431/531 Class Notes 7
5.7 Transistor Dierential Amplier
Dierential ampliers are in general very useful. They consist of two inputs and one output,
as indicated by the generic symbol in Fig. 24. The output is proportional to the
dierence
between the two inputs, where the proportionality constant is the gain. One can think of
this as one of the two inputs (labelled \
,
") being inverted and then added to the other
non-inverting input (lab elled \+"). Operational ampliers (\op amps"), whichwe will soon
study, are fancy dierential ampliers, and are represented by the same symbol as that of
Fig. 24.
+
-
in1
in2
out
Figure 24: Symbol for a dierential amplier or op amp.
This technique is commonly used to mitigate noise pickup. For example, a signal which
is to be transmitted and subject to noise pickup can rst be replicated and inverted. This
\dierential pair" is then transmitted and then received by a dierential amplier. Any
noise pickup will be approximately equal for the two inputs, and hence will not appear in
the output of the dierential amplifer. This \common mode" noise is rejected. This is often
quantied by the common-mode rejection ratio (CMRR) which is the ratio of dierential
gain to common-mo de gain. Clearly, a large CMRR is good.
5.7.1 A Simple Design
The circuit shown in Fig. 25 represents a dierential amplier design. It looks liketwo
common-emitter ampliers whose emitters are tied together at point A. In fact, the circuit
does behaveinthisway. It is simplest to analyze its output if one writes each input as the
sum of two terms, a sum and a dierence. Consider twosignals
v
1
and
v
2
. In general, we
can rewrite these as
v
1
=
<v>
+
v=
2and
v
2
=
<v>
,
v=
2, where
<v>
=(
v
1
+
v
2
)
=
2is
the average and
v
=
v
1
,
v
2
is the dierence. Therefore, we can break down the response
of the circuit to b e due to the resp onse to a common-mode input (
<v>
) and a dierence
(
v
) input.
Let's analyze the dierence signal rst. Therefore, consider two inputs
v
1
=
v=
2and
v
2
=
,
v=
2. The signals at the emitters then follow the inputs, as usual, so that at pointA
wehave
v
A
=
v
E
1
+
v
E
2
=
v
1
+
v
2
=0. Following the common-emitter amplier derivation,
wehave
v
out1
=
,
i
C
R
C
, where
i
C
i
E
=
v
E
=R
E
=
v
in1
=R
E
. Hence,
v
out1
=
,
(
R
C
=R
E
)
v
1
and
v
out2
=
,
(
R
C
=R
E
)
v
2
.We dene the
dierential gain
G
di
as the ratio of the output to
the input dierence. So
G
di1
v
out1
=
v
=
,
(
R
C
=R
E
)
v
1
=
(2
v
1
)=
,
R
C
=
(2
R
E
)
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