Gate timing jitter

Gate timing jitter is shot-to-shot variation in the timing of a detection time gate relative to the signal being measured. It differs from a fixed delay error: repeated gates may have the correct mean delay while admitting different portions of a rapidly varying detector signal. The SR250 catalogue describes a trigger-controlled gate, finite delay jitter and a gate-monitor output that can be overlaid with the signal on an oscilloscope.^[ref]

For an original sensitivity derivation, let a reproducible baseline-corrected electric current waveform be $i(t)$ and the intended integrated electric charge beSmall edge errors giveIf both edges shift by the same amount, the gate width is unchanged butThus a gate translating within a flat plateau has little first-order sensitivity, while a gate whose edges intersect different signal levels can be sensitive even at fixed width.

For stipulated edge currents $i(t_0)=100\mathrm{nA}$ and $i(t_1)=20\mathrm{nA}$, a common timing error with standard deviation $2\mathrm{ns}$ contributes approximately $0.16\mathrm{fC}$ charge standard deviation. This calculation assumes smooth waveform values near both edges and timing excursions small enough for linearization. A gate crossing an abrupt onset requires the actual waveform integral.

Gate-width jitter is a separate effect. For a constant plateau current $I$, $Q=I(t_1-t_0)$, so $\delta Q=I\delta T_g$ even though a common gate translation would cancel. More generally, the edge-error contribution has varianceThe covariance determines whether two individually noisy edges largely preserve the width.

An apparatus check records both the gate monitor and signal waveform over many triggers, using the same time reference, to estimate relative delay and width distributions. A single aligned trace establishes neither distribution. Timing motion shared by the pulse and gate can cancel in their relative delay; the uncertainty relevant to the measured charge is their relative timing, not solely a gate generator's standalone specification.

Gate-width jitter is shot-to-shot variation in the duration of a detection time gate. If its opening and closing times are $t_0,t_1$, then $T_g=t_1-t_0$. Both edges can have substantial gate timing jitter while their difference remains stable. A common shift changes delay without changing width.

For small timing fluctuations,With equal edge standard deviations ${\sigma }_e$ and correlation coefficient $\rho$, this becomes ${\sigma }_T={\sigma }_e\sqrt{2(1-\rho )}$. The covariance identity is exact whenever those variances exist. It separates width stability from the jitter of either edge measured alone.

For an original example, let both edges have standard deviation $100\mathrm{ps}$. Independent edge errors give ${\sigma }_T=141.4\mathrm{ps}$; correlation $\rho =0.99$ instead gives $14.14\mathrm{ps}$. At nominal width $10\mathrm{ns}$, those are relative width fluctuations of about 1.414 percent and 0.1414 percent. Assuming independence would overestimate the second width uncertainty by a factor of ten.

If a flat, baseline-corrected electric current $I$ fills the gate, the integrated electric charge is $Q=I{T}_g$, so ${\sigma }_Q=|I|{\sigma }_T$. At $I=2\mu \mathrm{A}$ the nominal charge is $20\mathrm{fC}$, with respective standard deviations $0.2828$ and $0.02828\mathrm{fC}$. A varying waveform also introduces sensitivity to where the edges fall; the gate timing jitter article gives the general edge-current formula.

A gate-normalized detector output can report $Q/T_g$ instead of charge. For an exactly constant current and accurately known actual width, that ratio is $I$ despite width variation. Dividing by a fixed nominal width instead retains the width-induced variation. The SR250 documentation describes integration followed by gate-width normalization, and provides a gate monitor for checking timing.^[ref]

An apparatus check measures both edges relative to a common reference over repeated triggers and computes their difference for each shot. Measuring the two edge jitter distributions separately without their covariance cannot determine width jitter. Readout time resolution and the threshold used to define an edge are also part of that measurement.