,"wgIsRedirect":!1,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles lacking in-text citations from April 2009","All articles lacking in-text citations","Commons category link is on Wikidata","Signal processing"],"wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Pulse-width_modulation",
"wgRelevantArticleId":81242,"wgIsProbablyEditable":!0,"wgRelevantPageIsProbablyEditable":!0,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgMediaViewerOnClick":!0,"wgMediaViewerEnabledByDefault":!0,"wgPopupsFlags":10,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":!0,"nearby":!0,"watchlist":!0,"tagline":!1},"wgWMESchemaEditAttemptStepOversample":!1,"wgULSCurrentAutonym":"English","wgNoticeProject":"wikipedia","wgCentralAuthMobileDomain":!1,"wgEditSubmitButtonLabelPublish":!0,"wgULSPosition":"interlanguage","wgWikibaseItemId":"Q585184"};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","noscript":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.styles.legacy":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready",
"ext.uls.interlanguage":"ready","ext.wikimediaBadges":"ready","wikibase.client.init":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","ext.math.scripts","site","mediawiki.page.ready","mediawiki.toc","skins.vector.legacy.js","ext.gadget.ReferenceTooltips","ext.gadget.charinsert","ext.gadget.extra-toolbar-buttons","ext.gadget.refToolbar","ext.gadget.switcher","ext.centralauth.centralautologin","mmv.head","mmv.bootstrap.autostart","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.compactlinks","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.centralNotice.geoIP","ext.centralNotice.startUp"];</script>
<script>(RLQ=window.RLQ||[]).push(function(){mw.loader.implement("user.options@1hzgi",function($,jQuery,require,module){/*@nomin*/mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"});
});});</script>
<link rel="stylesheet" href="/w/load.php?lang=en&amp;modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cskins.vector.styles.legacy%7Cwikibase.client.init&amp;only=styles&amp;skin=vector"/>
<script async="" src="/w/load.php?lang=en&amp;modules=startup&amp;only=scripts&amp;raw=1&amp;skin=vector"></script>
<meta name="ResourceLoaderDynamicStyles" content=""/>
<link rel="stylesheet" href="/w/load.php?lang=en&amp;modules=site.styles&amp;only=styles&amp;skin=vector"/>
<meta name="generator" content="MediaWiki 1.36.0-wmf.37"/>
<meta name="referrer" content="origin"/>
<meta name="referrer" content="origin-when-crossorigin"/>
<meta name="referrer" content="origin-when-cross-origin"/>
<meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/PWM%2C_3-level.svg/1200px-PWM%2C_3-level.svg.png"/>
<meta property="og:title" content="Pulse-width modulation - Wikipedia"/>
<meta property="og:type" content="website"/>
<link rel="preconnect" href="//upload.wikimedia.org"/>
<link rel="alternate" media="only screen and (max-width: 720px)" href="//en.m.wikipedia.org/wiki/Pulse-width_modulation"/>
<link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Pulse-width_modulation&amp;action=edit"/>
<link rel="edit" title="Edit this page" href="/w/index.php?title=Pulse-width_modulation&amp;action=edit"/>
<link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"/>
<link rel="shortcut icon" href="/static/favicon/wikipedia.ico"/>
<link rel="search" type="application/opensearchdescription+xml" href="/w/opensearch_desc.php" title="Wikipedia (en)"/>
<link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"/>
<link rel="license" href="//creativecommons.org/licenses/by-sa/3.0/"/>
<link rel="canonical" href="https://en.wikipedia.org/wiki/Pulse-width_modulation"/>
<link rel="dns-prefetch" href="//login.wikimedia.org"/>
<link rel="dns-prefetch" href="//meta.wikimedia.org" />
</head>
<body class="mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Pulse-width_modulation rootpage-Pulse-width_modulation skin-vector action-view skin-vector-legacy"><div id="mw-page-base" class="noprint"></div>
<div id="mw-head-base" class="noprint"></div>
<div id="content" class="mw-body" role="main">
	<a id="top"></a>
	<div id="siteNotice" class="mw-body-content"><!-- CentralNotice --></div>
	<div class="mw-indicators mw-body-content">
	</div>
	<h1 id="firstHeading" class="firstHeading" >Pulse-width modulation</h1>
	<div id="bodyContent" class="mw-body-content">
		<div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div>
		<div id="contentSub"></div>
		<div id="contentSub2"></div>
		
