[time-nuts] Square to sine wave symmetrical conversion

[Bob Camp]

Hi

Just so this does not get to ghastly confusing for those trying to follow along:

 Vig, John R.; Ferre-Pikal, Eva. S.; Camparo, J. C.; Cutler, L. S.; Maleki, L.; Riley, W. J.; Stein, S. R.; Thomas, C.; Walls, F. L.; White, J. D. (26 March 1999), IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities, IEEE, ISBN <https://en.wikipedia.org/wiki/International_Standard_Book_Number> 0-7381-1754-4 <https://en.wikipedia.org/wiki/Special:BookSources/0-7381-1754-4>, IEEE Std 1139-1999

On page 2 defines phase noise as:

 ℒ(f)=Sφ(f)/2 where the "phase instability" Sφ(f) is the one-sided spectral density of a signal's phase deviation. 

(Yes, that’s a bit of cut and paste from Wikipedia. I believe that their citation is correct.) 

Put another way, it’s what a phase noise test set measures (HP 3048 or whatever). It’s also the part of the spectral noise (as opposed to AM noise) that goes up 
as 20*log(N) when you multiply the signal’s frequency by N. 

Phase jitter and cycle jitter are not the same quantity. 

Bob


> On Jul 27, 2015, at 1:28 PM, Charles Steinmetz <csteinmetz at yandex.com> wrote:
> 
> Bob wrote:
> 
>> In tis case the question is "do you *need* low harmonics in the oscillator
>> stage to get low phase noise?"
> 
> Note that there are actually two questions.  One is WRT the phase noise of the oscillator itself, and the other WRT the phase noise of a system that integrates the oscillator.  In particular, even harmonics in the oscillator proper generate additional phase noise in the system when the signal is AC-coupled and/or DC-restored, and when it is fed to a zero-cross detector or other circuit that is sensitive to the symmetry of the waveform.
> 
> NIST published a paper on this.[1]  There is other research describing and quantifying the phenomenon, as well.
> 
> Best regards,
> 
> Charles
> 
> 
> [1]  "The Effect of Harmonic Distortion on Phase errors in Frequency Distribution and Synthesis," Walls and Ascarrunz  <http://tf.nist.gov/timefreq/general/pdf/1437.pdf>
> 
> 
> 
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