Question

Ferthe zenc-crrent resoranl switch converter orla Determine Lr and Ge such thet tha maxium current Lr (ArPeale) As 9A, Deteanne the reguire sau china equency

Answer 1

Calculation of L_r & C_r_1 I_L_1 peak = I_0 + V_s/Z_0 9 = 3 + 50/20 C = 50/20 Z_0 = 8.333 ohm W_0 = 1/squareroot L_r C_r = 10^n rad/sec Z_0 = squareroot L_r/C_r = 8.333 ohm rightarrow w_0 = 1/squareroot L_r C_r times L_r/L_r = 10 = squareroot L^2_r/L_r C_r 1/L_r^2 w_0 = squareroot L_r/C_r 1/L_r \r\n w_0 = Z_0 1/L_r Therefore L_r = Z_0/w_0 = 8.333/10 L_r = 0.8333 k H Therefore Z_0 = squareroot L_r/C_r Z_0^2 = L_r/C_r C_r = L_r/Z_0^2 = 0.8333/8.333^2 C_r = 12 n F (b) calculation of required switching frequency V_0 = V_0 f_s (t/2 + (t_2 - t_1) + (t_3 - t_2)) t_1 = I_0 L_r/V_3 = 3 times 0.8334/50 = 0.05 m sec t_2 - t_1 = 1/w_0 [sin^- 1 (I_0 z_0/v_3) + pi] = 1/10^n (sin^- 1 (3 times 8.333/50) + pi) \r\n 1/10 (pi/6 + pi) = 0.1047 k sec t_3 - t_2 = -C_r V_3/I_0 (1 - C_0 (W_0 (t_2 - t_1)) = 12 times 10^- 9 times 50/3 (1 - cos (10 (0 - 1047 (w))) = 0.0334 n sec