		<div id="jump-to-nav"></div>
		<a class="mw-jump-link" href="#mw-head">Jump to navigation</a>
		<a class="mw-jump-link" href="#searchInput">Jump to search</a>
		<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><table class="box-More_footnotes plainlinks metadata ambox ambox-style ambox-More_footnotes" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></div></td><td class="mbox-text"><div class="mbox-text-span">This article includes a list of general <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">references</a>, but it remains largely unverified because <b>it lacks sufficient corresponding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a></b>.<span class="hide-when-compact"> Please help to <a href="/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check" class="mw-redirect" title="Wikipedia:WikiProject Fact and Reference Check">improve</a> this article by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations.</span>  <small class="date-container"><i>(<span class="date">April 2009</span>)</i></small><small class="hide-when-compact"><i> (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this template message</a>)</i></small></div></td></tr></tbody></table>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:PWM,_3-level.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/PWM%2C_3-level.svg/350px-PWM%2C_3-level.svg.png" decoding="async" width="350" height="242" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/PWM%2C_3-level.svg/525px-PWM%2C_3-level.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/PWM%2C_3-level.svg/700px-PWM%2C_3-level.svg.png 2x" data-file-width="688" data-file-height="475" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:PWM,_3-level.svg" class="internal" title="Enlarge"></a></div>An example of PWM in an idealized inductor driven by a <span style="color:blue; font-size:100%; line-height:1;" title="Blue">■</span> voltage source modulated as a series of pulses, resulting in a <span style="color:red; font-size:100%; line-height:1;" title="Red">■</span> sine-like current in the inductor. The rectangular voltage pulses nonetheless result in a more and more smooth current waveform, as the <i>switching frequency</i> increases.  Note that the current waveform is the integral of the voltage waveform.</div></div></div>
<style data-mw-deduplicate="TemplateStyles:r1013635363">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:#f8f9fa;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar a{white-space:nowrap}.mw-parser-output .sidebar-wraplinks a{white-space:normal}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding-bottom:0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em 0}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding-top:0.2em;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding-top:0.4em;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.4em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding-top:0}.mw-parser-output .sidebar-image{padding:0.2em 0 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em}.mw-parser-output .sidebar-content{padding:0 0.1em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.4em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%}.mw-parser-output .sidebar-collapse .sidebar-navbar{padding-top:0.6em}.mw-parser-output .sidebar-list-title{text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{text-align:center;margin:0 3.3em}@media(max-width:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar nomobile"><tbody><tr><th class="sidebar-title" style="background-color: #bdb"><a href="/wiki/Passband" title="Passband">Passband</a> <a href="/wiki/Modulation" title="Modulation">modulation</a></th></tr><tr><th class="sidebar-heading" style="background-color: #cfc">
<a href="/wiki/Modulation#Analog_modulation_methods" title="Modulation">Analog modulation</a></th></tr><tr><td class="sidebar-content hlist">
<ul><li><a href="/wiki/Amplitude_modulation" title="Amplitude modulation">AM</a></li>
<li><a href="/wiki/Frequency_modulation" title="Frequency modulation">FM</a></li>
<li><a href="/wiki/Phase_modulation" title="Phase modulation">PM</a></li>
<li><a href="/wiki/Quadrature_amplitude_modulation" title="Quadrature amplitude modulation">QAM</a></li>
<li><a href="/wiki/Space_modulation" title="Space modulation">SM</a></li>
<li><a href="/wiki/Single-sideband_modulation" title="Single-sideband modulation">SSB</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cfc">
<a href="/wiki/Digital_modulation" class="mw-redirect" title="Digital modulation">Digital modulation</a></th></tr><tr><td class="sidebar-content hlist">
<ul><li><a href="/wiki/Amplitude-shift_keying" title="Amplitude-shift keying">ASK</a></li>
<li><a href="/wiki/Amplitude_and_phase-shift_keying" title="Amplitude and phase-shift keying">APSK</a></li>
<li><a href="/wiki/Continuous_phase_modulation" title="Continuous phase modulation">CPM</a></li>
<li><a href="/wiki/Frequency-shift_keying" title="Frequency-shift keying">FSK</a></li>
<li><a href="/wiki/Multiple_frequency-shift_keying" title="Multiple frequency-shift keying">MFSK</a></li>
<li><a href="/wiki/Minimum-shift_keying" title="Minimum-shift keying">MSK</a></li>
<li><a href="/wiki/On-off_keying" class="mw-redirect" title="On-off keying">OOK</a></li>
<li><a href="/wiki/Pulse-position_modulation" title="Pulse-position modulation">PPM</a></li>
<li><a href="/wiki/Phase-shift_keying" title="Phase-shift keying">PSK</a></li>
<li><a href="/wiki/Quadrature_amplitude_modulation" title="Quadrature amplitude modulation">QAM</a></li>
<li><a href="/wiki/Single-carrier_FDMA" title="Single-carrier FDMA">SC-FDE</a></li>
<li><a href="/wiki/Trellis_modulation" title="Trellis modulation">TCM</a></li>
<li><a href="/wiki/Wavelet_modulation" title="Wavelet modulation">WDM</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cfc">
<a href="/wiki/Hierarchical_modulation" title="Hierarchical modulation">Hierarchical modulation</a></th></tr><tr><td class="sidebar-content hlist">
<ul><li><a href="/wiki/Quadrature_amplitude_modulation" title="Quadrature amplitude modulation">QAM</a></li>
<li><a href="/wiki/Wavelet_modulation" title="Wavelet modulation">WDM</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cfc">
<a href="/wiki/Spread_spectrum" title="Spread spectrum">Spread spectrum</a></th></tr><tr><td class="sidebar-content hlist">
<ul><li><a href="/wiki/Chirp_spread_spectrum" title="Chirp spread spectrum">CSS</a></li>
<li><a href="/wiki/Direct-sequence_spread_spectrum" title="Direct-sequence spread spectrum">DSSS</a></li>
<li><a href="/wiki/Frequency-hopping_spread_spectrum" title="Frequency-hopping spread spectrum">FHSS</a></li>
<li><a href="/wiki/Time-hopping" title="Time-hopping">THSS</a></li></ul></td>
</tr><tr><th class="sidebar-heading" style="background-color: #cfc">
See also</th></tr><tr><td class="sidebar-content hlist">
<ul><li><a href="/wiki/Category:Capacity-approaching_codes" title="Category:Capacity-approaching codes">Capacity-approaching codes</a></li>
<li><a href="/wiki/Demodulation" title="Demodulation">Demodulation</a></li>
<li><a href="/wiki/Line_code" title="Line code">Line coding</a></li>
<li><a href="/wiki/Modem" title="Modem">Modem</a></li>
<li><a href="/wiki/Angle_modulation" title="Angle modulation">AnM</a></li>
<li><a href="/wiki/Polar_modulation" title="Polar modulation">PoM</a></li>
<li><a href="/wiki/Pulse-amplitude_modulation" title="Pulse-amplitude modulation">PAM</a></li>
<li><a href="/wiki/Pulse-code_modulation" title="Pulse-code modulation">PCM</a></li>
<li><a href="/wiki/Pulse-density_modulation" title="Pulse-density modulation">PDM</a></li>
<li><a class="mw-selflink selflink">PWM</a></li>
<li><a href="/wiki/Delta-sigma_modulation" title="Delta-sigma modulation">ΔΣM</a></li>
<li><a href="/wiki/Orthogonal_frequency-division_multiplexing" title="Orthogonal frequency-division multiplexing">OFDM</a></li>
<li><a href="/wiki/Frequency-division_multiplexing" title="Frequency-division multiplexing">FDM</a></li>
<li><a href="/wiki/Multiplexing" title="Multiplexing">Multiplexing</a></li></ul></td>
</tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r992953826">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Modulation_techniques" title="Template:Modulation techniques"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Modulation_techniques" title="Template talk:Modulation techniques"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Template:Modulation_techniques&amp;action=edit"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table>
<p><b>Pulse width modulation</b> (<b>PWM</b>), or <b>pulse-duration modulation</b> (<b>PDM</b>), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of <a href="/wiki/Volt" title="Volt">voltage</a> (and <a href="/wiki/Electric_current" title="Electric current">current</a>) fed to the <a href="/wiki/Electrical_load" title="Electrical load">load</a> is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. Along with <a href="/wiki/Maximum_power_point_tracking" title="Maximum power point tracking">maximum power point tracking</a> (MPPT), it is one of the primary methods of reducing the output of solar panels to that which can be utilized by a battery.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">&#91;1&#93;</a></sup> PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching, because their inertia causes them to react slowly. The PWM switching frequency has to be high enough not to affect the load, which is to say that the resultant waveform perceived by the load must be as smooth as possible. 
</p><p>The rate (or frequency) at which the power supply must switch can vary greatly depending on load and application. For example, switching has to be done several times a minute in an electric stove; 120&#160;<a href="/wiki/Hertz" title="Hertz">Hz</a> in a lamp dimmer; between a few kilohertz (kHz) and tens of kHz for a motor drive; and well into the tens or hundreds of kHz in audio amplifiers and computer power supplies. The main advantage of PWM is that power loss in the switching devices is very low. When a switch is off there is practically no current, and when it is on and power is being transferred to the load, there is almost no voltage drop across the switch. Power loss, being the product of voltage and current, is thus in both cases close to zero. PWM also works well with digital controls, which, because of their on/off nature, can easily set the needed duty cycle. PWM has also been used in certain <a href="/wiki/Signalling_(telecommunication)" class="mw-redirect" title="Signalling (telecommunication)">communication systems</a> where its duty cycle has been used to convey information over a communications channel.
</p><p>In electronics, many modern <a href="/wiki/Microcontroller" title="Microcontroller">microcontrollers</a> (MCUs) integrate <b>PWM controllers</b> exposed to external pins as peripheral devices under <a href="/wiki/Firmware" title="Firmware">firmware</a> control by means of internal programming interfaces. These are commonly used for <a href="/wiki/Direct_current" title="Direct current">direct current</a> (DC) <a href="/wiki/Motor_controller" title="Motor controller">motor control</a> in <a href="/wiki/Robotics" title="Robotics">robotics</a> and other applications. 
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Duty_cycle"><span class="tocnumber">1</span> <span class="toctext">Duty cycle</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#History"><span class="tocnumber">2</span> <span class="toctext">History</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#Principle"><span class="tocnumber">3</span> <span class="toctext">Principle</span></a>
<ul>
<li class="toclevel-2 tocsection-4"><a href="#Delta"><span class="tocnumber">3.1</span> <span class="toctext">Delta</span></a></li>
<li class="toclevel-2 tocsection-5"><a href="#Delta-sigma"><span class="tocnumber">3.2</span> <span class="toctext">Delta-sigma</span></a></li>
<li class="toclevel-2 tocsection-6"><a href="#Space_vector_modulation"><span class="tocnumber">3.3</span> <span class="toctext">Space vector modulation</span></a></li>
<li class="toclevel-2 tocsection-7"><a href="#Direct_torque_control_(DTC)"><span class="tocnumber">3.4</span> <span class="toctext">Direct torque control (DTC)</span></a></li>
<li class="toclevel-2 tocsection-8"><a href="#Time_proportioning"><span class="tocnumber">3.5</span> <span class="toctext">Time proportioning</span></a></li>
<li class="toclevel-2 tocsection-9"><a href="#Types"><span class="tocnumber">3.6</span> <span class="toctext">Types</span></a></li>
<li class="toclevel-2 tocsection-10"><a href="#Spectrum"><span class="tocnumber">3.7</span> <span class="toctext">Spectrum</span></a></li>
<li class="toclevel-2 tocsection-11"><a href="#PWM_sampling_theorem"><span class="tocnumber">3.8</span> <span class="toctext">PWM sampling theorem</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-12"><a href="#Applications"><span class="tocnumber">4</span> <span class="toctext">Applications</span></a>
<ul>
<li class="toclevel-2 tocsection-13"><a href="#Servos"><span class="tocnumber">4.1</span> <span class="toctext">Servos</span></a></li>
<li class="toclevel-2 tocsection-14"><a href="#Telecommunications"><span class="tocnumber">4.2</span> <span class="toctext">Telecommunications</span></a></li>
<li class="toclevel-2 tocsection-15"><a href="#Power_delivery"><span class="tocnumber">4.3</span> <span class="toctext">Power delivery</span></a></li>
<li class="toclevel-2 tocsection-16"><a href="#Voltage_regulation"><span class="tocnumber">4.4</span> <span class="toctext">Voltage regulation</span></a></li>
<li class="toclevel-2 tocsection-17"><a href="#Audio_effects_and_amplification"><span class="tocnumber">4.5</span> <span class="toctext">Audio effects and amplification</span></a></li>
<li class="toclevel-2 tocsection-18"><a href="#Electrical"><span class="tocnumber">4.6</span> <span class="toctext">Electrical</span></a></li>
<li class="toclevel-2 tocsection-19"><a href="#Soft-blinking_LED_indicator"><span class="tocnumber">4.7</span> <span class="toctext">Soft-blinking LED indicator</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-20"><a href="#See_also"><span class="tocnumber">5</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-21"><a href="#References"><span class="tocnumber">6</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-22"><a href="#External_links"><span class="tocnumber">7</span> <span class="toctext">External links</span></a></li>
</ul>
</div>

