# p_margin

phase margin and associated crossover frequency

### Syntax

[phm,fr] = p_margin(h) phm = p_margin(h)

### Arguments

- h
a SISO linear system (see :syslin).

- phm
a number, the phase margin in degree if it exists or an empty matrix.

- fr
a number, the corresponding frequency (in Hz) or an empty matrix.

### Description

Given a SISO linear system in continuous or discrete time,
`p_margin`

returns `phm`

, the
phase margin in degree of `h`

and
`fr`

, the achieved corresponding frequency in
Hz.

The phase margin is the values of the phase at frequency
points where the nyquist plot of `h`

crosses the
unit circle. In other words the phase margin is the difference
between the phase of the frequency response of
`h`

and -180° when the gain of
`h`

is 1.

The algorithm uses polynomial root finder to solve the equations:

- h(s)*h(-s)=1
for the continuous time case.

- h(z)*h(1/z)=1
for the discrete time case.

### Examples

//continuous case h=syslin('c',-1+%s,3+2*%s+%s^2) [p,fr]=p_margin(h) [p,fr]=p_margin(h+0.7) show_margins(h+0.7,'nyquist') //discrete case h = syslin(0.1,0.04798*%z+0.0464,%z^2-1.81*%z+0.9048);//ok [p ,f]=p_margin(h) show_margins(h,'nyquist')

### See also

- g_margin — gain margin and associated crossover frequency
- show_margins — display gain and phase margin and associated crossover frequencies
- repfreq — frequency response
- black — Black-Nichols diagram of a linear dynamical system
- bode — Bode plot
- nicholschart — Nichols chart
- nyquist — nyquist plot

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