Question

A transistor in the common emitter mode can be used as an amplifier

1. Design a circuit to amplify an ac signal given in the input region

[Hint: Give forward biasing to input region, reverse biasing to output region and take output across a resistor]

2. Derive expressions for voltage gain, current gain and power gain in the above transistor configuration.

Answer 1

1. 

2. When we apply an AC signal as input, we get an AC base current denoted by i_B . Hence input AC voltage can be written as

V_i = i_Br ……..(1)

where ‘r’ is the effective input resistance. This AC input current produces an AC output current (i_c) which can ow through a capacitor. Hence the output voltage can be written as

V₀ = i_c × output resistance

If we take output resistance as R_L then v₀ becomes

V₀ = i_c R_L

V₀ = β_ACi_B x R_L .....(2)    \(\Big[sinceβ_{AC} =\frac{i_C}{i_B}\Big]\)

AC voltage gain A_v = \(\frac{AC\,output\,voltage}{AC\,input\,voltage}\)

i.e. A_v = \(\frac{V_0}{V_1}\)

Substituting eq(1) and eq(2),in the above equation we get

A_v = \(\frac{β_{AC}i_B\times R_L}{i_Br}\)

A_v = \(\frac{β_{AC}R_L}{r}\)

Power gain:

The power gain A_p can be expressed as the product of the current gain and voltage gain. ie. power gain A = β_ac x  A_v.