Magnus,
At 4:01 PM +0000 7/25/09, [email protected] wrote:
Message: 5
Date: Sat, 25 Jul 2009 16:38:23 +0200
From: Magnus Danielson <[email protected]>
Subject: Re: [time-nuts] Measuring phase shift between 1 Hz DMTD
signals by I+Q processing
To: Discussion of precise time and frequency measurement
<[email protected]>
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
hardware.
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.
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
suggested.
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
trouble.
The Costas loop will not by itself solve the problem of
transfer-oscillator noise.
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?
Joe Gwinn
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