<h2><span class="mw-headline" id="Duty_cycle">Duty cycle</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=1" title="Edit section: Duty cycle">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The term <i><a href="/wiki/Duty_cycle" title="Duty cycle">duty cycle</a></i> describes the proportion of 'on' time to the regular interval or 'period' of time; a low duty cycle corresponds to low power, because the power is off for most of the time. Duty cycle is expressed in percent, 100% being fully on. When a digital signal is on half of the time and off the other half of the time, the digital signal has a duty cycle of 50% and resembles a "square" wave. When a digital signal spends more time in the on state than the off state, it has a duty cycle of &gt;50%. When a digital signal spends more time in the off state than the on state, it has a duty cycle of &lt;50%. Here is a pictorial that illustrates these three scenarios:
</p>
<div class="thumb tnone"><div class="thumbinner" style="width:544px;"><a href="/wiki/File:Duty_Cycle_Examples.png" class="image"><img alt="Duty Cycle Examples.png" src="//upload.wikimedia.org/wikipedia/commons/b/b8/Duty_Cycle_Examples.png" decoding="async" width="542" height="342" class="thumbimage" data-file-width="542" data-file-height="342" /></a>  <div class="thumbcaption"></div></div></div>
<h2><span class="mw-headline" id="History">History</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=2" title="Edit section: History">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Some machines (such as a <a href="/wiki/Sewing_machine" title="Sewing machine">sewing machine</a> motor) require partial or variable power.  In the past, control (such as in a sewing machine's foot pedal) was implemented by use of a <a href="/wiki/Rheostat" class="mw-redirect" title="Rheostat">rheostat</a> connected in series with the motor to adjust the amount of current flowing through the motor.  It was an inefficient scheme, as this also wasted power as heat in the resistor element of the rheostat, but tolerable because the total power was low. While the rheostat was one of several methods of controlling power (see <a href="/wiki/Autotransformer" title="Autotransformer">autotransformers</a> and <a href="/wiki/Variac" class="mw-redirect" title="Variac">Variac</a> for more info), a low cost and efficient power switching/adjustment method was yet to be found. This mechanism also needed to be able to drive motors for fans, pumps and <a href="/wiki/Robotics" title="Robotics">robotic</a> <a href="/wiki/Servomechanism" title="Servomechanism">servos</a>, and needed to be compact enough to interface with lamp dimmers.  PWM emerged as a solution for this complex problem.
</p><p>One early application of PWM was in the <a href="/wiki/Sinclair_Radionics" title="Sinclair Radionics">Sinclair</a> X10, a 10&#160;W audio amplifier available in kit form in the 1960s. At around the same time PWM started to be used in AC motor control.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">&#91;2&#93;</a></sup>
</p><p>Of note, for about a century, some variable-speed electric motors have had decent efficiency, but they were somewhat more complex than constant-speed motors, and sometimes required bulky external electrical apparatus, such as a bank of variable power resistors or rotating converters such as the <a href="/wiki/Ward_Leonard_control" title="Ward Leonard control">Ward Leonard drive</a>.
</p>
<h2><span class="mw-headline" id="Principle">Principle</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=3" title="Edit section: Principle">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Duty_cycle_general.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Duty_cycle_general.svg/350px-Duty_cycle_general.svg.png" decoding="async" width="350" height="175" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Duty_cycle_general.svg/525px-Duty_cycle_general.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Duty_cycle_general.svg/700px-Duty_cycle_general.svg.png 2x" data-file-width="500" data-file-height="250" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Duty_cycle_general.svg" class="internal" title="Enlarge"></a></div>Fig. 1: a <a href="/wiki/Pulse_wave" title="Pulse wave">pulse wave</a>, showing the definitions of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle y_{\text{min}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>min</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{min}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd2a1d9572f917308f19cf93a8457d620dc1e21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.112ex; height:2.009ex;" alt="{\displaystyle y_{\text{min}}}"/></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle y_{\text{max}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>max</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{max}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f990a65e495ff47ae797bc7fb8516068b932cb2c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.43ex; height:2.009ex;" alt="{\displaystyle y_{\text{max}}}"/></span> and D.</div></div></div>
<p>Pulse-width modulation uses a <a href="/wiki/Rectangular_wave" class="mw-redirect" title="Rectangular wave">rectangular pulse wave</a> whose pulse width is modulated resulting in the variation of the <a href="/wiki/Average" title="Average">average</a> value of the waveform. If we consider a pulse waveform <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle f(t)}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mi>t</mi>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="f(t)"/></span>, with period <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle T}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>T</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle T}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="T"/></span>,   low value <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 y_{\text{min}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>min</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{min}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd2a1d9572f917308f19cf93a8457d620dc1e21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.112ex; height:2.009ex;" alt="{\displaystyle y_{\text{min}}}"/></span>, a high value <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 y_{\text{max}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>max</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{max}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f990a65e495ff47ae797bc7fb8516068b932cb2c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.43ex; height:2.009ex;" alt="{\displaystyle y_{\text{max}}}"/></span> and a <a href="/wiki/Duty_cycle" title="Duty cycle">duty cycle</a> D (see figure 1), the average value of the waveform is given by:
</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 {\bar {y}}={\frac {1}{T}}\int _{0}^{T}f(t)\,dt}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>y</mi>
              <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mn>1</mn>
            <mi>T</mi>
          </mfrac>
        </mrow>
        <msubsup>
          <mo>&#x222B;<!-- ∫ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>T</mi>
          </mrow>
        </msubsup>
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mi>t</mi>
        <mo stretchy="false">)</mo>
        <mspace width="thinmathspace" />
        <mi>d</mi>
        <mi>t</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\bar {y}}={\frac {1}{T}}\int _{0}^{T}f(t)\,dt}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1aa8d581326bc327485d203d6aa7997947df7607" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:17.871ex; height:6.176ex;" alt="{\displaystyle {\bar {y}}={\frac {1}{T}}\int _{0}^{T}f(t)\,dt}"/></span></dd></dl>
<p>As <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle f(t)}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mi>t</mi>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="f(t)"/></span> is a pulse wave, its value is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle y_{\text{max}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>max</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{max}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f990a65e495ff47ae797bc7fb8516068b932cb2c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.43ex; height:2.009ex;" alt="{\displaystyle y_{\text{max}}}"/></span> for <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 0&lt;t&lt;D\cdot T}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mn>0</mn>
        <mo>&lt;</mo>
        <mi>t</mi>
        <mo>&lt;</mo>
        <mi>D</mi>
        <mo>&#x22C5;<!-- ⋅ --></mo>
        <mi>T</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle 0&lt;t&lt;D\cdot T}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1937ebbac57c6fbcf91d69e129305a669fa55e5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:13.439ex; height:2.176ex;" alt="{\displaystyle 0&lt;t&lt;D\cdot T}"/></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle y_{\text{min}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>min</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{min}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd2a1d9572f917308f19cf93a8457d620dc1e21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.112ex; height:2.009ex;" alt="{\displaystyle y_{\text{min}}}"/></span> for <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 D\cdot T&lt;t&lt;T}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>D</mi>
        <mo>&#x22C5;<!-- ⋅ --></mo>
        <mi>T</mi>
        <mo>&lt;</mo>
        <mi>t</mi>
        <mo>&lt;</mo>
        <mi>T</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle D\cdot T&lt;t&lt;T}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe21a173fd77e7c0fedbc88d5b45f92aefa9955b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:13.912ex; height:2.176ex;" alt="{\displaystyle D\cdot T&lt;t&lt;T}"/></span>. The above expression then becomes:
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\begin{aligned}{\bar {y}}&amp;={\frac {1}{T}}\left(\int _{0}^{DT}y_{\text{max}}\,dt+\int _{DT}^{T}y_{\text{min}}\,dt\right)\\&amp;={\frac {1}{T}}\left(D\cdot T\cdot y_{\text{max}}+T\left(1-D\right)y_{\text{min}}\right)\\&amp;=D\cdot y_{\text{max}}+\left(1-D\right)y_{\text{min}}\end{aligned}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
            <mtr>
              <mtd>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>y</mi>
                      <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
                    </mover>
                  </mrow>
                </mrow>
              </mtd>
              <mtd>
                <mi></mi>
                <mo>=</mo>
                <mrow class="MJX-TeXAtom-ORD">
                  <mfrac>
                    <mn>1</mn>
                    <mi>T</mi>
                  </mfrac>
                </mrow>
                <mrow>
                  <mo>(</mo>
                  <mrow>
                    <msubsup>
                      <mo>&#x222B;<!-- ∫ --></mo>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mn>0</mn>
                      </mrow>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mi>D</mi>
                        <mi>T</mi>
                      </mrow>
                    </msubsup>
                    <msub>
                      <mi>y</mi>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mtext>max</mtext>
                      </mrow>
                    </msub>
                    <mspace width="thinmathspace" />
                    <mi>d</mi>
                    <mi>t</mi>
                    <mo>+</mo>
                    <msubsup>
                      <mo>&#x222B;<!-- ∫ --></mo>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mi>D</mi>
                        <mi>T</mi>
                      </mrow>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mi>T</mi>
                      </mrow>
                    </msubsup>
                    <msub>
                      <mi>y</mi>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mtext>min</mtext>
                      </mrow>
                    </msub>
                    <mspace width="thinmathspace" />
                    <mi>d</mi>
                    <mi>t</mi>
                  </mrow>
                  <mo>)</mo>
                </mrow>
              </mtd>
            </mtr>
            <mtr>
              <mtd />
              <mtd>
                <mi></mi>
                <mo>=</mo>
                <mrow class="MJX-TeXAtom-ORD">
                  <mfrac>
                    <mn>1</mn>
                    <mi>T</mi>
                  </mfrac>
                </mrow>
                <mrow>
                  <mo>(</mo>
                  <mrow>
                    <mi>D</mi>
                    <mo>&#x22C5;<!-- ⋅ --></mo>
                    <mi>T</mi>
                    <mo>&#x22C5;<!-- ⋅ --></mo>
                    <msub>
                      <mi>y</mi>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mtext>max</mtext>
                      </mrow>
                    </msub>
                    <mo>+</mo>
                    <mi>T</mi>
                    <mrow>
                      <mo>(</mo>
                      <mrow>
                        <mn>1</mn>
                        <mo>&#x2212;<!-- − --></mo>
                        <mi>D</mi>
                      </mrow>
                      <mo>)</mo>
                    </mrow>
                    <msub>
                      <mi>y</mi>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mtext>min</mtext>
                      </mrow>
                    </msub>
                  </mrow>
                  <mo>)</mo>
                </mrow>
              </mtd>
            </mtr>
            <mtr>
              <mtd />
              <mtd>
                <mi></mi>
                <mo>=</mo>
                <mi>D</mi>
                <mo>&#x22C5;<!-- ⋅ --></mo>
                <msub>
                  <mi>y</mi>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mtext>max</mtext>
                  </mrow>
                </msub>
                <mo>+</mo>
                <mrow>
                  <mo>(</mo>
                  <mrow>
                    <mn>1</mn>
                    <mo>&#x2212;<!-- − --></mo>
                    <mi>D</mi>
                  </mrow>
                  <mo>)</mo>
                </mrow>
                <msub>
                  <mi>y</mi>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mtext>min</mtext>
                  </mrow>
                </msub>
              </mtd>
            </mtr>
          </mtable>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\bar {y}}&amp;={\frac {1}{T}}\left(\int _{0}^{DT}y_{\text{max}}\,dt+\int _{DT}^{T}y_{\text{min}}\,dt\right)\\&amp;={\frac {1}{T}}\left(D\cdot T\cdot y_{\text{max}}+T\left(1-D\right)y_{\text{min}}\right)\\&amp;=D\cdot y_{\text{max}}+\left(1-D\right)y_{\text{min}}\end{aligned}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4674cefe2722c18aebd8db2ce69e3cac9dedd1e9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -6.838ex; width:38.269ex; height:14.843ex;" alt="{\displaystyle {\begin{aligned}{\bar {y}}&amp;={\frac {1}{T}}\left(\int _{0}^{DT}y_{\text{max}}\,dt+\int _{DT}^{T}y_{\text{min}}\,dt\right)\\&amp;={\frac {1}{T}}\left(D\cdot T\cdot y_{\text{max}}+T\left(1-D\right)y_{\text{min}}\right)\\&amp;=D\cdot y_{\text{max}}+\left(1-D\right)y_{\text{min}}\end{aligned}}}"/></span></dd></dl>
