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 Gain or GAIN may refer to: Science and technology * Gain (electronics), an electronics and signal processing term * Antenna gain * Gain (laser), the amplification involved in laser emission * Gain (projection screens) * Information gain in de ...

, expressed as a ratio or in

decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...

s, 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 the v ...

s and

oscillators 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 ...

, and more generally in both electronic and nonelectronic industrial

control system A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...

s 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 v ...

, determines the behavior of the device, and particularly whether the output is

stable A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...

, 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 Heinrich Georg Barkhausen (2 December 1881 – 20 February 1956), born in Bremen, was a German physicist. Growing up in a patrician Bremen family, he showed interest in natural sciences from an early age. He studied at the Technical Univer ...

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 Harry Nyquist (, ; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory. Personal life Nyquist was born in the village Nilsby of the parish Stora Ki ...

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 scientific development company owned by mult ...

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 Negative feedback (or balancing feedback) occurs when some function (Mathematics), function of the output of a system, process, or mechanism is feedback, fed back in a manner that tends to reduce the fluctuations in the output, whether caused by ...

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 The radian per second (symbol: rad⋅s−1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency, commonly denoted by the Greek letter ''ω'' (omega). ...

. 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.

References

External links

Loop Gain and its Effects on Analog Circuit Performance
Amplifiers {{FS1037C MS188

See also

References

External links