### Author Topic: An advanced question - sampling an oscillator's signal for analysis  (Read 13840 times)

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#### JohnnyMalaria

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #75 on: June 14, 2018, 05:01:28 am »
I don't have access to that reference. Can you not share what it says?

I truly do not understand why my description of how to calculate the variance is wrong. Indeed, as far as I can tell, my description of what it is and what it isn't is the same as yours (as I have stated). All I'm refering to is the calculation of the quantity given by Allan. I'm not in any way alluding to interpretation, mechanistic understanding, application or if other modified versions of his approach are more often used. I'm just suggesting a method for calculating a quantity from a specific mathematical equation given my experience in developing highly efficient calculations for very similar equations.
Tell me it can't be done and I'll do it. Or die trying.

#### tomato

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #76 on: June 14, 2018, 05:11:14 am »
I don't have access to that reference. Can you not share what it says?

The link was in an earlier post (#21?) by GerryBags.

#### DimitriP

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #77 on: June 14, 2018, 05:30:08 am »
It seems to me you are trying to determine how much "off frequency " you are going to be based on the ADEV  of the oscillator.
So far you have not mentioned (or I missed it) what your target frequency is.

A 1x10-6 stable oscillator  will be "off"  10Hz @10 MHz and 100KHz "off" @ 10GHz  ;is that what you are looking for ?

If three 100  Ohm resistors are connected in parallel, and in series with a 200 Ohm resistor, how many resistors do you have?

#### JohnnyMalaria

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #78 on: June 14, 2018, 07:23:10 am »
I don't have access to that reference. Can you not share what it says?

The link was in an earlier post (#21?) by GerryBags.

Thank you.

Equation 10 is what I described. The only potential source of confusion is y vs. ybar. I implied (i.e., didn't say) that y is the average value of the signal over time interval tau.

This really is very similar to the principles behind autocorrelation of photodetector signals from light scattered by moving nanoparticles. For my processes, I have a sinusoidal oscillating phase of known period but unknown amplitude in a very noisy signal caused by random diffusion of the particles. Historically, autocorrelation has been used but I developed a novel way to remove the random noise from the signal and pull out the phase change information with far greater accuracy. Autocorrelators are still widely used and evolved significantly from their advent in the mid-60s, going from 1-bit linear single tau to today's multichannel multiple tau USB single photon digital correlators.
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#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #79 on: June 14, 2018, 10:06:30 am »
This was a reference in one of the previous links.  It's HP AN1289:

http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf

I think it important to keep in mind that with current computational resources much more elaborate analyses than the Allan deviation are quite practical.  Bendat & Piersol specifically treat hard clipping of non-stationary series in chapter 12 which is exactly what the OP wants to do.

#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #80 on: June 14, 2018, 10:26:01 am »
It seems to me you are trying to determine how much "off frequency " you are going to be based on the ADEV  of the oscillator.
So far you have not mentioned (or I missed it) what your target frequency is.

A 1x10-6 stable oscillator  will be "off"  10Hz @10 MHz and 100KHz "off" @ 10GHz  ;is that what you are looking for ?

The "target frequency", if I understand your question, is 10 MHz. I have a bunch of 10 MHz oscillators that I want to compare.

I don't think a 10 MHz oscillator with an Allan Variance of 1x10-6 will be "off" 10 Hz. That isn't the nature of this measure of stability.

The reason I have not walked away from this discussion as it increasingly goes on walkabout is I am building a poor man's time lab. I intend to measure the performance of the oscillators alluded to above, but I need to know what data to gather. Without understanding this, I am likely to measure attributes of the oscillators that have no practical value (I am beginning to think Allan Variance falls into this category). Also, if I have no idea how to analyze the data, after gathering it, what the heck am I going to do with it? So, I will keep reading and keep asking questions until someone provides useful advice (I'm not saying some haven't done this already; they have. But there is a lot chaff in this thread).

#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #81 on: June 14, 2018, 10:58:57 am »
A brief comment on data collection.

The traditional Wiener - Shannon - Nyquist approach is regular sampling.  Regular sampling performs a multiplication in the time domain which is a convolution in the frequency domain.   The Fourier transform of a closely spaced set of spikes in one domain is widely separated spikes in the other domain.  This it the mathematical reason that aliasing takes place.  The signal spectrum is convolved with the spike series and if the spectrum of the signal is broader than one half the spike spacing, aliasing occurs.