<p>This latter expression can be fairly simplified in many cases where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle y_{\text{min}}=0}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>min</mtext>
          </mrow>
        </msub>
        <mo>=</mo>
        <mn>0</mn>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle y_{\text{min}}=0}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2bcfdd5420aabc2fa94b6a2cffc5676be0f6e5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:8.373ex; height:2.509ex;" alt="{\displaystyle y_{\text{min}}=0}"/></span> as <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 {\bar {y}}=D\cdot y_{\text{max}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>y</mi>
              <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo>=</mo>
        <mi>D</mi>
        <mo>&#x22C5;<!-- ⋅ --></mo>
        <msub>
          <mi>y</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mtext>max</mtext>
          </mrow>
        </msub>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\bar {y}}=D\cdot y_{\text{max}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6342fc950d4168b10189e1fcb779be6b32987649" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:12.434ex; height:2.509ex;" alt="{\displaystyle {\bar {y}}=D\cdot y_{\text{max}}}"/></span>. From this, the average value of the signal (<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 {\bar {y}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>y</mi>
              <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
            </mover>
          </mrow>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\bar {y}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b298744237368f34e61ff7dc90b34016a7037af" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.302ex; height:2.343ex;" alt="{\bar {y}}"/></span>) is directly dependent on the duty cycle D.
</p>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Pwm.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pwm.svg/350px-Pwm.svg.png" decoding="async" width="350" height="292" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pwm.svg/525px-Pwm.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pwm.svg/700px-Pwm.svg.png 2x" data-file-width="600" data-file-height="500" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Pwm.svg" class="internal" title="Enlarge"></a></div>Fig. 2: A simple method to generate the PWM pulse train corresponding to a given signal is the intersective PWM: the signal (here the red sine wave) is compared with a sawtooth waveform (blue). When the latter is less than the former, the PWM signal (magenta) is in high state (1). Otherwise it is in the low state (0).</div></div></div>
<p>The simplest way to generate a PWM signal is the intersective method, which requires only a <a href="/wiki/Sawtooth_wave" title="Sawtooth wave">sawtooth</a> or a <a href="/wiki/Triangle_wave" title="Triangle wave">triangle</a> waveform (easily generated using a simple <a href="/wiki/Electronic_oscillator" title="Electronic oscillator">oscillator</a>) and a <a href="/wiki/Comparator" title="Comparator">comparator</a>. When the value of the reference signal (the red sine wave in figure 2) is more than the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state.
</p>
<h3><span class="mw-headline" id="Delta">Delta</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=4" title="Edit section: Delta">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Delta_modulation" title="Delta modulation">Delta modulation</a></div>
<p>In the use of delta modulation for PWM control, the output signal is integrated, and the result is compared with limits, which correspond to a Reference signal offset by a constant. Every time the integral of the output signal reaches one of the limits, the PWM signal changes state.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">&#91;3&#93;</a></sup> Figure 3
</p>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Delta_PWM.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Delta_PWM.svg/350px-Delta_PWM.svg.png" decoding="async" width="350" height="210" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Delta_PWM.svg/525px-Delta_PWM.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Delta_PWM.svg/700px-Delta_PWM.svg.png 2x" data-file-width="500" data-file-height="300" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Delta_PWM.svg" class="internal" title="Enlarge"></a></div>Fig. 3&#160;: Principle of the delta PWM. The output signal (blue) is compared with the limits (green). These limits correspond to the reference signal (red), offset by a given value. Every time the output signal (blue) reaches one of the limits, the PWM signal changes state.</div></div></div>
<h3><span class="mw-headline" id="Delta-sigma">Delta-sigma</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=5" title="Edit section: Delta-sigma">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Delta-sigma_modulation" title="Delta-sigma modulation">Delta-sigma modulation</a></div>
<p>In delta-sigma modulation as a PWM control method, the output signal is subtracted from a reference signal to form an error signal. This error is integrated, and when the integral of the error exceeds the limits, the output changes state. Figure 4
</p>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Sigma-delta_PWM.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Sigma-delta_PWM.svg/350px-Sigma-delta_PWM.svg.png" decoding="async" width="350" height="292" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Sigma-delta_PWM.svg/525px-Sigma-delta_PWM.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Sigma-delta_PWM.svg/700px-Sigma-delta_PWM.svg.png 2x" data-file-width="600" data-file-height="500" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Sigma-delta_PWM.svg" class="internal" title="Enlarge"></a></div>Fig. 4&#160;: Principle of the sigma-delta PWM. The top green waveform is the reference signal, on which the output signal (PWM, in the bottom plot) is subtracted to form the error signal (blue, in top plot). This error is integrated (middle plot), and when the integral of the error exceeds the limits (red lines), the output changes state.</div></div></div>
<h3><span class="mw-headline" id="Space_vector_modulation">Space vector modulation</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=6" title="Edit section: Space vector modulation">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Space_vector_modulation" title="Space vector modulation">Space vector modulation</a></div>
<p>Space vector modulation is a PWM control algorithm for multi-phase AC generation, in which the reference signal is sampled regularly; after each sample, non-zero active switching vectors adjacent to the reference vector and one or more of the zero switching vectors are selected for the appropriate fraction of the sampling period in order to synthesize the reference signal as the average of the used vectors.
</p>
<h3><span id="Direct_torque_control_.28DTC.29"></span><span class="mw-headline" id="Direct_torque_control_(DTC)">Direct torque control (DTC)</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=7" title="Edit section: Direct torque control (DTC)">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Direct_torque_control" title="Direct torque control">Direct torque control</a></div>
<p>Direct torque control is a method used to control AC motors. It is closely related with the delta modulation (see above). Motor torque and magnetic flux are estimated and these are controlled to stay within their hysteresis bands by turning on a new combination of the device's semiconductor switches each time either signal tries to deviate out of its band.
</p>
<h3><span class="mw-headline" id="Time_proportioning">Time proportioning</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=8" title="Edit section: Time proportioning">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>Many digital circuits can generate PWM signals (e.g., many <a href="/wiki/Microcontrollers" class="mw-redirect" title="Microcontrollers">microcontrollers</a> have PWM outputs). They normally use a <a href="/wiki/Counter_(digital)" title="Counter (digital)">counter</a> that increments periodically (it is connected directly or indirectly to the <a href="/wiki/Clock_signal" title="Clock signal">clock</a> of the circuit) and is reset at the end of every period of the PWM. When the counter value is more than the reference value, the PWM output changes state from high to low (or low to high).<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">&#91;4&#93;</a></sup> This technique is referred to as <b>time proportioning,</b> particularly as <b>time-proportioning control</b><sup id="cite_ref-5" class="reference"><a href="#cite_note-5">&#91;5&#93;</a></sup> – which <i>proportion</i> of a fixed cycle time is spent in the high state.
</p><p>The incremented and periodically reset counter is the discrete version of the intersecting method's sawtooth. The analog comparator of the intersecting method becomes a simple integer comparison between the current counter value and the digital (possibly digitized) reference value. The duty cycle can only be varied in discrete steps, as a function of the counter resolution. However, a high-resolution counter can provide quite satisfactory performance.
</p>
<h3><span class="mw-headline" id="Types">Types</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=9" title="Edit section: Types">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Three_PWM_types.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Three_PWM_types.svg/350px-Three_PWM_types.svg.png" decoding="async" width="350" height="292" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Three_PWM_types.svg/525px-Three_PWM_types.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Three_PWM_types.svg/700px-Three_PWM_types.svg.png 2x" data-file-width="600" data-file-height="500" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Three_PWM_types.svg" class="internal" title="Enlarge"></a></div>Fig. 5&#160;: Three types of PWM signals (blue): leading edge modulation (top), trailing edge modulation (middle) and centered pulses (both edges are modulated, bottom). The green lines are the sawtooth waveform (first and second cases) and a triangle waveform (third case) used to generate the PWM waveforms using the intersective method.</div></div></div>
<p>Three types of pulse-width modulation (PWM) are possible:
</p>
<ol><li>The pulse center may be fixed in the center of the time window and both <a href="/wiki/Signal_edge" title="Signal edge">edges</a> of the pulse moved to compress or expand the width.</li>
<li>The lead edge can be held at the lead edge of the window and the tail edge modulated.</li>
<li>The tail edge can be fixed and the lead edge modulated.</li></ol>
<h3><span class="mw-headline" id="Spectrum">Spectrum</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=10" title="Edit section: Spectrum">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The resulting <a href="/wiki/Spectrum" title="Spectrum">spectra</a> (of the three cases) are similar, and each contains a <a href="/wiki/Direct_current" title="Direct current">dc</a> component—a base sideband containing the modulating signal and phase modulated <a href="/wiki/Carrier_signal" class="mw-redirect" title="Carrier signal">carriers</a> at each <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> of the  frequency of the pulse. The amplitudes of the harmonic groups are restricted by a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle \sin x/x}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>sin</mi>
        <mo>&#x2061;<!-- ⁡ --></mo>
        <mi>x</mi>
        <mrow class="MJX-TeXAtom-ORD">
          <mo>/</mo>
        </mrow>
        <mi>x</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \sin x/x}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/186c83abf80a10cb248374b107a9205f81c0d687" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:7.065ex; height:2.843ex;" alt="\sin x/x"/></span> envelope (<a href="/wiki/Sinc_function" title="Sinc function">sinc function</a>) and extend to infinity.
The infinite bandwidth is caused by the nonlinear operation of the pulse-width modulator. In consequence, a digital PWM suffers from <a href="/wiki/Aliasing" title="Aliasing">aliasing</a> distortion that significantly reduce its applicability for modern <a href="/wiki/Communications_systems" class="mw-redirect" title="Communications systems">communications system</a>. By limiting the bandwidth of the PWM kernel, aliasing effects can be avoided.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">&#91;6&#93;</a></sup>
</p><p>On the contrary, the delta modulation is a random process that produces continuous spectrum without distinct harmonics.
</p>
<h3><span class="mw-headline" id="PWM_sampling_theorem">PWM sampling theorem</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=11" title="Edit section: PWM sampling theorem">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The process of PWM conversion is non-linear and it is generally supposed that low pass filter signal recovery is imperfect for PWM. The PWM sampling theorem<sup id="cite_ref-7" class="reference"><a href="#cite_note-7">&#91;7&#93;</a></sup> shows that PWM conversion can be perfect. The theorem states that "Any bandlimited baseband signal within ±0.637 can be represented by a pulsewidth modulation (PWM) waveform with unit amplitude. The number of pulses in the waveform is equal to the number of Nyquist samples and the peak constraint is independent of whether the waveform is two-level or three-level."
</p>
<ul><li>Nyquist-Shannon Sampling Theorem: "If you have a signal that is perfectly band limited to a bandwidth of f<sub>0</sub> then you can collect all the information there is in that signal by sampling it at discrete times, as long as your sample rate is greater than 2f<sub>0</sub>."<sup id="cite_ref-8" class="reference"><a href="#cite_note-8">&#91;8&#93;</a></sup></li></ul>
<h2><span class="mw-headline" id="Applications">Applications</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=12" title="Edit section: Applications">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<h3><span class="mw-headline" id="Servos">Servos</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=13" title="Edit section: Servos">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>PWM is used to control <a href="/wiki/Servomechanism" title="Servomechanism">servomechanisms</a>; see <a href="/wiki/Servo_control" title="Servo control">servo control</a>.
</p>
<h3><span class="mw-headline" id="Telecommunications">Telecommunications</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=14" title="Edit section: Telecommunications">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>In <a href="/wiki/Telecommunications" class="mw-redirect" title="Telecommunications">telecommunications</a>, PWM  is a form of signal <a href="/wiki/Modulation#Pulse_modulation_methods" title="Modulation">modulation</a> where the widths of the pulses correspond to specific data values encoded at one end and decoded at the other.
</p><p>Pulses of various lengths (the information itself) will be sent at regular intervals (the carrier frequency of the modulation).
</p>
<pre>          _      _      _      _      _      _      _      _     
         | |    | |    | |    | |    | |    | |    | |    | |    
Clock    | |    | |    | |    | |    | |    | |    | |    | |    
       __| |____| |____| |____| |____| |____| |____| |____| |____

