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Draw approximate hybrid π model of CE transistor amplifier and derive expressions for Av, Ai, Zi and Zo.

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

Marks: 10M

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enter image description here

Hence Hybrid π equivalent circuit becomes,

enter image description here

Av(Voltage Gain) :

The output voltage is,

VO=(ro||Rc||RL)gmVbe…………………..(1)

The base emitter voltage Vbe, which controls the collector current, Vbe is voltage across Zi, Applying voltage divider rule,

Vbe=R1||R2||rπRs+R1||R2||rπVs

Substituting value of Vbe in equation (1),

Vo=(ro||Rc||RL)gmR1||R2||rπRs+(R1||R2||rπ)Vs

This gives voltage gain Rs,

Av=VoVs=(R1||R2||rπ)(ro||Rc||RL)gmRs+(R1|R2||rπ)

Av=(R1||R2||rπ)×(ro||Rc||RL)gmRs+(R1||R2||rπ)

Ai( Current Gain) :

Current Io flows through load resistance RL. Hence applying current divider rule at C,

Io=gmVbe×(ro||Rc)(ro||Rc)+RL----------------------------(2)

From Figure 2,

Vbe=Ibrπ

Apply current divider rule at b,

Ib=R1||R2rπ+(R1||R2)Ii

Vbe=(R1||R2)rπrπ+(R1||R2)Ii

Vbe=(R1||R2||rπ)Ii

Substitute Vbe in equation (2),

Ai=IoIi=gm(R1||R2||rπ)×(ro||Rc)(ro||Rc)+RL

Ai=gm(R1||R2||rπ)×(ro||Rc)(ro||Rc)+RL

Zi (Input Resistance):

Zi'=Vb/Ib

But

Vb=Ibrπ

Hence,

Zi=rπ

Zi = R1||R2||Zi’

Zi=R1||R2||rπ

Zo (Output Resistance):

For Output Resistance:

Step 1: Set Vs=0V

Step 2: Open the load.

Step 3: Connect an imaginary voltage source Vs at output terminal

enter image description here

Hence an imaginary voltage source delivers current through parallel combination ro and Rc. Where,ro=VA/ICQ

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