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

[Magnus Danielson]

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