If the three$-$phase inverter drawn in $($a$)$ has resistive load of $Z$ per phase and is fed from a d$.$c$.$ supply voltage rail of $V_{dc}.$ If the six$-$step method is used, and the triggering mode is where three switches conduct simultaneously, that is $180$ degrees conduction mode.

$($i$)$ Sketch the gate signal voltages waveforms of $V_{S1},V_{S2},V_{S3},V_{S4},V_{S5}$ and $V_{S6}.$

$($ii$)$ Indicate which of the six switches are conducting during each $60$ degrees interval of the cyclic period.

$($iii$)$ Deduce the phase voltages of $V_{an},V_{bn},$ and $V_{cn}$ and the line voltages of $V_{ab},V_{bc},$ and $V_{ca}$ for switches conducting during each $60$ degrees interval.

$($iv$)$ Sketch the phase voltages waveforms of $V_{an},V_{bn},$ and $V_{cn}$ and line voltages waveforms of $V_{ab},V_{bc},$ and $V_{ca}.$

QUESTION THREE

$(20$ Marks$)$

$($a$).$ What is safe operating area $($SOA$)$ of power semiconductor devices.

$($b$).$ Sketch the curve of safe operating area $($SOA$)$ of power semiconductor and explain the various limitations of the device.

$($c$).$ Sketch the switching characteristics curve of Insulated Gate Bipolar Transistor $($IGBT$)$ and indicate on the curve the switching ON and OFF.

$($d$).$ Consider the switching waveform for power semiconductor device if the load is resistive show that, the total switching dissipation is given by;

$W_{on}=\frac{V_{\text{b}\text{u}\text{s}}{I}_{\text{l}\text{o}\text{a}\text{d}}(t_{on}+t_{\text{o}\text{f}\text{f}})f}{6}$

QUESTION FOUR

$($a$)$ Sketch and explain the circuit and waveforms of a single $-$phase full bridge inverter

$($b$)$ Construct a table to indicate the following on it for both positive and negative cycle

$($i$)$ Load voltage, current and conducting devices

$($c$)$ A single$-$phase half rectifier feeds a $15$ resistance. The supply voltage is $230$ V $($ mms $).$ The firing angle is $\frac{}{2},$ find $($i$)V_{dc},I_{dc},V_{rms}$ and $I_{rms}$