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Derive equation of voltage gain, input resistance and output resistance of voltage divider based JFET amplifier.

Mumbai University > Electronics Engineering > Sem 4 > Discrete Electronic Circuits

Marks: 10M

Year: Dec 2016

1 Answer
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enter image description here

Figure 1: Circuit Diagram of Common Source amplifier.

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

enter image description here

Figure 2: Small signal equivalent circuit

Voltage Gain (AV):

VO=IORD

But IO=Ids

VO=IdsRD ....(1)

Apply KCL at drain terminal,

Ids=I1+gmVgs

I1=VOrd

Ids=VOrd+gmVgs .....(2)

substitute equation (2) in (1),

VO=(VOrd+gmVgs)RD

VO+VOrdRD=gmVgsRD

VO(1+RDrd)=gmVgsRD

VO(rd+RDrd)=gmVgsRD

VO=gmVgs(RDrdrd+RD)

VO=gmVgs(RD||rd)

From input side we get vin = vgs,

hence, VO=gmVin(RD||rd)

AV=VOVin=gm(RD||rd)

Input Resistance (Rin):

Rin=VinIin

Since Iin passes only through R1||R2,

Rin=VinIin=R1||R2

Output Resistance (RO):

RO can be obtained using following steps:

i. Set Vin=0.

ii. Connect and imaginary voltage source VO that delivers current IO.

RO=VOIO

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Figure 3 : AC equivalent for RO

RO=VOIO=RD||rd

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