AN256 Datasheet, PDF (1/8 Pages) Silicon Laboratories – INTEGRATED PHASE NOISE

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INTEGRATED PHASE NOISE
1. Introduction
Phase noise is commonly used to describe the performance of oscillators and is a measure of the power spectral
density of the phase angle. Noise in the phase angle of a sinusoid is visible on the power spectral density of the
carrier sinusoid as a spread of the true carrier tone. Phase noise in the frequency domain is equivalent to jitter in
the time domain. In this application note, we will refer to phase noise power integrated over a bandwidth as phase
jitter. Phase jitter, when calculated from phase noise, is an RMS quantity.
In addition to noise, there are other repeating phenomena that generate additional tones, usually much lower than
the carrier. Such tones are labeled as "spurs." The word "spur" comes from the word "spurious", which means "not
the original." Spurs are signals close to the primary/carrier frequency but that are not the primary signal. Such
signals can be problematic for some applications but may have no effect on other systems. Typically, the term
"spurs" refers to those that are not harmonics of the carrier signal; so, many devices specify non-harmonic
spurious power separately. Spurs require additional consideration when calculating the integrated jitter.
2. Power Spectral Density Measurements
Phase noise is typically plotted on a per Hertz basis. This means that the power level is considered to be uniform
across a 1 Hz brick-wall bandwidth (also called the resolution bandwidth). Unfortunately, it would take a very long
time to sweep a 1 Hz band-pass filter in 1 Hz steps across the entire frequency spectrum in order to obtain the
phase noise data. Instead, a larger resolution bandwidth is used depending on the frequency range offset from the
carrier. For example, a 1 MHz resolution bandwidth may be used for the offset range from 10 to 100 MHz, thereby
reducing the number of frequency bins from 90 million to 90.
Once the frequency bins have been measured, the noise in a 1 Hz band can be calculated by subtracting 10 dB for
every decade frequency drop from the resolution bandwidth to 1 Hz. For example, a 1 MHz resolution bandwidth
bin would be scaled by:
10 x Log10(1 MHz/1Hz) = 60 dB.
Using a smaller resolution bandwidth, a second pass across the frequency range may be made in order to improve
the spurious signal’s height above the noise floor.
3. Calculating Phase Jitter from Phase Noise
To obtain the time integral of the phase jitter, one can simply take the frequency integral of the phase noise. This is
the direct result from Parseval's Theorem, which, simply stated, says that the time integral of the square of a signal
is equal to the frequency integral of the square of its Fourier Transform.
Since real phase noise data cannot be collected across a continuous spectrum, a summation must be performed in
place of the integral. The summation can be performed using a rectangular or trapezoidal approximation or even
Simpson's rule, depending on personal preference. Lastly, phase noise data is typically plotted on a log-log scale,
whereas the integration should be performed on a linear-linear scale. The conversion from d/b/a/Hz to seconds/Hz
is derived in " Appendix—Mathematical Treatment of Spurs" on page 5 and is restated here:
1_----0_---^L_---^d_--^B_---⁽_-^f_--⁾_---^⁄_-²_---⁰_-
πf₀
=
T_j
Rev. 0.2 3/06
Copyright © 2006 by Silicon Laboratories
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