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