# [time-nuts] GPSDO TC

Magnus Danielson magnus at rubidium.dyndns.org
Thu Jan 8 18:08:49 EST 2009

```>> 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

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