BJT: large and small signal models

Question

I am a bit rusty on my BJT circuit analysis and relooking at my college notes I can't remember the cross-over point when you switch between large signal and small signal models.

The large signal model is just a diode between base and emitter with a current source between collector and emitter whose equation is β.I_b.

The small signal model is the T or PI model where there is the AC dynamic resistance of the diode re between base and emitter and a current source again β.I_b although this can be replaced with a voltage controlled current source gm.v_be where v_be is the small signal voltage across the base and emitter.

Now when you design the bias of the circuit you use the large signal model. When you look at the gain of your circuit you use the small signal model. However when you come to the analysis for instance of a push-pull amplifier I have seen texts use the large signal model and sometimes consider re although it will be negligible at high currents (re = 25mV/I_c(mA)). I just want to get it set in stone in my head so I have a design procedure approach for all situations and trying to remember all this from 30 years ago :-)

Answer 1

I just want to get it set in stone in my head so I have a design procedure approach for all situations ...

Both large signal and small signal regions are models, just our approximations for how the circuit behaves.

In some situations, it's obvious whether to use one or the other. In other situations, like the output stage of a push-pull amplifier, it's appropriate to consider both.

Stability will always require consideration of the small signal model if a transistor is in the active amplifying region, whether it's in a small signal or large signal environment. If the large signal operation takes it through several different bias currents, then you will need to redo your linear model for each.

Answer 2

Quote: "...when you come to the analysis for instance of a push-pull amplifier I have seen texts use the large signal model and sometimes consider re although it will be negligible at high currents (re = 25mV/Ic(mA))."

Perhaps it helps to remember the physical meaning of the quantity re=26mV/Ic.

This "resistance" re (which really is NOT a classical two-pole resistance) is nothing else than the inverse transconductance re=1/gm with gm=d(Ic)/d(Vbe) [slope of the Ic=f(Vbe) curve] at the corresponding opearational point. This quantity gm is an important parameter for finding the small-sigal gain of an amplifier.

However, also under large-signal conditions (push-pull applications) the Ic=f(Vbe) characteristic is dominant because it describes the connection between the input Vbe and output (Ic). Therefore, it is also possible to express this relation in some formulas using the corresponding slope gm=1/re, which will vary under large-signal conditions.

Hence, although re=1/gm is a small-signal parameter it can in some cases appear in formulas for large signal applications - but it would be not correct to say that a small-signal analysis is used for push-pull analyses.