# CMRR

```CMRR
• One important measure of the goodness of an opamp or an opamp circuit is
the common mode rejection ratio (CMRR)
• Ideally, opamps are expected to amplify the differences between v1 and v2
with nearly infinite gain
• Due to transistor nonidealities, some small amount of amplification occurs
due to the common signal of both inputs
open
loop
gain
common
mode
gain
v1
v2
vcm
vo
vo
A = ----------------v2 – v1
vo
vo
A cm = --------v cm
A
CMRR = ---------A cm
Lecture 8-1
CMRR
• We would like to have an infinite CMRR
v id = v 2 – v 1
v1
v2 + v1
v Icm = ----------------2
v2
v o = Av id + Acm v Icm
• A typical CMRR is 80-100dB at low frequency
• Would the CMRR improve, or get smaller with increasing frequency?
Lecture 8-2
CMRR
• Not really a problem for inverting amplifier configurations --- why?
R2
R1
Vo
Vin
• But definitely a problem for noninverting amplifier configurations --- why?
R2
R1
Vo
Vin
Lecture 8-3
Difference Amplifier
• Also a problem for difference amplifiers
R2
R1
Vo
Va
Vb
Lecture 8-4
Difference Amplifier
• We have to scale the voltage vb to achieve balanced amplification of vb-va
R2
R1
R1
Va
Vb
Vo
R2
Lecture 8-5
CMRR
• Opamp data sheets specify the CMRR for the opamp itself, but the opamp
differential amplifier circuit also has a CMRR
Rf
Even with ideal opamp model
you will see some common
mode gain if there is a mismatch
in the resistor values
Rs
vo
vin
vp
R1
R2
Lecture 8-6
Input-Currents and -Resistances
• There is some small dc current flowing into/out of the inputs at all times --
input bias current
v1 _
v id
v2
+
IB1
IB2
• There is also a component of input current that changes with input voltage
(both common mode and differential) --- input resistances
v Icm
Rcm
v1 _
v id
v2
+
Rid
Lecture 8-7
Input Resistance
• These resistances are generally quite large: Rcm ~ 100MΩ, and Rid ~ 1MΩ
• These resistances are even larger for MOS opamps
1
2Rcm
Rid
2
2Rcm
Lecture 8-8
Input Resistance
• These opamp input resistances do not affect an inverting amplifier
configuration as long as R1 is much less than Rid and Rcm
R2
R1
Vo
Vin
• But these resistances are what determines the input resistance of a non-
inverting amplifier configuration
R2
R1
Vo
Vin
Lecture 8-9
Input Resistances
• The resistors R1 and R2 should be kept significantly smaller than the input
resistances for the gain to be close to ideal
R2
R1
v1
2Rcm
vo
Rid
iin
v2
+
2Rcm
A ( v2 – v1 )
vin
Rin
_
Lecture 8-10
Input Resistances
R2
R1
v1
2Rcm
vo
Rid
iin
v2
+
2Rcm
A ( v2 – v1 )
vin
Rin
_
Lecture 8-11
Nonzero Output Resistance
• We also have to keep in mind that the opamp output cannot source an infinite
amount of current --- so we can’t drive arbitrarily small resistance loads
• This is modeled by an output resistance, Ro
R2
if
vin &lt; 0
R1
iL
Ro
A ( v 2 – v1 )
RL
note that vo
definition is
changed when
output resistance
the model
Lecture 8-12
Measuring Output Resistance
R2
R1
Ro
A ( v2 – v1 )
Lecture 8-13
Modeling Output Resistance
• Since the open loop gain depends on frequency, so does the opamp circuit
output impedance
Lecture 8-14
Input Bias Current
• The input bias current is not frequency dependent, but can cause an unwanted
dc output response
R2
R1
IB1
IB2
Lecture 8-15
Compensating for IB
• In practice, a resistor is added so that the bias current drops are compensated
properly between the two ports
Rf
Rs
vo
vin
Rcomp
Lecture 8-16
Compensating for IB
R2
R1
R3
IB1
IB2
Lecture 8-17
dc Offset Voltage
• Another unwanted dc output signal is due to the dc offset voltage
• A dc differential input is required for a real opamp to zero the output
• This offset is due to mismatch in transistor parameters, and is temperature
dependent --- more on this later in the course
VOS ~ 1-5mV
1
2
VOS
Lecture 8-18
dc Input Offset Voltage
• Calculate output voltage due to dc input offset voltage
Rf
Rs
vo
vin
VOS
Lecture 8-19
ac Coupling
• We can avoid this offset voltage at the output by using ac coupling
Rf
CC
Rs
vo
vin
VOS
Lecture 8-20
```