(Solved): 2.1 Analysis and design of a buck-boost converter: A buck-boost converter is illustrated in Fig. 2 ...

2.1 Analysis and design of a buck-boost converter: A buck-boost converter is illustrated in Fig. 2.28a, and a practical implementation using a transistor and diode is shown in Fig. \( 2.28 \) b. (a) Fig. 2.28 Buck-boost converter of Problem 2.1: (a) ideal converter circuit, (b) implementation using MOSFET and diode (a) Find the dependence of the equilibrium output voltage \( V \) and inductor current \( I \) on the duty ratio \( D \), input voltage \( V_{g} \), and load resistance \( R \). You may assume that the inductor current ripple and capacitor voltage ripple are small. (b) Plot your results of part (a) over the range \( 0 \leq D \leq 1 \). (c) Dc design: for the specifications \[ \begin{array}{ll} V_{g}=30 \mathrm{~V} & V=-20 \mathrm{~V} \\ R=4 \Omega & f_{s}=40 \mathrm{kHz} \end{array} \] (i) Find \( D \) and \( I \) (ii) Calculate the value of \( L \) that will make the peak inductor current ripple \( \Delta i \) equal to ten percent of the average inductor current \( I \). (iii) Choose \( C \) such that the peak output voltage ripple \( \Delta v \) is \( 0.1 \mathrm{~V} \). (d) Sketch the transistor drain current waveform \( i_{T}(t) \) for your design of part (c). Include the effects of inductor current ripple. What is the peak value of \( i_{T} \) ? Also sketch \( i_{T}(t) \) for the case when \( L \) is decreased such that \( \Delta i \) is \( 50 \% \) of \( I \). What happens to the peak value of \( i_{T} \) in this case?