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Derive the equations for AV, Ai, Ri and Ro for a NPN transistor in CE mode voltage divider bias configuration with RE unbiased.

Mumbai University > Electronics and telecommunication engineering > Sem 3 > Analog electronics 1

Marks: 10M

Years: May 15

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AC equivalent circuit:

Let us draw the AC equivalent circuit of voltage divider bias configuration with RE unbiased

enter image description here

Approximate h-parameter equivalent circuit:

Now replace the transistor in the AC equivalent circuit fig by its hybrid equivalent circuit.

Obtain the expression for Ri and Ri:

Ri=VbIb … (1)

But Vb=Ibrπ+IeRE=Ibrπ+(1+β)IbRE

Vb=Ib[rπ+(1+β)RE] ….. (2)

Substituing eq 2 in 1

Ri=(Ib[rπ+(1+β)RE])Ib=rπ+(1+β)RE

Ri=rπ+(1+β)RE

Ri=R1||R2||rπ+(1+β)RE

Obtain the expression of voltage gain AVS:

AVS=VoVs

enter image description here

Vo= Voltage across ( RC||RL)

Vo=βIb(RC||RL) …. (3)

Now refer circuit Fig4.2,

Vb=IbRi

Substitute this in eq 3

Vo=(βIb(RC||RL))Ri

But Vb=Ri(Ri+Rs) X VS

Vo=(βRiVS)(Ri+RS) X ((RC||RL))Ri

AVS = VoVs = (βRi)(Ri+RS) X ((RC||RL))Ri

But Ri=rπ+(1+β)RE

AVS=(β(RC||RL))(rπ+(1+β)RE) X Ri(Ri+RS)

If Ri>>RSand(1+β)>>rπ then

AVS=((RC||RL))RE

This is the expression for voltage gain.

Output resistance:

Let VS = 0, and Vx is connected between the output terminals and current supplied by this source be Ix.

enter image description here

As VS = 0, Ib will reduce to zero. Hence βIb = 0 so the dependent current source is replaced by an open circuit.

Therefore, Ro = VxIx = ( RC||RL)

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