Data Source & Methodology

  • IEEE Std 1139-2022 — Standard Definitions for Fundamental Frequency and Time Metrology—Random Instabilities. Methods and quantities for phase/frequency instability and time-domain measures. Standard access.
  • Analog Devices MT-008 — Converting Oscillator Phase Noise to Time Jitter, W. Kester. Derivation and practical integration guidance. PDF.
  • Analog Devices (article) — Clock Jitter and Phase Noise Conversion. Link.
  • Skyworks AN279 — Estimating Period Jitter from Phase Noise. PDF.

All calculations strictly follow the formulas and data definitions provided by these sources.

The Formula Explained

Single-sideband phase noise \(L(f)\) [dBc/Hz] relates to phase-noise spectral density \(S_\phi(f)\) [rad\(^2\)/Hz] as:

\[ S_\phi(f) \;=\; 2 \cdot 10^{\,L(f)/10} \]

The RMS time jitter is:

\[ \sigma_t \;=\; \frac{1}{2\pi f_0}\;\sqrt{ \int_{f_1}^{f_2} S_\phi(f)\, df } \;=\; \frac{1}{2\pi f_0}\;\sqrt{ \int_{f_1}^{f_2} 2\cdot 10^{L(f)/10} \, df } \;. \]

Additional conversions:

\[ \sigma_\phi \;=\; 2\pi f_0 \,\sigma_t,\qquad \text{pp jitter} \approx N\,\sigma_t,\qquad \%UI = 100 \cdot \sigma_t \cdot R_b, \]

For a sinusoid at \( f_{\text{in}} \):

\[ \mathrm{SNR_{jitter}} \,[\mathrm{dB}] \;=\; -20 \log_{10} \!\big( 2\pi f_{\text{in}} \sigma_t \big). \]

Glossary of Variables

  • \(f_0\): carrier/clock frequency (Hz).
  • \(L(f)\): single-sideband phase noise at offset \(f\) (dBc/Hz).
  • \(S_\phi(f)\): phase-noise spectral density (rad\(^2\)/Hz), \(=2\cdot 10^{L/10}\).
  • \([f_1,f_2]\): integration band (Hz).
  • \(\sigma_t\): RMS time jitter (s).
  • \(\sigma_\phi\): RMS phase jitter (radians).
  • \(R_b\): data rate (Hz) for UI conversion.
  • \(N\): sigma multiplier for peak-to-peak estimate (Gaussian RJ assumption).

How It Works: A Step-by-Step Example

Given: \(f_0=100\;\mathrm{MHz}\); integrate from \(10^3\) to \(10^7\) Hz; phase-noise points: (1k, −90), (10k, −110), (100k, −130), (1M, −150), (10M, −160) dBc/Hz.

  1. Interpolate \(L(f)\) between points in the log-frequency domain; convert to \(S_\phi(f)=2\cdot10^{L/10}\).
  2. Numerically integrate \(S_\phi(f)\) over \([10^3,10^7]\) Hz (trapezoidal rule on linear \(f\)).
  3. Compute \(\sigma_t = \frac{1}{2\pi f_0}\sqrt{\int S_\phi(f) df}\).
  4. For \(N=14.1\), get peak-to-peak \(= N\sigma_t\). For \(R_b=10\;\mathrm{Gb/s}\), \(\%UI=100\,\sigma_t\,R_b\).
  5. At \(f_{\text{in}}=10\,\mathrm{MHz}\), compute \(\mathrm{SNR_{jitter}}\).

The live calculator reproduces these steps precisely.

FAQ

Which integration limits should I pick?

It depends on your signal chain and any filtering. Common choices: from a few Hz or kHz up to a fraction of the carrier, the ADC Nyquist rate, or clock bandwidth. See IEEE 1139 and vendor notes for context.

Why is there a factor of 2 in \(S_\phi(f)=2\cdot10^{L/10}\)?

Because \(L(f)\) is single-sideband (SSB) phase noise. Converting to two-sided phase-noise spectral density in rad\(^2\)/Hz introduces the factor of two.

Is peak-to-peak jitter well-defined?

Not for unbounded Gaussian noise. Engineers quote a multiple of σ (e.g., 14.1σ for BER≈10⁻¹²). Use N-sigma appropriate for your target BER.

Does this include deterministic jitter (DJ)?

No—this integration computes random jitter from phase noise. Budget DJ separately (e.g., ISI, periodic interference) and combine as appropriate.

Can I input integrated phase noise directly?

Enter two points bounding your band and use a flat L(f) (or several flat segments) to approximate; future versions may add direct input for integrated values.

Why log-domain interpolation?

Phase-noise plots are usually on log-frequency with slopes in dB/decade; log-domain interpolation better matches typical spectra between measured offsets.

Tool developed by Ugo Candido. Technical content reviewed by CalcDomain Editorial Board.
Last accuracy review: