Gate-normalized detector output (${\bar{v}}_g$)

A gate-normalized detector output reports an integrated detector signal divided by the duration of the detection time gate. For an input electric potential difference waveform $v(t)$ and a gate from $t_0$ to $t_0+T_g$, the input-referred average isIts units are those of electric potential difference, whereas the integral has units of electric potential difference times time. The SR250 gated integrator implements integration followed by gate-width normalization and an adjustable amplification stage.^[ref]

For an original idealized detector pulse, take $v(t)=2\mathrm{mV}$ from0 to4nanoseconds and zero outside that interval. A gate covering0–4nanoseconds integrates $8\mathrm{mV}\mathrm{ns}$ and reports an average of2millivolts. A gate covering0–8nanoseconds integrates the same area but reports1millivolt. Thus unchanged admitted pulse area need not give an unchanged normalized output.

The gate average also differs from the average over a full repetition period. For the same pulse repeated once per microsecond, the full-period mean is only8microvolts. Comparing instruments therefore requires knowing whether the reported quantity is pulse area, within-gate average or full-period average.

A constant baseline $b$ contributesGate-width normalization does not remove that baseline. A separate reference or subtraction measurement is needed to distinguish it from the desired signal.

An apparatus check overlays the gate monitor and detector waveform on an oscilloscope, then varies the gate width while keeping its start fixed. A flat plateau should retain its input-referred average while the gate remains inside it; a short pulse diluted by additional quiet time behaves like the example above. Gate timing jitter and gate-width jitter can alter which signal portion is admitted and which duration is used for normalization.^[ref]