(Solved): A DCM boost converter is to be designed to operate under the following conditions: \[ \begin{array ...

A DCM boost converter is to be designed to operate under the following conditions: \[ \begin{array}{l} 18 \mathrm{~V} \leq V_{g} \leq 36 \mathrm{~V} \\ 5 \mathrm{~W} \leq P_{\text {had }} \leq 100 \mathrm{~W} \\ V=48 \mathrm{~V} \\ f_{i}=150 \mathrm{kHz} \end{array} \] You may assume that a feedback loop will vary to transistor duty cyele as necessary to maintain a constant output voltage of \( 48 \mathrm{~V} \). Design the converter, subject to the following considerations: The converter should operate in the discontinuous conduction mode at all times. To ensure an adequate design margin, the discontinuous subinterval length \( D_{3} T_{3} \) should be no less than ten percent of the switching period \( T_{s} \), at all operating points. Given the above requirements, choose the element values to minimize the peak inductor current The output voltage peak ripple should be less than IV Specify: (a) The inductor value \( L \) (b) The output capacitor value \( C \) (c) The worst-case peak inductor current \( i_{\mu k} \) (d) The maximum and minimum values of the transistor duty cycle \( D \). (e) The maximum and minimum values of the discontinuous subinterval length \( D_{j} T_{x} \).