Common emitter amplifier characteristics
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
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,
Therefore, the partial small-signal voltage gain is
• 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):
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
which is much more favorable for an amplifier