When an amplifier with a gain A(s) is put in a
feedback loop as shown in Figure 1, the closed loop gain, V o /V in = A CL
The system is unstable when the loop gain, ß A(s), equals -1. That is, ß A(s) has a magnitude of one and a phase of -180
degrees. An unstable system oscillates. A system close to being unstable has a large ringing overshoot in response to a step input.
The phase margin is a measure of how close the phase of the loop gain is to -180 degrees, when the magnitude of the loop gain is one. The phase margin is the additional phase required to bring the phase of the loop gain to -180 degrees. Phase Margin = Phase of loop gain - (-180). The loop gain has a dominant pole at
. Higher order poles can be
represented by an equivalent pole at . The amplifier is approximated by a function with two poles as shown in Equation 2.
Since for frequencies of interest where the loop gain magnitude is close to unity,
∙ PM is the phase margin.
∙ w t is the unity gain frequency (rad/sec).
∙ w eq is the frequency of the equivalent higher order pole (rad/sec).
∙ Q is the system Quality factor.
∙ OS is the Over Shoot.