[time-nuts] Measuring phase shift between 1 Hz DMTD signals by I+Q processing
joegwinn at comcast.net
Sun Jul 26 00:23:07 UTC 2009
At 4:01 PM +0000 7/25/09, time-nuts-request at febo.com wrote:
>Date: Sat, 25 Jul 2009 16:38:23 +0200
>From: Magnus Danielson <magnus at rubidium.dyndns.org>
>Subject: Re: [time-nuts] Measuring phase shift between 1 Hz DMTD
> signals by I+Q processing
>To: Discussion of precise time and frequency measurement
> <time-nuts at febo.com>
>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 [conjugate] 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 arbitrarily 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.
It would be nice, but I need to think about this. I'm not sure that
you don't have to use a real physical delay out in the analog
>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
But, unlike ZCD-triggered counters, there is no disadvantage or
difficulty if the phase difference is adjusted exactly to zero, where
the two 1 Hz sinewaves coincide.
>An alternative approach is to use the Costas tracking loop as Bruce
A Costas loop is far more complex, but they do work well. Given near
constant phase delay, don't know if a Costas loop is worth the
The Costas loop will not by itself solve the problem of
>Regardless this first stage of digital processing can be done in a FPGA
>frontend and bring the resulting signal bandwidth into very reasonable
>rates, just as for a GPS receiver.
Yes. Is 0.01 Hz slow enough?
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