Step 1 :

Calculate $r_d$ - 

$r_d=\dfrac{1}{Y_{os}}$

$\therefore r_d=\dfrac{1}{20 \times 10^{-6}}$

$\therefore r_d=50k \Omega$

Step 2 :

Calculate $g_m$

$\therefore g_m=\dfrac{I_D}{V_{DSQ}}$

But $I_D=\dfrac{V_{DD}-V_{DSQ}}{R_D}$

 $\therefore I_D=\dfrac{10-2.75}{3.3}=2.197mA$

$\therefore g_m=\dfrac{2.197}{2.75}=0.7989mS$

Analysis with $r_d$

Step 1 :

Calculate $A_V$

$\therefore A_V=\dfrac{V_0}{V_i}=\dfrac{-g_mV_{gs}(r_d\mid\mid R_D \mid\mid R_F)}{V_gs}=-g_m(r_d\mid\mid R_D \mid\mid R_F)$

$\therefore A_V=-0.7989 \times 10^{-3}[50k \mid\mid3.3k\mid\mid10M]$

$\therefore A_V=-0.7989 …