$($b$)$ For the single$-$phase full$-$bridge grid connected voltage source inverter shown in Fig. $1\mathrm{.}3,$ the grid voltage is $230$ V and $50$ Hz $.$

$($i$)$ What is the minimum DC link voltage required for the single$-$phase full bridge grid connected voltage source inverter.

$[1$ mark$]$

$($ii$)$ Explain how the line current $\backslash ($ i$\_\{$g$\}\backslash )$ is controlled in phase with grid voltage $\backslash ($ v$\_\{$g$\}\backslash )$ by the voltage source inverter.

$[3$ marks$]$

$($iii$)$ Explain how the bipolar sinusoidal pulse width modulation $($PWM$)$ control signals are generated for the inverter and comment upon the effect of PWM switching frequency on the harmonics of the line current $\backslash ($ i$\_\{$g$\}\backslash )$ and the inverter efficiency.

$[4$ marks$]$