For an ideal/lossless buck converter, i.e., no power loss is associated with the switches (MOSFET and diode), inductors and capacitors, - 1. Derive the transfer function G(s) = V. (s)/V/(s) when the MOSFET is on and the diode is off. Hint: load resistance should be considered.

Solution

In the ideal states diode and MOSFET will act as switches with zero losses;

2. Draw the bode plot of G(s) using MATLAB. The system parameters are given below:

 • Circuit parameters: L = 2 mH, C = 20 uF, R. = 5 •

MTALAB code :

close all

clear all

num=[5];% enter the value of numerator

den= [0.0000002 0.002 5];% enter the value of denominator in SI units

G=tf(num,den);% transfer function

bode(G)% bode plot of transfer function

grid on

 For the lossless buck converter in the following figure, derive the state space model with state variable vector X as {ių, vc}, input variable vector U as {Vi, 1.}, output variable vector Y as {v,}. Hint: Need to derive the matrix coefficients in the model below. Note that duty cycle d should be considered and included.

Solution

State space model of buck converter