                 _      __     ____          ____   _
PWM signal      | |    |  |   |    |        |    | | |
                | |    |  |   |    |        |    | | |
       _________| |____|  |___|    |________|    |_| |___________

Data       0     1       2      4      0      4     1      0
</pre>
<p>The inclusion of a <a href="/wiki/Clock_signal" title="Clock signal">clock signal</a> is not necessary, as the leading edge of the data signal can be used as the clock if a small offset is added to each data value in order to avoid a data value with a zero length pulse.
</p>
<pre>                _      __     ___    _____   _      _____   __     _   
               | |    |  |   |   |  |     | | |    |     | |  |   | | 
PWM signal     | |    |  |   |   |  |     | | |    |     | |  |   | |  
             __| |____|  |___|   |__|     |_| |____|     |_|  |___| |_____

Data            0       1      2       4     0        4      1     0
</pre>
<h3><span class="mw-headline" id="Power_delivery">Power delivery</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=15" title="Edit section: Power delivery">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>PWM can be used to control the amount of power delivered to a load without incurring the losses that would result from linear power delivery by resistive means. Drawbacks to this technique are that the power drawn by the load is not constant but rather discontinuous (see <a href="/wiki/Buck_converter" title="Buck converter">Buck converter</a>), and energy delivered to the load is not continuous either.  However, the load may be inductive, and with a sufficiently high frequency and when necessary using additional passive <a href="/wiki/Electronic_filter" title="Electronic filter">electronic filters</a>, the pulse train can be smoothed and average analog waveform recovered.  Power flow into the load can be continuous. Power flow from the supply is not constant and will require energy storage on the supply side in most cases. (In the case of an electrical circuit, a capacitor to absorb energy stored in (often parasitic) supply side inductance.)
</p><p>High <a href="/wiki/Frequency" title="Frequency">frequency</a> PWM power control systems are easily realisable with semiconductor switches. As explained above, almost no power is dissipated by the switch in either on or off state. However, during the transitions between on and off states, both voltage and current are nonzero and thus power is dissipated in the switches. By quickly changing the state between fully on and fully off (typically less than 100 nanoseconds), the power dissipation in the switches can be quite low compared to the power being delivered to the load.
</p><p>Modern semiconductor switches such as <a href="/wiki/MOSFET" title="MOSFET">MOSFETs</a> or <a href="/wiki/Insulated-gate_bipolar_transistor" title="Insulated-gate bipolar transistor">insulated-gate bipolar transistors</a> (IGBTs) are well suited components for high-efficiency controllers. Frequency converters used to control AC motors may have efficiencies exceeding 98%. Switching power supplies have lower efficiency due to low output voltage levels (often even less than 2 V for microprocessors are needed) but still more than 70–80% efficiency can be achieved.
</p><p>Variable-speed <a href="/wiki/Computer_fan_control" title="Computer fan control">computer fan controllers</a> usually use PWM, as it is far more efficient when compared to a <a href="/wiki/Potentiometer" title="Potentiometer">potentiometer</a> or <a href="/wiki/Rheostat" class="mw-redirect" title="Rheostat">rheostat</a>. (Neither of the latter is practical to operate electronically; they would require a small drive motor.)
</p><p>Light dimmers for home use employ a specific type of PWM control. Home-use light dimmers typically include electronic circuitry which suppresses current flow during defined portions of each cycle of the AC line voltage. Adjusting the brightness of light emitted by a light source is then merely a matter of setting at what voltage (or phase) in the AC half-cycle the dimmer begins to provide electric current to the light source (e.g. by using an electronic switch such as a <a href="/wiki/TRIAC" title="TRIAC">triac</a>). In this case the PWM duty cycle is the ratio of the conduction time to the duration of the half AC cycle defined by the frequency of the AC line voltage (50&#160;Hz or 60&#160;Hz depending on the country).
</p><p>These rather simple types of dimmers can be effectively used with inert (or relatively slow reacting) light sources such as incandescent lamps, for example, for which the additional modulation in supplied electrical energy which is caused by the dimmer causes only negligible additional fluctuations in the emitted light. Some other types of light sources such as light-emitting diodes (LEDs), however, turn on and off extremely rapidly and would perceivably flicker if supplied with low frequency drive voltages. Perceivable flicker effects from such rapid response light sources can be reduced by increasing the PWM frequency. If the light fluctuations are sufficiently rapid (faster than the <a href="/wiki/Flicker_fusion_threshold" title="Flicker fusion threshold">flicker fusion threshold</a>), the human visual system can no longer resolve them and the eye perceives the time average intensity without flicker.
</p><p>In electric cookers, continuously variable power is applied to the heating elements such as the hob or the grill using a device known as a <a href="/wiki/Energy_regulator" class="mw-redirect" title="Energy regulator">simmerstat</a>. This consists of a thermal oscillator running at approximately two cycles per minute and the mechanism varies the duty cycle according to the knob setting. The thermal time constant of the heating elements is several minutes, so that the temperature fluctuations are too small to matter in practice.
</p>
<h3><span class="mw-headline" id="Voltage_regulation">Voltage regulation</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=16" title="Edit section: Voltage regulation">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">Switched-mode power supply</a></div>
<p>PWM is also used in efficient <a href="/wiki/Voltage_regulator" title="Voltage regulator">voltage regulators</a>. By switching voltage to the load with the appropriate duty cycle, the output will approximate a voltage at the desired level. The switching noise is usually filtered with an <a href="/wiki/Inductor" title="Inductor">inductor</a> and a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a>.
</p><p>One method measures the output voltage. When it is lower than the desired voltage, it turns on the switch. When the output voltage is above the desired voltage, it turns off the switch.
</p>
<h3><span class="mw-headline" id="Audio_effects_and_amplification">Audio effects and amplification</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=17" title="Edit section: Audio effects and amplification">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>Varying the duty cycle of a pulse waveform in a synthesis instrument creates useful timbral variations. Some synthesizers have a duty-cycle trimmer for their square-wave outputs, and that trimmer can be set by ear; the 50% point (true square wave) was distinctive, because even-numbered harmonics essentially disappear at 50%. Pulse waves, usually 50%, 25%, and 12.5%, make up the <a href="/wiki/Video_game_music" title="Video game music">soundtracks of classic video games</a>. The term PWM as used in sound (music) synthesis refers to the ratio between the high and low level being secondarily modulated with a <a href="/wiki/Low_frequency_oscillation" class="mw-redirect" title="Low frequency oscillation">low frequency oscillator</a>. This gives a sound effect similar to chorus or slightly detuned oscillators played together. (In fact, PWM is equivalent to the sum of two <a href="/wiki/Sawtooth_wave" title="Sawtooth wave">sawtooth waves</a> with one of them inverted.)<sup id="cite_ref-9" class="reference"><a href="#cite_note-9">&#91;9&#93;</a></sup> 
</p><p>A new class of audio amplifiers based on the PWM principle is becoming popular. Called <a href="/wiki/Class-D_amplifier" title="Class-D amplifier">class-D amplifiers</a>, they produce a PWM equivalent of the analog input signal which is fed to the <a href="/wiki/Loudspeaker" title="Loudspeaker">loudspeaker</a> via a suitable filter network to block the carrier and recover the original audio. These amplifiers are characterized by very good efficiency figures (≥ 90%) and compact size/light weight for large power outputs. For a few decades, industrial and military PWM amplifiers have been in common use, often for driving <a href="/wiki/Servomotor" title="Servomotor">servo motors</a>. Field-gradient coils in <a href="/wiki/MRI" class="mw-redirect" title="MRI">MRI</a> machines are driven by relatively high-power PWM amplifiers.
</p><p>Historically, a crude form of PWM has been used to play back <a href="/wiki/PCM" class="mw-redirect" title="PCM">PCM</a> digital sound on the <a href="/wiki/PC_speaker" title="PC speaker">PC speaker</a>, which is driven by only two voltage levels, typically 0 V and 5 V. By carefully timing the duration of the pulses, and by relying on the speaker's physical filtering properties (limited frequency response, self-inductance, etc.) it was possible to obtain an approximate playback of mono PCM samples, although at a very low quality, and with greatly varying results between implementations.
</p><p>In more recent times, the <a href="/wiki/Direct_Stream_Digital" title="Direct Stream Digital">Direct Stream Digital</a> sound encoding method was introduced, which uses a generalized form of pulse-width modulation called <a href="/wiki/Pulse_density_modulation" class="mw-redirect" title="Pulse density modulation">pulse density modulation</a>, at a high enough sampling rate (typically in the order of MHz) to cover the whole <a href="/wiki/Acoustics" title="Acoustics">acoustic</a> frequencies range with sufficient fidelity. This method is used in the <a href="/wiki/Super_Audio_CD" title="Super Audio CD">SACD</a> format, and reproduction of the encoded audio signal is essentially similar to the method used in class-D amplifiers.
</p>
<h3><span class="mw-headline" id="Electrical">Electrical</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=18" title="Edit section: Electrical">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>SPWM (Sine–triangle pulse width modulation) signals are used in micro-inverter design (used in solar and wind power applications). These switching signals are fed to the <a href="/wiki/FET" class="mw-redirect" title="FET">FETs</a> that are used in the device. The device's efficiency depends on the harmonic content of the PWM signal. There is much research on eliminating unwanted harmonics and improving the fundamental strength, some of which involves using a modified carrier signal instead of a classic sawtooth signal<sup id="cite_ref-10" class="reference"><a href="#cite_note-10">&#91;10&#93;</a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11">&#91;11&#93;</a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12">&#91;12&#93;</a></sup> in order to decrease power losses and improve efficiency. Another common application is in robotics where PWM signals are used to control the speed of the robot by controlling the motors.
</p>
<h3><span class="mw-headline" id="Soft-blinking_LED_indicator">Soft-blinking LED indicator</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=19" title="Edit section: Soft-blinking LED indicator">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>PWM techniques would typically be used to make some indicator (like a <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">LED</a>) "soft blink". The light will slowly go from dark to full intensity, and slowly dimmed to dark again. Then it repeats. The period would be several soft-blinks per second up to several seconds for one blink. An indicator of this type would not disturb as much as a "hard-blinking" on/off indicator. The indicator lamp on the <a href="/wiki/IBook" title="IBook">Apple iBook G4, PowerBook 6,7 (2005)</a> was of this type. This kind of indicator is also called "pulsing glow", as opposed to calling it "flashing".