It has come to light in the last few years that if you randomly sample so that the sampling process is not correlated with itself, then the Fourier transform of the sampling process is a spike at DC and aliasing does not take place.  I suspect that this was recognized by some long ago, but the power of it really needs a high performance computer to get the full benefit.

If the clock ticks at which a sample is collected are selected randomly, then the counts at regular intervals will be uncorrelated with any of the signals such as the MCU clock or the clocks under test.  So all the signal structure can be extracted by computing autocorrelations of the counts over various time periods.

I only came to understand the power of this a few years ago after some 30 years of data analysis in which regularizing data to remove minor deviations from regular sampling was a perennial topic at the annual professional society meetings and many PhDs were awarded for "solving" it.

#### KE5FX

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #82 on: June 14, 2018, 12:27:56 pm »
It seems to me you are trying to determine how much "off frequency " you are going to be based on the ADEV  of the oscillator.
So far you have not mentioned (or I missed it) what your target frequency is.

A 1x10-6 stable oscillator  will be "off"  10Hz @10 MHz and 100KHz "off" @ 10GHz  ;is that what you are looking for ?

The "target frequency", if I understand your question, is 10 MHz. I have a bunch of 10 MHz oscillators that I want to compare.

I don't think a 10 MHz oscillator with an Allan Variance of 1x10-6 will be "off" 10 Hz. That isn't the nature of this measure of stability.

The reason I have not walked away from this discussion as it increasingly goes on walkabout is I am building a poor man's time lab. I intend to measure the performance of the oscillators alluded to above, but I need to know what data to gather. Without understanding this, I am likely to measure attributes of the oscillators that have no practical value (I am beginning to think Allan Variance falls into this category). Also, if I have no idea how to analyze the data, after gathering it, what the heck am I going to do with it? So, I will keep reading and keep asking questions until someone provides useful advice (I'm not saying some haven't done this already; they have. But there is a lot chaff in this thread).

Have you read any of Bill Riley's work yet?  Spend some time with the Stable32 manual and see what you think.  (Stable32 is actually free now, and is worth becoming familiar with.)

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#### awallin

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #83 on: June 14, 2018, 02:25:51 pm »
FWIW to test AllanTools there's a Kasdin&Walter noise-generator that generates phase-noise with different power-law coefficients and one can then plot ADEV, MDEV, phase-PSD and frequency-PSD like so:
https://github.com/jleute/colorednoise

the example-code that generates that figure contains the relations between phase-PSD, frequency-PSD, ADEV, and MDEV. Your patches for e.g. HDEV etc are welcome
https://github.com/jleute/colorednoise/blob/master/example_noise_slopes.py
Some of the theoretical expressions for ADEV/MDEV are in the IEEE-1139 standard (but not all IIRC).

A simulation with suitable power-law noise components and possibly some deterministic drift added should allow you to explore a lot of scenarios..
For the Arduino stuff a resonable start is the TICC https://www.tapr.org/kits_ticc.html
an alternative could be the digilent analog discovery which was used in a recent "sine-wave fitting ADEV" paper https://arxiv.org/abs/1711.07917

cheerio,
A

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#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #84 on: June 14, 2018, 02:51:24 pm »
Have you read any of Bill Riley's work yet?  Spend some time with the Stable32 manual and see what you think.  (Stable32 is actually free now, and is worth becoming familiar with.)

I had heard of Stable32, but had not pursued it. One problem is it only runs on Windows. I have a Windows 10 installation running on Parallels, which is a virtual machine application running on my Mac. I'll see if it runs on it (it's Windows 10, so there may be some issues). Also, I could try it on Linux running over Wine.

Anyway, thanks for reminding me of it. For anyone else interested in Stable32, the user manual is here.

#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #85 on: June 14, 2018, 02:57:14 pm »
FWIW to test AllanTools there's a Kasdin&Walter noise-generator that generates phase-noise with different power-law coefficients and one can then plot ADEV, MDEV, phase-PSD and frequency-PSD like so:
https://github.com/jleute/colorednoise

the example-code that generates that figure contains the relations between phase-PSD, frequency-PSD, ADEV, and MDEV. Your patches for e.g. HDEV etc are welcome
https://github.com/jleute/colorednoise/blob/master/example_noise_slopes.py
Some of the theoretical expressions for ADEV/MDEV are in the IEEE-1139 standard (but not all IIRC).

