[time-nuts] Measuring phase shift between 1 Hz DMTD signals by I+Q processing

[Bruce Griffiths]

If one uses a mixer output frequency of several kHz then one can avoid
the flicker noise region if one uses a high pass filter between the ADCs
and the mixer preamps.

Does such a system have a performance advantage over direct RF sampling?
Perhaps it does if and only if the phase noise floor of the lower
bandwidth ADCs that are used is lower than the noise floor of the ADCs
that would be required to sample the RF signals directly?
The noise floor of state of the art ADCs suitable for direct RF sampling
is around -150dBFS/Hz.
The noise floor of  "typical" high resolution ADC(AD7762, AD7641)
capable of sampling at around 1MSPS or so appear to be similar.

Bruce

Magnus Danielson wrote:
> Joe Gwinn wrote:
>> It occurs to me that there is a possible alternative to the ZCD-chain
>> approach typical in DMTDs, if one is willing to provide two mixers
>> and two ADCs per channel, with a 90 degree phase offset between LO
>> signals provided to the mixers of a channel.  The output of the four
>> ADCs will be a pair of I+Q signals, one pair per DMTD channel.
>>
>> The key observation is that if one has two signals, one being a time
>> delayed replica of the other, if one multiplies one signal by the
>> complex complement of the other signal, the result is Exp[j(phase
>> difference)].  This is true whatever the waveform of the signal, so
>> long as the only difference in signals is a delay.  The mathematical
>> argument function of this exponential is the desired phase.
>>
>> In practice, one will sample far faster than 1 Hz, say 1 MHz, and
>> will heavily average the resulting stream of products.
>>
>> Now I have not gone through the math to estimate performance compared
>> to the traditional ZCD approach, but the complex multiply and average
>> approach should be quite robust against noise, and is easily
>> implemented in a DSP or FPGA.
>
> The time-difference between the two sampling points could be minimized
> in such an approach as the phase could be shifted arbitrarilly in the
> post-processing such that the effective phase difference between the
> two chains reduces to near zero and hence the correlation between the
> channels for the transfer oscillator would be better in phase and
> cancel the transfer oscillator out better.
>
> The postprocessing would then slowly tune the I/Q phase and keep a
> phase adjustment track such that post-correlation could turn it back
> for proper phase-trace.
>
> An alternative approach is to use the Costas tracking loop as Bruce
> suggested.
>
> Regardless this first stage of digital processing can be done in a
> FPGA frontend and bring the resulting signal bandwidth into very
> reasnoble rates, just as for a GPS receiver.
>
> Cheers,
> Magnus
>
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