An advanced question - sampling an oscillator's signal for analysis

[tomato]

My intention was to explore the phase noise bandwidth issue, not to obtain definitive measurement values.

Oscillator	Lower	Upper	Bandwidth
GSPDO	9.589	10.402	813 KHz
Rubidium	9.669	10.328	659 KHz
Rigol	9.688	10.309	621 KHz

Setting your markers to where the curve falls off the bottom of the screen is not a valid way to measure the bandwidth.  Adjust your vertical scale and measure the actual width of the curve.

[dnessett]

Setting your markers to where the curve falls off the bottom of the screen is not a valid way to measure the bandwidth.  Adjust your vertical scale and measure the actual width of the curve.

As another poster (Borghese) pointed out, the phase noise of my SA isn't low enough to directly measure the phase noise of the oscillators. So, I am looking for another way to get an estimate of the oscillator phase noise bandwidth in order to spec out the requirements for a data acquisition system other than my oscilloscope.

[dnessett]

You can read "Choosing a Phase Noise Measurement Technique" from HP or Agilent.

Thanks for the references. In prepping for specing a data acquisition system other than my oscilloscope, I read Phase Noise and AM noise measurement in the Frequency Domain and Frequency Stability Specification and Measurement: High Frequency and Microwave Signals, which are very old (but useful, nevertheless). The references you provided update the material in those reports.

One problem I have is using the techniques described in these (and your) references requires an existing test setup. The one I have been using has the disadvantage that the data capture device is my Rigol 1104Z oscilloscope. The lowest sample rate I can select is 25 Msa/s and since I have only 6 Mpts of memory depth, the longest sample I can capture is 240 msec. While I can process the data from such a sample using software filters and FFT based spectral analysis, I am worried that this short sample limitation may not allow me to get an estimate of the noise bandwidth I will need to handle when I start looking at longer sample intervals. I need that estimate to determine the rate of sampling I need to support, which influences the backend data storage system design.

I have been using an AD8302 as a phase difference detector, which separates the AM and Phase noise components of the oscillator output. My intention is to digitize the phase difference output signal from the AD8302 and process it offline. But, do I need to sample this signal at 2 Msa/s, 10 Msa/s, 20 Msa/s, ....? If I have an estimate of phase noise bandwidth, I can double that and arrive at a reasonable sample rate that I can then use in the data acquisition design.

Other than reading the references you provided (which I intend to do), do you have any ideas how to get an estimate of phase noise bandwidth for the purposes of designing the DAQ system? The estimate doesn't have to be precise; using a technique that provides an upper bound would be reasonable.

[rhb]

One problem I have is using the techniques described in these (and your) references requires an existing test setup. The one I have been using has the disadvantage that the data capture device is my Rigol 1104Z oscilloscope. The lowest sample rate I can select is 25 Msa/s and since I have only 6 Mpts of memory depth, the longest sample I can capture is 240 msec. While I can process the data from such a sample using software filters and FFT based spectral analysis, I am worried that this short sample limitation may not allow me to get an estimate of the noise bandwidth I will need to handle when I start looking at longer sample intervals. I need that estimate to determine the rate of sampling I need to support, which influences the backend data storage system design.

A 240 ms sample length limits your RBW to a fraction of a Hz.  That's quite adequate.  The bigger limitation of using the DSO is the dynamic range.  The solution for that is to collect a lot of samples, sum them and normalize the peak to 1.0.

[tomato]

One problem I have is using the techniques described in these (and your) references requires an existing test setup. The one I have been using has the disadvantage that the data capture device is my Rigol 1104Z oscilloscope. The lowest sample rate I can select is 25 Msa/s and since I have only 6 Mpts of memory depth, the longest sample I can capture is 240 msec.

Are you sure about that?  It's impossible to believe any scope would be that hamstrung.

[dnessett]

Are you sure about that?  It's impossible to believe any scope would be that hamstrung.

Your challenge motivated me to go back and try to get the lowest sample rate that I could on the 1104Z. To make a long story short, there is no way to directly select the sample rate - you change it by changing the sweep rate. However, I keep getting inconsistent results when I attempt to change the sample rate using the horizontal timebase controls. I have downloaded the latest version of the firmware and will load it and see if that improves things.

[dnessett]

Are you sure about that?  It's impossible to believe any scope would be that hamstrung.

