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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Restwelligkeit</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Wenn eine <a href="Gleichspannung" title="Gleichspannung">Gleichspannung</a> aus sinusförmiger <a href="Wechselspannung" title="Wechselspannung">Wechselspannung</a> durch <a href="Gleichrichtung" class="mw-redirect" title="Gleichrichtung">Gleichrichtung</a> entstehen soll, so entsteht immer eine <a href="Mischspannung" title="Mischspannung">Mischspannung</a> aus Gleich- und überlagerter Wechselspannung. Einfache Schaltungen zur Verminderung des Wechselanteils verwenden einen <a href="Gl%C3%A4ttungskondensator" title="Glättungskondensator">Glättungskondensator</a> oder eine <a href="Gl%C3%A4ttungsdrossel" title="Glättungsdrossel">Glättungsdrossel</a>, oft beides zusammen. Die Tatsache, dass trotz Glättung noch ein (dann meistens unerwünschter) Wechselspannungsanteil bestehen bleibt, wird mit <b>Restwelligkeit</b> bezeichnet. Auch geregelte <a href="Netzteil" title="Netzteil">Netzteile</a> und <a href="Schaltnetzteil" title="Schaltnetzteil">Schaltnetzteile</a> haben eine, wenn auch wesentlich geringere, Restwelligkeit.
</p>
<div class="mw-heading mw-heading2"><h2 id="Definitionen">Definitionen</h2></div>
<p>Die nachfolgenden Definitionen gelten in gleicher Weise für <a href="Elektrische_Spannung" title="Elektrische Spannung">elektrische Spannung</a> und <a href="Stromst%C3%A4rke" class="mw-redirect" title="Stromstärke">Stromstärke</a>. Zur Vereinfachung beschränkt sich dieser Text auf die Spannung.
</p><p>Eine Mischgröße <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>u</mi>
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<annotation encoding="application/x-tex">{\displaystyle u}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}" loading="lazy"></span> setzt sich zusammen aus einem Gleichanteil und einem Wechselanteil
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=U_{-}+u_{\sim }\ .}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>u</mi>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
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<mo>+</mo>
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<mi>u</mi>
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<mo>∼<!-- ∼ --></mo>
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<mtext> </mtext>
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<annotation encoding="application/x-tex">{\displaystyle u=U_{-}+u_{\sim }\ .}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6849dd56ed4ef962f5ec8516c4c40323906692af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.435ex; height:2.509ex;" alt="{\displaystyle u=U_{-}+u_{\sim }\ .}" loading="lazy"></span></dd></dl>
<p>Zur quantitativen Beschreibung des Wechselanteils gibt die hierzu maßgebliche <a href="Normung" title="Normung">Norm</a> DIN 40110-1 („Wechselstromgrößen“; März 1994) drei Größenverhältnisse an:
</p>
<ul><li><i>Schwingungsgehalt</i> als Verhältnis <a href="Effektivwert" title="Effektivwert">Effektivwert</a> des Wechselanteils <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\sim }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{\sim }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3d514c3d8f63553a117dcdd8f0eba21a31d4b5f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.132ex; margin-bottom: -0.54ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle U_{\sim }}" loading="lazy"></span> zu Effektivwert der gesamten Mischgröße <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>U</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/458a728f53b9a0274f059cd695e067c430956025.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}" loading="lazy"></span></li></ul>
<dl><dd><dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{u}={\frac {U_{\sim }}{U}}\ ,}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>s</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>u</mi>
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</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
</mrow>
</msub>
<mi>U</mi>
</mfrac>
</mrow>
<mtext> </mtext>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle s_{u}={\frac {U_{\sim }}{U}}\ ,}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0f4461fd41c946975b162c39d35c34c66e2b5c21.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.523ex; height:5.343ex;" alt="{\displaystyle s_{u}={\frac {U_{\sim }}{U}}\ ,}" loading="lazy"></span></dd></dl></dd></dl>
<ul><li><i>Welligkeit</i> als Verhältnis Effektivwert des Wechselanteils <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\sim }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{\sim }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3d514c3d8f63553a117dcdd8f0eba21a31d4b5f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.132ex; margin-bottom: -0.54ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle U_{\sim }}" loading="lazy"></span> zu Betrag des <a href="Gleichwert" title="Gleichwert">Gleichwertes</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{-}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{-}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0343e3195e2d26d8b0b64707c4a4c9c10cdfd552.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle U_{-}}" loading="lazy"></span></li></ul>
<dl><dd><dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{u}={\frac {U_{\sim }}{|U_{-}|}}\ ,}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>u</mi>
