= Input-referred resolution
\b[Input-referred resolution] expresses an output increment or distinguishable output change in units of the quantity applied to a <measuring system>. For local response $y=f(x)$ with nonzero <transducer sensitivity> $S=dy/dx$, an output increment $q_y$ corresponds approximately to
$$
q_x=\frac{q_y}{|S|}.
$$
State what output criterion is being referred: one converter-code step, a noise-based threshold and a repeatably distinguishable input change are different specifications. Walt Kester's converter tutorial distinguishes code transitions, <input-referred noise> and noise-based resolution measures.<MT-004 by Walt Kester>[pp1–4, code-transition noise, grounded-input histograms and noise-free/effective resolution]{ref}
For an original pressure readout, suppose a transducer has $S=5\,\mathrm{mV\,kPa^{-1}}$, followed by an ideal 12-bit <analog-to-digital converter> spanning $2.048\,\mathrm V$. Its code step is $q_V=2.048/4096=0.0005\,\mathrm V$, corresponding to $q_p=0.1\,\mathrm{kPa}$. This arithmetic specifies a nominal increment, rather than demonstrating that two pressures separated by that amount can be reliably distinguished.
Place an ideal <amplifier> of gain ten before the converter. The combined sensitivity becomes $50\,\mathrm{mV\,kPa^{-1}}$, so the converter step corresponds to $0.01\,\mathrm{kPa}$. With zero offset in this model, the pressure span mapping onto the converter simultaneously shrinks from $409.6$ to $40.96\,\mathrm{kPa}$. Gain trades converter coverage against nominal input increments; it does not create an unlimited input range.
Suppose the transducer itself contributes $0.25\,\mathrm{mV}$ rms output noise. That is $0.05\,\mathrm{kPa}$ input-referred noise. The added ideal gain scales both that signal and that noise, leaving this pressure-noise contribution unchanged. More display digits therefore need not improve the useful <measurement resolution>.
For a nonlinear response, repeat the conversion at the relevant operating point and account for the actual observation bandwidth and processing. Near <detector saturation>, sensitivity can approach zero and the local conversion becomes uninformative. A complete <measurement result> also includes <measurement uncertainty>, which contains calibration and other contributions beyond the chosen resolution criterion.
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