[time-nuts] Re: What phase variations to expect in a DMTD due to temperature fluctuations?

[Carsten Andrich]

Hi Erik,

spectral leakage only occurs with the DFT due to its implicit 
rectangular window applied to the input samples. The appeal of the 
digital down conversion (DDC) implemented with the NCO is that coherence 
does not matter and spectral leakage does not occur. It's simply a 
perfect, digital implementation of the down mixing you perform in the 
analog domain. Its purpose is to shift the frequency of the signal to 
enable reduction of the sample rate to reasonable levels (a few kSa/s 
instead of >= 25 MSa/s) via decimation. The decimation can also be seen 
as averaging, so this approach also uses every available sample.

Additionally, the use of complex down-conversion enables straightforward 
phase estimates. Relative to the sampling clock by taking the phase 
angle of the complex samples of a single channel. Between two channels 
by taking the phase angle of fraction of two channels' complex samples. 
If you unwrap the phase angles and apply linear regression, you can 
compute the average frequency difference.

Best regards,
Carsten

On 24.10.22 15:35, Erik Kaashoek wrote:
> Hi Carsten
>
> Thanks for the very interesting article. As my DMTD uses an audio ADC, 
> the 10MHz inputs first have to be down mixed to the selected audio IF. 
> This probably will add to long term instability.
> Although in the article "Measurement of Phase Difference Using DSP 
> Algorithms by Non-Coherent Sampling" by Michal Krumpholc and Milos 
> Sedlacek it is explained that DFT is not an optimal choice for a DMTD, 
> I decided to use DFT. This because a bit true simulation showed the 
> impact of the spectral leakage to be below the performance ambition 
> and using all samples reduced noise. Also a PLL is used to sync the 
> sampling with the reference input to reduce the worst impact of the 
> non-coherent sampling.
> In your "DSP for Sine Wave Reference Signals " method you only have 
> one NCO, how do you avoid the non-coherent sampling and spectral 
> leakage problem with two non coherent inputs?
> In my measurements there is a clear difference in noise between using 
> coherent inputs (e.g. single clock send to both inputs) and non 
> coherent inputs, even if the frequency difference is in the order of 
> 10 micro Hertz, but this could be due to the noise from the DDS used 
> to generate the dual signals with very small frequency differences. As 
> I have no access to very stable clocks the DDS is the only tool I can 
> use for stability measurements.
> Erik.
>
> On 24-10-2022 10:10, Carsten Andrich wrote:
>> Hi Erik,
>>
>> only the ADC clock should matter and the used ADC should be of the 
>> simultaneous sampling type. If it's not, its multiplexer may have a 
>> detrimental temperature-dependent effect on the phase measurement.
>>
>> I've implemented a fully digital DMTD using USRP N210 with LFRX 
>> daughterboards [1]. To analyze stability of the system itself, I 
>> compared a split 10 MHz signal. Over the course of 4 days, the 
>> measured standard deviation was 359 fs [1, Fig. 11]. I don't have 
>> temperature measurements available, but the lab wasn't air 
>> conditioned, populated, and diurnal difference between two SRS FS725 
>> was clearly observable (another measurement not in the paper).
>>
>> The high stability could be explained by the N210's dual-channel ADC 
>> that directly sampled both 10 MHz signals. I believe, temperature 
>> differences between the preceding analog components (most importantly 
>> the LFRX daughterboard) probably have a very limited effect on 
>> account of the negligible relative bandwidth of the measured 10 MHz 
>> signals' true frequency (a few (dozen) mHz vs. 10 MHz). If the 10 MHz 
>> were down-mixed to a few Hz in the analog domain, the relative 
>> bandwidth would increase substantially. Of course, that's just an 
>> educated guess. I did not investigate temperature stability when I 
>> wrote the paper.
>>
>> Best regards,
>> Carsten
>