# [time-nuts] ensemble oscillators for better stability

Magnus Danielson magnus at rubidium.dyndns.org
Fri Dec 28 23:54:26 UTC 2012

```Hi Corby,

On 28/12/12 20:12, cdelect at juno.com wrote:
> Hi,
>
> I've been playing around with 2 HP 5065A standards to see if averaging
> them will give better stability.
>
> The results so far are:
>
>                       1 sec        10 sec    100 sec
> unitA            1.28-12    3.83-13   1.33-13
> unitB            9.31-13    3.44-13   1.18-13
> combined     8.95-13    3.09-13   8.95-14
>
> Each unit was adjusted for equal amplitude into a resistive power
> combiner and also adjusted so their phase was coincident prior to
> starting the plots.
> The main problem was getting their relative frequencies close enough so
> that there was no drift during the measurements.
> Not a trivial accomplishment for the 100 sec tau!
>
> I'm thinking now of a way to loosely lock the phase of one unit to the
> other to simplify the setup.
>
> One different idea I had that I'd like some feedback on:
>
> If I take both units into a double balanced mixer, then take the
> resulting 10MHz and divide it back to 5MHz would I get the same
> improvement?

Interesting that you take up the concept of ensembles, as I have been

My first idea would be to mutually lock the oscillators. You can even do
weighted locking without much difficulty. You toss the oscillators into
a mixer, use it as a phase detector, do the usual PI control and then
steer both oscillators the same EFC but with opposite sign. One can add
a common EFC steering to both:

Vd is the detected phase from the mixer (low-pass filtered)
VI = VI + I*Vd
EFC_loop = VI + P*Vd
EFC_A = EFC_common + EFC_loop/2
EFC_B = EFC_common - EFC_loop/2

With the right sign, the loop will steer the oscillators towards each
other and the common frequency will be the average. Weighting can be
applied in how much the EFC_loop steers the oscillator, and should be
assigned to how great part they have in the noise compared to the
ensemble noise, noisier gets more steering.

The benefit of mutual locking (which really just is two oscillators
locked together with the other as reference) as well as mixing is that
high-frequency noise gets averaged.

Another way would be to measure them and then steer one to represent the
ensemble. This is what people like NIST do, but they use a microstepper
to re-synthesize but it is essentially the same thing. This method
however does not get the high-frequency noise benefit, as the output of
the individual clocks isn't combined.

Mixing would work, but you will not be able to weight the oscillators.
The simple combination provides rather fixed weighting (actually not,
but for rubidiums the difference in frequency is small enough not to
have large effect on the weighting between the oscillators), but can be
useful in that context.

> This method would be much simpler!

It would. The downside is that you won't be able to get best possible
performance out of the ensemble, but you can get pretty good results for
the cost of combining them.

> Happy New Year!

Happy New Year!

Cheers,
Magnus

```