Circuit Response
every model has an edge, and the figure carries it
Concept

Aperture jitter — where it appears

The uncertainty in the instant a converter samples, which arrives as an amplitude error equal to the signal's slope times the timing error. A specification in picoseconds root-mean-square fixes the total error power and not its spectrum, so two clocks with the same figure can differ by twenty decibels in their worst line.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

What 10 ps of aperture jitter is worth, in bits. computed by solving, not by drawing. Samples are taken at instants displaced by a seeded Gaussian of 10 ps and the error is measured against the same sinusoid sampled exactly. The line is −20 log(2π f × jitter), which the measurement matches to 0.12 dB across three decades. The penalty is exactly twenty decibels a decade of input frequency, because the error is the signal's slope times the timing error and nothing else — so a converter holds 16 bits only up to 199 kHz and 12 bits up to 3.18 MHz. An aperture figure quoted without an input frequency states no resolution at all.

A picosecond, read as bits

Every other boundary in this collection has a frequency, an amplitude or a size on its axis. This one has a duration. A converter that samples at t + δ instead of t gets a value wrong by the slope times δ, so the damage is proportional to input frequency and to nothing else about the part: ten picoseconds holds sixteen bits up to 199 kHz and twelve bits up to 3.18 MHz, falling at exactly twenty decibels a decade. An aperture figure quoted without an input frequency states no resolution at all.

digital · Aperture jitter Same 2 ps of jitter: a floor at -121 dB, or a line at -91. computed by solving, not by drawing. A 3.337 MHz sinusoid sampled at 10 MHz with two clocks of identical root-mean-square jitter. One clock's timing error is independent gaussians and the other's is a sinusoid at 130 kHz. The total error power is the same — -87.43 and -87.55 decibels below the signal, against the closed form's -87.55 — and the pictures are not. The random clock spreads it over 2048 bins, -120.5 dB each; the modulated one puts it into two lines at 3.337 ± 0.130 MHz, -91.5 dB down. A specification in picoseconds does not choose between them.

A floor, or a line

Two clocks with identical two-picosecond jitter sample the same sinusoid, and the total error power is the same to a tenth of a decibel — the closed form the rung below computed, right for both. One of them puts that error across two thousand bins at −120 dB each; the other puts it into two lines at −91.5. The gap is the processing gain, it grows with the record length because a density falls and a line does not, and nothing in a specification quoted in picoseconds root-mean-square distinguishes the two cases.

digital · Aperture jitter

Named alongside it

The objects these essays reach for when they reach for this one.

Dynamic rangeEffective bitsMeasurement conditionNoise floorPhase noiseProcessing gainSample rateSampled dataSlew rateSpectrum

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