# opamp input bias voltage vs. common mode rejection ratio

Common Mode Rejection Ratio (CMRR) is often explained as the ratio of out and V1 in a circuit like the one below:

simulate this circuit – Schematic created using CircuitLab

This ignores Input Offset Voltage.

Input Offset Voltage (Vos) is usually explained as the V1 that makes out to be zero in a schema like that:

simulate this circuit

This in turn ignores CMRR.

Usually only upper limits are provided for Vos, but no information on how it depends on common mode voltage or frequency.

Is Vos dependent on common mode voltage?

The point I'm trying to make is that when the Vos may change with common mode voltage, then what's the point of CMRR? Or is Vos considered to be a fixed voltage for each device?

I have the same problem with the currents. The datasheet gives me limits, but no indication on how 'stable' they are with frequency or common mode voltage.

Consider a typical example of an op-amp having 1 mV offset voltage and 100 dB CMR.

CMRR is $\dfrac{differential\space gain}{common\space mode\space gain}$

So, if the differential gain is 1000 and the CMR is 100dB (100,000), then the common mode gain is 1000/100,000 = 0.01

It can be seen that differential offsets are by far more liable to produce an output error compared to common mode voltages. For this reason it is sensible to assume that the offset voltage of an op-amp has no contribution from the common mode voltage.

Regards input offsets being affected by frequency, remember that all op-amp offsets are a dc quantity. I'm not saying that high frequency EMI doesn't tweak these offsets a little - there are a lot of examples where EMI can produce a pseudo DC offset at the input due to input protection rectifying the high frequencies to a small DC value.

• What is "diffential gain" for a regular (non-instrument) op-amp? Is this the open-loop gain of the op-amp (~120db)? Or say, I'm using the opamp in a inverted amplifier configuration with R1/R2 = 10, is that the gain? Commented Feb 9, 2015 at 13:44
• @Stefan the formula for CMRR applies to any amplifier whether configured with resistors to produce a stable gain of 1 to an op-amp run open loop. In your comment the differential gain will be 10. Commented Feb 9, 2015 at 13:48
• Just to be sure, if I build an attenuator, say R1/R2=0.01, and I AC-couple the output, Vos won't affect me, and CMRR influence will be microscopic. Sound almost too good to be true. Commented Feb 9, 2015 at 14:03
• If R1 is the feedback resistor and R2 is the input resistor to the inverting input then the effect of Vos on the output will be at the one-tenth level (compared to unity inverting gain) and, as pointed out in my answer the influence of common mode signals is really quite small. Don't forget about bias currents - try and keep impedances small !! Commented Feb 9, 2015 at 14:20