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=20" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><a href="/wiki/Analog_signal_to_discrete_time_interval_converter" title="Analog signal to discrete time interval converter">Analog signal to discrete time interval converter</a></li>
<li><a href="/wiki/Class-D_amplifier" title="Class-D amplifier">Class-D amplifier</a></li>
<li><a href="/wiki/Computer_fan_control" title="Computer fan control">Computer fan control</a></li>
<li><a href="/wiki/Continuously_variable_slope_delta_modulation" title="Continuously variable slope delta modulation">Continuously variable slope delta modulation</a></li>
<li><a href="/wiki/Delta-sigma_modulation" title="Delta-sigma modulation">Delta-sigma modulation</a></li>
<li><a href="/wiki/H-bridge" title="H-bridge">H-bridge</a></li>
<li><a href="/wiki/Pulse-amplitude_modulation" title="Pulse-amplitude modulation">Pulse-amplitude modulation</a></li>
<li><a href="/wiki/Pulse-code_modulation" title="Pulse-code modulation">Pulse-code modulation</a></li>
<li><a href="/wiki/Pulse-density_modulation" title="Pulse-density modulation">Pulse-density modulation</a></li>
<li><a href="/wiki/Pulse-position_modulation" title="Pulse-position modulation">Pulse-position modulation</a></li>
<li><a href="/wiki/Radio_control" title="Radio control">Radio control</a></li>
<li><a href="/wiki/Servomechanism#RC_servos" title="Servomechanism">RC servo</a></li>
<li><a href="/wiki/Sliding_mode_control" title="Sliding mode control">Sliding mode control</a> - produces smooth behavior by way of discontinuous switching in systems</li>
<li><a href="/wiki/Space_vector_modulation" title="Space vector modulation">Space vector modulation</a></li>
<li><a href="/wiki/Sound_chip" title="Sound chip">Sound chip</a></li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=21" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r1011085734">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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">
<div class="mw-references-wrap mw-references-columns"><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"><style data-mw-deduplicate="TemplateStyles:r999302996">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),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 a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.homepower.com/articles/solar-electricity/design-installation/sizing-grid-tied-pv-system-battery-backup">"Sizing a Grid-Tied PV System ...with Battery Backup"</a>. <i>Home Power Magazine</i>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Home+Power+Magazine&amp;rft.atitle=Sizing+a+Grid-Tied+PV+System+...with+Battery+Backup&amp;rft_id=https%3A%2F%2Fwww.homepower.com%2Farticles%2Fsolar-electricity%2Fdesign-installation%2Fsizing-grid-tied-pv-system-battery-backup&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" class="Z3988"></span></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:r999302996"/><cite id="CITEREFSchönungStemmler,_H.1964" class="citation journal cs1">Schönung, A.; Stemmler, H. (August 1964). "Geregelter Drehstrom-Umkehrantrieb mit gesteuertem Umrichter nach dem Unterschwingungsverfahren". <i>BBC Mitteilungen</i>. <b>51</b> (8/9): 555–577.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=BBC+Mitteilungen&amp;rft.atitle=Geregelter+Drehstrom-Umkehrantrieb+mit+gesteuertem+Umrichter+nach+dem+Unterschwingungsverfahren&amp;rft.volume=51&amp;rft.issue=8%2F9&amp;rft.pages=555-577&amp;rft.date=1964-08&amp;rft.aulast=Sch%C3%B6nung&amp;rft.aufirst=A.&amp;rft.au=Stemmler%2C+H.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" class="Z3988"></span></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFDuRobertson2017" class="citation journal cs1">Du, Ruoyang; Robertson, Paul (2017). <a rel="nofollow" class="external text" href="https://www.repository.cam.ac.uk/bitstream/1810/263361/1/Cost%20effective%20grid%20connected%20inverter%20for%20microCHP%20system.pdf">"Cost Effective Grid-Connected Inverter for a Micro Combined Heat and Power System"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Transactions on Industrial Electronics</i>. <b>64</b> (7): 5360–5367. <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%2FTIE.2017.2677340">10.1109/TIE.2017.2677340</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a>&#160;<a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0278-0046">0278-0046</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=IEEE+Transactions+on+Industrial+Electronics&amp;rft.atitle=Cost+Effective+Grid-Connected+Inverter+for+a+Micro+Combined+Heat+and+Power+System&amp;rft.volume=64&amp;rft.issue=7&amp;rft.pages=5360-5367&amp;rft.date=2017&amp;rft_id=info%3Adoi%2F10.1109%2FTIE.2017.2677340&amp;rft.issn=0278-0046&amp;rft.aulast=Du&amp;rft.aufirst=Ruoyang&amp;rft.au=Robertson%2C+Paul&amp;rft_id=https%3A%2F%2Fwww.repository.cam.ac.uk%2Fbitstream%2F1810%2F263361%2F1%2FCost%2520effective%2520grid%2520connected%2520inverter%2520for%2520microCHP%2520system.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" 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:r999302996"/><cite id="CITEREFBarr2001" class="citation web cs1">Barr, Michael (1 September 2001). <a rel="nofollow" class="external text" href="https://barrgroup.com/Embedded-Systems/How-To/PWM-Pulse-Width-Modulation">"Introduction to Pulse Width Modulation (PWM)"</a>. <i>Barr Group</i>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Barr+Group&amp;rft.atitle=Introduction+to+Pulse+Width+Modulation+%28PWM%29&amp;rft.date=2001-09-01&amp;rft.aulast=Barr&amp;rft.aufirst=Michael&amp;rft_id=https%3A%2F%2Fbarrgroup.com%2FEmbedded-Systems%2FHow-To%2FPWM-Pulse-Width-Modulation&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" 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"><i>Fundamentals of HVAC Control Systems,</i> by Robert McDowall, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UMk1EUp-W-UC&amp;pg=PA21&amp;dq=%22time+proportioning%22">p. 21</a></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:r999302996"/><cite id="CITEREFHausmairShuli_ChiPeter_SingerlChristian_Vogel2013" class="citation journal cs1">Hausmair, Katharina; Shuli Chi; Peter Singerl; Christian Vogel (February 2013). "Aliasing-Free Digital Pulse-Width Modulation for Burst-Mode RF Transmitters". <i>IEEE Transactions on Circuits and Systems I: Regular Papers</i>. <b>60</b> (2): 415–427. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a>&#160;<span class="cs1-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.454.9157">10.1.1.454.9157</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/10.1109%2FTCSI.2012.2215776">10.1109/TCSI.2012.2215776</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=IEEE+Transactions+on+Circuits+and+Systems+I%3A+Regular+Papers&amp;rft.atitle=Aliasing-Free+Digital+Pulse-Width+Modulation+for+Burst-Mode+RF+Transmitters&amp;rft.volume=60&amp;rft.issue=2&amp;rft.pages=415-427&amp;rft.date=2013-02&amp;rft_id=%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.454.9157%23id-name%3DCiteSeerX&amp;rft_id=info%3Adoi%2F10.1109%2FTCSI.2012.2215776&amp;rft.aulast=Hausmair&amp;rft.aufirst=Katharina&amp;rft.au=Shuli+Chi&amp;rft.au=Peter+Singerl&amp;rft.au=Christian+Vogel&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" 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">J. Huang, K. Padmanabhan, and O. M. Collins, “The sampling theorem with constant amplitude variable width pulses”, IEEE transactions on Circuits and Systems, vol. 58, pp. 1178 - 1190, June 2011.</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:r999302996"/><cite id="CITEREFWescott2018" class="citation web cs1">Wescott, Tim (August 14, 2018). <a rel="nofollow" class="external text" href="http://www.wescottdesign.com/articles/Sampling/sampling.pdf">"Sampling: What Nyquist Didn't Say, and What to Do About It"</a> <span class="cs1-format">(PDF)</span>. Wescott Design Services. <q>The Nyquist-Shannon sampling theorem is useful, but often misused when engineers establish sampling rates or design anti-aliasing filters.</q></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Sampling%3A+What+Nyquist+Didn%E2%80%99t+Say%2C+and+What+to+Do+About+It&amp;rft.pub=Wescott+Design+Services&amp;rft.date=2018-08-14&amp;rft.aulast=Wescott&amp;rft.aufirst=Tim&amp;rft_id=http%3A%2F%2Fwww.wescottdesign.com%2Farticles%2FSampling%2Fsampling.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APulse-width+modulation" class="Z3988"></span></span>
</li>
<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.soundonsound.com/sos/Mar03/articles/synthsecrets47.asp">Synthesizing Strings: PWM &amp; String Sounds</a></span>
</li>
<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Hirak Patangia, Sri Nikhil Gupta Gourisetti, "A Harmonically Superior Modulator with Wide Baseband and Real-Time Tunability", IEEE International Symposium on Electronic Design (ISED), India, Dec.11.</span>
</li>
<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Hirak Patangia, Sri Nikhil Gupta Gourisetti, “Real Time Harmonic Elimination Using a Modified Carrier”, CONIELECOMP, Mexico, Feb 2012.</span>
</li>
<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Hirak Patangia, Sri Nikhil Gupta Gourisetti, “A Novel Strategy for Selective Harmonic Elimination Based on a Sine-Sine PWM Model”, MWSCAS, U.S.A, Aug 2012.</span>
</li>
</ol></div></div>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit&amp;section=22" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:#f9f9f9;border:1px solid #aaa;color:#000">
<tbody><tr>
<td class="mbox-image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="noviewer" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></td>
<td class="mbox-text plainlist">Wikimedia Commons has media related to <i><b><a href="https://commons.wikimedia.org/wiki/Category:Pulse_width_modulation" class="extiw" title="commons:Category:Pulse width modulation"><span style="">Pulse width modulation</span></a></b></i>.</td></tr>
</tbody></table>
<ul><li><a rel="nofollow" class="external text" href="http://www.beis.de/Elektronik/DeltaSigma/DeltaSigma.html">An Introduction to Delta Sigma Converters</a></li>
<li><a rel="nofollow" class="external text" href="http://www.pidlab.com/en/pwm-demo">Pulse Width Modulation in PID control loop - free simulator</a></li>
<li><a rel="nofollow" class="external text" href="http://www.tftcentral.co.uk/articles/pulse_width_modulation.htm">Pulse Width Modulation in Desktop monitors - monitor flicker</a></li></ul>
<!-- 
NewPP limit report
Parsed by mw1267
Cached time: 20210402154806
Cache expiry: 2592000
Dynamic content: false
Complications: [vary‐revision‐sha1]
CPU time usage: 0.508 seconds
Real time usage: 0.664 seconds
Preprocessor visited node count: 1059/1000000
Post‐expand include size: 25517/2097152 bytes
Template argument size: 576/2097152 bytes
Highest expansion depth: 13/40
Expensive parser function count: 1/500
Unstrip recursion depth: 1/20
Unstrip post‐expand size: 26995/5000000 bytes
Lua time usage: 0.259/10.000 seconds
Lua memory usage: 4727744/52428800 bytes
Number of Wikibase entities loaded: 1/400
-->
<!--
Transclusion expansion time report (%,ms,calls,template)
100.00%  494.560      1 -total
 40.84%  201.964      1 Template:Reflist
 27.05%  133.762      3 Template:Cite_web
 18.09%   89.445      1 Template:More_footnotes
 15.74%   77.868      1 Template:Modulation_techniques
 11.57%   57.212      1 Template:Commons_category
 11.40%   56.404      1 Template:Ambox
 10.78%   53.291      1 Template:Sister_project
 10.12%   50.058      1 Template:Side_box
  5.89%   29.146      3 Template:Cite_journal
-->

