Let's start with arbitrary transfer function as an example, such as:

obj = tf([1 2],[1 0 2 5]);
grid on;
axis([-2 2 -2 2]); axis equal

As far as I do understand what is gain (expressed in dB), I am unable to figure out, nor find any information about circles that appear after we use grid. For some reason there is vertical line at Re=-0.5 associated with 0 dB value. On the left and right of this line we see non coincident circles in the shape of peacock's eye with decreasing or increasing values. Circles converge to points [-1,0] and [0,0].

We can see that system's curve starts at point [-0.4,0] which corresponds to -7.9588 dB gain, crosses -10 dB circle twice, where on both occurrences system's gain doesn't match -10 dB value.

Moreover, just from the fact that that we have infinite line denoted with 0 dB value, one can infer that it has absolutely nothing to do with actual gain, which on Nyquist plot should be circular around point [0,0]. In this case my question is simple: what does those dB values and circles mean?

Nyquist plot with grid on


1 Answer 1


See doc nyquist:

The nyquist function has support for M-circles, which are the contours of the constant closed-loop magnitude. M-circles are defined as the locus of complex numbers where

$$T(j\omega) = \left|\dfrac{G(j\omega)}{(1+G(j\omega))}\right|$$

is a constant value. In this equation, $\omega$ is the frequency in radians/TimeUnit, where TimeUnit is the system time units, and $G$ is the collection of complex numbers that satisfy the constant magnitude requirement.

  • $\begingroup$ M-circles is the phrase that I have been looking for. I checked Matlab documentation before, but I must have miss this section. I also found some more information about this in The Control Handbook, section 9.2.2, page 140. It is available on [Google][1]. [1]: books.google.pl/… $\endgroup$
    – Maverick
    Jun 21, 2017 at 21:23

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