= Transducer sensitivity
{title2=$S=dy/dx$}
\b[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 uses
$$
S(x_0)=\left.\frac{dy}{dx}\right|_{x=x_0},\qquad
\Delta y\simeq S(x_0)\Delta x.
$$
VIM 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.<International vocabulary of metrology by JCGM>[VIM3entry4.12, definition and notes1–2]{ref} The <derivative> is the smooth local limit of that response ratio.
For an original pressure-to-potential transducer, stipulate
$$
V(p)=0.010\,\mathrm V+(0.002\,\mathrm{V\,kPa^{-1}})p
+(10^{-5}\,\mathrm{V\,kPa^{-2}})p^2.
$$
Its <transducer sensitivity> is
$$
S(p)=0.002\,\mathrm{V\,kPa^{-1}}+
(2\times10^{-5}\,\mathrm{V\,kPa^{-2}})p.
$$
At $p=100\,\mathrm{kPa}$, the output is $0.310\,\mathrm V$ and the sensitivity is $4\,\mathrm{mV\,kPa^{-1}}$. Across the finite interval from $100$ to $110\,\mathrm{kPa}$, output changes by $41\,\mathrm{mV}$, so the measured response ratio is instead $4.1\,\mathrm{mV\,kPa^{-1}}$. 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>.
Back to article page
