The duty cycle of the switch (S1) is given as D. The load current is given as la. The switching period is given as T. Assume the converter is working in continuous conduction mode. Assume the input voltage of the buck converter (battery voltage) is constant and the output voltage (terminal voltage) ripple is very small. Sketch the following waveforms for two switching periods. Align the time axis of all graphs. Express axis values in terms of Vin, Vt, Ia, D, T, L, and C. i. Sketch inductor current it and inductor voltage vz. on the same time axis. ii. Sketch the current waveform ic of the capacitor. iii. Sketch the voltage and current waveform of switch S1 on the same time axis. iv. Sketch the voltage and current waveform of diode S2 on the same time axis. v. Determine the maximum instantaneous voltage and the maximum instantaneous current for diode S2 and switch S1. (Attention: You can ignore the battery internal resistance for this question, but actually a drop in the battery voltage which is due to the battery current exists.) Vbat Battery Rbat + Input Filter Cin Lin + Vin S Buck Converter Controller D L + 1 PM DC motor la Ra La + E Ea Wheels System Parameters Battery voltage (Vbat) Battery internal resistance (Rhat) Input capacitance (Cin) Buck converter inductance (L) Buck converter capacitance (C) Armature resistance (Ra) Armature inductance (La) Machine constant (Ka) Motor rated terminal voltage (Va) Motor inertia (Ja) Motor rated power Values 52 V 0.2 100 F 400 pH 100 F 73.8 120 0.3416 V rad/sec 48V 0.0130 kg.m 250W