[time-nuts] Framework for simulation of oscillators

[Magnus Danielson]

Hi,

On 03/21/2016 10:52 PM, Attila Kinali wrote:
> 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].
>

Chuck Greenhall have a nice overview of methods for flicker noise, and 
goes in to some depth on it.

>> 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.

Depending on the tau of interest, temperature variations may or may not 
affect your plots.

Noise on EFC will be filtered, and then integrated.

Cheers,
Magnus