Derive the expressions for closed-loop gain Avf, input resistance Rif, and output resistance Rof of the following image.© BrainMass Inc. brainmass.com December 24, 2021, 5:01 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
This is a schematic of the basic emitter follower circuit. Just a transistor and a single resistor from the emitter to ground.
Writing the voltage equation around the input loop,
Vi - Vbe - Vo = 0 ---------- 1
Making Vbe very small or the gain large, we have, Vi =(approx.) = Vo
The output follows the input. thats why this circuit is called an emitter follower.
The voltage gain Vo/Vi is less than but near unity in magnitude.
From the load in the emitter circuit,
Vo = Re (Ib + Ic) = (1+hfe)*Re * Ib -----Since Ic = hfe Ib
At the input we have Vbe = hie * Ib
Substituting these back to our equation 1,
Vi = [hie + (1 + hfe)*Re ]* Ib ------------ 2
The input resistance of the amplifier follows as,
Rie = Vi/Ib = hie + (1 + hfe)*Re = approx. = hie + hfe*Re ---- 3
To find the output resistance,
(refer to the attached figure) The output resistance at the 2,2 port is found by making the independent source Vi = 0.
With hie parallel with Re,
Output resistance, Roc = hie * Re/[hie + Re] --------4
Voltage gain, Avf = -Ai Re/Ri
= hfe *Re/hie[1 + gm Re] where gm = hfe/hie
= gm*Re/[1+gm*Re] ---------5© BrainMass Inc. brainmass.com December 24, 2021, 5:01 pm ad1c9bdddf>