Consider the common$-$emitter $($CE$)$ amplifier circuit shown in the below figure. Do the following:

$($a$)$ Draw the de bias circuit. This $npn$ BJT has $=100,V_{BE}=0\mathrm{.}7V$ in the active mode and $V_T=25mV.$

$($b$)$ Using the dc bias circuit in part $($a$),$ determine the values of $I_m{I}_a{I}_B{g}_m$ and $r_n$

With the results, prove that the transistor is operating in the active mode.

$($c$)$ Using the hybrid$-$ model $(g_m{V}_{}-$ version$),$ draw the small$-$signal equivalent circuit. Neglect the early voltage effect $(r_o).$

$($d$)$ Using the circuit in part $($c$),$ determine the values of the input resistance $(R_m),$ the output resistance $(R_q)$ and the overall gain $G_v(\frac{v}{v_{}}).$

$($Hint$)$ Refer to In$-$Class Problems $03$ and $04$ on pages $11$ and $12$ of the "ELEN$3363\_$Lecture$10"$ slides.