Question

MOSFET Diode 0 Fig. 1. Buck converter with non-ideal switches 2. Based on the small-signal model derived in Problem 1, assume Vin and io are ideal with no variations (i.e., the perturbations of vin and io equal zero), rewrite the state space equations. Note that in the updated state space equations, only the perturbation of duty cycle d is considered in the vector of input variables 3. Understand the function of the MATLAB commands 'ss' and 'bode'1. Use the command 'ss to build the model/system (i.e., the state space equations with updated coefficient matrices) derived in Problem 2 in an m-script, and use the command 'bode' to plot the bode figures with the duty cycle d as 20%, 40% and 60%. The system parameters are shown below: Circuit parameters : L-400 μΗ, C-60 μF, Rons-20 nO. Rond-40 n(2. Vİ-20 V Frequency range in bode figure: 0.5 Hz~200 kHz

Answer 1

Given that During ON From KCl V_c/R + I_c - I_L = 0 V_c/R + c d v_c/dt - I_L = 0 C d v_c/dt = I_L - v_c/dt = I_L - v_c/R gives d v_c/dt = I_L/c - v_c/R_c from KVL V_i - I_L Rons - v_L - v_c = 0 v_i - I_L Rons - L dI_L/dt - v_c = 0 L d_I L/dt = v_i - I_L Rons - v_c dIL/dt = v_i/L - I_L Rons/L - v_c/L v_0 - v_C from 1, 2 and 3 dIL/dt = v_i/L - I_l Rons/L - v_c/L dv_c/dt = I_L/c - v_c/R_c \r\n v_0 = v_c [dIL/dt dv_c/dt] = [-Rons/L 1/c -1/L -1/Rc][IL v_0] + [1/L 0]v_i v_0 = [0 1] [I_L v_c] DT < t < T from KCl I_L = I_c + I_0 I_L = c dv_c/dt + v_c/R gives dv_c/dt = I_L/c - v_c/R_c from KVL -I_L Ron -v_L - v_c = 0 gives L dI L/dt = -v_c - I_L Rond dI L/dt = -v_c/L - I_L Rond dIL/dt = -v_c/L