Question

Difference between gain crossover frequency and phase crossover frequency ?

Answer 1

Gain Crossover Frequency: 

Gain crossover frequency is that frequency at which, [G(jω)], the magnitude of the open loop transfer function is unity. 

The Phase margin PM is 180° plus the phase angle φ of the open loop transfer function at the gain crossover frequency.

PM = (180°(+φ)at GCF)

Phase Crossover Frequency:

Phase crossover frequency is that frequency at which, ∠G(jω), the phase angle of the open loop transfer function equals ‐180°.   

Thus, Gain Margin,  

GM = (1/jG(jω))_{at PCF}

In terms of decibels,

GM dB = 20 logIG(jω))_{at PCF}