# Estimate the phase margin of a loop gain

The loop gain is $$\10^6 /[(s+1)(1+s10^5)]\$$. Below I have the Bode plot. How can I derive the unity gain frequency from the Bode Plot? How can I find the phase margin from the phase plot of the Bode?

• From your drawing, it looks like unity gain is around $10^{5.5} \approx 320 kHz$. With that value calculate $AB(j \omega_f)$ and find the angle of the resulting complex value. – jDAQ Oct 23 '19 at 4:06
• You have already identified the phase margin on your Bode plot. The 0dB crossover frequency can be read from the log frequency scale, which you have also identified already. But the diagram needs to be plotted on log-linear graph paper for accuracy. – Chu Oct 23 '19 at 6:17
• @jDAQ how do I get an exact value for the unity gain frequency? – Hector Oct 23 '19 at 19:00
• @Chu I try setting the linear loop gain to zero, but I cannot seem to get value for omega – Hector Oct 23 '19 at 19:01
• @Hector to find the unity gain frequency solve $10^6 / | (j \omega_0 +1)(1+j \omega_0 10^5) | = 1$ – jDAQ Oct 23 '19 at 20:47