D $10\mathrm{.}97$ The amplifier in Fig. P$10\mathrm{.}97$ is biased to operate at $g_m=2m\frac{A}{V}.$ Neglect $r_o.$

Figure P$10\mathrm{.}97$

$($a$)$ Determine the value of $R_D$ that results in a midband gain of $-20\frac{V}{V}.$

$($b$)$ Determine the value of $C_S$ that results in a pole frequency of $100$ Hz $.$

$($c$)$ What is the frequency of the transmission zero introduced by $C_S?$

$($d$)$ Give an approximate value for the $3-$dB frequency $f_L.$

$($e$)$ Sketch a Bode plot for the gain of this amplifier. What does the plot tell you about the gain at dc$?$ Does this make sense? Why or why not?