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The amplifier input common-mode range is the set of common-mode voltages for which an electronic amplifier meets its operating requirements at the specified differential input, gain, supplies and load. A high common-mode rejection ratio describes rejection within a usable operating region; it does not extend that region. An instrumentation amplifier can have saturated internal stages even when its ideal final output fits the amplifier output range.^[ref]

An original simplified three-amplifier model makes the constraint visible. Let the input-stage output potentials bewhere $v_c=(v_{+}+v_{-})/2$ and $v_d=v_{+}-v_{-}$. Suppose each internal output must stay between $0.4$ and $4.6\mathrm{V}$. ThenFor $G_1=20$ and $v_d=0.10\mathrm{V}$, the permitted common interval is $1.4$–$3.6\mathrm{V}$. Choosing $v_c=0.8\mathrm{V}$ predicts internal outputs $1.8$ and $-0.2\mathrm{V}$ and violates the stipulated limit. A unity-gain difference stage with reference $2.5\mathrm{V}$ would nevertheless predict a plausible final $4.5\mathrm{V}$. That final prediction alone is insufficient.

This is an illustrative architecture model, not a device specification; input-device limits can impose further restrictions. A practical test holds $v_d$ fixed while sweeping both inputs together, recording differential gain error and distortion. Repeat at the intended gain and differential amplitudes. The resulting operating region is more informative than a single common-mode interval quoted without its test conditions.

The common-mode rejection ratio compares a receiver's differential gain $A_d$ with its gain $A_c$ for common-mode voltage. In a linear small-signal model,A high value means that equal disturbances on the two inputs have relatively little effect on the output. It does not specify the maximum common input range before saturation.^[ref]

For $A_d=100$ and CMRR $=80$ dB, the ratio is $10000$ and $|A_c|=0.01$. A 1 V common disturbance then creates 10 mV of output error, equivalent to 0.1 mV at the differential input. A measurement applies equal input changes while keeping their difference fixed, subtracts the initial output, and compares the measured common gain with a separate differential-gain measurement. Both gains depend on frequency, so a DC specification alone does not describe rejection of a rapidly changing disturbance.

Eamon Nash is an applications engineer whose technical writing connects amplifier models with measurements of real circuits. His A Practical Review of Common Mode and Instrumentation Amplifiers by Eamon Nash explains how finite common-mode rejection ratio converts a shared input disturbance into output error, even when the desired signal is differential.^[ref]

His later RF-modeling article compares simulated and measured amplifier behavior. Small-signal scattering parameters describe linear gain and matching, but additional data are needed for noise and nonlinear compression. One demonstrated limitation is especially instructive: a model can reproduce amplitude compression while missing signal-dependent phase distortion because its input data contain only small-signal phase. That makes the disagreement scientifically useful evidence about what information the model lacks.^[ref]

An instrumentation amplifier amplifies a differential input while presenting high input impedance and rejecting a common component. A useful ideal relation isIts common-mode rejection ratio describes finite unwanted response to common-mode voltage. This is distinct from the amplifier input common-mode range over which the circuit can operate without internal saturation.^[ref]

For an original example, stipulate $v_{+}=2.501\mathrm{V}$, $v_{-}=2.499\mathrm{V}$, $G=100$ and $V_{\mathrm{ref}}=2.5\mathrm{V}$. The differential signal is $2\mathrm{mV}$ and the ideal output is $2.7\mathrm{V}$, assuming all input and output limits are satisfied.

Now suppose the differential-to-common gain ratio is $10^4$, or $80\mathrm{dB}$. The common-mode gain is then $100/10^4=0.01$. A $1\mathrm{V}$ common-input change contributes $10\mathrm{mV}$ at the output, five percent of the desired $0.20\mathrm{V}$ signal contribution. A high rejection ratio therefore does not mean zero error.

A source that changes both inputs together tests rejection; a source that changes their difference tests differential gain. Both tests must respect input common-mode limits, amplifier output range, load and frequency response. A plausible ideal output value alone does not prove that every internal stage remains linear.