= Reset error budget with a persistent pedestal
A \b[reset error budget with a persistent pedestal] assigns separate tolerance to a decaying pre-reset residual and an offset created when the reset switch opens. Increasing the preceding discharge time can reduce the former without reducing the latter. The <integrator reset settling time> article derives the basic worst-case bound and its logarithmic reset-duration requirement.
A focused extension includes leakage during a fixed post-opening readout delay $d$. Let the pre-reset residual magnitude be at most $R$, its decay <time constant> be $\tau$, the opening <reset charge-injection pedestal> magnitude be at most $p$, and subsequent <electric current> magnitude be at most $I_{\max}$ on fixed <capacitance> $C$. The <triangle inequality> gives
$$
|e|\leq Re^{-T/\tau}+p+\frac{I_{\max}d}{C}.
$$
This separates a duration-controlled term from an error floor $F=p+I_{\max}d/C$. For $R>0$ and a required guarantee $|e|\leq\varepsilon$, finite reset time is possible from this bound only when $\varepsilon>F$, and
$$
T\geq\max\!\left(0,\tau\log\frac{R}{\varepsilon-F}\right).
$$
For an original chosen circuit, take $R=0.10\,\mathrm V$, $\tau=5\,\mathrm{\mu s}$, $p=0.50\,\mathrm{mV}$, $C=100\,\mathrm{pF}$, $I_{\max}=1.0\,\mathrm{nA}$ and $d=20\,\mathrm{\mu s}$. Leakage consumes $0.20\,\mathrm{mV}$. A $1.0\,\mathrm{mV}$ total tolerance leaves $0.30\,\mathrm{mV}$ for the old residual, requiring about $29.0\,\mathrm{\mu s}$ of reset. A $0.60\,\mathrm{mV}$ tolerance requires changing the stipulated pedestal or readout conditions; reset duration alone cannot guarantee it.
These are worst-case bounds, not root-sum-square <standard uncertainties>. Test the discharge by varying $T$, the opening step with zero-input records, and the subsequent drift by varying $d$. Real charge transfer depends on switching sequence, and prior overload can require separate recovery.<ACF2101 Low Noise, Dual Switched Integrator datasheet>[p11, Charge Transfer and Droop; p10, Output Overload]{ref} Accidental cancellation of signed errors is not a reproducible worst-case margin.
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