As I am a poor programmer and also lazy (includes hardware and software), I 
would like to ask the following question: How much better would a GPSDO like 
the Arduino GPSDO be with added sawtooth correction? 

Let’s say we assume the 1ns resolution TIC is perfect, no jitter from the uP 
and the DAC have a perfect frequency setting resolution of 1E-13. The receiver 
in my case is a M12 set in position hold mode after a survey and my measured 
ADEV starts at 2E-8 for 1sec and is 2E-11 at 1000secs. The MDEV is 2E-8 at 1sec 
and 2E-12 at 1000sec (very similar to what found on the leapsecond.com M12 
page). The oscillator is my “8663”-type OCXO that I have measured to have an 
ADEV just above 1E-12 over the range 1-10000secs. Let’s say the oscillator is 
perfect at 2E-12 over 1-10000secs.

The Arduino GPSDO control loop works as follows, as far as I understand, if set 
to a time constant =1000secs and damping =2 :

TIC value is pre-filtered similar to an RC filter with 250seconds time constant 
(I like to refer to analog RC-filters being an RF and analog engineer)


The filtered TIC value is divided by the time constant 1000 and adjusts the DAC 
proportional to this.


The filtered TIC value integrates the DAC value after dividing it by (time 
constant * time constant * damping) = (/1000/1000/2).


My explicit question is how much better the ADEV of the GPSDO oscillator output 
will be with sawtooth correction added in the software? Another question is how 
much better the ADEV will be if the TIC had a resolution of 0.1nsec instead? 
Maybe a third question could be if the DAC only had 1E-12 resolution?

Is some more important factors needed to be known to calculate this to a 
reasonable accuracy? e.g. room temperature variations of the M12. 

In my own measurements, with about the same conditions as above with a time 
constant of 1000s, I got an output ADEV of about 3E-12 at Tau 1000s measured 
with an HP5370 against an LPRO Rb (plot was attached to Arduino GPSDO thread 
Feb 12 2014). This value looks very similar to the combination of the 1PPS MDEV 
and OCXO ADEV. Is that just a coincidence?

Lars
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