Question

Derive the expression for the voltage gain of a transistor amplifier in CE configuration in terms of the load resistance R_L, current gain β_a and input resistance.
Explain why input and output voltages are in the opposite phase.

Answer 1

 Let R_i be the input resistance of the emitter-base circuit. When an input signal voltage V_i is applied to the emitter-base circuit, let ΔI_b, ΔI_c be the change in base current and collector current respectively.

Then, V_i = ΔI_b × R_i

Then ac current gain of the transistor is,

Current gain, `beta_"a" = (Delta "I"_"C")/(Delta "I"_"B")`

⇒ Δ I_C = β_a × ΔI_B

Also, V_CE = V_CC -I_CR_L

As the change in the base current changes the collector current but not V_CC, so,

ΔV_CE = 0 - ΔI_CR = - (β_a Δ I_B) R_L

Output voltage, V₀ = ΔV_CE - β_a Δ I_BR_L

The voltage gain of the common emitter amplifier,

`"AV" = "V"_0/"V"_"i" = (-beta Delta "I"_"B""R"_"L")/(Delta "I"_"B""R"_"i") = -beta_"a" "R"_"L"/("R"_"i")`

`"AV" -beta_"a" "R"_"L"/("R"_"i")`

Here, -ve sign shows that the output voltage is 180^o out of phase with the input voltage. i.e. input voltage and output voltage are in the opposite phase. As the input voltage rises, so the current increases through the base circuit, this increases the current through the collector circuit. This results in the voltage between the collector and emitter terminals falling.