Biomedical Engineering Reference
In-Depth Information
Next, we eliminate
v
n
by substituting
v
1
into the inverting input KCL equation, as follows:
1
2
v
n
¼
ð
v
1
þ
v
o
Þ
1
2
¼
ð
v
o
2
V
s
þ
v
o
Þ
¼
v
o
V
s
Finally, we substitute the solutions for
v
1
and
v
n
into the node 1 KCL equation, giving
R
1
v
n
þ
ð
2
R
1
þ
R
2
Þ
v
1
R
1
v
o
¼
0
R
1
v
o
V
s
ð
Þ þ
ð
2
R
1
þ
R
2
Þ
v
o
ð
2
V
s
Þ
R
1
v
o
¼
0
After simplification, we have
ð
3
R
1
þ
2
R
2
Þ
v
o
¼
V
s
R
2
Example Problems 9.23 and 9.24 illustrate an op amp circuit that differentiates and inte-
grates by using a capacitor.
EXAMPLE PROBLEM 9.23
Find
v
0
for the following circuit.
i
R
R
+
v
C
−
i
C
−
+
+
C
+
+
+
−
V
S
v
n
v
0
v
p
−
−
−
Solution
With the noninverting input connected to ground, we have
v
p
¼
0
¼
v
n
. From KVL
v
C
¼
V
s
Continued
