Editing Loop gain

{{short description|Sum of the gain around a feedback loop}}
In [[electronics]] and [[Control Systems Engineering|control system theory]], '''loop gain''' is the sum of the [[Gain (electronics)|gain]], expressed as a ratio or in [[decibel]]s, around a [[feedback loop]].   Feedback loops are widely used in electronics in [[amplifier]]s and [[electronic oscillator|oscillators]], and more generally in both electronic and nonelectronic industrial [[control system]]s to control industrial plant and equipment.  The concept is also used in [[biology]].  In a feedback loop, the output of a device, process or plant is sampled and applied to alter the input, to better control the output.  The loop gain, along with the related concept of loop [[phase shift]], determines the behavior of the device, and particularly whether the output is [[BIBO stability|stable]], or unstable, which can result in [[oscillation]].  The importance of loop gain as a parameter for characterizing electronic feedback amplifiers was first recognized by [[Heinrich Barkhausen]] in 1921, and was developed further by [[Hendrik Wade Bode]] and [[Harry Nyquist]] at [[Bell Labs]] in the 1930s.

[[Image:Block Diagram for Feedback.svg|thumb|A block diagram of an electronic amplifier with feedback.]]
A [[block diagram]] of an electronic amplifier with [[negative feedback]] is shown at right.  The input signal is applied to the amplifier with [[open-loop gain]] ''A'' and amplified.  The output of the amplifier is applied to a feedback network with gain ''β'', and subtracted from the input to the amplifier.  The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied.  In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, ''−Aβ''.  The minus sign is because the feedback signal is subtracted from the input.  

The gains ''A'' and ''β'', and therefore the loop gain, generally vary with the [[frequency]] of the input signal, and so are usually expressed as functions of the [[angular frequency]] ''ω'' in [[radians per second]].  It is often displayed as a graph with the horizontal axis frequency ''ω'' and the vertical axis gain.     In amplifiers, the loop gain is the difference between the open-loop gain curve and the closed-loop gain curve (actually, the 1/β curve) on a dB scale.<ref>{{Cite web|url = https://training.ti.com/system/files/docs/1332%20-%20Stability%202%20-%20slides.pdf|title = TI Precision Labs - Op-amps - Stability 2|quote = To find the magnitude of AolB, we can simply subtract 1/B from Aol.}}</ref><ref>{{Cite web|url = http://www.analog.com/media/en/training-seminars/tutorials/MT-033.pdf|title = MT-033 TUTORIAL Voltage Feedback Op Amp Gain and Bandwidth|quote = The difference between the open-loop gain and the closed-loop gain is known as the loop gain}}</ref><ref>{{Cite web
| url = http://www.ti.com/lit/an/slyt374/slyt374.pdf
| title = Operational amplifier gain stability, Part 2: DC gain-error analysis
| quote = ... shows the simplified open-loop gain ... along with the closed-loop gain ... The difference between these two curves is the loop gain, β×AOL.
}}</ref>  

== See also ==
* [[Phase margin]] and [[gain margin]]
* [[Nyquist plot]]
* In telecommunications, the term "loop gain" can refer to the total usable [[Power (physics)|power]] gain of a [[carrier signal|carrier]] [[terminal (telecommunication)|terminal]] or two-wire [[repeater]]. The maximum usable gain is determined by, and may not exceed, the losses in the closed path. 
*[[Negative-feedback amplifier#Summary of terms|Summary of negative feedback amplifier terms]]

== References ==
<references />

== External links ==
* [http://www.linear.com/solutions/5587 Loop Gain and its Effects on Analog Circuit Performance]
* [https://kenkundert.com/docs/cd2001-01.pdf Striving for Small-Signal Stability] Ieee Circuits and Devices Magazine, vol. 17, no. 1, pp. 31-41, January 2001.  <!-- Widely cited paper -->

[[Category:Electronic amplifiers]]
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