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Example problem 1
Find the output voltage 
u
o
for the following circuit.
Solution
Using the op amp model shown in figure 33, we may apply KCL at the inverting terminal and
gain the following:
i
1
+ i
2
=0
since currents do not flow into the op amp’s input terminals. Replacing the current using ohm’s
law gives:
V
s
−V
n
R
1
+
V
o
−V
n
R
2
=0
Multiplying by R
1
R
2
and collecting like terms, we could gain:
R
2
V
s
=
(
R
1
+ R
2
)
V
n
− R
1
V
o
Now 
V
o
= A
(
V
p
−V
n
)
, and since the no inverting terminal is connected to the ground, 
V
p
=0
,
Figure 34. Idealized mode of the op amp
Biomedical Sensor, Device and Measurement Systems
http://dx.doi.org/10.5772/59941
217

---

V
o
= − AV
n
Substituting 
V
n
into the KCL inverting input equation gives
R
2
V
s
=
(
R
1
+ R
2
)
(
−
V
o
A
)
− R
1
V
o
Namely, 
V
o
= −
R
2
V
s
R
1
+
R
1
+ R
2
A
When a goes to infinity, the above equations could be simplified into:
V
o
= −
R
2
R
1
V
s
Interestingly, with A going to infinity, output voltage 
V
o
remain finite due to the resistor
R
2
.This happens because a negative feedback path exists between the output and the inverting
input terminal through resistor 
R
2
. This circuit is called the inverting scaling operation circuit.
Of course, similar circuits have differential circuit, integrating circuit, summing circuit, index
circuit, logarithmic circuit and dividing circuit. These circuits could be found and read in the
analog circuit textbook.