[time-nuts] Checking accuracy of Rubidium standards

Bruce Griffiths bruce.griffiths at xtra.co.nz
Sun Nov 9 21:36:16 UTC 2008


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
>   
Steve

The effect of the finite resolution of the sound card ADC can be
estimated as follows:
For a 16 bit ADC and a sinusoidal beat frequency signal with 10MHz mixer
inputs a 16 bit ADC has a quantisation noise of about 8.8 ppm of the
amplitude of a full scale sinewave.
This corresponds to a zero crossing measurement jitter of about 140fs
(at 10MHz).
This result is independent of the beat frequency.
The corresponding system noise level due to the finite ADC resolution is
about 1.4E-13/Tau.

This is a gross approximation and the corresponding system noise will be
somewhat larger.
Thus it is advisable to either use an ADC with greater resolution to
achieve such low noise, or to increase the beat frequency signal slew
rate at the zero crossing.
The finite signal bandwidth of the sound card will limit the maximum
slope amplification to around 100X or so.
If one uses a mixer where both the RF and LO ports are saturated then
the beat frequency waveform will be trapezoidal with a slew rate at the
zero crossing about 3X that if the signal were sinusoidal.

Bruce




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