Biomedical Engineering Reference
In-Depth Information
contains only the signal of interest uncontaminated by noise from the environment. The noise is
typically called a
. A common-mode signal comes from lighting, 60-Hz power
line signals, inadequate grounding, and power supply leakage. A differential amplifier with
appropriate filtering can reduce the impact of a common-mode signal.
common-mode signal
The response of a differential amplifier can be decomposed into differential-mode and
common-mode components:
v
dm
¼
v
b
v
a
and
v
cm
¼
v
a
þ
v
b
ð
Þ
2
As described, the common-mode signal is the average of the input voltages. Using the
two previous equations, one can solve
v
a
and
v
b
in terms of
v
dm
and
v
cm
as
v
a
¼
v
cm
v
d
2
and
v
b
¼
v
cm
þ
v
d
2
When substituted into the response in Example Problem 9.21, we get
R
R
2
R
R
R
ð
R
1
þ
R
Þ þ
R
ð
R
1
þ
R
Þ
1
1
2
2
2
2
2
v
0
¼
v
cm
þ
v
dm
¼
A
cm
v
cm
þ
A
dm
v
dm
R
1
R
1
þ
R
2
ð
Þ
2
R
1
R
1
þ
R
2
ð
Þ
Notice the term multiplying
, is zero, characteristic of the ideal op amp that ampli-
fies only the differential-mode of the signal. Since real amplifiers are not ideal and resistors
are not truly exact, the common-mode gain is not zero. So when one designs a differential
amplifier, the goal is to keep
v
cm
,
A
cm
A
cm
as small as possible and
A
dm
as large as possible.
The rejection of the common-mode signal is called
common-mode rejection
, and the mea-
sure of how ideal the differential amplifier is called the
common-mode rejection ratio,
given as
20 log
10
A
dm
CMRR
¼
A
cm
where the larger the value of
CMRR,
the better. Values of
CMRR
for a differential amplifier
for EEG, ECG, and EMG are 100 to 120 db.
The general approach to solving op amp circuits is to first assume that the op amp is
ideal and
. Next, we apply KCL or KVL at the two input terminals. In more complex
circuits, we continue to apply our circuit analysis tools to solve the problem, as Example
Problem 9.22 illustrates.
v
p
¼
v
n
