Este guia está disponível atualmente em inglês.
Technology / Technical guide
Sampling Jitter: Timing Error, Signal Slope & SNR
An error in the instant of observation can become an error in the reported waveform value. The effect depends on how quickly the waveform changes at that instant. Sampling jitter therefore concerns the time base of conversion, not simply the time zone or arrival timestamp attached to a later record.
Time uncertainty interacts with waveform slope.
Follow the small timing displacement into amplitude error before interpreting a conditional signal-to-noise relation.
01 / Time model
Actual sample instants can differ from a uniform grid.
Write an actual instant as nTs+δt[n], where nTs is the nominal uniform grid and δt is the timing deviation.
Write an actual instant as nTs+δt[n], where nTs is the nominal uniform grid and δt is the timing deviation. A constant offset shifts all observations alike; varying timing error changes their relative placement.
Clock timing, converter aperture uncertainty and delivery latency belong to different boundaries. The lag guide compares retained patterns, but their alignment does not independently identify the instant when analogue conversion occurred.
02 / Local slope
A small displacement produces a first-order value error.
For a differentiable waveform and sufficiently small δt, x(t+δt)−x(t) is approximately x′(t)δt.
For a differentiable waveform and sufficiently small δt, x(t+δt)−x(t) is approximately x′(t)δt. Timing error has seconds as its unit; slope has signal units per second, leaving the corresponding amplitude-error unit.
The same time deviation produces little first-order error near a stationary point and more on a steep portion. This is a local approximation, not a statement that the complete waveform error always follows one fixed amplitude offset.
03 / Sine conditions
A statistical relation needs independent small timing error.
For x = A sin(2πf_in t), the RMS slope over the represented cycles is 2πf_in A/√2.
For x = A sin(2πf_in t), the RMS slope over the represented cycles is 2πf_in A/√2. With small zero-mean random timing error, RMS σ_t, independent of signal phase, the first-order RMS error is approximately 2πf_in Aσ_t/√2.
Analog Devices derives this sine-wave jitter relationship. Dividing signal RMS A/√2 by that error gives SNR_j ≈ −20log10(2πf_inσ_t) dB. Here f_in is input-waveform frequency, not sampling frequency; the argument is dimensionless.
04 / Numerical model
Input frequency changes the ideal jitter contribution.
Hypothetical values: f_in = 100 Hz and σ_t = 10 microseconds give 2πf_inσ_t ≈ 0.00628 and jitter-only SNR about 44.0 dB.
Hypothetical values: f_in = 100 Hz and σ_t = 10 microseconds give 2πf_inσ_t ≈ 0.00628 and jitter-only SNR about 44.0 dB. The small phase-error condition is retained in this illustration.
At 200 Hz with the same σ_t, the model gives about 38.0 dB, approximately 6.02 dB lower. These invented frequencies and jitter describe one theoretical contribution, not a sensor sample rate, product SNR or allowable timing requirement.
05 / Noise structure
RMS timing spread does not specify the entire spectrum.
Periodic timing modulation can create structured spectral components, whereas other timing statistics can produce different error patterns.
Periodic timing modulation can create structured spectral components, whereas other timing statistics can produce different error patterns. Two timing processes with equal RMS need not have identical spectral content. Independence cannot be inferred from an RMS value alone.
Additional voltage noise and distortion can further limit the total signal-to-error ratio. Independent variance contributions can be combined under their model; shared or correlated timing paths need their proper relationships rather than automatic root-sum-square addition.
06 / Scope
A timing model cannot infer converter performance by itself.
Non-sinusoidal signals need their actual slopes and statistics; large time deviations can invalidate the first-order expansion.
Non-sinusoidal signals need their actual slopes and statistics; large time deviations can invalidate the first-order expansion. The quantisation guide covers another error mechanism, while the PSD guide describes frequency-distributed squared quantities.
No MARSTON clock jitter, aperture specification or SNR is asserted. This explanation provides no clock replacement, live test, synchronisation change or acquisition setting; it states the conditions behind a mathematical timing-error estimate.
Related technical guides: ADC Quantisation, Bit Count & Effective Number of Bits · Cross-Correlation: Lag Sign, Similarity & Time Delay · Discrete Control & Zero-Order Hold: Between Samples.
General background: Analog Devices MT-007: Aperture timing and conditional sine-wave jitter error. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| δt[n] | Deviation of conversion time, seconds | Different from a later arrival timestamp. |
| x′(t) | Local waveform slope | Determines the small-error amplitude mapping. |
| σ_t | RMS timing error in the stated model | Independence and spectrum are separate properties. |
| f_in | Input sine frequency, Hz | Not the sample rate. |
| SNR_j | −20log10(2πf_inσ_t) | Small random jitter, sine and phase assumptions apply. |
Engineering questions.
Is fixed timing offset identical to random jitter?
No. Their effects and statistical descriptions differ.
Does every waveform point have equal jitter error?
No. Its local slope matters.
Is f_in the sample frequency in the equation?
No. It is the represented input sine frequency.
Does jitter-only SNR equal total measured SNR?
Not generally; other error contributions remain.
Does one RMS value establish white timing noise?
No. Its spectrum and dependencies need their own description.
Are 44 dB and ten microseconds product values?
No. They belong to the hypothetical small-error model.
Technical enquiry
Discuss the technical question.
An error in the instant of observation can become an error in the reported waveform value. Share the model and applicable operating or design information for an engineering discussion.