AN279 Datasheet, PDF (4/8 Pages) Silicon Laboratories – ESTIMATING PERIOD JITTER FROM PHASE NOISE

AN279
By contrast, if we weight L(f) using the period jitter weighting function and integrate the resulting curve over 10 Hz
to 160 MHz, we obtain a total phase noise power = –56.84 dBC, equivalent to RMS period jitter of 2.025 ps or
0.00204 radians; so, we can estimate the period jitter as being roughly 2 ps RMS, based solely on the available
phase noise measurement. This estimate can be correlated with measurements from complementary time domain
equipment when available. See Smith (2006) for example.
The estimation process may be simplified further by treating the period jitter weighting function as if it was a single-
pole, high-pass filter function out to fc/2 only. As noted in Figure 2, the J_PER weighting function, based on the
4sin2(πfτ) weighting factor in dB, looks like a +20 dB/dec sloped line until it gets close to the half-carrier frequency,
where it starts to curve down. If one instead approximates the weighting function as 4(πfτ)² in dB, this yields a
straight +20 dB/dec line. The maximum or intercept at the half-carrier frequency is, therefore,
10log(4(π(fc/2)τ)²) = 10log(π²) = 9.94 dB or approximately 10 dB. Integrating the weighted phase noise in this
fashion, one obtains –57.62 dBc, equivalent to RMS period jitter of 1.849 ps or 0.00186 radians. In this particular
example, the simplified “single pole filter” weighting out to the half carrier frequency resulted in a roughly 9% lower
estimate. This is a less conservative approach, which may still yield a sufficiently accurate estimate depending on
the application.
Since this approach does not directly measure period jitter in the time domain, we cannot make definitive
statements about the peak-to-peak values of the period jitter. However, if other evidence suggests that the edge
jitter or period jitter distribution is Gaussian, we can apply the usual statistical estimates.
5. Summary
This application note has reviewed how RMS period jitter may be estimated from phase noise data. The key points
to keep in mind are as follows:
„ Period jitter is dominated by high-frequency phase noise.
„ Channel bandwidth plays a determining role in the apparent jitter observed.
„ Spurs contribute very little to the period jitter unless they are large and located in the vicinity of the half-carrier
frequency.
Generally speaking, hybrid crystal oscillators, such as the Si5xx series devices, have excellent period jitter due to
their relatively low noise floor.
6. References
Drakhlis, Boris, "Calculate Oscillator Jitter By Using Phase-Noise Analysis,"
Microwaves & RF, Jan. 2001 pp. 82-90, 157.
Underhill, M. J. and P. J. Brown, "Estimation of Total Jitter and Jitter Probability Density Function from the Signal
Spectrum", Proc. 18th EFTF (European Time and Frequency Forum), University of Surrey, Guildford, UK, 5-7 April
2004.
Smith, Kevin G., “Practical Issues Correlating Theoretical Period Jitter vs. T1A Measured Period Jitter”, Austin
Conference on Integrated Systems & Circuits, 2006.
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