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Nichols plot

Chart of a transfer function's phase response vs. magnitude

Wikipedia contributorsAdapted for Fathomly · View authors
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Source updated March 18, 2026
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The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.

01Use in control design

Given a transfer function,

G(s)={\frac {Y(s)}{X(s)}}

with the closed-loop transfer function defined as,

M(s)={\frac {G(s)}{1+G(s)}}

the Nichols plots displays 20\log _{10}(|G(s)|) versus \arg(G(s)). Loci of constant 20\log _{10}(|M(s)|) and \arg(M(s)) (so-called Hall circles) are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency \omega is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - 20\log _{10}(|G(s)|) versus \log _{10}(\omega ) and \arg(G(s)) versus \log _{10}(\omega )) - are plotted.

In feedback control design, the plot is useful for assessing the stability and robustness of a linear system. This application of the Nichols plot is central to the quantitative feedback theory (QFT) of Horowitz and Sidi, which is a well known method for robust control system design.

In most cases, \arg(G(s)) refers to the phase of the system's response. Although similar to a Nyquist plot, a Nichols plot is plotted in a Polar coordinate system while a Nyquist plot is plotted in a Cartesian coordinate system.

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Sources and credits

This article is adapted from the Wikipedia article “Nichols plot”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Hall circles

Hall circles are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis.

Bode plot

In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude of the frequency response, and a Bode phase plot, expressing the phase shift.

Nyquist stability criterion

In control theory and stability theory, the Nyquist stability criterion or Strecker-Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a linear dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system.