A Nyquist plot is used in automatic control and signal processing for assessing the stability of a system with feedback. It is represented by a graph in polar coordinates in which the gain and phase of a frequency response are plotted. The plot of these phasor 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 — magnitude and phase — on a single graph, with frequency as a parameter along the curve. The Nyquist plot is named after Harry Nyquist, a former engineer at Bell Laboratories. Signal processing is the processing, amplification and interpretation of signals and deals with the analysis and manipulation of signals. ... Feedback is (generally) information about actions. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... In electronics, gain is usually taken as the mean ratio of the signal output of a system to the signal input of the system. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Frequency response is the measure of any systems response to frequency, but is usually used in connection with electronic amplifiers and similar systems, particularly in relation to audio signals. ... See wikibooks book on Phasors A phasor is a constant complex number representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. ... The Bode plot for a first-order Butterworth filter A Bode plot, named after Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot: A Bode magnitude plot is a graph of log magnitude against log frequency often used in signal processing to show... Harry Nyquist (February 7, 1889 - April 4, 1976) was an important contributor to information theory. ... Bell Telephone Laboratories or Bell Labs was originally the research and development arm of the United States Bell System, and was the premier corporate facility of its type, developing a range of revolutionary technologies from telephone switches to specialized coverings for telephone cables, to the transistor. ...

The Nyquist plot is very useful in assessing the stability of a negative feedback system. An application of Cauchy's Argument principle to the open loop transfer function, the Nyquist plot identifies singularities in the semicircle of infinite radius in the right half of the s-plane, the presence of which indicates instability in the feedback system. Negative feedback is the process of feeding back to the input a part of a systems output, so as to reverse the direction of change of the output. ... The contour C (black), the zeros of f (blue) and the poles of f (red). ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. ... The S plane is a mathematical domain, where instead of viewing processes in the time domain, modelled with time based functions they are viewed, as equations, in the frequency domain. ... Instability in systems is generally characterized by some of the outputs or internal states growing without bounds. ...

Nyquist and related plots are classic methods of assessing stability; they 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

• Nyquist stability criterion
• Bode plot
• Transfer function
• Frequency response
• Nichols plot
• Cauchy's Argument Principle

The Nyquist stability criterion, named for Harry Nyquist, provides a simple test for stability of a closed-loop control system by examining the open-loop systems Nyquist plot. ... The Bode plot for a first-order Butterworth filter A Bode plot, named after Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot: A Bode magnitude plot is a graph of log magnitude against log frequency often used in signal processing to show... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... Frequency response is the measure of any systems response to frequency, but is usually used in connection with electronic amplifiers and similar systems, particularly in relation to audio signals. ... A Nichols plot is a graph used in signal processing in which the magnitude and phase of a frequency response are plotted on orthogonal axes. ... The contour C (black), the zeros of f (blue) and the poles of f (red). ...

External link

• The Nyquist Plot
• The Barkhausen Stability Criterion - a simple and intuitive yet completely incorrect method of assessing the stability of a feedback system.