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Emitter Follower and Differential Amplifiers

Emitter Follower and Differential Amplifiers
The next two amplifier circuits we will discuss are very important to electrical engineering in general, and to the NorCal 40A specifically.However, neither of these amplifiers appears in discrete form in the NorCal 40A. Instead, you will find these amplifiers performing their important functions inside ICs.
Emitter Follower (aka Common Collector) Amplifier
A typical emitter follower amplifier is shown in

There are two big differences between this amplifier and the common emitter amplifier:
1. there is no collector resistor,
2. the output voltage is taken at the emitter. There are four important characteristics of the emitter follower amplifier (presented here without derivation):
1. voltage gain ?? 1,
2. current gain > 1,
3. high input impedance,
4. low output impedance (?1 ?).
Consequently, the emitter follower is useful as
1. a buffer amplifier,
2. an almost ideal voltage source.
In the NorCal 40A, emitter followers can be found internally in the:
1. Audio Amplifier U3 (LM 386). See the equivalent schematic on p. 399.
2. Oscillator circuits of the Product Detector U2 and the Transmit Mixer U4. Both are SA602 ICs. See the equivalent circuit shown in Fig. 4 on p. 419 of the text.
Differential Amplifier
This is probably a new circuit for you. The differential amplifier is an interesting circuit in that it amplifies only a difference in the two input voltages.
Actually, you’ve used differential amplifiers for years now, though you probably didn’t know it. A differential amplifier appears as the input circuit for an operational amplifier. It is this circuit that gives rise to the familiar v0= A(v+ ?V?) relationship for the op amp (where A is the open-loop gain). The differential amplifier also appears in the Audio Amplifier and the SA602 mixer ICs in the NorCal 40A. In the latter case, the diff amps appear in the form of Gilbert Cells (see p. 227). We will spend some time here on the operation of the differential amplifier, considering its importance to the mixing process.
A typical differential amplifier is shown in

It’s important that the circuit have matched transistors and resistors for satisfactory performance (more specifically, to ensure symmetry in the circuit).
This diff amp is a moderately complicated circuit to analyze. A relatively simple method of analysis, however, is to consider two special cases of input signals:
1. vi1 = ?vi2 , called the differential (or “odd”) input,
2. vi1 = vi2 , called the common-mode (or “even”) input.
After determining the response of the diff amp to each of these two excitations, arbitrary combinations of inputs can be analyzed as weighted combinations of these two.
I. Differential Input,vi1 = ?vi2 : For these input voltages,
Ie1=-ie2 Þ it=ie1+ie2=0
With each amplifier effectively grounded at Rt, then we can use the common-emitter amplifier gain

To give

And

The output voltage for this specific input combination is defined as the differential output voltage vd as


where vid ? vi1 ? vi2 is the differential input voltage. Therefore, the differential gain Gd is

Note that this is the same gain for just one half of the differential amplifier.
II. Common-Mode Input, vi1 = vi2 : For these input voltages,
ie1 = ie2 ? ite = ie1 + ie2
Applying KVL through the transistor bases to Rt and then to ground, the input voltages can be expressed as
vi1 = Re i e1+ Rt it =( Re + 2R t)ie1
vi2 = Re i e2+ R ti t=( Re + 2Rt) ie2
The last equalities use the relationships it = 2i e2 and it = 2ie2 ,respectively.
Next, using KVL from Vcc to v1 (ac signals only) gives

Similarly, it can be shown that

Notice that with this common-mode input, both v1 and v2 are equal. Consequently, the output voltage is
v0= v1 ? v2 = 0
This last result clearly shows that the differential amplifier does not amplify signals that are common to both inputs. Cool! Since these voltages v1 and v2 are the same, we define either of them as the common-mode voltage vc
v c= v1 = v2
so that

Using

where vic = vi1 = vi2 . Hence, the common-mode gain Gc is

Differential Amplifiers in the SA602 Mixers
As mentioned previously, the differential amplifier plays a critical role in the SA602 mixer. Specifically, the diff amp appears as the two input terminals 1 and 2 (see p. 419). However, in the NorCal 40A, only one diff amp input is connected to the signal (SA602 pin 1). The other input (pin 2) is connected to ground (through a dc block capacitor). This input configuration is not one of the two considered earlier. We can account for this type of input, however, simply as a weighted sum of differential and common-mode inputs. That is, in order to account for the inputs vi1 = vi and vi2 = 0, use (1) and
(2) to yield:

Let’s check that weighted sums of these two inputs (9.70) and (9.71) are indeed equivalent to the desired inputs vi1 = vi and vi2 =0 . First, calculate (9.70)+2?(9.71) (i.e., the sum vid + 2vic ) giving

Next, calculate 2?(9.71)-(9.70) (i.e., the sum 2 vic ?v ) giving

Summary of Common and Differential Inputs
The check we just performed illustrates the usefulness of the common and differential input analysis. We began with

Then we asked: What v and vic (differential and commonmode inputs) yield the same v1 and v2 as for the non-symmetric inputs shown above? The answers, as we just saw, are

Expanding these two results, we find from (9.59) that
Vd=V1-V2=GdVid=GdVi
And



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