Problem 1. Calculate the rms value of the following waveforms
(1) v(t) =15 sin(2g600
(2) v0) = 15 I sin(2z600 I
(3) What is the loop transfer function and the transfer function in the following system?

Problem 2. In a Buck converter, the input voltage V,„=24V. The output voltage V. is 6V. The switching frequency fs=400kHz. Assuming an ideal switching power-pole, calculate the pulse width Tu. of the switching signal, and the duty-ratio dA of the power pole.

Problem 3. In a Buck converter, L=2501. It is operating in dc steady state under the following conditions: Vin=42V, D=0.3, Po=24W, and fs=400kHz. Assume ideal components.

(1)   Calculate and draw the waveforms of q, vA, v₁ IL,ripple, iL, and i n

(2)   Draw the inductor voltage and current waveforms if P_o=12W. all else is unchanged. Compare the ripple in the inductor current with that in (1)

(3)   In this converter, the output load is changing. Calculate the critical value of the output load P_c below which the converter will enter the discontinuous conduction mode of operation.

(4)   Explain the function of the capacitor

Problem 4

In a Buck-Boost converter, L=25kH. It is operating in dc steady state under the following conditions: Vin=13V, D=0.6, P_o=36W. and fs=400kHz. Assume ideal components.

(1)  Calculate and draw the waveforms of q, v_ti Vu IL,ripplet iLt Lode and i_s

(2)  Draw the inductor voltage and current waveforms if P₀=20W; all else is unchanged. Compare the ripple in the inductor current with that in (1).

(3)  Calculate the critical value of the output load Po below which the converter will enter the DCM.

(4)  Calculate the critical value of the inductance L below which the converter enter the DCM of the operation at Po=5W.