Measure phase difference sub-picosecond between two 200-700Hz signals

[steaky1212]

Hi,

I've just seen the release of the 53100A from Microsemi and that got me thinking about a problem at work.

I have a system whereby I have 2 sinusoidal waveforms (at least they should be sinusoidal!!) between nominally 200-700Hz, and I need to measure the phase difference between these two signals down to sub-picosecond accuracy.

Can anyone suggest a piece of equipment that would be able to do this?

Thanks in advance

[KE5FX]

Awesome, our marketing must be working.   (53100A dev here)

The 53100A is rated for use on (sinewave) RF carriers at 1 to 200 MHz, but it actually has the ability to select DC signal paths for baseband measurement, and it was originally rated "DC-200 MHz" for that reason.  I haven't enabled DC path support in the software yet, but it's still planned, and in principle you could make this measurement when that happens.  That said, the 53100As no longer advertise DC-1 MHz support because I don't anticipate good performance in that region compared to a dedicated audio analyzer.  It's a superb instrument for HF/VHF stability measurement, but there are likely to be much better solutions for LF.

In terms of what would handle your application, subpicosecond resolution in the audio range is hard to achieve.  That's such a small fraction of the signal period that it's debatable whether it's even meaningful to talk about.  At 10 MHz, a picosecond of jitter corresponds to a (full-band) SNR of about 84 dB, but at 600 Hz that's more like -170 dB.

For instance, if you tell TimeLab to scale a rubidium standard's phase noise profile at 5 MHz down to a hypothetical 600 Hz, in order to simulate what you might see with an equally-hypothetical instrument capable of this sort of measurement, you might obtain a plot like this:



You'll need 10 watts or so just to reach the thermal floor.  Unless you work at LIGO, I have to wonder if the problem is really this demanding.  Can you talk a bit more about what you're actually doing?

[nctnico]

Hi,

I've just seen the release of the 53100A from Microsemi and that got me thinking about a problem at work.

I have a system whereby I have 2 sinusoidal waveforms (at least they should be sinusoidal!!) between nominally 200-700Hz, and I need to measure the phase difference between these two signals down to sub-picosecond accuracy.

Can anyone suggest a piece of equipment that would be able to do this?

Getting to sub-picosecond is hard. As KE5FX wrote: what are you trying to do?
One way of doing it would be to measure the frequency of both signals over a long enough period to determine their relative frequency difference. From there you can derive the phase change. But this would only work if the phase shift changes between the signals; after all a phase shift also means the frequency has to change.

[steaky1212]

I work for a company designing equipment that uses the relative phase difference between two signals to determine a measured value - the two signals will have an identical frequency. 
Up until 25 or 30 years ago, this would be achieved using a zero-crossing detection scheme, but since then it's used quite a bit of complex maths.

[David Hess]

I have a system whereby I have 2 sinusoidal waveforms (at least they should be sinusoidal!!) between nominally 200-700Hz, and I need to measure the phase difference between these two signals down to sub-picosecond accuracy.

If an integrated measurement over many cycles is acceptable, then even old universal counters which support averaging can easily get down to 10 picoseconds of resolution.  Single shot resolution which would be necessary to characterize high frequency noise and jitter is an entirely different matter.

[KE5FX]

I have a system whereby I have 2 sinusoidal waveforms (at least they should be sinusoidal!!) between nominally 200-700Hz, and I need to measure the phase difference between these two signals down to sub-picosecond accuracy.

If an integrated measurement over many cycles is acceptable, then even old universal counters which support averaging can easily get down to 10 picoseconds of resolution.  Single shot resolution which would be necessary to characterize high frequency noise and jitter is an entirely different matter.

Yep, the hard part is taking advantage of averaging while preserving the statistical properties that you're after.  A sonar operator can't afford to wait 10 hours for a reading that tells them where the enemy sub might have been. 

Averaging with a counter can be loosely compared to postdetection audio/video filtering in a receiver.  It can be a big help, but it can also never be a perfect substitute for IF filtering.  Once broadband noise is allowed to enter the detector, good luck getting rid of it later. 

It doesn't sound like steaky1212 is at liberty to go into too much detail, so it's hard to say if averaging would be helpful.  Are the two signals already the result of a demodulation process?   Did you get the two signals by downmixing from higher frequencies, or by dividing?  Is there a lock-in process (synchronous detection), and if not, can that be considered?

Probably the #1 question would be, how long can you afford to wait for a reading?

[nctnico]

In the digital domain it might be doable using a very sharp notch filter. That can push the noise out. Perhaps that is where the but since then it's used quite a bit of complex maths statement is hinting at.

[AndyC_772]

Getting to sub-picosecond is hard. As KE5FX wrote: what are you trying to do?

I'd bet that this is a coriolis flow meter, probably quite a small one at that frequency.

I have a great deal of experience with them, both use and design. Even if I'm wrong and this application is something different, the problem of accurately measuring a very small phase difference between two signals is the same.

Can anyone suggest a piece of equipment that would be able to do this?

This sounds like an interesting project that I can definitely help with - please PM me with a few more details.

[ogden]

This sounds like an interesting project that I can definitely help with - please PM me with a few more details.

Interesting indeed. Please provide at least some info here in this forum, like operating principles of device in question.

[Sighound36]

Steaky

If it is a works budget then these are decent, we have one of these rather good.

http://www.holzworth.com/analyzers.htm


Out of interest how much is the  53100A KE5FX?

[steaky1212]

I have a system whereby I have 2 sinusoidal waveforms (at least they should be sinusoidal!!) between nominally 200-700Hz, and I need to measure the phase difference between these two signals down to sub-picosecond accuracy.

If an integrated measurement over many cycles is acceptable, then even old universal counters which support averaging can easily get down to 10 picoseconds of resolution.  Single shot resolution which would be necessary to characterize high frequency noise and jitter is an entirely different matter.

How would this be set up?

[KE5FX]

Out of interest how much is the  53100A KE5FX?

I honestly couldn't tell you at this point, as I'm a long way out of that particular loop.  The original introductory pricing in single-unit quantities was in the 15K USD neighborhood, but that was with a completely different distributor.  Current pricing will have to come from a Microchip representative, which I'm not.  It's safe to say it will vary based on quantity and market region.

[unitedatoms]

Sorry if I go off topic. But the posted problem is unsolvable with current technology. Except may be using a lab grown trained blind ninja who can dissect a mosquito (fat one for 200 Hz) with a 100 ft sword in a echoless  thermally stabilized room.

[ogden]

Seems like many confuse phase noise (jitter) to phase difference measurements.

[gf]

I'm in fact wondering whether these phase noise analyzers can also measure and report the phase difference between two (phase-locked) input signals (granted that they have two inputs)?

[KE5FX]

A direct digital test set does both phase-difference and phase noise measurements extremely well, just not at this level.    No phase locking is necessary.

The first commercial model was the TSC 5120A, circa 2008.  That's the place to start Googling if you're interested in this sort of thing.

[gf]

A direct digital test set does both phase-difference and phase noise measurements extremely well, just not at this level.

Isn' the (statisitically) achievable level more or less just a matter of the number of samples being averaged (i.e. a matter of the granted maximum duration of the measurement interval)?

No phase locking is necessary.

What does it report then? The average phase difference in the measurement interval?

[KE5FX]

Isn' the (statisitically) achievable level more or less just a matter of the number of samples being averaged (i.e. a matter of the granted maximum duration of the measurement interval)?

In theory, yes.  In practice, a lot of different factors, both systematic and random, conspire to make it difficult to achieve precise phase measurements at low frequencies. 

In this particular problem, AM-PM conversion will be one of the big stumbling blocks.  If you try to measure the phase shift of an RF attenuator at the picosecond level, for example, you'll find that no two instruments in the house give you quite the same numbers as the attenuator is switched on and off.  A high-performance counter with averaging will show phase differences that don't agree perfectly with a different brand of counter, which won't agree with the phase measurement button on your DSO, which won't agree with a direct-digital stability analyzer, and so on.  These discrepancies are already in the single-digit picosecond range when measuring at 1 MHz, and they will grow as the carrier frequency falls. 

One way to think of it is to remember that 'phase' is ultimately defined by zero-crossing times, even if you're not directly measuring the zero crossings themseves.  To characterize the timing of the zero crossings, you have to pin down their position.  That, in turn, is affected by the harmonic content of the waveform in conjunction with its slew rate.  Harmonic distortion and IMD will consist of both tonal and noise-like components that arise in every stage of the signal chain, from the crystal or atomic resonators where the signals originate to the measuring instrument itself.  To one extent or another, every stage the signals pass through will turn amplitude variations into phase distortion.

Anyway, the TL, DR is that LF phase measurement is harder than it appears at first.  The OP isn't trying to measure an attenuator, presumably, but the example is illustrative because similar factors will confound both measurements. 

