Figure 1 : Circuit Diagram of CS-CS Amplifier

At mid frequency all connected capacitors acts as short circuit. Hence AC equivalent using JFET becomes,

Figure 2 : AC equivalent circuit

Av (Voltage Gain) :

Av2 = $\frac{Vo}{Vo1}$

Vo= Io Rd2 …..(1)

Io= $\frac{-gmVgs2×rd}{rd+Rd2}$ ……..(2) by CDR

Substitute equation (2) in (1),

Vo= $\frac{-gmVgs2×rd×Rd2}{rd+Rd2}$

Vo = - gm Vgs2 (rd || Rd2)

Since Vgs2 and Vo1 are in parallel. Hence, Vo1=Vgs2

Vo = - gm Vo1 (rd || Rd2)

Av2= $\frac{Vo}{Vo1}$ = - gm (rd||Rd2)

Av1 is obtained by considering following circuit,

Figure 3 : Part of AC equivalent Circuit

Vo1 = Io1×Rg2

But,

Io1=" $\frac{-gmVgs1×(Rd1||rd)}{(Rd1||rd )+Rg2}$ By CDR

Vo1=$\frac{-gmVgs1×(Rd1||rd)×Rg2}{(Rd1||rd)+Rg2}$

Vo1 = -gmVgs1×(Rd1||rd||Rg2)

But Vgs1 & Vin are in parallel, hence Vgs1=Vin

Av1=$\frac{Vo1}{Vin}$ = -gm(Rd1 || rd || Rg2)

Multiply Av1 & Av2 to obtain Av,

AV = Av1×Av2

Zi (Input Resistance) :

Zi = Rg1

Zo (Output Resistance) :

Zo can be obtained using following steps

1. Set Vin=0.
2. Open load resistance.
3. Connect and imaginary voltage source Vo that delivers current Io.

Figure 4 : AC equivalent for Zo

Vo = Io(Rd2||rd)

$\frac{Vo}{Io}$ = Zo= (Rd2|| rd)

Zo= (Rd2|| rd)