[time-nuts] Framework for simulation of oscillators

Attila Kinali attila at kinali.ch
Mon Mar 21 17:52:32 EDT 2016


Good evening

On Sun, 20 Mar 2016 22:33:15 +0100
Magnus Danielson <magnus at rubidium.se> wrote:

> As you read the appendixes of ITU-T Rec. G.823, G.824 and G.825 they 
> will not give very detailed information, but hints. The flicker noise 
> model comes from Jim Barnes and Chuck Greenhalls PTTI 19 article "Large 
> Sample Simulation of Flicker Noise". 

So far I have seen three approaches to 1/f^a simulation:
* filter in the time domain
* filter in the frequency domain
* simulate a random process with the right properties

Barnes&Greenhall[1], Park&Muhammad&Roy[2] on which Brooker&Inggs[3]
is based on fall into the first category.
Kasdin[4] and Ashby[5] falls into category two (Kasdin also gives a nice
overview of the problem space and the solutions applied there).
>From the third category, i've sofar only read Milotti[6].

 
> If this simulation approach is sufficient for either of your efforts, or 
> not, depends on what you try to capture. For instance, the oscillators 
> performance have been idealized in assuming fully linear EFC, fully 
> linear integrator of the crystal, assuming noise profile etc. This may 
> or may not be sufficient. Inherent lowpass filtering may be important or 
> not.

The modeling of the EFC and temperature dependence is orthogonal to the
noise modeling, AFAIK. And if I understand the physical properties of
a crystal, resp. the oscillator correctly, they can be modeled completely
independent without degrading the accuracy. Of course, noise on the EFC
signal will have an influence on the crystal noise, and this noise can
be of 1/f^a type itself as well.
 
			Attila Kinali


[1] "Large Sample Simulation of Flicker Noise", by Barnes and Greenhall, 1987
http://www.dtic.mil/dtic/tr/fulltext/u2/a495531.pdf
And its correction:
http://tycho.usno.navy.mil/ptti/1992papers/Vol%2024_44.pdf

[2] "Efficient Modeling of 1/f^2 Noise Using Multirate Process",
by Park, Muhammad, Roy, 2006
http://dx.doi.org/10.1109/TCAD.2005.855953

[3]"Efficient Generation of f^a Noise Sequences for Pulsed Radar Simulation",
by Brooker, Inggs, 2010
http://dx.doi.org/10.1109/TAES.2010.5461653 

[4] "Discrete Simulation of Colored Noise and Stochastic Processes and 1/f^a
Power Law Noise Generation", by Kasdin, 1995
http://www.umbc.edu/photonics/Menyuk/Phase-Noise/kasdin_ProcIEEE_950501n.pdf

[5] "Probability Distributions and Confidence Intervals for Simulated
Power Law Noise", by Neil Ashby, 2015
http://dx.doi.org/10.1109/TUFFC.2013.006167 (open access)

[6] "Exact numerical simulation of power-law noises", by Milotti, 2005
http://dx.doi.org/10.1103/PhysRevE.72.056701


-- 
Reading can seriously damage your ignorance.
		-- unknown


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