What does it report then? The average phase difference in the measurement interval?

Phase measurements between two signals at different frequencies are effectively scaled by that frequency difference.  So if you know the nominal or expected frequencies of the two signals (and you generally do), you can scale the readings to make it appear that the signals were measured at the same frequency. 

In a measurement where one signal is designated as a the "reference" and the other as the "DUT," the reference phase is typically scaled to conform to the nominal DUT frequency.  This makes the phase-difference measurement independent of the frequency of the reference in use.  For the OP's problem, the two signals are presumed to be at the same frequency, so this extra complication doesn't apply.

[ogden]

Right. At any frequency sub-picosecond is hard. During 1ps light in the vacuum travels whooping 0.3mm, in FR4 microstrip signal travels 0.175mm (6.9 mils)

[JohnPi]

ps cycle-by-cycle resolution on a 600 Hz signal using just zero crossings (like a time analyzer or frequency counter basically uses) would require unachievable SNR (at least at room temperature); for example if your signals was around 1 V peak, and your zero crossing comparator had 1 mV offset (and ps delay difference), you would an error of about 1mV/1V.π/2, or about 1.6 mrad which is equivalent to about 400 ns already. You also have to assume that the signals you are measuring have no noise added (at the nV level).

However, if you know the frequencies (and they are identical), you could improve this by using some signal processing -- basically sample each signal with an ADC, and cross-correlate the signals with a (sinusoidal) reference -- so, each signal would be cross-correlated with the reference (==> S1 = sum(ADC_1*sin(reference), C1=sum(ADC_1*cos(reference), & S2 = sum(ADC_2*sin(reference), C2=sum(ADC²*cos(reference)). Now your phase angle between the 2 signals is ATAN(C1,S1) - ATAN(C2,S2). Your resolution will be limited by ADC errors & resolution and matching/calibration etc.  A full analysis is somewhat complex.

[steaky1212]

So the next question would be, assuming 2x sinusoidal waveforms 200-700Hz 1V pkpk. Frequency is identical, but with a phase shift. What kit is there for measuring down to the 10's of picoseconds? or 100s of picoseconds?

I'm not an analogue guy, and I get that this is a difficult measurement to perform. But we are engineers, right. Surely there's got to be something doable?

[gf]

So the next question would be, assuming 2x sinusoidal waveforms 200-700Hz 1V pkpk. Frequency is identical, but with a phase shift. What kit is there for measuring down to the 10's of picoseconds? or 100s of picoseconds?

To assess what's doable, and what's not, it would be rather necessary to analyze/assess your signals (and their imperfections) in the first place. Nobody here has seen your actual signals on any analyzer, and you are unfortunately not very verbose regarding details. If you would explain the intended use case and the origin of the signals, then some people might have an idea regarding the typically expected signal characteristics and the feasibility limits for the particular use case.

Some of the aspects of interest are:

What's the a priori SNR of the signals (and what's their noise spectrum)?

What is the THD of the signals? Is it really low enough in order that "assuming sine waves" holds up to the desired accuracy level? An algorithm which works only for perfect sine waves will likely not meet your accuracy goals if your actual signals are not perfect sine waves.

What is the actual result you need? Do you really need a phase angle (degrees), or rather a time delay (seconds)?

Do you really need the absolute phase angle for each single measurements, or does the difference between the phase angles from two subsequent measurements suffice (w/o touching the whole measurement setup between the measurements)? The former will add an additional complication for calibrating the the zero-point for a particular measurement setup (e.g. to account for slightly different cable lenghts or other delays in the signal chains - remember odgen's message: 0.3mm ~ 1ps !).

How much time do you grant for taking a single measurement?
Could you afford minutes or even hours? (in order to capture and process a really huge number of samples)
Are your signals stable over such a time interval?

[AndyC_772]

You also have to assume that the signals you are measuring have no noise added (at the nV level).

The signals in question can be a *long* way from being noiseless or, indeed, sinusoidal.

The required measurement rate is, I'd expect, somewhere between 10 and 100 measurements/sec (assuming the test equipment is required to deliver results with the same kind of dynamic bandwidth as the finished product).

It can, of course, be done, though I'm not aware of any off-the-shelf test equipment that would be suitable. It's a bit of a specialist area and there are other factors (nothing to do with electronics) which have a dramatic effect on the accuracy and usefulness of the end result.

[sorin]

Correct me if I´m wrong, but I think that this is used as Sonar to detect  Submarine, and is not a simple sonar but is used to detect stealth (silent) Submarines.