 Range-overlap calibration

Range-overlap calibration establishes or checks the relationship between instrument settings using inputs that both can measure validly. In gain ranging, it tests whether changing sensitivity preserves the inferred measurand. It can determine relative scale and offset between ranges, but agreement between ranges alone does not establish their absolute accuracy or independent metrological traceability.

For an original two-range measurement model, let the same stable electric current $I$ produceEliminating $I$ givesAn overlap experiment therefore needs enough distinct, stable input levels to distinguish relative gain from offset. One common input gives one equation for $a$ and $c$ and cannot identify both without additional information.

For example, suppose $G_L=0.10V/nA$, $b_L=0.01\mathrm{V}$, $G_H=0.50V/nA$ and $b_H=0.02\mathrm{V}$. Currents of $1$, $2$ and $3\mathrm{nA}$ give output pairs $(0.11,0.52)$, $(0.21,1.02)$ and $(0.31,1.52)\mathrm{V}$. They satisfy $V_H=5V_L-0.03\mathrm{V}$. Dividing raw outputs by their nominal gains without removing the offsets would not give consistent current estimates.

A practical test can drive a switchable transimpedance amplifier from a stable current source, record multiple overlap levels, and alternate the setting order to reveal instrumental drift. Avoid amplifier clipping, allow settling time, and retain the bandwidth and temperature conditions. The manufacturer tables show why range-dependent noise and gain drift must be included rather than assumed equal.^[ref]

At each level, compare corrected estimates $I_H$ and $I_L$ through their difference $d=I_H-I_L$. The measurement uncertainty of that difference depends on covariance:A common reference can move both estimates together and disappear from this difference. Thus good overlap agreement checks a relative relationship; it cannot by itself exclude a shared calibration error. The general uncertainty-combination law explicitly retains correlated contributions.^[ref]