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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.

Transducer sensitivity describes how much the output of a measuring transducer changes when its input changes. For an output $y$ responding smoothly to input $x$, a local model usesVIM defines sensitivity of a measuring system through the quotient of corresponding indication and input changes, noting that sensitivity can depend on the input value and that the changes used must be appreciable relative to resolution.^[ref] The derivative is the smooth local limit of that response ratio.

For an original pressure-to-potential transducer, stipulateIts transducer sensitivity isAt $p=100\mathrm{kPa}$, the output is $0.310\mathrm{V}$ and the sensitivity is $4\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Across the finite interval from $100$ to $110\mathrm{kPa}$, output changes by $41\mathrm{mV}$, so the measured response ratio is instead $4.1\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Specify the operating point or interval rather than treating these two slopes as contradictory.

An output increment $q=0.2\mathrm{mV}$ corresponds locally to input-referred resolution $q/|S|=0.05\mathrm{kPa}$ at the first operating point. This conversion is not a complete uncertainty statement. Increasing electronic gain can enlarge output noise as well as the signal; detector saturation can flatten the response and destroy local invertibility.

Estimate transducer sensitivity with known input steps, repeated outputs and checks for changing zero, loading and temperature. In a linear response $y=Sx+b$, a constant offset $b$ cancels from differences; a changing offset does not. Retain both the sensitivity relation and its uncertainty in measurement calibration, and propagate the relevant contributions when reporting a measurement result.