Why gain crossover frequency must be lower than phase crossover frequency for stable systems?

Asked Mar 25 '18 at 17:08

Active Dec 29 '19 at 18:56

Viewed 1,084 times

As far as I understood from here, phase margin means the amount of phase that needs to be added in order to coincide with 0 db gain and -180 degrees phase. Likewise for the gain margin it means means the amount of gain that needs to be added in order to coincide with 0 db gain and -180 degrees phase. But i don't understand why do they both necessarily have to be positive for stable systems?

Re-stating my question. I want to know: Why gain crossover frequency must be lower than phase crossover frequency for stable systems?

Relevant: Can a phase margin become bigger than 180° and is this bad?

edited Dec 29 '19 at 18:56

asked Mar 25 '18 at 17:08

aadil095

Positive gain and phase margin for stable systems is just convention. – Chu Mar 25 '18 at 19:00
You might also look up "stability margin" which is the shortest distance from the Nyquist curve to the critical point. It captures the other two ideas. – jonk Mar 25 '18 at 19:41
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Look up Barkhausen's criterion. The old joke, is "my amplifiers oscillate, and my oscillators don't". – Whit3rd Mar 25 '18 at 20:05
Read about Harry Nyquist. – analogsystemsrf Mar 25 '18 at 22:06
@Chu I want to know the reasoning behind the convention – aadil095 Dec 29 '19 at 18:48
It's just a convention - no deeper implication. Like the universally accepted convention that clockwise is off for flow control valves and water taps. – Chu Dec 29 '19 at 19:00

Why gain crossover frequency must be lower than phase crossover frequency for stable systems?

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