$2.(45$ points$)$ DC $/$ DC Boost converter. A boost converter has an input of $3$ Volts DC and an output of $7\mathrm{.}5$ Volts DC$.$ It switches at a $450$ kHz rate. The load resistance is $5$ ohms. Assume no voltage is dropped across the transistor $($switch$)$ or diode.

a$.(10$ points$)$ Draw an appropriate circuit diagram for this boost converter, labeling input and output voltages. You need not label other components.

b$.(10$ points$)$ Sketch at least one cycle of the voltage waveform across the switch. Label significant values of voltage and time.

C$.(5$ points$)$ Find the rms value of the voltage across the switch that you found in part $2$a above.

d$.(10$ points$)$ The boost converter's inductor is $\backslash (15\backslash$mu $\backslash$mathrm$\{$H$\}\backslash ).$ Assume that the pover tosses are negligible. Sketch the inductor current. What is the peak inductor current?

e$.(10$ points$)$ Sketch the capacitor currents and label the peak and minimum value and appropriate time axis numbers.