Magnus Danielson magnus at rubidium.dyndns.org
Wed Jun 16 05:57:34 UTC 2010

```On 06/16/2010 05:45 AM, Charles P. Steinmetz wrote:
> Warren wrote:
>
>> Charles posted:
>>> but the locked frequency will be different from both oscillators'
>>> free-running frequency and
>>> the EFC will not correctly indicate the test oscillator deviation
>>> because it isn't the only control input in the system.
>>
>> Good point and No argument (except for the deviation part)
>> Because the EFC is the only control input THAT IS VARYING.
>
> No, it's not. The strength with which each oscillator pulls on the other
> also varies as the equilibrium frequency (the result of all three
> recursive control inputs) moves around relative to the two instantaneous
> free-running frequencies. How much EFC is required depends, in part, on
> the strength of the pulling. There are three varying inputs.
>
> Magnus suggested that the effect of injection locking may be enough
> smaller than the EFC input that it has little practical significance.
> That may be so, but when dealing with measurement accuracy in the
> hundreds or tens ot ppt, this needs to be verified by the results of
> carefully constructed experiments and hopefully also supported by
> mathematical analysis.

What you get is a scale error. Consider that you have an amplifier gain
of 1000 and the injection locking provide a gain of 1, that will result
in actual gain of 1001 and the gain error on the EFC will become
1000/1001. Considering that Allan deviation estimation has problem of
its own, this scale error is not significant. What you do need to check
is that the relationship between intended gain and injection gain is
sufficiently different. Since oscillator frequency from EFC may not be
completely correct, we already want calibration of that scale factor
(K_O) and the gain error due to injection locking would be included into
that correction factor.

So, sufficiently small amount of injection locking gain will change the
apparent EFC coefficient K_O [Rad/sV] on which the scale of TPLL
frequency measurements depends. The fractional frequency observed is

y(t) = 2*pi*f_0 / K_O,eff EFC(t)

Cheers,
Magnus

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