We will now begin the analysis of the three basic types of
linear BJT small-signal amplifiers:
1. Common emitter (CE)
2. Common base (CB)
3. Common collector (CC),
which is oftentimes called the emitter follower amplifier.
We’ll study the CE amplifier in this lecture and the next,
followed by the CB and CC amplifiers. The CE amplifier is
excited at the base of the BJT with the output taken at the
emitter:
The capacitor CE is called a bypass capacitor. At the operating
frequency, its purpose is to shunt out the effects of the DC
current source from the time varying signal. In other words, CE
sets an AC ground at this node at the frequency of operation.
There are a number of ways to bias this amplifier, other than
that shown above. What we’re primarily interested in here is the
small-signal characteristics.
Common Emitter Small-Signal Amplifier Analysis
The small-signal equivalent circuit for the CE amplifier above
is shown below. Because the emitter is located at an AC ground
is the reason this type of amplifier is called a “common
emitter” amplifier.
Notice that we’ve included ro in this small-signal model. This
is the finite output resistance of the BJT. This accounts for
thefinite slope of the characteristic curves of iC versus vCE
mentioned briefly in
where VA is called the Early voltage. Usually ro is fairly
large, on the order of many tens of kb Our quest in the
small-signal analysis of this amplifier is to determine these
quantities: input resistance Rin, the “overall” small-signal
voltage gain GV = vo/ vsig ,
the “partial” small-signal voltage gain v o i Av=
vo v i , the overall small-signal
current gain Gi= i0/ I i ,
the short circuit small-signal current gain is os i
Ais= ias ii ,and the output
resistance Rout.
• Input resistance, Rin. Directly from the small-signal
equivalent circuit, we see that
Rin= RB || r p
Oftentimes we select RB rp so that
i Rin rp
Oftentimes we select RB rp so that
r p will often be a few kb, which means this CE amplifier
presents a moderately large value of input impedance.
• Overall small-signal voltage gain, Gv. By “overall” voltage
gain we mean
which is the actual small-signal voltage gain that would be
realized in the circuit above. At the output of this circuit
Vo=-gmVp(ro||Rc
||Rl)
while at the input
Substituting (4) into (3) gives an expression for the overall
(i.e., realized) gain of this CE amplifier
In the usual case that B RB>> rp , then
Recall that rp = ß/gm If it also turned
out Rsig>> rp , then we see from (6)
that Gv would be directly dependent on b. This is not a
favorable condition since, as we learned when discussing biasing
of such BJT circuits, bita can vary considerably between
transistors. • Partial small-signal voltage gain, Av. This is
only a partial voltage gain since we are calculating
At the input, vi = Vp while at the output,
V0=-gmVp(ro||Rc
||RL)
Therefore, the partial small-signal voltage gain is
Av=-gm(ro||Rc||RL
• Overall small-signal current gain, Gi. By definition
Referring to the small-signal equivalent circuit shown above, we
see that
Forming the ratio of these two currents, we find that the
current gain is
or, using (9)
• Short circuit small-signal current gain, Ais. This is the
smallsignal current gain of the amplifier but with a short
circuitedload ( R L = 0):
Equivalently,
A is=G i| R l=0
Using (11) in (13) with R l=0 . gives
A is=-g m(r p||R
B)
In the usual case that R B r p then A
is »-bita This result is not unexpected because
bita is by definition the short circuit current gain for the BJT
when operating in the active mode.
• Output resistance Rout. Using the small-signal equivalent
circuit above, we short out the source vsig =0 which
means that vp =0 as well. Therefore, gm
vp = 0, which is an open circuit for a current
source. Consequently,
Rout= Rc|| r o
which is generally fairly large.
Summary of CE Amplifier Characteristics
Summary for theCommon_Emitter_Amplifier: Big voltage and current
gains are possible. Input resistance is moderately large.
Output resistance is fairly large.
This last characteristic is often not desirable. Why? Consider
this simple Thévenin equivalent for the output of a small-signal
amplifier:
The output signal voltage provided to this resistive load is
Now, if Rout<< RL then
This is not a favorable result if this Thévenin equivalent
circuit is for an amplifier because the output voltage is
beingattenuated. Con versely, if there were a small output
resistance such that Rout<< RL then then
(17) becomes
vout vo
which is much more favorable for an amplifier.
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