Question

Find the op-amp common mode configuration

I got this question in a national level competition.

The question is from Common Mode Configuration and  Rejection Ratio in portion Practical Limitations of Op Amp Circuits of Linear Integrated Circuits

Answer 1

The common mode configuration of an operational amplifier (op-amp) occurs when the same signal is applied to both the inverting and non-inverting inputs of the op-amp. This configuration is crucial for evaluating how well an op-amp rejects signals that appear at both inputs equally, which is characterized by the Common-Mode Rejection Ratio (CMRR).

In a common-mode condition:

• Both input terminals receive the same voltage.
• Ideally, an op-amp should not respond to common-mode signals; it should only amplify the difference between the two inputs (differential mode). However, due to imperfections, real op-amps still respond to common-mode signals, and the ability to reject these signals is quantified by CMRR.

The common-mode gain in such a scenario is ideally zero for an ideal op-amp, but for a real op-amp, it is nonzero but much smaller than the differential gain. The CMRR is the ratio of the differential gain to the common-mode gain and is typically expressed in decibels (dB).

For example, if the differential gain of an op-amp is AdA_dAd​ and the common-mode gain is AcmA_{cm}Acm​, the CMRR is calculated as:

CMRR=AdAcm\text{CMRR} = \frac{A_d}{A_{cm}}CMRR=Acm​Ad​​

In dB, it is expressed as:

CMRR (dB)=20×log⁡10(AdAcm)\text{CMRR (dB)} = 20 \times \log_{10}\left(\frac{A_d}{A_{cm}}\right)CMRR (dB)=20×log10​(Acm​Ad​​)

This means a high CMRR is desirable for rejecting unwanted common-mode signals (such as noise). For example, an op-amp with a high CMRR will not amplify noise that appears equally at both inputs.

In practical terms:

• Common mode rejection is crucial in systems where the input signals are small and noise might be common to both input terminals, such as in instrumentation amplifiers or precision measurements.