[time-nuts] statistical distribution of initial frequency error in tcxos

[jimlux]

On 3/13/19 9:17 AM, Attila Kinali wrote:
> Hoi Jim,
> 
> On Wed, 13 Mar 2019 08:39:24 -0700
> jimlux <jimlux at earthlink.net> wrote:
> 
>> For instance, if I'm buying 10MHz oscillators with a spec of 5ppm,
>> they'll all fall in a band +/- 50 Hz.  But how many are within 1 Hz?
>> within 0.1Hz?
> 
> I have never measured TCXOs, but I've seen data of other devices
> that are adjusted at the manufacturer. What you end up with is
> something between a uniform distribution and truncated Gauss.
> It is also very likely that most are withing 1ppm or even less,
> depending on how much margin the manufacturer put into the spec.
> Aging and environment will spread the values in a Gauss like fashion
> (think of a (anomalous) diffusion process).
> 
> Would it be rude to ask for more details on what you are planing to do?
> It sounds interesting.
> 

I'm looking at various radio issues with large swarms of tiny spacecraft 
- specifically for making a radio telescope. Unlike terrestrial 
interferometers where you have reference distribution (local) or cesium 
clocks and masers (VLBI), we have to have some other way to solve the 
problem.

Fortunately, you can do a lot of post processing, so it's more a matter 
of "knowledge" not "control" of the local frequency source on the swarm 
nodes.

One scheme to propagate references is to radiate your reference 
oscillator so that all the other nodes can receive it, and each node can 
then say "I'm node A, and relative to me, nodes B is 1% high, Node C is 
0.5% low, etc." and from that you can (maybe) solve for the ensemble. 
One can also get some information about the relative positions of nodes 
(by looking at the phase of the signal).

(one does need at least one single "good" reference to tie them all to.. 
in the case of most swarm schemes, there's a mother ship to relay data 
back to Earth that can provide a broadcast reference, or if you're close 
enough to Earth, you can radiate a high quality signal from Earth).

This whole scheme breaks horribly if too many signals are too close 
together, and I suspect that this is the actual case.  So we need to 
have a way to explicitly move the signals around.

when you're building 1000 nodes, you would really like them to be
a) all the same parts list and construction
b) not require any customization
c) and have the minimum number of parts on the parts list.

(recognizing that I can probably do something like modulate the 
reference broadcast with a single bit from some existing part and do 
CDMA in some form - but it was a thought..)

--
It's funny - folks have spent a lot of time over the years making 
oscillators that are "on frequency" - but with modern processing 
techniques, a lot of times it's more about "good phase noise close in" 
and "a way to measure and estimate the frequency" (the latter requires 
decent ADEV if you're not making the measurement simultaneously) but no 
real aging requirement.  (Which is good in space applications, because 
radiation causes frequency shifts.)

Take the NTIA 20Hz carrier frequency control requirement for SSB voice 
radios in HF (to provide natural sounding voice without needing a 
clarifier control). At 30MHz, that's <1ppm, and tough with a cheap 
crystal. But if you have an integrated GPS receiver with 1pps, you 
measure the current crystal frequency and adjust the DDS or PLL as 
needed to compensate.