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>

{{Unreferenced stub|auto=yes|date=December 2009}}

The '''open-loop gain''' of an [[operational amplifier]] is the [[Gain (electronics)|gain]] obtained when no [[feedback]] is used in the [[electrical network|circuit]].

Open loop gain is usually exceedingly high; in fact, an ideal operational amplifier has infinite open-loop gain. Typically an op-amp may have a maximal open-loop gain of around <math>10^5</math>. Normally, feedback is applied around the op-amp so that the gain of the overall [[electrical network|circuit]] is defined and kept to a figure which is more usable. The very high open-loop gain of the op-amp allows a wide range of feedback levels to be applied to achieve the desired performance.

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]].

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 [[Bandwidth (signal processing)|bandwidth]].

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.

==Definition==

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.)

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

== Role in non-ideal gain ==

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 operationoperational amplifier that is often finite in comparison 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:

== Role in non-ideal gain ==

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

However, including the finite open-loop gain <math>A</math> reduces the gain slightly, to:

The open-loop gain is a physical attribute of an operation amplifier that is often finite in comparison 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.

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

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

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:

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

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

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.

However, with the use of open-loop gain, the equation becomes:

==Operational amplifiers==

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

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 ==

Notice that the equation becomes effective the same for the ideal case as <math>A</math> approaches infinity.

*[[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==

In this manner, the open-loop gain is important for computing the actual gain for a given non-ideal operational amplifier network in situations where the ideal model of an operational amplifier begins to become inaccurate.

{{reflist}}

== See also ==

* [[Loop gain]]

{{DEFAULTSORT:Open-Loop Gain}}

[[Category:Electrical parameters]]

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