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Problem $4$: For the amplifier shown, $v_{in}$ is an ideal ac source. Given that $I_C=0\mathrm{.}925mA$ and $=100.$

$($a$)$ What is the main function of $R_E?$

$($b$)$ Calculate $g_m$ and $r_{}.$

$($c$)$ Draw its small signal equivalent circuit using the $-$model.

$($d$)$ Calculate the voltage gain $\frac{v_{\text{o}\text{u}\text{t}}}{v_{in}}.$

$($e$)$ Calculate its input resistance $R_{in}.$

$($f$)$ Calculate its output resistance $R_{\text{o}\text{u}\text{t}}.$

$($g$)$ Without calculations, what will happen to the overall gain if the ac source were not ideal?

$($h$)$ What are your options to further increase the gain?