In
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
and
control system theory, loop gain is the sum of the
gain, expressed as a ratio or in
decibels, around a
feedback loop
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled c ...
. Feedback loops are widely used in electronics in
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost t ...
s and
oscillators, and more generally in both electronic and nonelectronic industrial
control systems to control industrial plant and equipment. The concept is also used in
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
. 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
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it ...
, determines the behavior of the device, and particularly whether the output is
stable, or unstable, which can result in
oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
. 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
Hendrik Wade Bode ( ; ;Van Valkenburg, M. E. University of Illinois at Urbana-Champaign, "In memoriam: Hendrik W. Bode (1905-1982)", IEEE Transactions on Automatic Control, Vol. AC-29, No 3., March 1984, pp. 193–194. Quote: "Something should be ...
and
Harry Nyquist at
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial Research and development, research and scientific developm ...
in the 1930s.
A
block diagram
A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships of the blocks. of an electronic amplifier with
negative feedback is shown at right. The input signal is applied to the amplifier with
open-loop gain
The open-loop gain of an electronic amplifier is the gain obtained when no overall feedback is used in the circuit.
The open-loop gain of many electronic amplifiers is exceedingly high (by design) – an ''ideal'' operational amplifier (op-amp) ...
''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
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of the input signal, and so are usually expressed as functions of the
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
''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.
See also
*
Phase margin and
gain margin
*
Nyquist plot
* In telecommunications, the term "loop gain" can refer to the total usable
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
gain of a
carrier terminal or two-wire
repeater
In telecommunications, a repeater is an electronic device that receives a signal and retransmits it. Repeaters are used to extend transmissions so that the signal can cover longer distances or be received on the other side of an obstruction. Som ...
. The maximum usable gain is determined by, and may not exceed, the losses in the closed path.
*
Summary of negative feedback amplifier terms
References
External links
Loop Gain and its Effects on Analog Circuit Performance
Amplifiers
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