A simulation with suitable power-law noise components and possibly some deterministic drift added should allow you to explore a lot of scenarios..
For the Arduino stuff a resonable start is the TICC https://www.tapr.org/kits_ticc.html
an alternative could be the digilent analog discovery which was used in a recent "sine-wave fitting ADEV" paper https://arxiv.org/abs/1711.07917

cheerio,
A

Even though I am unconvinced of the practical usefulness of Allan Variance and its derivatives, I appreciate the links.

#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #86 on: June 15, 2018, 06:36:59 am »
The formulae for AVAR, MVAR and TVAR in terms of spectral transfer functions can be found on pp 104-106  of:

https://tf.nist.gov/general/pdf/1168.pdf

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#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #87 on: June 15, 2018, 08:58:15 am »
The formulae for AVAR, MVAR and TVAR in terms of spectral transfer functions can be found on pp 104-106  of:

https://tf.nist.gov/general/pdf/1168.pdf

#### tomato

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #88 on: June 15, 2018, 09:09:59 am »
Even though I am unconvinced of the practical usefulness of Allan Variance and its derivatives, I appreciate the links.

All the physicists and engineers working in the time & frequency divisions of national standards labs around the globe will be very disappointed to hear that the main diagnostic tool they have used for decades has no practical usefulness.

#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #89 on: June 15, 2018, 09:27:06 am »
The formulae for AVAR, MVAR and TVAR in terms of spectral transfer functions can be found on pp 104-106  of:

https://tf.nist.gov/general/pdf/1168.pdf

I thought you'd received enough unhelpful comments and might find something with actual mathematical details refreshing.  From looking at the transfer functions, I think the intent is to filter out noise that cannot be suppressed except by ensembles of reference oscillators.  In the HP app note they make the point that even the worst oscillator in the ensemble improves the performance of the ensemble.  That pretty much implies that Gaussian noise (e.g. flicker and thermal)  can only be suppressed by 1/sqrt(n) and that other types of errors can be suppressed by modeling the individual oscillator performance over time.

Those comments suggest that you may well do best by using the GPSDO and the three other oscillators in an ensemble.  I decided just to use a GPSDO from Leo Bodnar, at least until I need a 3rd frequency.

The HP app note goes through an experiment the authors did with three of  the cheapest available digital stop watches.  It's quite well written as it presents the mathematics without making them intimidating.

#### KE5FX

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #90 on: June 15, 2018, 09:57:47 am »
Also:

The designer couldn't care less what is the Allan Varience of the oscillator or the power law exponents of the component noise sources. He wants to know the jitter bounds. If you can't get the jitter bounds from the Allan Variance, then it has no value in this particular application.

Some may criticize this example, pointing out that I know very little about doppler radar. That is absolutely correct. So, if there are any out there reading this thread who have experience in either professional or amateur doppler radar, I welcome their comments.

Radar people don't tend to use Allan deviation.  They care about phase noise at offsets close to the carrier -- which, again, is the same basic measurement as ADEV, but without the ambiguity in the frequency domain.  ("Jitter" is just another way of saying "phase noise" within specified limits of integration.  "Jitter bounds" isn't a recognized technical term.)

Specifically, radar people don't care about ADEV because the long-term stability of the reference is not of interest.  Ordinary frequency drift is disregarded by the signal-processing math simply because radar is inherently a residual measurement, where the returned echo is compared to the transmitter output.

Time-oriented folks are more likely to care about ADEV and related metrics.  Need to know which oscillator keeps better time over intervals ranging from minutes to months?  Measure the ADEV.  Need to know which oscillator keeps better time from microseconds to seconds?  Measure the PN.

Hard to see how to make it much more clear than this... but speaking as someone who occasionally needs to write user manuals and tutorials on the subject, I'm always open to suggestions.

#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #91 on: June 15, 2018, 10:41:25 am »
Radar people don't tend to use Allan deviation.  They care about phase noise at offsets close to the carrier -- which, again, is the same basic measurement as ADEV, but without the ambiguity in the frequency domain.  ("Jitter" is just another way of saying "phase noise" within specified limits of integration.  "Jitter bounds" isn't a recognized technical term.)

