Topic: Control Systems
The closed loop frequency response of a dc-dc converter is shown in following figure. What are the gain and phase margins?
(The graph plots Gain in dB and Phase in degrees against frequency. The phase plot crosses 0 degrees at a point where the gain is roughly 20 dB, and the gain crosses 0 dB where the phase is roughly 120 degrees.)
- A. 20 dB, $80^{\circ}$
- B. 26 dB, $80^{\circ}$
- C. 20 dB, $120^{\circ}$
- D. 26 dB, $120^{\circ}$
Answer: C. 20 dB, $120^{\circ}$
Explanation: Since it is a closed loop system, i.e. $1+G(s)H(s)=0$, the phase margin is calculated above $0^{\circ}$ rather than $180^{\circ}$ (for $G(s)H(s)=-1$). Similarly, the gain margin is calculated for $1+G(s)H(s)=0$. From the plot, the Gain margin = $0 - (-20) = 20 \text{ dB}$ and phase margin = $0 + 120^{\circ} = 120^{\circ}$.