Phase Noise and Jitter Conversion: Formula and Calculator

Phase noise and jitter are critical parameters in frequency domain systems, impacting signal integrity. Converting between the two requires precise formulas and calculations. This guide provides an in-depth explanation of phase noise, jitter, their relationship, and a handy conversion calculator for accurate analysis.

Phase noise

Phase noise is the purity measurement of crystal oscillators/synthesizers. Ideally oscillator should have all the energies concentrated at the operating frequency as desired if we view the single sided spectrum on spectrum analyzer. But practically it will produce phase modulated noise sidebands in the close vicinity. These small noise sidebands results in phase noise concept. The most popular crystal oscillator we have used was 10 MHz OCXO, from Vectron International.
Phase noise measurement :
There are various methods for phase noise measurements, the one using spectrum analyzer is shown in the fig.1. As shown in the figure phase noise is measured very near to the carrier at 10Hz, 100Hz, 1KHz, 10KHz, 100KHz away. Phase noise is the difference in level between peak of the carrier and magnitude at some frequency away say 1KHz. To get the final phase noise 10 log₁₀(RBW) to be added to the difference obtained above. If sidebands are not visible then D is the difference between peak of the carrier and noise level at offset frequency desired.
➨ RF phase noise measurement setup➤

Phase jitter

Time domain name of phase noise is phase jitter, measured in radians (rms) or pico-second (rms). Variation in the period or cycle of the time domain waveform is the primary cause of jitter. This happens due to power supply provided to the oscillator, Electro-magnetic radiation, interference from other sources and so on. There are many types of jitter for example absolute jitter, cycle to cycle jitter and so on. Difference between measured and ideal cycle of the time domain waveform gives cycle to cycle jitter. Phase Jitter causes signal to shift in horizontal and hence causes ISI.
Phase jitter measurement :
➨ Refer Application note from Maxim Integrated no. AN 3359 for phase jitter measurement method.

Phase noise to jitter conversion

As shown in the figure first integrated phase noise is derived from f1 to f5, let this integrated phase noise is A. From this integrated phase noise, rms phase jitter is obtained using following equation.
A= 10*log₁₀ (A1+A2+A3)
Phase jitter (radians) φ = (2 x 10^A/10)^1/2
Phase jitter (seconds) = φ/(2 x pi x fc)
Here fc is the carrier frequency of the oscillator/synthesizer of which we are finding phase noise/phase jitter.

Example calculation

Let us assume that we have broadband phase noise of about -120 dBc/Hz from 1 KHz to 1 MHz, and oscillator frequency fc is 10 MHz. Integrated phase noise (A) = -120 + 10 log₁₀ ( 10x 10 ⁶ - 0.001 x 10 ⁶)
= -120dBc + 70dB
= -50dBc
RMS phase jitter (radian), φ = ( 2 x 10^-5.0 )^1/2
= 4.72 x 10^-4 radians
RMS phase jitter (seconds) = φ /(2 x pi x 10 MHz) = 0.711 ps

Phase noise/jitter reduction techniques

• Use filter capacitor and bypass capacitor which will eliminate low frequency(power supply noise) and high frequency signals(surge) respectively.
• Follow proper PCB layout design rules for crystal/synthesizer mounting. For example avoid long traces, keep power and ground signals nearby and so on.
• Use ferrite beads in the circuit.
• Do proper shielding of crystal oscillator which will eliminate Electro-Magnetic radiation effect to the crystal oscillator.
• Use highly stabilized power supply with less ripple as source of power for the oscillator.
• Use shield box for covering the oscillator, if space limitation is not there.
• Cooling mechanism either in the form of heat sink or fan should be provided.

• www.jittertime.com/resources/pncalc.shtml
• www.raltron.com/cust/tools/osc.asp

RF Phase Noise Measurement using Spectrum Analyzer

➨Refer RF phase noise measurement➤ which mentions settings required in Spectrum Analyzer for phase noise measurement.

Conclusion

Understanding the correlation between phase noise and jitter ensures better system performance. Utilize the provided formula and calculator to simplify complex conversions in frequency systems.

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RF and Wireless Terminologies