3/7/2011
Example The Input Offset Voltage lecture
1/7
Example: The Input
Offset Voltage
Consider an inverting amp constructed with an op-amp exhibiting an input offset
voltage of Vos:
R2
i2
R1
vin
i1
v-
-
Vos
v+
+
Jim Stiles
ideal
vout
+
- +
The Univ. of Kansas
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
2/7
v- not equal to v+
We know that because of the input offset voltage:
v − = v + +Vos
For the circuit above, the non-inverting terminal of the op-amp is connected to
ground (i.e., v + = 0 ), and so the virtual “ground” is now described by:
v − =Vos
The current into each terminal of the op-amp is still zero, so that from KCL:
i1 = i2
where form KCL and Ohm’s Law:
i1 =
and:
i2 =
Jim Stiles
vin − v − vin −Vos
=
R1
R1
v − − vout Vos − vout
=
R2
R2
The Univ. of Kansas
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
3/7
The output has a DC offset!
Combining, we find:
vin −Vos Vos − vout
=
R1
R2
Performing a little algebra, we can solve this equation for output voltage vout :
vout =
Vos R1 +Vos R2 − vin R2
R1
R2
and rearranging:
R ⎞
⎛R ⎞
⎛
vout = − ⎜ 2 ⎟vin + ⎜ 1 + 2 ⎟Vos
R1 ⎠
⎝ R1 ⎠
⎝
i2
R1
vin
i1
v-
-
Vos
v+
+
Jim Stiles
The Univ. of Kansas
ideal
vout
+
- +
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
4/7
Superposition is your friend
Q: Hey! Couldn’t we have easily found this result by applying superposition?
R2
A: Absolutely!
i2
R1
vin
i1
Note that if the input offset voltage is
zero (its ideal value), this expression
simply reduces to the normal inverting
amplifier expression:
v-
ideal
vout
+
v+
+
⎛R ⎞
vout = − ⎜ 2 ⎟vin
⎝ R1 ⎠
Jim Stiles
The Univ. of Kansas
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
5/7
It’s the non-inverting amplifier!
Likewise, if we set the input voltage source to ground potential (i.e., vin = 0 ), it is
evident that we have a non-inverting amplifier:
R2
i2
R1
i1
v-
-
-
Vos
v+
+
ideal
vout
+
- +
And so the output voltage is:
⎛
vout = ⎜ 1 +
⎝
Jim Stiles
R2 ⎞
⎟V
R1 ⎠ os
The Univ. of Kansas
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
6/7
Look at the DC offset!
The sum of these two results provides our previous answer:
R ⎞
⎛R ⎞
⎛
vout = − ⎜ 2 ⎟vin + ⎜ 1 + 2 ⎟Vos
R1 ⎠
⎝ R1 ⎠
⎝
Note the term:
R2 ⎞
⎛
+
1
⎜
⎟Vos
R
⎝
1 ⎠
is a constant with respect to vin —its value does
vout
not change, even if the input voltage is zero!.
Thus, the term represents an output offset
voltage.
⎛
Voff = ⎜ 1 +
⎝
R2 ⎞
⎟V
R1 ⎠ os
vin
⎛R ⎞
−⎜ 2 ⎟
⎝ R1 ⎠
Jim Stiles
The Univ. of Kansas
Dept. of EECS
3/7/2011
Example The Input Offset Voltage lecture
7/7
How do we define gain?
Q: But what is the gain of this amplifier? The ratio vout vin is not a constant!
⎛R ⎞ ⎛
vout
R ⎞V
= − ⎜ 2 ⎟ + ⎜ 1 + 2 ⎟ os
R1 ⎠ vin
vin
⎝ R1 ⎠ ⎝
????
A: Remember, it is more accurate and more general to define gain in terms of
the derivative:
Avo d vout
d vin
Which for this case provides the same result for the inverting amplifier:
⎛ R2 ⎞
⎟
R
⎝ 1⎠
Avo = − ⎜
Jim Stiles
The Univ. of Kansas
Dept. of EECS