Question

3. a) Consider a boost converter shown in the figure below. Briefly explain the principle of operation of the circuit as a step-up converter, ie, how the input voltage is stepped up and how energy transfer occurs from input to the output in each cycle. Find expressions for vi(l) when the switch is closed and when it is off. Sketch it for one eycle and find its average value, Vu. Find the relationship between input and output voltages by setting Vi-O b) Consider an ideal boost converter, operating in CCM mode, and assume input voltage, V,-10 V Output voltage, Vo-40 V, output power delivered to a resistive load, Po- 15 W, and inductor current ratio (LIR ratio), Δǐ/L-04. Sketch the inductor current, iL(t), switch current, in(t), and diode current, io(), over one cycle, indicating the minimum and maximum values. Also, calculate the average values of I, Iax, and Io.

Answer 1

Boast converter [stepup] Let us consider a large value of I_0 filter capacitance across the load so that the v_Tp remains constant Let us consider it is a lossless and the load is high inductive so that i_0 remains constant 0 lessthanorequalto t lessthanorequalto t_ON I_c = -I_0 V_l = V_s v_L implies a di_c/dt = v_s implies integral^I_max/_i_min dt = V_s/L intgeral^T_m_0 dt 1 I_L = V_s/L T_On T_On < t delta I_L = propositional V_s/fL t_On lessthanorequalto t lessthanorequalto T CH rightarrow D rightarrow On i_L = i_c + i_0 v_s = v_l + v_0 v_L = v_s - v_0 V_l = -(v_0 = v_s) rightarrow (v_l)_avg = 0 v_s T_On - (v_0 -v_S) T_OFF = 0 implies V_st = v_0 T_OFF implies v_s T = v_0(1 - alpha) T implies v_0 = v_s/1 - alpha \r\n by power balance equation p_0 = p_in v_o I_0 = v_s I_s implies v_0.v_s = I_s/I_0 = 1/a - alpha I_s = I_0/1 - alpha rightarrow delta Q