[time-nuts] Checking accuracy of Rubidium standards

[Bruce Griffiths]

Steve Rooke wrote:
> 2008/11/9 Bruce Griffiths <bruce.griffiths at xtra.co.nz>:
>   
>> When one is measuring the beat frequency between an offset standard and
>> the DUT, the sound card timebase doesn't have to be more accurate than
>> the the DUT as it is only measuring the error in the small offset
>> between the DUT and the offset standard.
>> However the local standard against which the DUT is being compared does.
>>     
>
> So as this is just measuring a beat, there is no requirement for
> absolute accuracy in the measuring system, it just needs the reference
> frequency to be as accurate as the desired measure of absolute
> accuracy. Yes, I can see that.
>
>   
>> For example with a 10MHz DUT and a 10MHz local standard offset by 100Hz
>> from 10MHz, the sound card only has to measure the  100Hz offset
>> frequency ( between the DUT and the offset standard) to an accuracy of
>> 1E-7 in order to determine the frequency of the DUT to an accuracy of
>> 1E-12.
>>     
>
> So 100Hz offset from 10MHz is 1E-5 and if I can measure the 100Hz to
> an accuracy of 1E-7 that would give an overall measurement of 1E-12.
> So that would mean that the sound card device would somehow have to
> sample with at least 1E-7 accuracy. That would mean taking enough
> samples of sufficient accuracy to determine this 1E-7 accuracy. A
> sound card has a sample frequency of approx 44KHz but to see an offset
> of 1E-7 would that not take a fairly long sample time? How would this
> affect the ability of such a system to determine ADEV for small tau?
>
>   
>> When one uses a dual mixer system to compare 2 non offset 10MHz signals,
>> most of the error contributions from the offset source and ADC sampling
>> clock are common to both channels and tend to cancel on subtraction.
>>     
>
> I can see that, assuming both channels are sampled at the same time.
>
> Thanks Bruce.
>
> 73, Steve
>   
If the signal has sufficiently high SNR the measurement time need not be
very long.
For example if the noise is an additive random Gaussian signal then a 40
dB SNR is equivalent to a period jitter of 0.3%.
For a 100Hz signal the corresponding time jitter is 30us.
If the measurement time is 1 second then the corresponding rms error in
measuring the 100Hz signal is 4.2E-5 or 4.2E-10 of the 10MHz signal.
Thus a measurement time of 420 sec or more would reduce the noise to
1E-12 rms or less.
In practice the beat frequency signal will, with low noise sources, have
a somewhat higher SNR.
Some filtering of the beat signal to reduce the noise will be required.
With a 100Hz beat frequency the shortest value of Tau achievable using
this technique is 10ms.

As long as the requirements of the sampling theorem are satisfied the
choice of sampling rate isnt critical as one can accurately interpolate
between samples to produce as high an effective sampling rate as
required. An effective sampling rate of 10MHz or more is sufficient to
achieve a resolution of 1E-12 or better (at 10MHz) with a 100Hz beat
frequency.
However calculating all the interpolated samples for a 10MHz clock isnt
the most efficient technique since only the zero crossings are of interest.

An alternative technique is to implement a Costas receiver in software.
Such a receiver has both in phase and quadrature outputs allowing the
phase of the receiver output signal to be calculated for each sample.

Bruce