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Input-referred noise expresses observed or modeled output noise as an equivalent disturbance at a system's input. For a locally linear response $y=Gx$ with constant nonzero gain over the relevant measurement band, an output-noise root mean square $n_{\mathrm{out}}$ corresponds toThis is a way to compare noise with the input signal; it does not locate every physical noise source at the input. Walt Kester's ADC tutorial explicitly models converter noise as an equivalent series input source and describes its measurement through repeated codes under a fixed input.^[ref]

For an original amplifier with voltage gain $100$, output noise $1\mathrm{mV}$ rms is equivalent to $10\mu \mathrm{V}$ rms at the input. Changing gain can change this quotient without removing the device's own physical noise. State the measurement bandwidth and processing, since a longer averaging interval or different filter changes the observed rms value.

An original two-stage example shows why the position of noise matters. Let gains be $G_1,G_2$ and independent input-equivalent noise contributions be $e_1,e_2$ for the respective stages. The output-noise variance isso referring it to the original input givesWith $e_1=2\mu \mathrm{V}$, $e_2=30\mu \mathrm{V}$ and $G_1=10$, this is $\sqrt{13}\simeq 3.61\mu \mathrm{V}$. Increasing $G_1$ to $100$ reduces the equivalent total to about $2.02\mu \mathrm{V}$, approaching the first-stage contribution. The independent-noise assumption matters; correlated contributions require covariance terms.

A quiet output code does not by itself establish a small total error, and rms noise is not the same criterion as input-referred resolution. Kester distinguishes noise-based resolution from dynamic converter measures and notes the conditions needed for averaging to help.^[ref] Retain offsets, gain uncertainty and instrumental drift separately in the measurement model.

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 toState 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.^[ref]

For an original pressure readout, suppose a transducer has $S=5\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, 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 $50\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, 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.