Phase Noise To Jitter Calculator

Calculate RMS phase jitter from phase-noise points and integration limits, and estimate ADC/input SNR from jitter and input frequency.

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Phase Noise to Jitter Formula

The standard relationship between single-sideband (SSB) phase noise and RMS time jitter is obtained by integrating the phase-noise spectrum over an offset-frequency band:

\sigma_t = \frac{1}{2\pi f_0}\sqrt{2\int_{f_1}^{f_2} 10^{L(f)/10}\,df},\qquad J_{pp}\approx 6\sigma_t

The calculator above uses a simplified, single-point approximation where phase noise is assumed flat at the entered level across an integration bandwidth \(\Delta f\):

J_{pp} \approx \frac{6}{2\pi f_0}\sqrt{2\cdot 10^{L/10}\cdot \Delta f}

Variables:

• \(L(f)\) is the SSB phase noise in dBc/Hz at offset frequency \(f\) (a power ratio per 1 Hz bandwidth)
• \(f_0\) is the carrier frequency (Hz)
• \(f_1\) to \(f_2\) define the offset-frequency integration limits (Hz), and \(\Delta f = f_2-f_1\) for a flat-noise approximation
• \(J_{pp}\approx 6\sigma_t\) is a common “6σ” peak-to-peak estimate (≈ ±3σ) for Gaussian random jitter; true peak-to-peak of a Gaussian process is unbounded

To calculate jitter, convert phase noise from dBc/Hz to linear units, integrate the spectrum to obtain RMS phase variance (rad²), take the square root to get RMS phase jitter (rad), and then convert to RMS time jitter using the carrier frequency. If desired, multiply RMS time jitter by 6 to estimate peak-to-peak jitter.

What is Phase Noise?

Phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, and it is related to time-domain jitter. It is a key parameter in the characterization of oscillators and timing components in electronic systems, affecting the performance of communication systems, radars, and other sensitive equipment.

How to Calculate Jitter from Phase Noise?

The following steps outline how to calculate jitter from phase noise:

1. Determine the phase noise \(L(f)\) in dBc/Hz as a function of offset frequency.
2. Choose an offset-frequency integration range \(f_1\) to \(f_2\) (Hz) that matches your application (or an equivalent integration bandwidth \(\Delta f\) for a simplified approximation).
3. Convert the phase noise to linear scale using: \(L_\text{lin}(f) = 10^{L(f)/10}\).
4. Compute RMS phase jitter (radians) by integrating the spectrum: \(\sigma_\phi = \sqrt{2\int_{f_1}^{f_2} 10^{L(f)/10}\,df}\). (For a flat-noise approximation, \(\sigma_\phi \approx \sqrt{2\cdot 10^{L/10}\cdot \Delta f}\).)
5. Convert RMS phase jitter to RMS time jitter: \(\sigma_t = \sigma_\phi/(2\pi f_0)\), where \(f_0\) is the carrier frequency.
6. If you need a peak-to-peak estimate, a common approximation for Gaussian random jitter is \(J_{pp}\approx 6\sigma_t\) (≈ ±3σ).
7. Use the calculator above to perform the same flat-noise approximation.

Example Problem:

Use the following variables as an example problem to test your knowledge (flat-noise approximation over \(\Delta f\)).

Phase Noise (L) = -100 dBc/Hz

Integration Bandwidth (Δf) = 10 kHz

Carrier Frequency (f₀) = 1 GHz

Using the calculator’s flat-noise approximation, the estimated peak-to-peak jitter is about 1.35 ps (0.00135 ns).