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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>The <b>open-loop gain</b> of an electronic <a href="Amplifier" title="Amplifier">amplifier</a> is the <a href="Gain_(electronics)" title="Gain (electronics)">gain</a> obtained when no overall <a href="Feedback" title="Feedback">feedback</a> is used in the <a href="Electrical_network" title="Electrical network">circuit</a>.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>The open-loop gain of many electronic amplifiers is exceedingly high (by design) – an <i>ideal</i> <a href="Operational_amplifier" title="Operational amplifier">operational amplifier</a> (op-amp) has infinite open-loop gain. Typically an op-amp may have a maximal open-loop gain of around <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 10^{5}}">

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<annotation encoding="application/x-tex">{\displaystyle 10^{5}}</annotation>

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</math></span><img src="./d7310d2ac4ddefd259b8a2c7c8fb89c6a9ea11a8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.676ex;" alt="{\displaystyle 10^{5}}" loading="lazy"></span>, or 100 <a href="Decibel" title="Decibel">dB</a>. An op-amp with a large open-loop gain offers high precision when used as an <a href="Inverting_amplifier" class="mw-redirect" title="Inverting amplifier">inverting amplifier</a>.

</p><p>Normally, <a href="Negative_feedback" title="Negative feedback">negative feedback</a> is applied around an amplifier with high open-loop gain, to reduce the gain of the complete <a href="Electrical_network" title="Electrical network">circuit</a> to a desired value.

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<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>

<p>The definition of open-loop gain (at a fixed frequency) is

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<annotation encoding="application/x-tex">{\displaystyle A_{\text{OL}}={\frac {V_{\text{out}}}{V^{+}-V^{-}}},}</annotation>

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</math></span><img src="./ac57c24785541e95e8a557785abbe6c82b4ba7b4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:18.559ex; height:5.509ex;" alt="{\displaystyle A_{\text{OL}}={\frac {V_{\text{out}}}{V^{+}-V^{-}}},}" loading="lazy"></span><sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></dd></dl>

<p>where <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 V^{+}-V^{-}}">

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<annotation encoding="application/x-tex">{\displaystyle V^{+}-V^{-}}</annotation>

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</math></span><img src="./b6626fa802296b6353c9d4f432dd77f225a21c5f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.696ex; height:2.676ex;" alt="{\displaystyle V^{+}-V^{-}}" loading="lazy"></span> is the input voltage difference that is being amplified. (The dependence on frequency is not displayed here.)

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<div class="mw-heading mw-heading2"><h2 id="Role_in_non-ideal_gain">Role in non-ideal gain</h2></div>

<p>The open-loop gain is a physical attribute of an operational amplifier that is often finite in comparison to the ideal gain. While open-loop gain is the gain when there is no feedback in a circuit, an operational amplifier will often be configured to use a feedback configuration such that its gain will be controlled by the feedback circuit components.

</p><p>Take the case of an inverting operational amplifier configuration. If the resistor between the single output node and the inverting input node is <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_{2}}">

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<annotation encoding="application/x-tex">{\displaystyle R_{2}}</annotation>

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</math></span><img src="./35f571121c264178676d1df8ab899f238a39bc2c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle R_{2}}" loading="lazy"></span> and the resistor between a source voltage and the inverting input node is <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_{1}}">

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<annotation encoding="application/x-tex">{\displaystyle R_{1}}</annotation>

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</math></span><img src="./c1d63c96f59d98589d923c4f0b04222feaa7283e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle R_{1}}" loading="lazy"></span>, then the calculated gain of such a circuit at the output terminal is defined, assuming infinite gain in the amplifier, is:

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<annotation encoding="application/x-tex">{\displaystyle G=-{\frac {R_{2}}{R_{1}}}}</annotation>

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</math></span><img src="./1eddfe04ff0781b72c37d3b71c321c59739dd9ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.388ex; height:5.509ex;" alt="{\displaystyle G=-{\frac {R_{2}}{R_{1}}}}" loading="lazy"></span></dd></dl>

<p>However, including the finite open-loop gain <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 A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> reduces the gain slightly, to:

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<annotation encoding="application/x-tex">{\displaystyle G={\frac {-{\frac {R_{2}}{R_{1}}}}{1+(1+{\frac {R_{2}}{R_{1}}}){\frac {1}{A}}}}}</annotation>

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</math></span><img src="./d3ab3ee5459cd9bd42e5024142c895009f89aea5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:20.56ex; height:9.509ex;" alt="{\displaystyle G={\frac {-{\frac {R_{2}}{R_{1}}}}{1+(1+{\frac {R_{2}}{R_{1}}}){\frac {1}{A}}}}}" loading="lazy"></span></dd></dl>

<p>For example, if <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 {\frac {R_{2}}{R_{1}}}=2}">

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<annotation encoding="application/x-tex">{\displaystyle {\frac {R_{2}}{R_{1}}}=2}</annotation>

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</math></span><img src="./00a4452bc3df9f04e9ce2119633c20113bbb166e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:7.915ex; height:5.509ex;" alt="{\displaystyle {\frac {R_{2}}{R_{1}}}=2}" loading="lazy"></span> and <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 A=10^{4}}">

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</math></span><img src="./1fdbc1c172832934ec512b866ec60bb65bda92dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.221ex; height:2.676ex;" alt="{\displaystyle A=10^{4}}" loading="lazy"></span>, then <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 G=}">

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<annotation encoding="application/x-tex">{\displaystyle G=}</annotation>

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</math></span><img src="./eb05bfee3ea6feb86f0005a82945ce08939910be.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.28ex; height:2.176ex;" alt="{\displaystyle G=}" loading="lazy"></span> −1.9994 instead of exactly −2.

</p><p>(The second equation becomes effectively the same as the first equation as <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 A}">

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> approaches infinity.)

</p><p>The open-loop gain can be important for computing the actual gain of an operational amplifier network, where the assumption of infinite open-loop gain is inaccurate.

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<div class="mw-heading mw-heading2"><h2 id="Operational_amplifiers">Operational amplifiers</h2></div>

<p>The open-loop gain of an operational amplifier falls very rapidly with increasing <a href="Frequency" title="Frequency">frequency</a>. Along with <a href="Slew_rate" title="Slew rate">slew rate</a>, this is one of the reasons why operational amplifiers have limited <a href="Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>.

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<ul><li><a href="Gain%E2%80%93bandwidth_product" title="Gain–bandwidth product">Gain–bandwidth product</a></li>

<li><a href="Loop_gain" title="Loop gain">Loop gain</a> (includes both the open-loop gain and the feedback attenuation)</li>

<li><a href="Negative-feedback_amplifier#Summary_of_terms" title="Negative-feedback amplifier">Summary of negative feedback amplifier terms</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://developerhelp.microchip.com/xwiki/bin/view/products/amplifiers-linear/operational-amplifier-ics/introduction/open-loop-gain/">"Open Loop Gain - Developer Help"</a>. <i>developerhelp.microchip.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-13</span></span>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sciencedirect.com/topics/engineering/open-loop-gain">"Open-Loop Gain - an overview | ScienceDirect Topics"</a>. <i>www.sciencedirect.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-13</span></span>.</cite></span>

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