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 v_{0}= 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. v_{i1} = ?v_{i2} , called the differential (or “odd”) input,
2. v_{i1} = v_{i2} , 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,v_{i1} = ?v_{i2} : For these input voltages,
I_{e1}=-i_{e2} Þ i_{t}=i_{e1}+i_{e2}=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 v_{d} as

where v_{id} ? v_{i1} ? v_{i2} is the differential input voltage. Therefore,
the differential gain G_{d} is

Note that this is the same gain for just one half of the
differential amplifier.
II. Common-Mode Input, v_{i1} = v_{i2} : For these input voltages,
i_{e1} = i_{e2} ? i_{te} = i_{e1} + i_{e2}
Applying KVL through the transistor bases to Rt and then to
ground, the input voltages can be expressed as
v_{i1} = R_{e} i _{e1}+ R_{t} i_{t} =( R_{e} + 2R _{t})i_{e1}
v_{i2} = R_{e} i _{e2}+ R _{t}i _{t}=( R_{e} + 2R_{t}) i_{e2}
The last equalities use the relationships i_{t} = 2i _{e2} and i_{t} = 2i_{e2} ,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
v_{0}= v_{1} ? v_{2} = 0
This last result clearly shows that the differential amplifier
does not amplify signals that are common to both inputs. Cool!
Since these voltages v_{1} and v_{2} are the same, we define either of
them as the common-mode voltage vc
v _{c}= v_{1} = v_{2}
so that

Using

where v_{ic} = v_{i1} = v_{i2} . Hence, the common-mode gain G_{c} 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 v_{i1} = v_{i} and v_{i2} = 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 v_{i1} = v_{i} and v_{i2} =0 .
First, calculate (9.70)+2?(9.71) (i.e., the sum v_{id} + 2v_{ic} ) giving

Next, calculate 2?(9.71)-(9.70) (i.e., the sum 2 v_{ic} ?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 v_{ic} (differential and commonmode
inputs) yield the same v_{1} and v_{2} 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
V_{d}=V_{1}-V_{2}=G_{d}V_{id}=G_{d}V_{i}
And