Which model does this equation come from in fixed bias circuit?

Question

In fixed bias circuit

I calculated voltage gain by this :

I measured the DC response in simulation as:

Ic = 3.73 mA Ib = 15.7 uA Vc = 11.3 mV Vbe = 824 mV I calculated re (ac emitter resistance)

re = 25mV/Ic = 25mV/3.73 mA = 6.67 ohm I calculated voltage gain from

A = (R1//R3)/re = 4761/6.67 = 713

Which Multisim voltage gain is not match my calculation. And I asked question about this and found answer that :

"For a fixed bias amplifier like this the correct (and overkill formula) should be

Av=−α∗(RC//RLoad//RB)/re

where

re=Vth/Ie=kT/(qIe) α=0.996 "

Which model did they use in second voltage gain? And where does this equation from?

Answer 1

The mentioned gain formula A=-(Rc||RL)/re=-gm*(Rc||RL) is a rough expression only. It neglects the finite output resistance rce of the transistor (not an ideal current source) as well as some other non-dealities which are covered in the Ebers-Moll equations (core of the BJT models used in the simulators).

See here: Measuring BJT (Ebers-Moll) parameters