Q$6.$ A single$-$phase, full$-$bridge inverter controls the power in a resistive load. The nominal value of the input dc voltage is $100$ V $,$ and a multiple pulse$-$width modulation is used for the control of the inverter.

a$)$ Determine the rms voltage across the load at amplitude modulation of $0\mathrm{.}2$ and $0\mathrm{.}8$ and with $2$ pulses per cycle.

b$)$ Determine the rms of the $3$rd and $5$th voltage harmonic across the load at amplitude modulation of $0\mathrm{.}2$ and $0\mathrm{.}8$ and with $2$ pulses per cycle.

c$)$ Determine the rms of the $3$rd and $5$th voltage harmonic across the load at amplitude modulation of $0\mathrm{.}2$ and $0\mathrm{.}8$ and with $4$ pulses per cycle.

d$)$ Comment on your calculations of parts $\text{'}\backslash ($ b $\backslash )\text{'}$ and $\text{'}\backslash ($ c $\backslash )\text{'}.$