The third, and final, small-signal BJT amplifier we will consider is the common collector amplifier shown below:
The small-signal equivalent circuit is shown in
We’ve included ro in this model since it can have an appreciable effect on the operation of this amplifier.
Notice that ro is connected from the emitter to an AC ground. We can simplify the AC small-signal analysis of this circuit by moving the collector-side lead of ro to the DC ground, as shown in
Similar to the previous BJT amplifiers, we’ll determine the
characteristics of this one by solving for Rin, Gv, Gi, Ais, and Rout.
• Input resistance, Rin. Looking into the base of the BJT,
From the circuit above, we see that
Vb=ie(re+r0||RL
Substituting this and 1b=i e/( ß +1) into (1) yields
Rib=( ß +1)(r e+r 0||R L)
This expression for Rib follows the so-called resistance
reflection rule: the input resistance is ( ß+1) times the total
resistance in the emitter lead of the amplifier. (We saw a
similar result in Lecture 19 for the CE amplifier with emitter degeneration.)
In the special case when r e<< R L<< r 0 then
R ab » (ß +1)RL
which can potentially be a large value.
Referring to circuit above, the input resistance to the amplifier is
• Small-signal voltage gain, Gv. We’ll first calculate the partial voltage gain
Beginning at the output,
from which we can directly determine that
The overall (from the input to the output) small-signal voltage gain Gv is defined as
We can equivalently write this voltage gain as
with Av given in (8). By simple voltage division at the input to the small-signal equivalent circuit
Substituting this result into (10) yields an expression for the
overall small-signal voltage gain
We can observe directly that each of the two factors in this
expression are less than one, so this overall small-signal
voltage gain is less than unity.
In the special instance that r0<< RL then (12) simplifies to
and if RB >>( ß+1)( re+RL) then this further simplifies to
We see from this expression that under the above two
assumptions and a third
RL>>re+ Rsig (ß + 1) , the smallsignal voltage gain is less than but approximately equal to one. This means that
Because of this result, the common collector amplifier is also called an emitter follower amplifier.
• Overall small-signal current gain, Gi. By definition
Using current division at the output of the small-signal
equivalent circuit above
while using current division at the input
Substituting this into (17) gives
from which we find that
• Short circuit current gain, Ais. In the case of a short circuit
load (RL = 0), Gi in (21) reduces to the short circuit current
gain:
In the case that RB >>( ß + 1)(re+RL)=( ß + 1)re, as was used earlier, then
Ais» ß + 1
which can be very large. So even though the amplifier has a voltage gain less than one (and approaching one in certain circumstances), it has a very large small-signal current gain. Overall, the amplifier does provide power gain to the AC signal.
• Output resistance, Rout. With vsig = 0 in the small-signal
equivalent circuit, we’re left with
It is a bit difficult to determine Rout directly from this circuit
because of the dependent current source. The trick here is to apply a signal source vx and then determine ix. The output
resistance is computed from the ratio of these quantities as
Applying KVL from the output through the input of this
circuit gives
Using KCL at the output
Substituting (26) into (25)
Forming the ratio of vx and ix in (27) gives
Summary
Summary of the CC (emitter follower) small-signal amplifier:
1. High input resistance.
2. Gv less than one, and can be close to one.
3. Ais can be large.
4. Low output resistance.These characteristics mean that the emitter follower amplifier is highly suited as a voltage buffer amplifier.
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