# Common Collector Amplifier or Emitter Follower Circuit

Common Collector Emitter Follower Amplifier

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