At some point you have to convert phase noise to frequency bounds (what I called "Jitter bounds", which, I admit, is a term I made up in an attempt to get my point across - what would be the recognized technical term?) Take the example I gave of doppler radar. Unless I completely misunderstand how it works (a real possibility), if you want to specify the error bounds on object velocity, you have to factor in the error in the frequency source - how its output varies in frequency around the desired carrier frequency. Phase noise is normally specified as dBm/Hz at several narrow side bands of the carrier. If you know how to convert that into errors in velocity estimates I would be extremely interested in learning about it (either by explaining it or pointing me to an appropriate reference).

Specifically, radar people don't care about ADEV because the long-term stability of the reference is not of interest.  Ordinary frequency drift is disregarded by the signal-processing math simply because radar is inherently a residual measurement, where the returned echo is compared to the transmitter output.

Time-oriented folks are more likely to care about ADEV and related metrics.  Need to know which oscillator keeps better time over intervals ranging from minutes to months?  Measure the ADEV.  Need to know which oscillator keeps better time from microseconds to seconds?  Measure the PN.

Hard to see how to make it much more clear than this... but speaking as someone who occasionally needs to write user manuals and tutorials on the subject, I'm always open to suggestions.

Here's the thing. I doubt there are many hobbyists or amateurs who plan to implement a national time standard. This is why ADEV was invented. Allan worked at NBS (now NIST) in Boulder, CO in the department responsible for keeping accurate time and distributing it (e.g., over WWV). I don't know what are the objectives of what you call "Time-oriented folks", but my guess is they are interested in keeping time, not using it in an application. Or, perhaps more accurately, keeping time is the application.

My interests are different. I want to know what makes one oscillator better than another when used in an application. My original interest was along the lines of "what oscillator should I use to synchronize my equipment (e.g., frequency counter, oscilloscope, spectrum analyzer) when making measurements?" That kind of grew into a general interest of what makes one particular oscillator better than another in general applications (other than very long-term time keeping). Could I test some oscillators and come up with a characterization that would help others make an intelligent choice? If a non-temperature controlled oscillator module is good enough, why use an ocxo?

So, I need a way of characterizing oscillators (initially 10 MHz oscillators) that those who want to use them would find helpful. Obviously, I don't want to invent something myself. That would be pretty nutty. I have neither the time nor interest in the journey that would entail.

Now, I understand some engineers might think this stupid. They just grab something and try it out. If it works, they're done. If not, they try something else. I have no quarrel with them. A lot of time that works. What I am doing isn't going to appeal to them. They think it is a huge waste of time.

However, perhaps over-optimistically, I think there are other engineers that would at least like some information that would help them make an intelligent first choice. From there they can try options. On the other hand, if no one else is interested, I am. So, I will keep plodding along until my curiosity is satisfied.

Added Later: Phase Noise is generally measured in dBc/Hz, not dBm/Hz
« Last Edit: June 15, 2018, 11:49:03 am by dnessett »

#### KE5FX

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #92 on: June 15, 2018, 11:12:56 am »
Radar people don't tend to use Allan deviation.  They care about phase noise at offsets close to the carrier -- which, again, is the same basic measurement as ADEV, but without the ambiguity in the frequency domain.  ("Jitter" is just another way of saying "phase noise" within specified limits of integration.  "Jitter bounds" isn't a recognized technical term.)

At some point you have to convert phase noise to frequency bounds (what I called "Jitter bounds", which, I admit, is a term I made up in an attempt to get my point across - what would be the recognized technical term?) Take the example I gave of doppler radar. Unless I completely misunderstand how it works (a real possibility), if you want to specify the error bounds on object velocity, you have to factor in the error in the frequency source - how its output varies in frequency around the desired carrier frequency. Phase noise is normally specified as dBm/Hz at several narrow side bands of the carrier. If you know how to convert that into errors in velocity estimates I would be extremely interested in learning about it (either by explaining it or pointing me to an appropriate reference).

It would come down to the core math behind Doppler radar.  Doppler shift in Hz is proportional to the speed of the target as well as the frequency of the radar signal carrier, since you're basically talking about how much the return signal is stretched or compressed in time by being bounced off of a moving target.  The shift is also scaled downward if the target isn't heading straight towards the radar site or away from it, which should be obvious from simple trig.  So it's easy to see how the error bars on a Doppler reading are proportional to how well you know the phase of the carrier.  That, in turn, is proportional to how sure you about what the carrier phase was x microseconds ago when the particular carrier cycles that you're receiving left your transmitter antenna.  This is the realm of phase noise, not ADEV.

