In
electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...
and
control system theory, loop gain is the sum of the
gain, 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, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
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 handle ...
. 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 is a two-port electronic circuit that uses electric power from a power su ...
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 ...
s to control industrial plant and equipment. The concept is also used in
biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
. 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 (symbol φ or ϕ) of a wave or other 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 expressed in such a s ...
, determines the behavior of the device, and particularly whether the output is
stable
A stable is a building in which working animals are kept, especially horses or oxen. The building is usually divided into stalls, and may include storage for equipment and feed.
Styles
There are many different types of stables in use tod ...
, 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 and
Harry Nyquist at
Bell Labs
Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...
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 ...
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) h ...
''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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
of the input signal, and so are usually expressed as functions of the
angular frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
''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
In electronic amplifiers, the phase margin (PM) is the difference between the phase (waves), phase lag (< 0) and -180°, for an amplifier's output signal (relative to its input) at zero dB gain - i.e. unity gain, or that the output signal has the ...
and
gain margin
*
Nyquist plot
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry ...
* In telecommunications, the term "loop gain" can refer to the total usable
power 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. Some ...
. 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 PerformanceStriving for Small-Signal StabilityIeee Circuits and Devices Magazine, vol. 17, no. 1, pp. 31-41, January 2001.
Electronic amplifiers
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