In chasing down the sample rate limit, I have learned that the DS1104Z has some pretty bizarre behavior when changing its sample rate. The formula the scope uses to select the sample rate when there is only one channel active and 12 Mpts selected is:

Sample_rate = 12 Mpts/(12*Time_scale)

So, I set the Time_scale to 50 secs with only channel one selected (using it for triggering). I then waited several minutes to see if the sample rate changed. It didn't (Figure 1 shows the result).

Figure 1 -

I then left the room for several minutes and returned. In the interval, the sample rate had changed to 20 Ksa/s.

It seems the scope re-calculates sample rate slowly when the Time_scale is long, which is why I thought it would only go as low as 25 Msa/s at 6 Mpts (I had 2 channels enabled when I observed those values).

Given this new data, I could capture 50 second samples at 20 Ksa/s or 5 second samples at 200 Ksa/s. In any case, eventually I want to observe longer intervals than this. So, 2 questions arise: 1) how do I determine the phase noise bandwidth during a 50 second interval; in particular, will a 20 Ksa/s rate be sufficient to obtain an upper limit on phase noise bandwidth over 50 seconds (given the Nyquist limit, this would assume phase noise bandwidth is less than or equal to 10 KHz), and 2) will the phase noise bandwidth in these sub-minute samples accurately represent the phase noise bandwidth in longer intervals?

My guess about the first question is 20 Ksa/s is probably not sufficient to achieve the objective. My guess about the second question is no.

[rhb]

Read Bendat & Piersol.  The time window controls your RBW. The sample rate controls  the Nyquist BW. 

If you collect 6 Mpts at 50 MSa/S you will have an RBW of 8.33 Hz and a Nyquist of 25 MHz.  If you collect 1024 such 8 bit series you should have about 16 bits, 96 dB, of dynamic range after summing the amplitude spectra.

Although in principle addition is commutative, in practice you need to remove the phase, hence the need to average amplitude spectra rather than compute the amplitude spectrum of the averaged traces.

Seismic data are non-stationary due to attenuation.  So a routine operation is to compute the average amplitude spectrum for a series of 500-1000 mS windows with 50% overlap.  Generally this is done for a sliding spatial window of 500 to 1000 traces from the start of the trace to the end.  Then the spatial variation of the attenuation in X & T will be plotted or the mean and standard deviation for each time window generated.

[tomato]

2) will the phase noise bandwidth in these sub-minute samples accurately represent the phase noise bandwidth in longer intervals?

Why do you think it is necessary to sample the phase noise for ~minutes to determine the bandwidth of the phase noise?

[dnessett]

Read Bendat & Piersol.  The time window controls your RBW. The sample rate controls  the Nyquist BW. 

I plan on getting back to Bendat & Piersol when I start getting some data that isn't corrupted by poor measurement techniques. Right now I am focusing on getting the test setup and test procedures properly designed.

[dnessett]

Why do you think it is necessary to sample the phase noise for ~minutes to determine the bandwidth of the phase noise?

Right now I am attempting to design a test setup that I can use to explore oscillator properties in the face of any eventualities. Some of what I have read suggests some components of oscillator phase noise are cyclostationary. Other authors dispute this, but indicate that the noise sources are correlated in such a way that provides the appearance of cyclostationarity (see Cyclostationary Noise in RF Circuits).

I don't want to build the test setup under the assumption that all oscillator noise sources are i.i.d., since somewhere down the road I may find out this is not true. Limiting samples to a short time period could hide properties (like non-stationarity or cyclostationarity) that may turn out to be important. Getting a handle on phase noise bandwidth defined over reasonably long sample periods will allow me to design the test system to handle whatever turns up. Actually, I don't need the exact phase noise bandwidth observed over long periods; I need an upper bound on phase noise bandwidth in order to properly design the data acquisition system.

If you can make a convincing argument (not just a proof by emphatic assertion) that 50 seconds of data at 20 Ksa/s is sufficient to develop the upper bound I am looking for, I would be deeply grateful.

[tomato]

Right now I am attempting to design a test setup that I can use to explore oscillator properties in the face of any eventualities. Some of what I have read suggests some components of oscillator phase noise are cyclostationary. Other authors dispute this, but indicate that the noise sources are correlated in such a way that provides the appearance of cyclostationarity (see Cyclostationary Noise in RF Circuits).