<!-- Saved in parser cache with key enwiki:pcache:idhash:81242-0!canonical!math=5 and timestamp 20210402154806 and revision id 1003507942. Serialized with JSON.
 -->
</div><noscript><img src="//en.wikipedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" title="" width="1" height="1" style="border: none; position: absolute;" /></noscript>
<div class="printfooter">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Pulse-width_modulation&amp;oldid=1003507942">https://en.wikipedia.org/w/index.php?title=Pulse-width_modulation&amp;oldid=1003507942</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">Categories</a>: <ul><li><a href="/wiki/Category:Signal_processing" title="Category:Signal processing">Signal processing</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_lacking_in-text_citations_from_April_2009" title="Category:Articles lacking in-text citations from April 2009">Articles lacking in-text citations from April 2009</a></li><li><a href="/wiki/Category:All_articles_lacking_in-text_citations" title="Category:All articles lacking in-text citations">All articles lacking in-text citations</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div>
	</div>
</div>
<div id='mw-data-after-content'>
	<div class="read-more-container"></div>
</div>

<div id="mw-navigation">
	<h2>Navigation menu</h2>
	<div id="mw-head">
		<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-personal" class="mw-portlet mw-portlet-personal vector-menu" aria-labelledby="p-personal-label" role="navigation" 
	 >
	<h3 id="p-personal-label" class="vector-menu-heading">
		<span>Personal tools</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="pt-anonuserpage">Not logged in</li><li id="pt-anontalk"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n">Talk</a></li><li id="pt-anoncontribs"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y">Contributions</a></li><li id="pt-createaccount"><a href="/w/index.php?title=Special:CreateAccount&amp;returnto=Pulse-width+modulation" title="You are encouraged to create an account and log in; however, it is not mandatory">Create account</a></li><li id="pt-login"><a href="/w/index.php?title=Special:UserLogin&amp;returnto=Pulse-width+modulation" title="You&#039;re encouraged to log in; however, it&#039;s not mandatory. [o]" accesskey="o">Log in</a></li></ul>
		
	</div>
</nav>

		<div id="left-navigation">
			<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-namespaces" class="mw-portlet mw-portlet-namespaces vector-menu vector-menu-tabs" aria-labelledby="p-namespaces-label" role="navigation" 
	 >
	<h3 id="p-namespaces-label" class="vector-menu-heading">
		<span>Namespaces</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="ca-nstab-main" class="selected"><a href="/wiki/Pulse-width_modulation" title="View the content page [c]" accesskey="c">Article</a></li><li id="ca-talk"><a href="/wiki/Talk:Pulse-width_modulation" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t">Talk</a></li></ul>
		
	</div>
</nav>

			<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-variants" class="mw-portlet mw-portlet-variants emptyPortlet vector-menu vector-menu-dropdown" aria-labelledby="p-variants-label" role="navigation" 
	 >
	<input type="checkbox" class="vector-menu-checkbox" aria-labelledby="p-variants-label" />
	<h3 id="p-variants-label" class="vector-menu-heading">
		<span>Variants</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"></ul>
		
	</div>
</nav>

		</div>
		<div id="right-navigation">
			<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-views" class="mw-portlet mw-portlet-views vector-menu vector-menu-tabs" aria-labelledby="p-views-label" role="navigation" 
	 >
	<h3 id="p-views-label" class="vector-menu-heading">
		<span>Views</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="ca-view" class="selected"><a href="/wiki/Pulse-width_modulation">Read</a></li><li id="ca-edit"><a href="/w/index.php?title=Pulse-width_modulation&amp;action=edit" title="Edit this page [e]" accesskey="e">Edit</a></li><li id="ca-history"><a href="/w/index.php?title=Pulse-width_modulation&amp;action=history" title="Past revisions of this page [h]" accesskey="h">View history</a></li></ul>
		
	</div>
</nav>

			<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-cactions" class="mw-portlet mw-portlet-cactions emptyPortlet vector-menu vector-menu-dropdown" aria-labelledby="p-cactions-label" role="navigation" 
	 >
	<input type="checkbox" class="vector-menu-checkbox" aria-labelledby="p-cactions-label" />
	<h3 id="p-cactions-label" class="vector-menu-heading">
		<span>More</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"></ul>
		
	</div>
</nav>

			<div id="p-search" role="search" >
	<h3 >
		<label for="searchInput">Search</label>
	</h3>
	<form action="/w/index.php" id="searchform">
		<div id="simpleSearch" data-search-loc="header-navigation">
			<input type="search" name="search" placeholder="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput"/>
			<input type="hidden" name="title" value="Special:Search"/>
			<input type="submit" name="fulltext" value="Search" title="Search Wikipedia for this text" id="mw-searchButton" class="searchButton mw-fallbackSearchButton"/>
			<input type="submit" name="go" value="Go" title="Go to a page with this exact name if it exists" id="searchButton" class="searchButton"/>
		</div>
	</form>
</div>

		</div>
	</div>
	
<div id="mw-panel">
	<div id="p-logo" role="banner">
		<a class="mw-wiki-logo" href="/wiki/Main_Page"
			title="Visit the main page"></a>
	</div>
	<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-navigation" class="mw-portlet mw-portlet-navigation vector-menu vector-menu-portal portal" aria-labelledby="p-navigation-label" role="navigation" 
	 >
	<h3 id="p-navigation-label" class="vector-menu-heading">
		<span>Navigation</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="n-mainpage-description"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z">Main page</a></li><li id="n-contents"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia">Contents</a></li><li id="n-currentevents"><a href="/wiki/Portal:Current_events" title="Articles related to current events">Current events</a></li><li id="n-randompage"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x">Random article</a></li><li id="n-aboutsite"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works">About Wikipedia</a></li><li id="n-contactpage"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia">Contact us</a></li><li id="n-sitesupport"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&amp;utm_medium=sidebar&amp;utm_campaign=C13_en.wikipedia.org&amp;uselang=en" title="Support us by donating to the Wikimedia Foundation">Donate</a></li></ul>
		
	</div>
</nav>

	<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-interaction" class="mw-portlet mw-portlet-interaction vector-menu vector-menu-portal portal" aria-labelledby="p-interaction-label" role="navigation" 
	 >
	<h3 id="p-interaction-label" class="vector-menu-heading">
		<span>Contribute</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="n-help"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia">Help</a></li><li id="n-introduction"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia">Learn to edit</a></li><li id="n-portal"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors">Community portal</a></li><li id="n-recentchanges"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r">Recent changes</a></li><li id="n-upload"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Add images or other media for use on Wikipedia">Upload file</a></li></ul>
		
	</div>
</nav>
<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-tb" class="mw-portlet mw-portlet-tb vector-menu vector-menu-portal portal" aria-labelledby="p-tb-label" role="navigation" 
	 >
	<h3 id="p-tb-label" class="vector-menu-heading">
		<span>Tools</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="t-whatlinkshere"><a href="/wiki/Special:WhatLinksHere/Pulse-width_modulation" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j">What links here</a></li><li id="t-recentchangeslinked"><a href="/wiki/Special:RecentChangesLinked/Pulse-width_modulation" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k">Related changes</a></li><li id="t-upload"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u">Upload file</a></li><li id="t-specialpages"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q">Special pages</a></li><li id="t-permalink"><a href="/w/index.php?title=Pulse-width_modulation&amp;oldid=1003507942" title="Permanent link to this revision of this page">Permanent link</a></li><li id="t-info"><a href="/w/index.php?title=Pulse-width_modulation&amp;action=info" title="More information about this page">Page information</a></li><li id="t-cite"><a href="/w/index.php?title=Special:CiteThisPage&amp;page=Pulse-width_modulation&amp;id=1003507942&amp;wpFormIdentifier=titleform" title="Information on how to cite this page">Cite this page</a></li><li id="t-wikibase"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q585184" title="Structured data on this page hosted by Wikidata [g]" accesskey="g">Wikidata item</a></li></ul>
		
	</div>
</nav>
<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-coll-print_export" class="mw-portlet mw-portlet-coll-print_export vector-menu vector-menu-portal portal" aria-labelledby="p-coll-print_export-label" role="navigation" 
	 >
	<h3 id="p-coll-print_export-label" class="vector-menu-heading">
		<span>Print/export</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li id="coll-download-as-rl"><a href="/w/index.php?title=Special:DownloadAsPdf&amp;page=Pulse-width_modulation&amp;action=show-download-screen" title="Download this page as a PDF file">Download as PDF</a></li><li id="t-print"><a href="/w/index.php?title=Pulse-width_modulation&amp;printable=yes" title="Printable version of this page [p]" accesskey="p">Printable version</a></li></ul>
		
	</div>
</nav>
<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-wikibase-otherprojects" class="mw-portlet mw-portlet-wikibase-otherprojects vector-menu vector-menu-portal portal" aria-labelledby="p-wikibase-otherprojects-label" role="navigation" 
	 >
	<h3 id="p-wikibase-otherprojects-label" class="vector-menu-heading">
		<span>In other projects</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li class="wb-otherproject-link wb-otherproject-commons"><a href="https://commons.wikimedia.org/wiki/Category:Pulse_width_modulation" hreflang="en">Wikimedia Commons</a></li></ul>
		
