Phase Noise → Jitter Calculator
Convert phase noise (dBc/Hz at offset) to RMS timing jitter (ps) for clock oscillators. Integrate single-point or multi-point phase-noise specs.
How to Use
- Enter carrier frequency and phase noise at a single offset (or use a flat-band approximation).
- Enter the integration bandwidth (f_low to f_high).
- Tool computes RMS integrated phase noise and converts to timing jitter in ps.
Show Work
Formulas
History of Phase Noise Analysis
David Leeson\'s 1966 Proc. IEEE paper, "A simple model of feedback oscillator noise spectrum," established the classical phase-noise model still used today. Leeson showed that an oscillator\'s phase noise spectrum has a characteristic 1/f² slope near the carrier and a flat noise floor at large offsets — governed by the resonator Q, feedback gain, and device flicker noise.
The phase-noise-to-jitter conversion (σ_t = σ_φ / 2πf₀) became critical in the 1990s as high-speed digital-communication systems pushed into the GHz range. An OC-192 SONET link at 10 Gbit/s requires < 1 ps RMS jitter integrated over 12 kHz to 20 MHz — a spec that demands ultra-low phase noise in the reference clock.
Modern 5G and coherent-optical receivers require sub-100 fs jitter, achievable only with high-Q SAW or MEMS oscillators (Q > 50,000) or with optical frequency combs. The mathematical relationship between phase noise and jitter hasn\'t changed in 60 years; only the numerical targets keep getting tighter.
About This Calculator
Enter carrier frequency f₀, flat-band phase noise L(f) in dBc/Hz, and your integration bandwidth (f_low to f_high). The tool computes RMS integrated phase σ_φ = √(2·L·BW) and converts to jitter σ_t = σ_φ / (2π·f₀).
This uses a flat-band approximation — if your phase-noise spec varies with offset (typical shape: slope of −30 dB/decade near carrier, flattening at large offsets), you need to integrate the L(f) curve piecewise. For first-pass design, this single-number approximation is within a factor of 2× for most real oscillators. Everything runs client-side.
Frequently Asked Questions
What is phase noise?
Random short-term frequency variations in an oscillator, expressed as single-sideband noise power relative to the carrier (dBc/Hz) at offset frequencies. Key spec for clock sources.
Jitter vs phase noise?
Same phenomenon in different units. Phase noise = frequency-domain, dBc/Hz at each offset. Jitter = time-domain, RMS picoseconds integrated over some bandwidth.
Integration bandwidth?
Depends on application. For 10GbE clock (156.25 MHz), integrate 12 kHz to 20 MHz. For SDR LO, 1 kHz to 100 MHz. Always specify BW when quoting jitter.
Common Use Cases
10 GbE Reference
Typical target: < 1 ps RMS jitter (12 kHz to 20 MHz).
5G Radio
< 100 fs RMS jitter; achievable with crystal oscillators with ultra-low phase noise.
ADC Clock
12-bit ADC at 1 GSPS: needs < 1 ps RMS to preserve SNR.
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