Question $2(25$ marks$)$

Assume that all diodes in Figure $2$ are ideal. The input signal $V_{in}$ is a sinusoidal waveform with peak voltage of $170V,50Hz.$ The transformer ratio is $17$:$1.$ Determine the following:

$($a$)$ Calculate the period of the input signal $V_{in}.$

$(5$ marks $)$

$($b$)$ Sketch $V_s$ and $V_{\text{o}\text{u}\text{t}}$ with respect to $V_{in}$ over $2$ cycles. Indicate the peak values clearly.

$(10$ marks $)$

$($c$)$ Calculate the average value of $V_{\text{o}\text{u}\text{t}\text{.}}$

$(5$ marks $)$

$($d$)$ Explain and sketch $V_{\text{o}\text{u}\text{t}}$ if Diode $D_2$ is spoilt and cannot conduct wurrent.

Figure $2$