Open-loop gain: Difference between revisions

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The '''open-loop gain''' of an electronic [[amplifier]] is the [[gain (electronics)|gain]] obtained when no overall [[feedback]] is used in the [[electrical network|circuit]].<ref name=":0" /><ref>{{Cite web |title=Open-Loop Gain - an overview {{!}} ScienceDirect Topics |url=https://www.sciencedirect.com/topics/engineering/open-loop-gain |access-date=2024-10-13 |website=www.sciencedirect.com}}</ref>

==Definition==

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

The open-loop gain of many electronic amplifiers is exceedingly high (by design) – an ''ideal'' [[operational amplifier]] (op-amp) has infinite open-loop gain. Typically an op-amp may have a maximal open-loop gain of around <math>10^5</math>, or 100 [[Decibel|dB]]. An op-amp with a large open-loop gain offers high precision when used as an [[inverting amplifier]].

<math>A_{\text{OL}}=\frac{V_{\text{out}}}{\left(V^+-V^-\right)},</math>

Normally, [[negative feedback]] is applied around an amplifier with high open-loop gain, to reduce the gain of the complete [[electrical network|circuit]] to a desired value.

where <math>V^+-V^-</math> is the input voltage difference that is being amplified. The dependence on frequency is not displayed here.

==Definition==

== Role in non-ideal gain ==

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

:<math>A_\text{OL} = \frac{V_\text{out}}{V^+ - V^-},</math><ref name=":0">{{Cite web |title=Open Loop Gain - Developer Help |url=https://developerhelp.microchip.com/xwiki/bin/view/products/amplifiers-linear/operational-amplifier-ics/introduction/open-loop-gain/ |access-date=2024-10-13 |website=developerhelp.microchip.com}}</ref>

where <math>V^ + -V^-</math> is the input voltage difference that is being amplified. (The dependence on frequency is not displayed here.)

The open-loop gain is a physical attribute of an operational amplifier that is often finite in comparison{{Clarify|date=March 2016}} to the usual gain, denoted <math>G</math>. 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.

== Role in non-ideal gain ==

Take the case of an inverting operational amplifier configuration. If the resistor between the single output node and the inverting input node is <math>R_2</math> and the resistor between a source voltage and the inverting input node is <math>R_1</math>, then the ideal gain for such a circuit at the output terminal is defined, ideally, to be:

The open-loop gain is a physical attribute of an operational amplifier that is often finite in comparison{{Clarify|date=March 2016}} to the usualideal gain, denoted <math>G</math>. 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.

Take the case of an inverting operational amplifier configuration. If the resistor between the single output node and the inverting input node is <math>R_2</math> and the resistor between a source voltage and the inverting input node is <math>R_1</math>, then the idealcalculated gain forof such a circuit at the output terminal is defined, ideally,assuming toinfinite begain in the amplifier, is:

:<math>G = - \frac{R_2}{R_1}</math>

However, withincluding the use offinite open-loop gain, <math>A</math> reduces the equationgain slightly, becomesto:

:<math>G = \frac{-\frac{R_2}{R_1}}{1 + (1+{\frac{R_2}{R_1}})\frac{1}{A}}</math>

For example, if <math>G = \frac{- \frac{R_2}{R_1}}{1 += \frac{2</math> -and \frac{R_2}{R_1}}{<math>A}} = 10^4</math>, then <math>G =</math> −1.9994 instead of exactly −2.

Notice(The that thesecond equation becomes effectively the same foras the idealfirst caseequation as <math>A</math> approaches infinity.)

In this manner, theThe open-loop gain iscan be important for computing the actual gain forof a given non-idealan operational amplifier network in situations, where the ideal modelassumption of aninfinite operationalopen-loop amplifiergain begins to becomeis inaccurate.

==Operational amplifiers==

The open-loop gain of an operational amplifier falls very rapidly with increasing [[frequency]]. Along with [[slew rate]], this is one of the reasons why operational amplifiers have limited [[Bandwidthbandwidth (signal processing)|bandwidth]].

== See also ==

== See also ==

* [[Loop gain]] (includes both the open-loop gain and the feedback attenuation)

*[[Gain–bandwidth product]]

* [[Loop gain]] (includes both the open-loop gain and the feedback attenuation)

*[[Negative-feedback amplifier#Summary of terms|Summary of negative feedback amplifier terms]]

==References==

{{DEFAULTSORT:Open-Loop Gain}}

{{reflist}}

[[Category:Electrical parameters]]

[[Category:Electrical parameters]]

{{Electronics-stub}}