= Sampling skew after matched ratiometric filters
{title2=$\delta t$}
<Sampling skew after matched ratiometric filters> is the timing difference between the signal and reference samples in a <ratiometric measurement>, after their analog paths have the same response. Shared wiring and matched filters cancel excitation at the same effective time; they do not make two different times interchangeable.
For constant sensor and reference resistances, let the common filtered excitation be $F(t)=(h*I)(t)$, where $h$ is the common <impulse response> and $*$ denotes <convolution>. With consistent initial conditions, the two filtered <electric potential differences> are $R_TF(t)$ and $R_{\rm ref}F(t)$. If the sensor is sampled at $t$ but the reference at $t+\delta t$, the measured <ratio> is
$$
r_{\rm skew}(t)=\frac{R_T}{R_{\rm ref}}\frac{F(t)}{F(t+\delta t)}.
$$
Both denominator factors must be nonzero. The sampling instants here mean the effective acquisition times; conversion-result arrival times need not be those instants. <Ratiometric cancellation with matched signal and reference filters> treats the equal-time cancellation, supported by the primary circuit report's matching requirement.<RTD Ratiometric Measurements and Filtering Using the ADS1148 and ADS1248 Family of Devices by Luis Chioye>[Abstract and §2, matching the signal and reference responses]{ref}
For positive differentiable $F$ and small skew, expanding the logarithm gives
$$
\log\frac{r_{\rm skew}}{R_T/R_{\rm ref}}
=-\delta t\frac{F'(t)}{F(t)}+O((\delta t)^2).
$$
A later reference sample during a rising excitation therefore makes the inferred resistance low. The relevant rate is the fractional slope $F'/F$, not the absolute slope alone. A <timing-skew bound for a ratiometric measurement> can express a worst-case requirement using a bound on this logarithmic slope.
For an original local example, suppose $F(t)=F_0e^{\kappa t}$ over the acquisition window, with $\kappa=20\,\mathrm{s^{-1}}$ and $\delta t=100\,\mathrm{\mu s}$. Then the exact scale error is $e^{-0.002}-1\approx-0.199800\%$. The small-skew estimate is $-0.200000\%$. Doubling the common amplitude $F_0$ leaves both errors unchanged; reversing the sample order changes their sign to first order. This is a stipulated short-window excitation model, not an instrument-performance claim.
A focused bench check replaces the sensor with a stable <resistor>, imposes a controlled excitation change, and compares simultaneous acquisition with deliberately delayed reference sampling. Recording the excitation on an <oscilloscope> supplies its fractional slope. Repeating on a settled plateau separates timing error from <reference-resistor error in ratiometric resistance measurement> and other steady scale errors.
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