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Nyquist plot
 
 
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A Nyquist plot is used in automatic control
Control system

A control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic gate, and feedback or linear controls....
 and signal processing
Signal processing

Signal processing is the analysis, interpretation, and manipulation of signal . Signals of interest include: audio signal processing, , time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others....
 for assessing the stability of a system with feedback
Feedback

Feedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
. It is represented by a graph in polar coordinates in which the gain
Gain

In electronics, gain is a measure of the ability of a electrical network to increase the Power or amplitude of a Signal . It is usually defined as the mean ratio of the Signalling of a system to the Signalling of the same system....
 and phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
 of a frequency response
Frequency response

Frequency response is the measure of any system's Frequency spectrum response at the output to a signal of varying frequency at its input. In the audible range it is usually referred to in connection with electronic amplifiers, microphones and loudspeakers....
 are plotted. The plot of these phasor
Phasor (electronics)

In physics and engineering, a phase vector is a representation of a sine wave whose amplitude , phase , and frequency are time-invariant. It is a subset of a more general concept called analytic signal....
 quantities shows the phase as the angle and the magnitude as the distance from the origin. This plot combines the two types of Bode plot
Bode plot

A Bode magnitude plot is a plot of logarithm magnitude versus frequency, plotted with a log-frequency axis, to show the transfer function or frequency response of a LTI system theory system....
 — magnitude and phase — on a single graph, with frequency as a parameter along the curve.






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A Nyquist plot is used in automatic control
Control system

A control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic gate, and feedback or linear controls....
 and signal processing
Signal processing

Signal processing is the analysis, interpretation, and manipulation of signal . Signals of interest include: audio signal processing, , time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others....
 for assessing the stability of a system with feedback
Feedback

Feedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
. It is represented by a graph in polar coordinates in which the gain
Gain

In electronics, gain is a measure of the ability of a electrical network to increase the Power or amplitude of a Signal . It is usually defined as the mean ratio of the Signalling of a system to the Signalling of the same system....
 and phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
 of a frequency response
Frequency response

Frequency response is the measure of any system's Frequency spectrum response at the output to a signal of varying frequency at its input. In the audible range it is usually referred to in connection with electronic amplifiers, microphones and loudspeakers....
 are plotted. The plot of these phasor
Phasor (electronics)

In physics and engineering, a phase vector is a representation of a sine wave whose amplitude , phase , and frequency are time-invariant. It is a subset of a more general concept called analytic signal....
 quantities shows the phase as the angle and the magnitude as the distance from the origin. This plot combines the two types of Bode plot
Bode plot

A Bode magnitude plot is a plot of logarithm magnitude versus frequency, plotted with a log-frequency axis, to show the transfer function or frequency response of a LTI system theory system....
 — magnitude and phase — on a single graph, with frequency as a parameter along the curve. The Nyquist plot is named after Harry Nyquist
Harry Nyquist

Harry Nyquist , was an important contributor to information theory....
, a former engineer at Bell Laboratories.

The high frequency response is at the origin. The plot provides information on the pole
Pole (complex analysis)

In complex analysis, a mathematical discipline, a pole of a meromorphic function is a certain type of mathematical singularity that behaves like the singularity of at ....
s and zero
Zero (complex analysis)

In complex analysis, a zero of a holomorphic function f is a complex number a such that f = 0....
s of the transfer function
Transfer function

A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a system analysis....
 (eg. from the angle at which the curve approaches the origin).

Assessment of the stability of a closed-loop negative feedback
Negative feedback

Negative feedback feeds part of a system's output, inverted, into the system's input; generally with the result that fluctuations are attenuated....
 system is done by applying the Nyquist stability criterion
Nyquist stability criterion

The Nyquist stability criterion, named after Harry Nyquist, provides a simple test for BIBO stability of a closed-loop control system by examining the open-loop system's Nyquist plot....
 to the Nyquist plot of the open-loop system (i.e. the same system without its feedback loop). This method is easily applicable even for systems with delays which may appear difficult to analyze by means of other methods.

Nyquist and related plots are classic methods of assessing stability, but have been supplemented or supplanted by computer-based mathematical tools in recent years. Such plots remain a convenient method for an engineer to get an intuitive feel for a circuit.

See also

  • Argument principle
    Argument principle

    In complex analysis, the Argument principle states that if f is ameromorphic function inside and on some closed contour C, with f having no Zero or Pole on C, then the following formula holdswhere N and P denote respectively the number of zeros and poles of f inside the contour C, with each zero and pole...
  • BIBO stability
    BIBO stability

    In electrical engineering, specifically signal processing and control theory, BIBO stability is a form of Control theory#Stability for linear system Signal s and systems that take inputs....
  • Nichols plot
    Nichols plot

    A Nichols plot is a Plot used in signal processing in which the logarithm of the magnitude is plotted against the phase of a frequency response on orthogonal axes....
  • Nyquist stability criterion
    Nyquist stability criterion

    The Nyquist stability criterion, named after Harry Nyquist, provides a simple test for BIBO stability of a closed-loop control system by examining the open-loop system's Nyquist plot....
  • Randles circuit
    Randles circuit

    A Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance RS in series with the parallel combination of the double-layer capacitance Cdl and an impedance of a faradaic reaction....
  • Electrochemical impedance spectroscopy
    Electrochemical impedance spectroscopy

    = Electrochemical Impedance Spectroscopy =...
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