Biomedical Engineering Reference
In-Depth Information
, and since the noninverting terminal is connected to ground,
Now
v
o
¼
Av
p
v
n
v
p
¼
0,
v
o
¼
Av
n
or
v
n
¼
v
o
A
Substituting
v
n
into the KCL inverting input equation gives
0
@
1
A
R
1
v
o
Þ
v
o
A
R
s
v
s
¼
R
1
þ
R
2
ð
0
@
1
A
v
o
R
1
þ
R
2
A
¼
þ
R
1
or
R
2
v
s
R
1
þ
R
1
þ
R
2
A
v
o
¼
As
A
goes to infinity, the previous equation goes to
v
o
¼
R
2
R
1
v
s
R
2
. This happens
because a negative feedback path exists between the output and the inverting input terminal
Interestingly, with
A
going to infinity,
v
0
remains finite due to the resistor
R
2
through
R
2
. This circuit is called an inverting amplifier with an overall gain of
R
1
.
An operational amplifier with a gain of infinity is known as an ideal op amp. Because of
the infinite gain, there must be a feedback path between the output and input, and we cannot
connect a voltage source directly between the inverting and noninverting input terminals.
When analyzing an ideal op amp circuit, we simplify the analysis by letting
v
n
¼
v
p
Consider the previous example. Because
v
p
¼
0,
v
n
¼
0. Applying KCL at the inverting
input gives
v
s
R
1
þ
v
o
2
¼
0
R
or
v
o
¼
R
2
R
1
v
s
Notice how simple the analysis becomes when we assume
v
n
¼
v
p
. Keep in mind that this
approximation is valid as long as
A
is very large (infinity) and a feedback is included.
