Common-Emitter Amplifier:

An exemplary common-emitter configuration is illustrated in Figure

Figure: An Exemplary Common-emitter Amplifier

For analyzing this circuit, we suppress the DC voltage (by setting V_cc = 0) and replace the transistor by its small signal AC equivalent circuit in terms of r_π and a current source β i_b, supposing r₀ → ∞, such an equivalent circuit is shown in Figure. The small signal voltage gain A_v, of this amplifier may be found as follows :

The loop equation of the base-emitter loop gives :

V_in  = i_b  r_π + (i_b  + β i_b ) R_E

so that we may find

R_ib = V _in  / i_b = r_π + (1 + β) R_E

The input resistance to the amplifier is, thus, specified by

R_i  = R₁ || R₂ || R_ib

Also,

Vin  = (R _i / R_i  + R_s) V_s

and

V₀  =- (β_ib ) R_c

Figure: AC Small Signal Equivalent Circuit of the Common-emitter Amplifier

Combining the above, we get

 A _v  = V₀   / V _in =- β R_c /  [r _π + (1 + β) R_E]( R_i / R_i  + R_S  )

From the above, we see that if R_i >> R_s and (1 + β) R_E >> r_π then

A_V  ≅    - β R_c/(1 + β) R_E  = - R_C/ R_E  , for large β.

Furthermore, if R_E = 0 and R_C >> R_S

A_v  ≅ (β/ r _π) R_C  ≅ - g_m R_c

Thus , It is seen that gain is negative which means that input and output of the amplifier are 180^o out of place.