= Phase calibration error in an admittance-based capacitance estimate
<Phase calibration error in an admittance-based capacitance estimate> can rotate a large in-phase conductance into a small capacitive quadrature. In the parallel port model $Y=G+i\omega C$ with $G\ge0$, $C>0$, and the $e^{i\omega t}$ convention, a relative <wave phase> error $\delta$ gives $Y_{\rm meas}=Ye^{i\delta}$. The exact estimate in <input capacitance inferred from measured admittance> therefore has relative error
$$
\frac{\widehat C-C}{C}=\cos\delta-1+\frac{G}{\omega C}\sin\delta.
$$
The ratio $G/(\omega C)$, not the DC resistance alone, determines sensitivity to a small <wave phase> rotation. The manufacturer's separate differential/common-mode port models motivate specifying the terminals and <operating point> before fitting an <input capacitance>.<MT-040: Op Amp Input Impedance by Analog Devices>[Printed pp. 1–2, Figure 1 and Op Amp Input Capacitance]{ref}
If $|\delta|\le\epsilon\le\pi/2$, the worst absolute relative error is bounded by
$$
\frac{|\widehat C-C|}{C}\le1-\cos\epsilon+\frac{G}{\omega C}\sin\epsilon.
$$
The negative endpoint $\delta=-\epsilon$ attains this bound. For target relative error $r>1-\cos\epsilon$, a sufficient <frequency> condition is
$$
f\ge\frac{G\sin\epsilon}{2\pi C\{r-(1-\cos\epsilon)\}}.
$$
This condition assumes the same $G+i\omega C$ model and the same phase-error bound remain valid over that <frequency> range.
For an original planning example, take $G=1\,\mathrm{\mu S}$, $C=50\,\mathrm{pF}$ and $\epsilon=0.5^\circ$. The bound is about $2.782\%$ at $1\,\mathrm{kHz}$ and $0.282\%$ at $10\,\mathrm{kHz}$. A one-percent target requires approximately $f\ge2.788\,\mathrm{kHz}$ in this model. Increasing <frequency> suppresses the conductance-mixing term, but leaves the $1-\cos\epsilon$ term and can expose other unmodelled parasitic effects.
A measurement uses the same voltage/current <wave phase> reference for the ratio $I/V$, checks that reference with a known port, and retains fixture admittance in the model or subtracts a validated value. Amplitude <measurement calibration> alone cannot establish this <wave phase> bound. The numbers above are chosen calculations, not device specifications or a claim that a high-frequency measurement is automatically more accurate.
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