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</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
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</msub>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
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</msub>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
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</mfrac>
</mrow>
<mtext> </mtext>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r_{u}={\frac {U_{\sim }}{|U_{-}|}}\ ,}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5cd92cf77abfd387e2b3b7aaa6075e7252765f4b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.775ex; height:6.009ex;" alt="{\displaystyle r_{u}={\frac {U_{\sim }}{|U_{-}|}}\ ,}" loading="lazy"></span></dd></dl></dd></dl>
<ul><li><i>Schwankungswelligkeit</i> (Riffelfaktor) als Verhältnis Schwingungsbreite <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{e}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>e</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{e}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e82b758ddad8d8d1ff96696823b51ab14f7d1e05.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.586ex; height:2.509ex;" alt="{\displaystyle U_{e}}" loading="lazy"></span> oder <a href="Spitze-Tal-Wert" title="Spitze-Tal-Wert">Spitze-Tal-Wert</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<munder>
<mover>
<mi>u</mi>
<msub>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∧<!-- ∧ --></mo>
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</msub>
</mover>
<msup>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∨<!-- ∨ --></mo>
</mrow>
</msup>
</munder>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fc878911f317ad189f33a3528a956b2a3ed939f3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:1.33ex; height:5.009ex;" alt="{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}" loading="lazy"></span> (früher Spitze-Spitze-Wert <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{ss}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>s</mi>
<mi>s</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{ss}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f655b2c567e0de5995ef4a88cb51787b42bd4ac9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.362ex; height:2.509ex;" alt="{\displaystyle U_{ss}}" loading="lazy"></span>) zu Betrag des Gleichwertes <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{-}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{-}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0343e3195e2d26d8b0b64707c4a4c9c10cdfd552.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle U_{-}}" loading="lazy"></span></li></ul>
<dl><dd><dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{u}={\frac {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}{|U_{-}|}}\ .}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>u</mi>
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</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<munder>
<mover>
<mi>u</mi>
<msub>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∧<!-- ∧ --></mo>
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</msub>
</mover>
<msup>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∨<!-- ∨ --></mo>
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</msup>
</munder>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
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</msub>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
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<mtext> </mtext>
<mo>.</mo>
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<annotation encoding="application/x-tex">{\displaystyle q_{u}={\frac {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}{|U_{-}|}}\ .}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8df795430d61195c761e015c7501e2e9b725156f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.764ex; height:8.509ex;" alt="{\displaystyle q_{u}={\frac {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}{|U_{-}|}}\ .}" loading="lazy"></span></dd></dl></dd></dl>
<p>Der Schwingungsgehalt kann Werte von 0 (bei Gleichspannung) bis 1 (Wechselspannung) bzw. 0 … 100 % annehmen. <br> Die Welligkeit und die Schwankungswelligkeit liegen im Bereich 0 (Gleichspannung) … ∞ (Wechselspannung). <br> Gelegentlich wird statt der Welligkeit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{u}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>u</mi>
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</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r_{u}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a1b33f1518fd9b64ad2cf5c1272813b77cab949a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.221ex; height:2.009ex;" alt="{\displaystyle r_{u}}" loading="lazy"></span> auch ihr <a href="Logarithmische_Gr%C3%B6%C3%9Fe#Maße" title="Logarithmische Größe">logarithmisches Maß</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lg r_{u}\cdot 20{\text{ dB}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>lg</mi>
<mo><!-- --></mo>
<msub>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>u</mi>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<mn>20</mn>
<mrow class="MJX-TeXAtom-ORD">
<mtext> dB</mtext>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lg r_{u}\cdot 20{\text{ dB}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6b254b31c755b8ae8e5e1c1ccade17bd56d62c9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.94ex; height:2.509ex;" alt="{\displaystyle \lg r_{u}\cdot 20{\text{ dB}}}" loading="lazy"></span> angegeben.
