1. Taking into account non-ideal characteristics of converter components, determine the following small-signal transfer functions of an open-loop buck converter. Neglect the equivalent series resistance of the output capacitor and assume that a switching load is connected to the output terminals:

transfer function relating inductor current to duty ratio,
transfer function relating output voltage to duty ratio,
transfer function relating input voltage to output voltage
transfer function relating input current to output current

2. A single-phase rectifier with capacitor voltage filter is connected to an AC circuit with negligible inductance. However, some inductance L_dc, is connected between the rectifier terminals and the capacitor voltage filter. Determine the minimum value of L_f in terms of V_s, ω and i_dc that will result in continuous. Consider the ripple V_dc in to be negligible.

3. A single-phase rectifier with capacitor voltage filter is connected to an ACc ircuit with finite supply-side inductance. Cables connecting the rectifier terminals to the filter capacitor can be considered to have negligible inductance. Sketch the rectifier terminal current graduating the current and time-axes (also show the angle or time at which the current peaks). V_s=120 V, f=50 Hz, L_s = 1 mH, V_dc=150 V.