A single$-$stage amplifier built with a $p-$channel enhancement$-$mode MOSFET is placed between a transducer $(E_{ST}$ and $R_{ST})$ and a load resistor $(R_L)$ as shown in Figure $453.M_1$ has low$-$frequency model parameters given below.

$g_{mf}=200S$

$x=0\mathrm{.}2$

$g_{ds}=0$

$r_s=0$

$r_b=0$

$($a$)$ Use these parameters and the component values shown on the schematic to calculate the value of the mid$-$band transducer voltage gain $G_{vs}$ that is defined as

$($b$)$ Calculate the value for the source resistor Rs that will produce a transducer voltage gain magnitude of $4\frac{V}{V}$; that is$.$

$|G_w|=4\mathrm{.}0\frac{V}{V}$