	</div>
</nav>

	<!-- Please do not use role attribute as CSS selector, it is deprecated. -->
<nav id="p-lang" class="mw-portlet mw-portlet-lang vector-menu vector-menu-portal portal" aria-labelledby="p-lang-label" role="navigation" 
	 >
	<h3 id="p-lang-label" class="vector-menu-heading">
		<span>Languages</span>
	</h3>
	<div class="vector-menu-content">
		<ul class="vector-menu-content-list"><li class="interlanguage-link interwiki-ar"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B6%D9%85%D9%8A%D9%86_%D8%B9%D8%B1%D8%B6_%D8%A7%D9%84%D9%86%D8%A8%D8%B6%D8%A9" title="تضمين عرض النبضة – Arabic" lang="ar" hreflang="ar" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-be"><a href="https://be.wikipedia.org/wiki/%D0%A8%D1%8B%D1%80%D0%BE%D1%82%D0%BD%D0%B0-%D1%96%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D1%8B%D1%8F" title="Шыротна-імпульсная мадуляцыя – Belarusian" lang="be" hreflang="be" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-ca"><a href="https://ca.wikipedia.org/wiki/Modulaci%C3%B3_per_amplada_de_polsos" title="Modulació per amplada de polsos – Catalan" lang="ca" hreflang="ca" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs"><a href="https://cs.wikipedia.org/wiki/Pulzn%C4%9B_%C5%A1%C3%AD%C5%99kov%C3%A1_modulace" title="Pulzně šířková modulace – Czech" lang="cs" hreflang="cs" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da"><a href="https://da.wikipedia.org/wiki/Pulsbreddemodulation" title="Pulsbreddemodulation – Danish" lang="da" hreflang="da" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de"><a href="https://de.wikipedia.org/wiki/Pulsdauermodulation" title="Pulsdauermodulation – German" lang="de" hreflang="de" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et"><a href="https://et.wikipedia.org/wiki/Pulsilaiusmodulatsioon" title="Pulsilaiusmodulatsioon – Estonian" lang="et" hreflang="et" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-es"><a href="https://es.wikipedia.org/wiki/Modulaci%C3%B3n_por_ancho_de_pulsos" title="Modulación por ancho de pulsos – Spanish" lang="es" hreflang="es" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eu"><a href="https://eu.wikipedia.org/wiki/Pultsu_zabalera_modulazio" title="Pultsu zabalera modulazio – Basque" lang="eu" hreflang="eu" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%88%D9%84%D8%A7%D8%B3%DB%8C%D9%88%D9%86_%D9%BE%D9%87%D9%86%D8%A7%DB%8C_%D9%BE%D8%A7%D9%84%D8%B3" title="مدولاسیون پهنای پالس – Persian" lang="fa" hreflang="fa" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr"><a href="https://fr.wikipedia.org/wiki/Modulation_de_largeur_d%27impulsion" title="Modulation de largeur d&#039;impulsion – French" lang="fr" hreflang="fr" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko"><a href="https://ko.wikipedia.org/wiki/%ED%8E%84%EC%8A%A4_%ED%8F%AD_%EB%B3%80%EC%A1%B0" title="펄스 폭 변조 – Korean" lang="ko" hreflang="ko" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hi"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A5%8D%E0%A4%AA%E0%A4%82%E0%A4%A6-%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%B0_%E0%A4%AE%E0%A5%89%E0%A4%A1%E0%A5%81%E0%A4%B2%E0%A4%A8" title="स्पंद-विस्तार मॉडुलन – Hindi" lang="hi" hreflang="hi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-it"><a href="https://it.wikipedia.org/wiki/Modulazione_di_larghezza_d%27impulso" title="Modulazione di larghezza d&#039;impulso – Italian" lang="it" hreflang="it" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-lv"><a href="https://lv.wikipedia.org/wiki/Impulsu_platuma_modul%C4%81cija" title="Impulsu platuma modulācija – Latvian" lang="lv" hreflang="lv" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-hu"><a href="https://hu.wikipedia.org/wiki/Impulzussz%C3%A9less%C3%A9g-modul%C3%A1ci%C3%B3" title="Impulzusszélesség-moduláció – Hungarian" lang="hu" hreflang="hu" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mn"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81_%D3%A9%D1%80%D0%B3%D3%A9%D0%BD%D0%B8%D0%B9_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86" title="Импульс өргөний модуляц – Mongolian" lang="mn" hreflang="mn" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-nl"><a href="https://nl.wikipedia.org/wiki/Pulsbreedtemodulatie" title="Pulsbreedtemodulatie – Dutch" lang="nl" hreflang="nl" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja"><a href="https://ja.wikipedia.org/wiki/%E3%83%91%E3%83%AB%E3%82%B9%E5%B9%85%E5%A4%89%E8%AA%BF" title="パルス幅変調 – Japanese" lang="ja" hreflang="ja" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no"><a href="https://no.wikipedia.org/wiki/Pulsbreddemodulasjon" title="Pulsbreddemodulasjon – Norwegian Bokmål" lang="nb" hreflang="nb" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-pl"><a href="https://pl.wikipedia.org/wiki/Modulacja_szeroko%C5%9Bci_impuls%C3%B3w" title="Modulacja szerokości impulsów – Polish" lang="pl" hreflang="pl" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt"><a href="https://pt.wikipedia.org/wiki/Modula%C3%A7%C3%A3o_por_largura_de_pulso" title="Modulação por largura de pulso – Portuguese" lang="pt" hreflang="pt" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ru"><a href="https://ru.wikipedia.org/wiki/%D0%A8%D0%B8%D1%80%D0%BE%D1%82%D0%BD%D0%BE-%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%BD%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D0%B8%D1%8F" title="Широтно-импульсная модуляция – Russian" lang="ru" hreflang="ru" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sk"><a href="https://sk.wikipedia.org/wiki/Impulzov%C3%A1_%C5%A1%C3%ADrkov%C3%A1_modul%C3%A1cia" title="Impulzová šírková modulácia – Slovak" lang="sk" hreflang="sk" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl"><a href="https://sl.wikipedia.org/wiki/Pulzno_%C5%A1irinska_modulacija" title="Pulzno širinska modulacija – Slovenian" lang="sl" hreflang="sl" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-fi"><a href="https://fi.wikipedia.org/wiki/Pulssinleveysmodulaatio" title="Pulssinleveysmodulaatio – Finnish" lang="fi" hreflang="fi" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv"><a href="https://sv.wikipedia.org/wiki/Pulsbreddsmodulering" title="Pulsbreddsmodulering – Swedish" lang="sv" hreflang="sv" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%81%E0%AE%9F%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81_%E0%AE%85%E0%AE%95%E0%AE%B2_%E0%AE%95%E0%AF%81%E0%AE%B1%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%87%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="துடிப்பு அகல குறிப்பேற்றம் – Tamil" lang="ta" hreflang="ta" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-uk"><a href="https://uk.wikipedia.org/wiki/%D0%A8%D0%B8%D1%80%D0%BE%D1%82%D0%BD%D0%BE-%D1%96%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%BD%D0%B0_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8F%D1%86%D1%96%D1%8F" title="Широтно-імпульсна модуляція – Ukrainian" lang="uk" hreflang="uk" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-vi"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%81u_ch%E1%BA%BF_%C4%91%E1%BB%99_r%E1%BB%99ng_xung" title="Điều chế độ rộng xung – Vietnamese" lang="vi" hreflang="vi" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-zh"><a href="https://zh.wikipedia.org/wiki/%E8%84%88%E8%A1%9D%E5%AF%AC%E5%BA%A6%E8%AA%BF%E8%AE%8A" title="脈衝寬度調變 – Chinese" lang="zh" hreflang="zh" class="interlanguage-link-target">中文</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/Q585184#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div>
	</div>
</nav>

</div>

</div>
<footer id="footer" class="mw-footer" role="contentinfo" >
	<ul id="footer-info" >
	<li id="footer-info-lastmod"> This page was last edited on 29 January 2021, at 09:30<span class="anonymous-show">&#160;(UTC)</span>.</li>
	<li id="footer-info-copyright">Text is available under the <a rel="license" href="//en.wikipedia.org/wiki/Wikipedia:Text_of_Creative_Commons_Attribution-ShareAlike_3.0_Unported_License">Creative Commons Attribution-ShareAlike License</a><a rel="license" href="//creativecommons.org/licenses/by-sa/3.0/" style="display:none;"></a>;
additional terms may apply.  By using this site, you agree to the <a href="//foundation.wikimedia.org/wiki/Terms_of_Use">Terms of Use</a> and <a href="//foundation.wikimedia.org/wiki/Privacy_policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a href="//www.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/Privacy_policy" class="extiw" title="wmf:Privacy policy">Privacy policy</a></li>
	<li id="footer-places-about"><a href="/wiki/Wikipedia:About" title="Wikipedia:About">About Wikipedia</a></li>
	<li id="footer-places-disclaimer"><a href="/wiki/Wikipedia:General_disclaimer" title="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-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Pulse-width_modulation&amp;mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li>
	<li id="footer-places-developers"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/How_to_contribute">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/Cookie_statement">Cookie statement</a></li>
</ul>

	<ul id="footer-icons" class="noprint">
	<li id="footer-copyrightico"><a href="https://wikimediafoundation.org/"><img src="/static/images/footer/wikimedia-button.png" srcset="/static/images/footer/wikimedia-button-1.5x.png 1.5x, /static/images/footer/wikimedia-button-2x.png 2x" width="88" height="31" alt="Wikimedia Foundation" loading="lazy" /></a></li>
	<li id="footer-poweredbyico"><a href="https://www.mediawiki.org/"><img src="/static/images/footer/poweredby_mediawiki_88x31.png" alt="Powered by MediaWiki" srcset="/static/images/footer/poweredby_mediawiki_132x47.png 1.5x, /static/images/footer/poweredby_mediawiki_176x62.png 2x" width="88" height="31" loading="lazy"/></a></li>
</ul>

</footer>


<script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgPageParseReport":{"limitreport":{"cputime":"0.508","walltime":"0.664","ppvisitednodes":{"value":1059,"limit":1000000},"postexpandincludesize":{"value":25517,"limit":2097152},"templateargumentsize":{"value":576,"limit":2097152},"expansiondepth":{"value":13,"limit":40},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":26995,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00%  494.560      1 -total"," 40.84%  201.964      1 Template:Reflist"," 27.05%  133.762      3 Template:Cite_web"," 18.09%   89.445      1 Template:More_footnotes"," 15.74%   77.868      1 Template:Modulation_techniques"," 11.57%   57.212      1 Template:Commons_category"," 11.40%   56.404      1 Template:Ambox"," 10.78%   53.291      1 Template:Sister_project"," 10.12%   50.058      1 Template:Side_box","  5.89%   29.146      3 Template:Cite_journal"]},"scribunto":{"limitreport-timeusage":{"value":"0.259","limit":"10.000"},"limitreport-memusage":{"value":4727744,"limit":52428800}},"cachereport":{"origin":"mw1267","timestamp":"20210402154806","ttl":2592000,"transientcontent":false}}});});</script>
<script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Pulse-width modulation","url":"https:\/\/en.wikipedia.org\/wiki\/Pulse-width_modulation","sameAs":"http:\/\/www.wikidata.org\/entity\/Q585184","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q585184","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":"2002-09-06T11:35:24Z","dateModified":"2021-01-29T09:30:51Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/8\/8e\/PWM%2C_3-level.svg","headline":"modulation technique"}</script>
<script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgBackendResponseTime":163,"wgHostname":"mw1364"});});</script>
</body></html>