Jitter from Phase Noise
Tj = √(2 × ∫L(f)df) / (2πf0)
Quick answer
This calculator solves Tj = √(2 × ∫L(f)df) / (2πf0) for RMS Jitter. With Integrated Phase Noise (rad² rms) 0.5, Carrier Frequency 10 MHz, the result is 15.92 ns.
Calculator
Formula
Description
Phase noise on a clock or oscillator signal translates directly to timing jitter. The integrated phase noise power over the bandwidth of interest determines the RMS jitter. Higher carrier frequencies have less jitter for the same phase noise because each radian of phase error represents a smaller fraction of the period. This relationship is critical for high-speed serial links (PCIe, USB, HDMI), ADC sampling clocks, and communication systems where jitter directly impacts bit error rate. Phase noise is typically integrated from 12 kHz to 20 MHz for serial link analysis.
Variables
- Tj — RMS timing jitter (s)
- ∫L(f)df — Integrated SSB phase noise power (rad² rms)
- f0 — Carrier (clock) frequency (Hz)
Practical Notes
For a 100 MHz clock with -100 dBc/Hz phase noise flat from 10 kHz to 10 MHz: integrated noise = 10⁻¹⁰ × 10⁷ = 10⁻³ rad², Tj ≈ 71 ps rms. PCIe Gen3 requires <1.5 ps rms jitter on the reference clock. DDR4 requires <3 ps rms. Low-jitter clock generators use crystal oscillators with PLL multiplication rather than RC oscillators.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Tj | RMS Jitter | ps | ps, ns, µs, ms, s, min, h |
| L_integrated | Integrated Phase Noise (rad² rms) | — | — |
| f0 | Carrier Frequency | MHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Integrated Phase Noise (rad² rms) 0.5, Carrier Frequency 10 MHz
- 2. The relation: Tj = √(2 × ∫L(f)df) / (2πf0)
- 3. Substitute: L_integrated = 0.5, f0 = 10 MHz
- 4. Result: RMS Jitter = 15.92 ns
Worked examples
Minimum range
Given: Integrated Phase Noise (rad² rms) 0.025, Carrier Frequency 100 kHz
Result: RMS Jitter = 0.3559 µs
Low range
Given: Integrated Phase Noise (rad² rms) 0.25, Carrier Frequency 1 MHz
Result: RMS Jitter = 112.5 ns
Typical
Given: Integrated Phase Noise (rad² rms) 0.5, Carrier Frequency 10 MHz
Result: RMS Jitter = 15.92 ns
High range
Given: Integrated Phase Noise (rad² rms) 0.8, Carrier Frequency 100 MHz
Result: RMS Jitter = 2.013 ns
Maximum range
Given: Integrated Phase Noise (rad² rms) 8, Carrier Frequency 1 GHz
Result: RMS Jitter = 0.6366 ns
How RMS Jitter changes with Integrated Phase Noise (rad² rms)
| Integrated Phase Noise (rad² rms) (input) | RMS Jitter (result) |
|---|---|
| 0.05 | 5.033 ns |
| 0.125 | 7.958 ns |
| 0.25 | 11.25 ns |
| 0.375 | 13.78 ns |
| 0.5 | 15.92 ns |
| 0.75 | 19.49 ns |
| 1 | 22.51 ns |
| 2 | 31.83 ns |
| 3.5 | 42.11 ns |
| 5 | 50.33 ns |
The same result in other units
| Unit | Value |
|---|---|
| ps | 15920 |
| ns | 15.92 |
| µs | 0.01592 |
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<p><a href="https://vbatpower.com/formulas/jitter-phase-noise/">Jitter from Phase Noise</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Jitter from Phase Noise?
Use Tj = √(2 × ∫L(f)df) / (2πf0). With Integrated Phase Noise (rad² rms) 0.5, Carrier Frequency 10 MHz, RMS Jitter works out to 15.92 ns.
What is the formula for Jitter from Phase Noise?
The formula is Tj = √(2 × ∫L(f)df) / (2πf0). Phase noise on a clock or oscillator signal translates directly to timing jitter.
What units does Jitter from Phase Noise use?
RMS Jitter is shown in ps, ns, µs. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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