Take a look at this article for some example numbers.  In practice, a radar designer would look at the area under the phase noise curve between selected integration limits, based on the performance range of interest.  The result of that integration can be express in RMS seconds of jitter, and the term "jitter bounds" would most likely refer to the limits of integration used to calculate it.

Quote
I don't know what are the objectives of what you call "Time-oriented folks", but my guess is they are interested in keeping time, not using it in an application. Or, perhaps more accurately, keeping time is the application.  My interests are different. I want to know what makes one oscillator better than another when used in an application.

Unfortunately I don't think anyone here has the faintest idea of the distinction you're trying to make.   Definitely read everything you can find by Bill Riley, though.  He can be considered a primary source for this stuff.

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#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #93 on: June 15, 2018, 12:42:33 pm »
Unfortunately I don't think anyone here has the faintest idea of the distinction you're trying to make.   Definitely read everything you can find by Bill Riley, though.  He can be considered a primary source for this stuff.

I freely admit I don't know the distinction I am trying to make. That is why I started posting questions here. If someone can say, "Dan, here is a book that explains how to choose an oscillator to use in an arbitrary application"; or "here is an article that does that", I would be ecstatic (presuming the referenced source actually solves the problem). But, so far all of the papers I have read have been mostly theoretical in nature and have left unclear how that theory is applied in practice.

I don't think this is a weird objective. If I am designing a digital circuit, I can go to various component data sheets and find out the parameters I need to know in order to use them. I am starting to design the circuit between the Arduino clone I have and the oscillator output that will be measured. I have to build a Schmitt trigger front-end, some digital counting logic (since the Arduino can't service interrupts fast enough to count the zero-crossings of a 10 MHz signal), some intermediate storage to hold the counting results temporarily to ensure there is no dead time in the zero-crossing counting process, etc. I chose an opamp based on its slew rate and its ability to run on a single voltage power supply. I am choosing the counter according to its speed, its ability to quickly dump its count to intermediate storage, etc. All that information is available in the components data sheets.

What do oscillator data sheets specify? Most specify phase noise at 2 or 3 side band frequencies, input voltage, temperature range, fundamental frequency, (Allan Variance, if the oscillator is intended for long-term clock applications), .... OK, how do engineers use this information to select an oscillator? As a concrete example, how would an engineer use this information to choose an oscillator for a doppler radar? And responses like, well you use the phase noise data to figure out the oscillator's stability are too vague. How exactly would an engineer do that? If someone can point me to an article or book that explains this, I will stop posting in this thread and devote more time to the measurement system I am building.

#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #94 on: June 15, 2018, 12:54:49 pm »
Take a look at this article for some example numbers.  In practice, a radar designer would look at the area under the phase noise curve between selected integration limits, based on the performance range of interest.  The result of that integration can be express in RMS seconds of jitter, and the term "jitter bounds" would most likely refer to the limits of integration used to calculate it.

The referenced article is the sort of thing I am looking for. It is fairly high level, but it specifies how phase noise plots (as opposed to phase noise spectral density values for a couple of side bands) are used to find a "noise pedestal" caused by the frequency synthesizer. The phase noise plots also show phase noise degrades at higher frequencies.

So, I have actually learned something useful from this brief survey. Don't just supply a couple of phase noise data points, produce a phase noise plot. Hurray!

#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #95 on: June 15, 2018, 10:02:18 pm »
I'm glad to read that KE5FX has supplied the sort of thing you are looking for.  Use of an oscillator in a clock is different from other uses of an oscillator and so different  metrics must be applied suited to each application.

With regard to stationarity and cyclostationarity,  current noise and thermal noise are non-stationary processes in the context of oscillator design where you are attempting to model performance over infinitessimal increments of time.  However, in the context of evaluating oscillator performance, it's not really relevant as you correctly concluded.  Over observational periods of many cycles the process is stationary.

I'm not familiar with analog correlators beyond knowing such things exist.  Hopefully KE5FX can supply more information, but mixing the signals from the DUTs and examining the baseband output seems as if it might be useful in evaluating close in phase noise.  A common DSO with the ability to capture long samples at 1 GSa/S will allow doing analysis in recorded time which is always more convenient than doing it in real time.  The caveat to that is that the stability of the DSO clock is almost certainly vastly inferior to the clocks you are trying to test.

