Question

Power Systems

Questions 7 to 14 pertain to the control-to-output transfer function Gyd(s) of a boost converter.This converter operates with the following element values and at the following quiescent operating point:

• Input voltage Vg = 12 V • Output voltage V = 30 V • Output power P = 60 W

• Inductance L = 120µH • Capacitance C = 100µF • Switching frequency fs = 200 kHz

You may assume that all components are ideal and neglect losses. You may assume that the load is resistive. First, solve the canonical model, with the parameters listed in Table 7.1, to find an expression for Gvd(s) of the boost converter.Second, construct the magnitude and phase asymptotes of the Bode plot of Gvd(s), using the methods described in the lectures. Semilog paper is linked to the Supplemental Materials which you can print out and use for this part. Compute all break frequencies and slopes. Then answer the questions below. Enter numerical values of frequency in Hz, rounded to the nearest 1 Hz.

7. (10 points) At what frequency do the magnitude asymptotes pass through 0 dB?

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