force this to converge after just 3 or 4 iterations. In general, though, we would never give something
this difficult on a test or exam. However, to build useful circuits in real life, you will often need to be
able to at least perform basic analysis of such complex circuits.
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241
This last lecture will cover the small signal model for the BJT. As we will see, it shares many
similarities with that of the MOSFET, so many of our old techniques still apply.
Current Topics: BJT SS Examples
The basic process for solving BJT small signal circuits is the same as what we studied for MOSFETs.
To begin, we must solve the BJT circuit at DC. Next, we replace capacitors and DC voltage sources
with a short circuit, and DC current sources with an open circuit. These steps are part of the general
smallsignal analysis process, and are identical for the MOSFET and BJT. The last step is to replace
the BJT with an equivalent smallsignal model.
BJT Small Signal Models
The basic smallsignal model for the BJT is called the hybridpi model. Like the default model for the
MOSFET, this is the generalpurpose replacement for the BJT in SS analysis. You will find it tends
to work best for finding opencircuit voltage gain (all cases), and input/output resistance when there
is no emitter resistor or commonbase connection. The primary difference from the MOSFET model
is the addition of the resistor from base to emitter,
, and the different formula for
. Like the
MOSFET, both of these smallsignal parameters are determined by the particular bias point (DC
current solution) of the circuit:
As with the NMOS and PMOS, the above model is valid for the NPN transistor. For the PNP model,
it is very important to note that the model is identically the same as to the NPN. There are no
changes in any voltage or current polarities. Be careful of this small detail. The governing equations
for the parameters of the above model are as follows:
Transconductance
BaseEmitter Resistance
Early Effect

 



As with the MOSFET, the BJT may be modeled with an added parallel resistance caused by what is
called the Early effect. Note that the formula for
for the BJT actually depends on
(while
Class Notes
–
BJT Small Signal Analysis
242
channellength modulation for the MOSFET did not depend on
). Usually this effect is small
compared to the magnitude of
, hence the approximation. As with the MOSFET, the values of
,
, and
come from our DC solution of the circuit. The value of
would be given if needed. Lastly,
the value of
is the same thermal voltage from the diode exponential model;
at
standard temperature. Note that the Early effect is less significant for the BJT at DC, and is
commonly ignored. It, however, often has a larger effect than the MOSFET in small signal domain.
Lastly, like the MOSFET, the BJT has an alternate model, also called the Tmodel.
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 Spring '17