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]] 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 an 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. However the very high gain of the op-amp enables considerable levels of feedback to be applied to achieve required performance. 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]].

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.

As you can see from the definition above, in an ideal amplifier where <math>V^+=V^-</math>, the open loop gain (<math>A_{\text{OL}}</math>) becomes infinite.

== See also 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.)

* [[Loop gain]]

==Role in non-ideal gain==

{{DEFAULTSORT:Open-Loop Gain}}

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.

[[Category:Electrical parameters]]

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 calculated gain of such a circuit at the output terminal is defined, assuming infinite gain in the amplifier, is:

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

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

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

(The second equation becomes effectively the same as the first equation as <math>A</math> approaches infinity.)

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.

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

==See also==

*[[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==

{{reflist}}

[[Category:Electrical parameters]]

{{Electronics-stub}}