[time-nuts] New Subscriber, DIY GPSDO project (yes, another one)

[Magnus Danielson]

H

On 2020-03-08 07:38, Poul-Henning Kamp wrote:
> --------
> In message <5583E434-4C72-4A4F-A60B-75A4204EF2D5 at n1k.org>, Bob kb8tq writes:
>
>> Backing up a bit …. the objective is not to minimize overshoot or 
>> keep the loop from oscillating. The issue here is optimizing the noise
>> output of the combination of GPS + OCXO when combined via
>> the control loop. It’s a very different objective ….
> Yes, but a PI loop is still the best mathematical tool for it,
> you just need the PI loop to have adjustable parameters.
>
> Adjusting those parameters after the initial capture is the hard
> part, because the signal you are looking for is in the "wander"
> domain.

First, a PID PLL degenerates into a PI loop. The P and D steering ends
up achieving the same thing as P in the PI, do there is no benefit of D.
I have shown such derivations in the past. Not too hard to do.

Second, a PI loop has trivial dimensioning from damping factor and
frequency, and the damping factor we know we need to keep high enough,
so say 3 or higher, so we end up only having the loop frequency, which
is the reciprocal of time-constant. These rules is easy to do, a page of
paper is enough or a whiteboard.

So, these basic facts is just the rule of the game.

> The best I have come up with, is to average the measured phase error
> to get rid of the GPS jitter/sawtooth, and adjust the PI loop
> parameters based on the time between sign-changes of that averaged
> signal.
Third, the averaging filter needs a limitation on how low it frequency
can go, before it starts to affect the pole-pair of the PI-loop, at
which time stability cannot be guaranteed. Corrections needs to be
performed to ensure stability and performance as it comes closer.
> If you plot the histogram of the time between sign-changes, you want
> the peak below the supposed "allan-intercept" and if you get time
> intervals more than double the "allan-intercept" you have probably
> tightend too much.

The Allan intercept is really where the cut-over from reference Allan
plot to the steered oscillator plot. The concept of Allan intercept is
actually not perfect science, but a concept. The actual physics would
make the cut-over analysis on the phase-noise plots make more sense, but
for the time-constants we talk, that's where the Allan deviation plot
has taken over typically. Actually doing the cut-over in Allan deviation
form carries with it biases values, making the Allan intercept value
biased. It gets you to the right neighborhood, sure, but do expect a few
trims for optimum stability.

Cheers,
Magnus