= Input capacitance
{title2=$C_{\mathrm{in}}$}
<Input capacitance> describes the capacitive part of an electrical port's small-signal <input impedance>, under stated bias, frequency, and termination conditions. In a simple parallel model with the $e^{i\omega t}$ convention, its <electrical admittance> is
$$
Y_{\rm in}=\frac{I}{V}=\frac1{R_{\rm in}}+i\omega C_{\rm in},\qquad
Z_{\rm in}=\frac1{Y_{\rm in}}.
$$
The <electric current> drawn by the <capacitance> grows with <angular frequency> even if the DC input resistance is enormous. Analog Devices distinguishes differential input paths from common-mode paths to ground: a quoted capacitance must identify which terminals are driven and how the remaining circuit is connected.<MT-040: Op Amp Input Impedance by Analog Devices>[Printed p. 1, Figure 1, differential and common-mode input paths; printed p. 2, Op Amp Input Capacitance]{ref}
For an original loading example, let $R_{\rm in}=10\,\mathrm{M\Omega}$ and $C_{\rm in}=20\,\mathrm{pF}$. At $10\,\mathrm{MHz}$, the capacitive reactance magnitude is only $1/(2\pi fC_{\rm in})\approx796\,\Omega$. A source with <electrical resistance> $R_s=1\,\mathrm{k\Omega}$ therefore has loaded-to-unloaded <phasor> ratio
$$
H=\frac1{1+R_s/R_{\rm in}+i2\pi fR_sC_{\rm in}},\qquad
|H|\approx0.623.
$$
The DC ratio is about $0.99990$. Thus a resistance-only reading would miss a substantial high-frequency <amplitude> reduction. The numbers are chosen examples, not a specification for a named device.
For this same model, the source-to-input <time constant> is $(R_s\mathbin\Vert R_{\rm in})C_{\rm in}$ and the DC-normalized half-power <signal bandwidth> is its reciprocal divided by $2\pi$. A complex-error requirement is instead governed by <capacitive bridging complex-error bandwidth>; these specifications answer different questions.
For <input capacitance inferred from measured admittance>, apply a small sinusoidal <electric potential difference>, measure the input <electric current> and its <phase shift>, and infer $\operatorname{Im}(I/V)/\omega$ within the parallel-capacitance approximation. Fixture, cable, and probe capacitances contribute to the measured port unless removed or included explicitly. Dependence on bias or frequency can make a single fitted $C_{\rm in}$ an inadequate model.
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