Common-collector (Emitter Follower) Amplifier:

The basic emitter follower arrangement is illustrated in Figure (a), while its small signal ac equivalent circuit is illustrated in Figure (b).

Figure (b) : Small Signal Equivalent of Common Collector Amplifier

From the circuit, we see that I₀ = (1 + β) i_b so that the output voltage V₀ may be written as

                                                     V₀  = (1 + β) i_b  (r₀  // R_E )

The loop equation of the base-emitter loop is

V_in  = i_b [r_π + (1 + β) (r₀  // R_E )

from where we get :

R_ib = V_in/ ib=  r_π + (1 + β) (r₀  // R_E )

Furthermore,

V_in  = (R_i / R_i  + R_s)V_s  where  R_i  = R₁ // R₂  // R_ib

From the above equations, at last we find

A  = V₀  / V _s  ( (1 + β) [r₀  // R_E ] /  r_π  + (1 + β) (r_o  // R_E ))(R_i/ R_i  + R_s )

Therefore, it is seen that gain is positive which means that output and input are in same phase.

 Also, if (1 + β) (r₀ // R_E) >> r_π and R_i >> R_s

A_v ≅ 1 (In practice, it is, though always slightly less than unity). The small signal output resistance of the circuit is specified by

R₀  =     ( r_π + (R₁  || R₂  || R₃ ) /(1 + β))|| R_E|| r₀

From the equivalent circuit, it follows that for V_s = 0 (or V_π = 0), the small signal resistance looking into the output terminal shall be equal to R_c, Thus,

                             R₀ = R_C