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SNR Loss from Sample Jitter

Find the jitter-limited SNR ceiling of a sampled sine — the number that kills your high-IF ADC's ENOB.

InputSNR_jitter = −20 · log₁₀( 2π · f_in · t_j ) , ENOB = (SNR − 1.76) / 6.02

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The engineering

When you sample a sine wave, timing uncertainty on the clock edge (aperture jitter) turns into voltage error proportional to the signal's slew rate. Because a sine slews fastest at its zero crossing and that slew rate scales with frequency, jitter-induced noise grows directly with input frequency — this is why a converter that hits 14 bits at baseband can collapse to 9 or 10 bits digitizing a 200 MHz IF.

This ceiling is independent of the ADC's own quantization noise; the total SNR is the RSS of the two. Rule of thumb: 1 ps RMS jitter caps you near 90 dB at 70 MHz but only ~73 dB at 500 MHz. If your high-IF SNR looks stuck no matter which converter you drop in, the clock source and its phase noise are the suspect, not the ADC.

Where this math comes from

The aperture-jitter SNR limit is standard data-converter lore, but Walt Kester of Analog Devices is the engineer who drilled it into a generation of designers. Through ADI seminar notes and tutorials from the 1990s onward, Kester reduced the phenomenon to the single tidy expression SNR = −20·log(2π·f·t_j) and hammered the practical point that clock jitter, not the ADC core, sets the limit at high input frequencies.

The underlying physics is older — it is just the derivative of a sine, dV/dt = 2πf·A·cos, folded into an RMS error — but the framing as a design budget line item, sitting alongside quantization and thermal noise in an RSS sum, belongs to the converter-application literature that Kester and his ADI colleagues codified.

  1. 1948Claude ShannonFormalizes sampling theory, making sample-timing error a quantifiable noise source.
  2. 1978Bernard Gordon / analog pioneersEarly ADC datasheets begin specifying aperture uncertainty as a limiting parameter.
  3. 1996Walt Kester (Analog Devices)Popularizes SNR = −20·log(2π·f·t_j) in ADI seminar and tutorial notes.
  4. 2010IEEE Std 1241Standardizes ADC dynamic-testing terminology including aperture jitter and effective bits.

See the full timeline of the math behind every calculator →

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