HW6+Solution

# HW6+Solution - ECE3072 HW6 Problem 1(a A buck converter is...

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ECE3072 HW6 Page 1 of 6 Problem 1 (a) A buck converter is shown in Figure 1, the switching frequency of the MOSFET is 20kHz, duty cycle D = 0.5, derive equivalent circuit models, which model the capacitor voltage ripple and the inductor current ripple. Assume the diode is ideal and there is no extra resistive loss. L I Figure 1. A buck converter. Mode 1: Inductor voltage L g v V V = Mode 2: Inductor voltage L v V = −

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ECE3072 HW6 Page 2 of 6 Inductor voltage and inductor current waveforms Inductor current slope during mode 1 ( ) g L V V di t dt L = Therefore, change in inductor current during mode 1 is 2 g L s V V i DT L Δ = 10 5 1 = 0.5 0.625 2 2 100 6 20 3 g L s V V i DT L e e Δ = × × = × Capacitor current and capacitor voltage waveforms The total charge q is equal to
ECE3072 HW6 Page 3 of 6 2 q C v = × Δ The total charge q is the area of the triangle 0.5 2 s L T q i = ×Δ × Therefore, the capacitor voltage ripple g1986g1874 =g1986 g1861 g3013 g1846 g3046 / g4666 8g1829g4667 = g1848g4666 1 −g1830g4667 g1846 g3046 g2870 / g4666 16g1838g1829g4667 =0 .0471 (b)

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