[time-nuts] GPSDO TC

[Magnus Danielson]

>> As always, the problem is how do you know that the time constant you are
>> using is anywhere near optimum?
>>
>>
>> Bruce
> 
> So what is optimum... from control theory we learn, that with an even
> better model of your system, you can push performance to the edge! But
> you always loose robustness in doing that. 

Trouble is, we have many more variables and our set of goodness 
measurements are the ADEV and friends, which is much more troublesome to 
analyse than traditional variance and noise bandwidth values.

The variance for a PLL is an integral over f multiplying the noise power 
function of f with the square of the amplitude response over f. It is 
traditional to simplify this by assume a white noise power N0 (V²/Hz) in 
which case the noise level creeps out of the integral (since it now is a 
variable independent of f) and the remaining integral is that of the 
squared amplitude response of the filter. This can then further be 
generalized to the noise bandwidth formula.

Notice how we started from the variance measure, our traditional sigma 
value. We already know that it is insufficient to qualify the noise 
since the the f^-n noise powers does not converge on integration. Using 
derivate formulations like noise bandwidth those inherit the analysis 
problems. It even becomes hard achieving something similar as it now is 
a balance between different noise powers and filtering combines them in 
new interesting ways.

I think we need to either do hard analysis or we notice the tendencies 
in measures and try to explain them in other general tendencies and 
knowledge and draw some simplified conclusions and get away with it.

> So what is the implication of a to large TC here? Nothing going instable
> in the control loop? We are just following the "freerunning" OCXO curve
> past the point where GPS goes downhill?

For a second degree loop it would mean loosing lock or not be able to 
pull in properly. The actual problem is dynamics. Loop bandwidth will 
scale drift rate numbers with the square.

Cheers,
Magnus