This forum has the highest proportion of PhDs, both credentialed and the common law, Jim Williams, variety of any group I've encountered outside of the annual professional society meetings I attend.

#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #96 on: June 16, 2018, 01:18:52 am »
With regard to stationarity and cyclostationarity,  current noise and thermal noise are non-stationary processes in the context of oscillator design where you are attempting to model performance over infinitessimal increments of time.  However, in the context of evaluating oscillator performance, it's not really relevant as you correctly concluded.  Over observational periods of many cycles the process is stationary.

The first thing I want to do when I get the sampling system designed and built is to test the fractional frequency data for stationarity. Tomato stated that he has never come across an oscillator that couldn't be modeled as a stationary process and several of the papers I have read state something similar. But, it never hurts to double check. Also, it will give me some experience in analyzing the data.

#### rhb

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #97 on: June 16, 2018, 02:55:33 am »
The difference in time scales between modeling a circuit and accounting for dynamic noise for design purposes and characterizing  a circuit for application are very different.  We know a priori that the thermal and current noise are not stationary over the course of a cycle.  However, we also know that for any point in the cycle, the noise is stationary.  So over the course of many cycles, the noise is stationary with a mean value equal to the mean value of the non-stationary noise over a cycle.

As I commented previously, it's a lexical minefield. Your question lies at the intersection of a lot of different disciplines, each with its own jargon and conventions.  The sign of the Fourier transform kernels is opposite each other in geophysics and electrical engineering.  Wandering among various disciplines as I am want to do, I have learned to be wary.

I found a circuit for an analog correlator and it's far too complex to justify building one unless you *really* have to.

Edit:

These look pretty good:

https://publications.npl.co.uk/npl_web/pdf/mgpg68.pdf

https://tf.nist.gov/general/tn1337/Tn190.pdf

Measuring phase noise is an interesting problem.  I noticed in the NIST update to 140 that improvements in practice must await better phase measurements.
« Last Edit: June 16, 2018, 09:39:15 pm by rhb »

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#### dnessett

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #98 on: June 16, 2018, 11:38:37 am »
These look pretty good:

https://publications.npl.co.uk/npl_web/pdf/mgpg68.pdf

https://tf.nist.gov/general/tn1337/Tn190.pdf

Measuring phase noise is an interesting problem.  I noticed in the NIST update to 140 that improvements in practice must await better phase measurements.

I couldn't get the npl link to load. However, the other two state that it is possible to make phase noise measurements with a spectrum analyzer. I thought so myself until I started reading about the subject. The problem is spectrum analyzers measure power, i.e., they display power spectral density. However, phase noise is measured in radians2/Hz (corrected 6/16/180), not watts/Hz. It is a spectral density, but not a power spectral density. The power spectral density close to a carrier is affected by both PM noise and AM noise; but, it is difficult, if not impossible to separate their effects within the power spectral density displayed by the spectrum analyzer. To use the power spectral density returned by a spectrum analyzer, you have to assume AM noise is insignifccant and then you have to do something (I still don't understand what) to convert the power expressed in watts to an angle expressed in Hz. Consequently, measuring phase noise is, as you point out in your message, not straightforward (at least when using only a spectrum analyzer).

I am hoping to find a way to extract the phase noise of the signal from the time domain fractional frequency data. This should be possible since instantaneous frequency is the time derivative of instantaneous phase.
« Last Edit: June 17, 2018, 01:10:06 am by dnessett »

#### Kleinstein

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##### Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #99 on: June 16, 2018, 09:09:24 pm »
The phase noise measurement described in the NIST link is using a mixer and reference signal of some kind to convert the signal, before sending it the the spectrum analyzer. If done in a way to mainly get the quadrature signal, the signal is rather insensitive to AM and mainly reflects phase modulation / phase noise.

Having the mixer part before the analysis helps in that the part behind the mixer can be considerably lower frequency and thus less critical with respect to sampling frequency stability. If one gets good time domain data, one can do essentially the same analysis numerically: start with a Hilbert transformation of some kind to get phase data. This can include a mixing step (I/Q like) to also go to a lower frequency domain - this is the kind of easy way to do the Hilbert transformation. So one will get phase and amplitude data an a somewhat slower time scale, which is usually sufficient and a nice reduction in data rate, without loosing significant information.

Smf