Reset charge-injection pedestal ($|\Delta v|=|Q_{\mathrm{inj}}|/C$)

A reset charge-injection pedestal is a step in the initial integrator output caused by charge transferred when the reset switch changes state. It can remain after an arbitrarily long preceding discharge. The integrator reset article distinguishes it from a decaying residual; the physical switched-integrator datasheet separately specifies charge-transfer errors.^[ref]

For an original example, let the net opening charge have magnitude $2\mathrm{pC}$ on an integration capacitance of $1\mathrm{nF}$. The output step has magnitude $2\mathrm{mV}$. If interpreted as photodiode signal charge with constant responsivity $0.50A/W$, it would imitate $Q/R=4\mathrm{pJ}$ of incident energy under the linear model. A positive step interpreted as signal would bias a true $20\mathrm{pJ}$ measurement by $20\%$. The actual polarity depends on the circuit.

Repeated zero-input acquisitions at the same post-opening delay estimate the mean pedestal. Subtracting that mean does not remove reset pedestal variance. For a fixed capacitance, an opening-charge standard deviation of $0.10\mathrm{pC}$ gives an output standard deviation of $0.10\mathrm{mV}$ in the same stipulated model.

Varying the preceding reset duration helps distinguish residual discharge from a step created by opening. Gain, capacitance, signal level and readout delay must remain comparable. Adding capacitance can reduce the step per unit charge but also changes the signal conversion and the full circuit's settling behavior.

Reset pedestal variance is the acquisition-to-acquisition variance of the output offset associated with integrator reset. In a model where the only fluctuating contribution is an opening charge $Q$ on fixed capacitance $C$,Subtracting the mean of the reset charge-injection pedestal removes its constant component, not the random spread. The physical datasheet distinguishes charge-transfer offset from output noise; its charge-transfer limit alone is not a statistical variance specification.^[ref]

Finite blank measurements introduce another contribution. Suppose independent pedestals have mean $\mu$ and standard deviation ${\sigma }_P$. Use $M$ independent zero-input acquisitions to estimate $\mu$, then subtract that same blank sample mean from each of $N$ new signal acquisitions. With a constant signal and no other noise, the corrected mean hasThis variance of a pedestal-corrected sample includes the uncertainty of the shared correction. Its second contribution does not shrink when more signal acquisitions reuse the same blank estimate. Covariance-based uncertainty propagation retains such shared terms.^[ref]

For original stipulated ${\sigma }_P=0.20\mathrm{mV}$, $N=100$ and $M=25$, the corrected mean has standard deviation $0.0447\mathrm{mV}$. An exactly known pedestal mean would give $0.0200\mathrm{mV}$. Repeated zero-input acquisitions at a fixed delay after switching measure the combined pedestal/readout spread; separating its mechanisms requires additional tests. Slow drift or correlations between acquisitions invalidate the independent-sample formula and must enter the measurement model.

The variance of a pedestal-corrected sample quantifies the random spread remaining after subtracting an estimated baseline from a signal acquisition. Subtracting a mean reset charge-injection pedestal removes an offset; it does not automatically remove reset pedestal variance. For a raw signal sample $Y$ and pedestal estimate $B$,The covariance term determines whether subtraction suppresses shared fluctuations or adds independent noise. The GUM's correlated-input rule gives this identity directly for the linear measurement model $f(Y,B)=Y-B$.^[ref]

Two correction procedures have different statistical consequences. First suppose signal acquisitions have independent pedestals $P_i$ of variance ${\sigma }_P^2$ and independent readout noise ${\eta }_i$ of variance ${\sigma }_{\eta }^2$. A separate mean of $M$ independent blank acquisitions, with individual variance ${\sigma }_B^2$, is reused for every signal sample:After removing any constant means, independence givesConsequently, averaging $N$ corrected samples givesThe shared blank correction creates a common uncertainty floor, as in shared calibration error.

Alternatively, a baseline and signal reading from the same acquisition can share a fluctuating pedestal. In an idealized correlated double sampling model, $R=B_0+e_R$ and $Y=s+B_0+e_Y$, so $Y-R=s+e_Y-e_R$: the common $B_0$ cancels. Independent readout noises remain and their variances add. More generally, if paired readings each have standard deviation0.20millivolt and correlation coefficient0.9, their difference has standard deviationTreating that pair as independent would predict0.283millivolt instead.

An experimental assessment records paired zero-input samples at the actual acquisition delays and estimates their covariance, then distinguishes that procedure from reusing a separate blank mean. The ACF2101 datasheet specifies output noise and charge-transfer errors separately; a charge-transfer limit is not itself a pedestal variance or evidence for a particular correlation.^[ref]