Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 9.22
Find
v
0
for the following circuit.
R
2
−
+
v
n
+
+
+
v
p
R
2
+
V
S
−
1
v
0
+
R
2
v
1
R
1
−
−−
−
Solution
With
v
n
¼
v
p
, we apply KCL at the inverting input
v
n
v
1
R
2
þ
v
n
v
o
2
¼
0
R
and
0
Next, we apply KVL from ground to node 1 to the noninverting input and back to ground,
giving
v
n
v
1
v
o
¼
2
v
1
V
s
þ
v
p
¼
0
and with
v
n
v
1
¼
V
s
:
Now we apply KCL at node 1, noting no current flows into the noninverting input terminal:
v
1
R
v
n
¼
v
p
, we have
1
þ
v
1
v
o
2
þ
v
1
v
n
2
¼
0
R
R
Combining like terms in the previous equation gives
0
With three equations and three unknowns, we first eliminate
R
1
v
n
þ
ð
2
R
1
þ
R
2
Þ
v
1
R
1
v
o
¼
v
1
by subtracting the inverting
input KCL equation by the KVL equation, giving
v
1
¼
v
o
2
V
s
