Q1. For the converter shown in Fig 1, consider all components to be ideal. When the converter is operating in DCM, derive the following:

a. Expression for the conditions under which the converter operates in the discontinuous conduction mode. Express your result in the form K < K_crit(D)and give the formulas for K and Kcrit(D).

b. Expression for the dc conversion ratio M(D, K) i.e. ratio of output voltage to input voltage.

c. If V_g = 5V, V₀ = 12V, L= 7µH, fsw = 200kHz, find the value of load resistance for which the converter operates at boundary of CCM and DCM.

Q2. For a converter shown in Fig 2, Vg = 50V, L= 5 mH, C = 20µF, R = 2?, D = 0.8, fsw = 200 kHz, Mosfet R_dson = 5m? and diode forward voltage drop Vd = 0.5V.

a) Draw the equivalent circuit of the converter.

b) Calculate the voltage conversion ratio and dc-component of inductor current.

c) Determine the efficiency of converter.

d) If K_crit(D) = (1-D)² & K= 2L/RTs, find the switching frequency f_sw at which the converter will go into discontinuous conduction mode.

Q3. A boost converter is designed for a 240 V input, 400 V output. The output power is 300 kW.

a. If the switching frequency is set to 10 kHz, determine the critical inductance (that is, minimum inductance for continuous conduction mode).

b. If the converter is operating in critical conduction mode, determine the average and peak current through the inductor.

c. If the inductance is chosen as 4.7 µ.H, determine the minimum switching frequency for continuous conduction mode (critical conduction).

Q4. A certain buck converter contains a synchronous rectifier, namely a synchronous buck converter, shown in figure below.

(a) Does this converter operate in discontinuous conduction mode at light load? Please explain.

(b) The load resistance is disconnected (R →∞), and the converter is operated with duty cycle 0.5. Sketch the inductor current waveform.

Q5. An unregulated dc input voltage varies over the range 35V ≤ Vg ≤ 70V. A buck converter reduces this voltage to 28 V; a feedback loop varies the duty cycle as necessary such that the converter output voltage is always equal to 28 V. The load power varies over the range 10W ≤ P_Load ≤ 1000W. The element values are:

L = 22 uH, C = 470 uF, fs = 75 kHz

Losses may be ignored.

a) Over what range of Vg and load current does the converter operate in CCM?

b) Determine the maximum and minimum values of the steady-state transistor duty cycle.

c) Simulate the circuit in PLECS and provide the waveforms for inductor current and diode current for

a. CCM (choose any operating point)

b. DCM (choose any operating point)

Q6. DCM mode boundary analysis of the Cuk converter of Fig. 5. The capacitor voltage ripples are small

(a) Sketch the diode current waveform for CCM operation. Find its peak value, in terms of the ripple magnitudes and the dc components I1 and I2 of the two inductor currents and respectively.

(b) Derive an expression for the conditions under which the Cuk converter operates in the discontinuous conduction mode. Express your result in the form K < Kcrit (D) and give formulas for K and Kcrit (D).