</p><p>Nicht in dieser Norm genannt wird die <i>Restwelligkeit</i> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ω<!-- ω --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \omega }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/48eff443f9de7a985bb94ca3bde20813ea737be8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" loading="lazy"></span>. Sie wird definiert als
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\sqrt {F^{2}-1}}\ .}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ω<!-- ω --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msup>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>1</mn>
</msqrt>
</mrow>
<mtext> </mtext>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \omega ={\sqrt {F^{2}-1}}\ .}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c5d4a03bfab94514e51b1bd9e361529ea6a5720e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.967ex; height:3.509ex;" alt="{\displaystyle \omega ={\sqrt {F^{2}-1}}\ .}" loading="lazy"></span></dd></dl>
<p>Darin ist der <a href="Formfaktor_(Elektrotechnik)" title="Formfaktor (Elektrotechnik)">Formfaktor</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>F</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/545fd099af8541605f7ee55f08225526be88ce57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}" loading="lazy"></span> das Verhältnis Effektivwert zu <a href="Gleichrichtwert" title="Gleichrichtwert">Gleichrichtwert</a>
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><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={\frac {U}{\,{\overline {|u|}}\,}}\ ,}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>F</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>U</mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
</mrow>
<mo accent="false">¯<!-- ¯ --></mo>
</mover>
</mrow>
<mspace width="thinmathspace"></mspace>
</mrow>
</mfrac>
</mrow>
<mtext> </mtext>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F={\frac {U}{\,{\overline {|u|}}\,}}\ ,}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f139f01060824a5ab804ed4ca19186d6699e9c7f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:10.415ex; height:6.676ex;" alt="{\displaystyle F={\frac {U}{\,{\overline {|u|}}\,}}\ ,}" loading="lazy"></span></dd></dl>
<p>wobei im vorliegenden Zusammenhang (Spannung ohne Vorzeichenwechsel) Gleichrichtwert dasselbe ist wie Betrag des Gleichwertes. Mit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U^{2}={U_{-}}^{2}+{U_{\sim }}^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>=</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U^{2}={U_{-}}^{2}+{U_{\sim }}^{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/17577d83f363187c72fdcbe95424cbee3ce715c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.139ex; height:3.009ex;" alt="{\displaystyle U^{2}={U_{-}}^{2}+{U_{\sim }}^{2}}" loading="lazy"></span> stimmt nach elementarer Umrechnung die Definition der Restwelligkeit mit der oben gegebenen Definition der Welligkeit überein.
</p><p>Als Kenngröße für die Restwelligkeit wird teilweise nur der Wechselanteil angegeben als <i>Effektivwert</i> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\sim }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>U</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∼<!-- ∼ --></mo>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle U_{\sim }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3d514c3d8f63553a117dcdd8f0eba21a31d4b5f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.132ex; margin-bottom: -0.54ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle U_{\sim }}" loading="lazy"></span> oder <i>Spitze-Tal-Wert</i> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<munder>
<mover>
<mi>u</mi>
<msub>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∧<!-- ∧ --></mo>
</mrow>
</msub>
</mover>
<msup>
<mrow class="MJX-TeXAtom-ORD">
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∨<!-- ∨ --></mo>
</mrow>
</msup>
</munder>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fc878911f317ad189f33a3528a956b2a3ed939f3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:1.33ex; height:5.009ex;" alt="{\displaystyle {\underset {{}^{\lor }}{\overset {{}_{\land }}{u}}}}" loading="lazy"></span>. Solche Angaben erfolgen in Millivolt oder Volt.
</p>
<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Andreas Friesecke: <i>Die Audio-Enzyklopädie.</i> Ein Nachschlagewerk für Tontechniker, 2. Auflage, Walter De Gruyter GmbH, Berlin 2014, ISBN 978-3-11-034013-6.</li>
<li>Theodor Wasserrab: <i>Schaltungslehre der Stromrichtertechnik.</i> Springer Verlag Berlin/Göttingen/Heidelberg, Berlin 1962.</li></ul>
<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>
<ul><li><a href="Stromflusswinkel" title="Stromflusswinkel">Stromflusswinkel</a></li>
<li><a href="Rippelstrom" title="Rippelstrom">Rippelstrom</a></li>
<li><a href="Klirrfaktor" title="Klirrfaktor">Klirrfaktor</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<ul><li><a rel="nofollow" class="external text" href="https://service.projektlabor.tu-berlin.de/projekte/sens-o-thek/unterlagen/referate/Folien_Spannung-Glaettung_Le-Dang_2009-06-25.pdf">Spannung glätten</a> (abgerufen am 21. Januar 2016)</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
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