Measuring phase shift between 1 Hz DMTD signals by I+Q processing
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.
Joe Gwinn
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
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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Bruce Griffiths wrote:
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.
Traditionally the beat frequency balance against the flicker noise in
which a lower beat frequency increases the "gain" where as eventually
flicker frequency comes and haunt us.
An alternative approach is to choose a higher initial beat frequency
around say 1 kHz, sample that using traditional audio samplers and then
digitally further mix down the signals before detection. That way you
can get say 1 Hz beat frequency with the noise performance dominated by
the 1 kHz noise. However, the processing could be performed on the
original 1 kHz waveform directly or for that matter a direct sampled
variant of the original waveforms.
A second mixdown requires that the first and second LOs is locked to
each other for best performance.
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.
Direct sampling is ofcourse another method to consider, but put higher
demands on up-front processing. It has however become fairly cheap.
Cheers,
Magnus