Single Stage Amplifier

For DC analysis, we usually want to know the currents and voltages through all the junctions. The followings are the equations which we need to calculate these values

Ic = Ie * a

Ib = Ie / (1 + b)

Ie = Ic / a

Ib = Ic / b

a = b / (1 + b)

Vc = Vcc - Ic * Rc

Ve = VBB (DC bias of Common-Base) - Ib * Rs - 0.7
 

For AC analysis, the equations we may need are followings:

gm = Ic / VT   (transconductance)
rpi = b /  gm = VT / Ib     (for hybrid-p model)
re = VT / Ie        (for T model)

ro = VA / Ic   (transistor output resistance)
 
 

Then, for the different type Amplifier, it will have different voltage gain, current gain, input resistance output resistance.

i) Common Emitter without Re

Ri=rpi

Ro=Rc || ro

Av =b* (Rc||ro)/(Rs + rpi)

Ai = b * ro / (ro + Rc)

ii) Common Emitter with Re

Ri = (a + 1) * (re + Re)

Ro = Rc

Av = - b * Rc / (Rs + (b +1) * (re + Re))

Ai = - b

iii) Common Base

Ri = re

Ro = Rc

Av= a * Rc / (Rs+re)

Ai = - a

iv) Common Collector  (or Emitter Follower)

Ri = (b +1) * ( re + ro||RL)

Ro = ro||(re + Rs / ( b + 1)

Av = (RL||ro) / (Rs / ( b +1) + re + RL||ro)

Ai = ( b +1) * ro / (ro+RL)