= Leakage-limited hold time
{title2=$T_{\max}=C\varepsilon/|I_{\rm leak}|$}
The <leakage-limited hold time> is the duration for which a stored <electric potential difference> remains within a stated drift allowance when unwanted <electric current> changes the stored <electric charge>. For a constant net leakage $I_{\rm leak}$ into a fixed <capacitance> $C$,
$$
C\frac{dv}{dt}=I_{\rm leak},\qquad |v(T)-v(0)|=\frac{|I_{\rm leak}|T}{C}.
$$
An allowed drift $\varepsilon>0$ therefore gives $T_{\max}=C\varepsilon/|I_{\rm leak}|$. This is a limit from a specified error mechanism, not the complete accuracy or usable duration of an instrument. The ACF2101 datasheet identifies amplifier bias, capacitor leakage and switch leakage as separate contributions to droop.<ACF2101 Low Noise, Dual Switched Integrator datasheet>[Printed p11, Droop]{ref}
For an original example, a4.7nanofarad <capacitor>,50picoamperes of net leakage and a0.20millivolt drift allowance give
$$
T_{\max}=\frac{(4.7\times10^{-9})(0.20\times10^{-3})}{50\times10^{-12}}\,\mathrm s
=18.8\,\mathrm{ms}.
$$
If the readout adds a further30picoamperes in the same direction, the correct total is80picoamperes and the duration falls to11.75milliseconds. The relevant <electric current> is the sum of all paths at the stored node, not necessarily the isolated <analog switch leakage current> specification.
For time-dependent leakage, the exact charge balance is
$$
\Delta v(T)=\frac1C\int_0^T I_{\rm net}(t)\,dt.
$$
A verified bound $|I_{\rm net}(t)|\leq I_{\max}$ guarantees $|\Delta v(T)|\leq I_{\max}T/C$. Oppositely signed contributions can cancel at one operating point without providing that bound elsewhere. <Temperature>, terminal potentials and board leakage must match the intended operating conditions.<MT-088: Analog Switches and Multiplexers Basics>[Printed pp4–5, Figures5–7, switch leakage equivalent circuits]{ref}
A bench check records the held node at several delays after the switching transient, using a known total <capacitance> and a readout whose input current is included in the model. The slope estimates net leakage. A step created at the transition is <analog switch charge injection>, not steady droop. If the initial step already uses part of a total error allowance, only the remaining allowance is available for calculating the <leakage-limited hold time>.
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