2/18/2011
Superposition and OpAmp Circuits lecture
1/6
Superposition and
Op-Amp Circuits
Consider this op-amp circuit, with two input voltages (v1 and v2):
R2
R1
v1
-
v2
ideal
R3
vout
+
R4
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/18/2011
Superposition and OpAmp Circuits lecture
2/6
Apply superpostion
The easiest way to analyze this circuit is to apply superposition! Recall that opamp circuits are linear, so superposition applies.
Our first step is to set all sources to zero, except v2 —in other words, set v1 =0
(connect it to ground potential):
R2
R1
-
v2
ideal
R3
v+
vo2
+
i+ = 0
R4
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/18/2011
Superposition and OpAmp Circuits lecture
3/6
v1 = 0
Since the current into the non-inverting input of the op-amp is zero (i+ = 0 ), it
is evident that:
v+ =
R4
R3 + R4
Likewise, the remainder of
the circuit is simply the
non-inverting amplifier,
where:
vo 2
vo 2
⎛
R ⎞ ⎛ R4 ⎞
= ⎜1 + 2 ⎟ ⎜
⎟ v2
+
R
R
R
⎝
1 ⎠ ⎝ 3
4 ⎠
Jim Stiles
R2
R1
-
⎛
R ⎞
= ⎜1 + 2 ⎟ v+
R1 ⎠
⎝
Combining these two
equations, we get:
v2
v2
ideal
R3
v+
vo2
+
R4
The Univ. of Kansas
Dept. of EECS
2/18/2011
Superposition and OpAmp Circuits lecture
4/6
v2 = 0
Now for the second step. Turn off all sources except v1 —in other words set v2
=0:
R2
R1
v1
i− = 0
v−
-
ideal
R3
v+
vo1
+
i+ = 0
R4
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/18/2011
Superposition and OpAmp Circuits lecture
5/6
An inverting amp
It is evident that the since the current into the non-inverting terminal of the
op-amp is zero, the voltage v+ is likewise zero.
Thus, the circuit above is simply an inverting amplifier, where:
vo 1 = −
R1
v1
i− = 0
R2
v
R1 1
v−
R2
-
ideal
R3
v+
vo1
+
i+ = 0
R4
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/18/2011
Superposition and OpAmp Circuits lecture
6/6
And the result
There are no more sources in this circuit, so that we can conclude from
superposition that the output voltage is the sum of our two, single-source
solutions:
⎛
⎛ R2 ⎞
R ⎞ ⎛ R4 ⎞
vout = vo 1 + vo 2 = ⎜ 1 + 2 ⎟ ⎜
v
−
⎟ 2 ⎜ ⎟ v1
+
R
R
R
⎝
⎝ R1 ⎠
1 ⎠ ⎝ 3
4 ⎠
v1
Note this circuit is
effectively a weighted
difference amplifier.
R2
R1
-
v2
ideal
R3
vout
+
R4
Jim Stiles
The Univ. of Kansas
Dept. of EECS