PLEASE ANSWER ALL PARTS

Problem $1$:

Sinusoidal PWM switching scheme for single$-$phase DC$-$AC Inverter $(25$ points$)$

The desired fundamental voltage peak value $\backslash (\backslash$left$(\backslash$widehat$\{$V$\}\_\{$A$\_\{0\}\}\backslash$right$)=120\backslash$mathrm$\{$~V$\}\backslash ),$ fundamental frequency $\backslash ($ f$=60\backslash$mathrm$\{$~Hz$\}\backslash ),$ switching frequency $\backslash ($ f$\_\{$s$\}=20\backslash$mathrm$\{$kHz$\}\backslash ).$

For better efficiency, you are asked to minimize the harmonic distortions of the single$-$phase inverter by employing a full bridge $($i$.$e$.,$ H bridge$)$ with sinusoidal PWM switching scheme. You may assume that the inverter's DC input voltage is constant and is equal to $360$ V $.$

A$.$ Determine the value of the inverter's modulation index $\backslash ($ m$\_\{$a$\}\backslash )$ and $\backslash ($ m$\_\{$f$\}\backslash ).(5$ points$)$

B$.$ Design your inverter using a single$-$phase full$-$bridge $($i$.$e$.,$ H$-$bridge$)$ configuration. Use PSIM or MATLAB$/$Simulink to answer the following: $(20$ points$)$

Show:

i$.$ Provide a screenshot of your circuit schematic. $(5$ points$)$

ii$.$ Plot the inverter's line$-$line open$-$circuit output voltage $\backslash ($ v$\_\{\backslash$mathrm$\{$AB$\}\}\backslash ).(5$ points$)$

iii. Plot the harmonic spectrum $($ FFT $)$ of your line$-$line open$-$circuit output voltage $\backslash ($ v$\_\{\backslash$mathrm$\{$AB$\}\}\backslash ).$ Determine the total harmonic distortion as a percentage of the fundamental frequency voltage $(\backslash \%$THD$).(10$ points$)$