= Input capacitance inferred from measured admittance
<Input capacitance inferred from measured admittance> is a parameter estimate from the quadrature component of a specified electrical port's response. In the parallel model of <input capacitance>, write its <electrical admittance> as $Y=G+i\omega C$ with the $e^{i\omega t}$ convention. A small sinusoidal excitation and simultaneous input-current measurement give
$$
\widehat C=\frac{\operatorname{Im}(I/V)}{\omega},\qquad
\widehat G=\operatorname{Re}(I/V).
$$
Both <amplitude> ratio and relative <wave phase> matter. The differential versus common-mode terminals and <operating point> conditions must be specified, as in the manufacturer's input-path diagrams.<MT-040: Op Amp Input Impedance by Analog Devices>[Printed p. 1, Figure 1; printed p. 2, Op Amp Input Capacitance]{ref}
For an original error calculation, suppose the <amplitude> ratio is exact but the measured current-to-voltage <wave phase> has offset $\delta$. Then $Y_{\rm meas}=Ye^{i\delta}$ and
$$
\widehat C=C\cos\delta+\frac{G}{\omega}\sin\delta.
$$
The <phase calibration error in an admittance-based capacitance estimate> can therefore mix a conductance term into the small capacitive estimate. For small $\delta$, the leading error is $(G/\omega)\delta$, not a fixed percentage of $C$.
Choose $G=10\,\mathrm{\mu S}$, $C=20\,\mathrm{pF}$, and $f=10\,\mathrm{kHz}$. The true susceptance is only $\omega C\approx1.257\,\mathrm{\mu S}$. A one-degree <wave phase> offset yields $\widehat C\approx22.775\,\mathrm{pF}$, an error of about $13.9\%$, despite perfect <amplitude> readings. These are chosen port-model values, not measured device specifications.
A useful measurement repeats the estimate over <frequency> and excitation <amplitude>. A nearly constant fitted $C$ and a residual consistent with $G+i\omega C$ support the assumed model; they do not prove that all parasitic effects were removed. A known fixture admittance adds to a parallel port and must be subtracted or retained in the model. At very small susceptance, uncertainty in the relative <wave phase> can dominate, so a high DC <input impedance> alone is not evidence for a precise <capacitance> measurement.
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