[time-nuts] GPSDO simulation tool

Joseph Gwinn joegwinn at comcast.net
Mon Mar 24 08:59:01 EDT 2014

On Sun, 23 Mar 2014 21:33:07 -0400, time-nuts-request at febo.com wrote:

> Message: 1
> Date: Mon, 24 Mar 2014 00:48:01 +0100
> From: Magnus Danielson <magnus at rubidium.dyndns.org>
> To: time-nuts at febo.com
> Subject: Re: [time-nuts] GPSDO simulation tool
> Jim,
> On 23/03/14 16:00, Jim Miller wrote:
>>> To handle higher tau performance I think we want a higher degree loop.
>>> Cheers,
>>> Magnus
>> Is a higher degree loop possible while maintaining stability? Commanding
>> frequency while measuring phase is one pole, integrating the result of the
>> phase comparison is a second pole and closing the loop will result in
>> oscillation unless a zero is inserted (the P in PID).
>> How would stability be maintained?
> A third degree PLL is stable if the pole-pair is suitably located. The 
> second degree PLL is kind of hard to bring into self-oscillation while 
> that is much easier with the third degree, so more care needs to go into it.
> When you think about it, putting an exponential averager just after the 
> phase-detector (AVG1 in gpsim1) is in fact making the PLL a third 
> degree, but since the time-constant needs to be constrained to be well 
> below the loop time-constant "for stability reasons" it is in fact to 
> avoid having the poles of this third-degree loop from deviating away 
> into instability.
> I did a temporary hack on the PID code to convert the D-term into I^2 
> term, by integrating the integrator output. First attempt was indeed 
> quite resonant just to show that I was in the unsafe region. Backing 
> down on the strength of the component sure did remove much of the 
> resonance, but I did not see any appreciable improvement in filtering 
> performance, so quick and dirty hacking isn't sufficient, darn.

I recall from an analysis of third-order PLLs read a few years ago that 
stability also depended on the amplitude of the signal to which the PLL 
was locking.  This sensitivity made 3rd-order PLLs difficult to use as 
radio receivers, but for use as a timing-chain component one can always 
arrange to have adequate amplitude (and have a level detector to warn 
if amplitude isn't adequate).  

I always suspected that the old Symmetricom 1050A disciplined 
oscillator was a 3rd-order loop, but was never able to find anybody who 

Joe Gwinn

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