Nyquist plot

A Nyquist plot is a type of graph used in signal processing in which the magnitude and phase of a frequency response are plotted on orthogonal axes. This plot combines the two types of Bode plot - magnitude and phase - on a single graph, with frequency as a parameter along the curve. It is useful for assessing the stability of a system with feedback.

The Nyquist plot shows the amplification/attenuation and phase-shift of the signal in the complex plane. The phase-shift of a signal with frequency ω is represented by the argument and the magnitude is represented by the length of a vector from the origin in the direction described by the argument.

The Nyquist plot is very useful in looking at the stability of an open negative-feedback-system. If the magnitude function of a frequency that is phase-shifted 180° is greater than or equal to unity then the closed system will be unstable.

The real use of Nyquist plot is in that the stability of the system can be easily predicted by plotting it's open loop polar plot along a path that goes along the jω axis and along a semicircle of infinite radius in the positive(real part) half of the s-plane. And at the same time the system stability and characteristics can be improved by modifying the plot graphically. All this has been made even simpler by some computer mathematical tools like matlab etc.

The Nyquist plot is named after Harry Nyquist, a former engineer at Bell Laboratories.