The input is applied to the gate and output is obtained at the source. The source follower amplifier is shown in fig .1. Ac equivalent circuit is drawn by connecting drain to ground

For voltage gain A_V: AV =Vo/Vi

Output voltage is measured across ro ||RS

Vo= gm Vgs (ro||RS) Vin=Vgs+Vo Vin=Vgs+gmVgs(ro||RS)=Vgs[1+gm(ro||RS)] Vgs=Vin/ (1+gm(ro||RS)

But Vin=Ri(Rsi+Ri) x ViVi where RiRi = R1||R1R1||R1

Vgs=((Ri(Rsi+Ri))Vi) / (1+gm(ro||RS))

Substitute this into expression for Vo to get,

Vo=((Ri(Rsi+Ri))gm(ro||RS)]) / (1+gm(ro||RS)) = (gm(ro||RS)])(1+gm(ro||RS))(Ri(Rsi+Ri))(gm(ro||RS)])(1+gm(ro||RS))(Ri(Rsi+Ri))

Input resistance (Ri):

Ri=R1||R2

Output resistance (Ro): The equivalent circuit to calculate Ro

Ro=Vo / Io

Apply KCL at node A to get,

Io+gmVgs=Ir+IRS

But Ir=Vo / ro and IRS=Vo / RS

Io+gmVgs=Vo(1 / ro+1 / RS)

Vgs=-Vo

Io=Vo(1 / ro+1 / RS)+gmVo =Vo[gm+1 / ro+1 / RS]Io

Ro=Vo / Io= = 1 / ([gm+1 / ro+1 / RS])

Ro=gm||1ro||1RS