(Solved): Boost converter. Please do not copy previous answers, thank you! Figure 2 A boost converter is im ...

Boost converter. Please do not copy previous answers, thank you!

Figure 2 A boost converter is implemented with a MOSFET and a p-n diode. The MOSFET is ideal, the diode has substantial reverse-recovery, with reverse recovery time \( \mathrm{t}_{\mathrm{r}} \) and recovered charge \( \mathrm{Q}_{\mathrm{r}} \). The inductor has winding resistance \( \mathrm{R}_{\mathrm{L}} \). a) Derive an equivalent circuit that models the dc components of the converter waveforms and that accounts for the loss elements described above. (3p) b) Solve your model to find an expression for the output voltage. (1p) c) Plot the output voltage vs. duty cycle over the range \( 0 \leqslant \mathrm{D}<1 \), for the following values: \( \mathrm{R}_{\mathrm{L}}=0.5 \Omega, \mathrm{f}_{\mathrm{s}}=200 \mathrm{kHz}, \mathrm{Q}_{\mathrm{r}}=2 \mu \mathrm{C}, \mathrm{t}_{\mathrm{r}}=100 \mathrm{~ns}, \mathrm{R}_{1}=60 \Omega, \mathrm{V}_{\mathrm{g}}=24 \mathrm{~V} .(1 \mathrm{p}) \)