= Amplifier input common-mode range
The \b[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>.<A Practical Review of Common Mode and Instrumentation Amplifiers by Eamon Nash>[Three Op-Amp Instrumentation Amplifier, Common Mode Range, Figure5]{ref}
An original simplified three-amplifier model makes the constraint visible. Let the input-stage output potentials be
$$
u_1=v_c+\frac{G_1v_d}{2},\qquad
u_2=v_c-\frac{G_1v_d}{2},
$$
where $v_c=(v_++v_-)/2$ and $v_d=v_+-v_-$. Suppose each internal output must stay between $0.4$ and $4.6\,\mathrm V$. Then
$$
0.4\,\mathrm V+\frac{|G_1v_d|}{2}
\leq v_c\leq
4.6\,\mathrm V-\frac{|G_1v_d|}{2}.
$$
For $G_1=20$ 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.
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