Bias Point Analysis:
Is = 5x10^-17
β = 100
Vτ = 0.026
(From Simulation)
Ic = 2.34 mΑ
Ib = Ic/β = 23.4 μΑ
Ιe = Ic + Ib = 2.36 mA
Ve = Re*Ie = 1.18 V
Small Signal Analysis:
gm = Ic/Vτ = 0.09 S = 1/11.111 (1/Ω)
Rπ = β/gm = 2254.79 Ω
Gain = Re/(Re + 1/gm) = 0.9783
(suppose Ro->Inf, so without Early Effect)
By observing the smaller than unity gain of the emitter follower, we can see that it doesn't amplify the input signal,it only increases it by Ve . Thats because the primary usage of an emitter follower is not to amplify a signal,but to act as an intermidiate buffer of high input impedance and small output impedance.
In the case in which we use a current source as biasing device of the emitter follower we get an gain of unity.
Input Impedance:
Rin = Rπ + (β+1)*Re = 52.75 kΩ
Output Impedance:
Rout = Re||(1/gm) = 10.8696 Ω