I don't want to build the test setup under the assumption that all oscillator noise sources are i.i.d., since somewhere down the road I may find out this is not true. Limiting samples to a short time period could hide properties (like non-stationarity or cyclostationarity) that may turn out to be important. Getting a handle on phase noise bandwidth defined over reasonably long sample periods will allow me to design the test system to handle whatever turns up. Actually, I don't need the exact phase noise bandwidth observed over long periods; I need an upper bound on phase noise bandwidth in order to properly design the data acquisition system.

If you can make a convincing argument (not just a proof by emphatic assertion) that 50 seconds of data at 20 Ksa/s is sufficient to develop the upper bound I am looking for, I would be deeply grateful.

You don't seem to have a lot of experience in this field, and I'm just trying to save you some effort.

I'm sorry, but I don't have time to write lengthy posts "proving" anything.  I will continue to make suggestions, but it doesn't offend me if you ignore them.

[dnessett]

You don't seem to have a lot of experience in this field, and I'm just trying to save you some effort.

I'm sorry, but I don't have time to write lengthy posts "proving" anything.  I will continue to make suggestions, but it doesn't offend me if you ignore them.

You are absolutely correct. I don't have a lot of experience in this field. And I appreciate the help you have given.

But, in order to learn, I have to understand what I am doing and why. Sometimes I learn by making mistakes. I don't like making mistakes, but that happens when you try something new. The reason I do a lot of reading is I am trying to learn from those who have made mistakes and learned from them - that is, I don't want to make the same mistakes others have turned into knowledge.

When I wrote "If you can make a convincing argument (not just a proof by emphatic assertion) ...", my point is that just telling someone new to the field to do something is useful, but limited. It is better to explain why they should do it - what is the experience on which the advise is based.

However, as I said, I am not unappreciative of the help you have provided.

[rhb]

Read Bendat & Piersol.  The time window controls your RBW. The sample rate controls  the Nyquist BW. 

I plan on getting back to Bendat & Piersol when I start getting some data that isn't corrupted by poor measurement techniques. Right now I am focusing on getting the test setup and test procedures properly designed.

Until you have read B&P cover to cover at least once, and in your case probably twice, you will not be able to acquire usable data.  To design the experiment you have to be able to write out and solve the equations which describe any experimental setup you are considering.

If you want to investigate cyclostationarity, you've got a lot of math to master.  I offered a design using comparators and multiple oscillators  which should work.  But you rejected that.

You are fundamentally limited by the phase noise of the instrument you use to make the measurements whether you use a DSO or an SA.  There are ways to address that, but until you have a good bit of experience with things like Wiener prediction error filters and can look at the equation for a time domain signal and immediately write out the  Fourier transform you're not going to get anywhere.

Wiener prediction error filters have a habit of blowing up, so designing them is a rather ticklish and typically iterative process.  This is why I suggested the comparator arrangement.

[dnessett]

Until you have read B&P cover to cover at least once, and in your case probably twice, you will not be able to acquire usable data.  To design the experiment you have to be able to write out and solve the equations which describe any experimental setup you are considering.

If you want to investigate cyclostationarity, you've got a lot of math to master.  I offered a design using comparators and multiple oscillators  which should work.  But you rejected that.

You are fundamentally limited by the phase noise of the instrument you use to make the measurements whether you use a DSO or an SA.  There are ways to address that, but until you have a good bit of experience with things like Wiener prediction error filters and can look at the equation for a time domain signal and immediately write out the  Fourier transform you're not going to get anywhere.

Wiener prediction error filters have a habit of blowing up, so designing them is a rather ticklish and typically iterative process.  This is why I suggested the comparator arrangement.

We are discussing two different things. I am focused at present on the design of the data acquisition system. Once an upper bound on input signal bandwidth exists (plus an estimate of the necessary precision), this is purely an acquisition system design problem (how to measure the signal data, how to capture it and archive it).

In the above quote, you address the data analysis problem. Once the type of signal (e.g., phase difference, zero-crossing count per unit time), the sample rate, error bounds, and precision of the data are known (there may be other factors, but these are the major ones), the data analysis problem need not consider how the data was captured.

Once I have designed and built the data acquisition system, I will concentrate on the data analysis problem. I may need to iterate and modify the data acquisition system at some point, but that will happen only after I have an initial version operating.

Added later: I forgot to mention that I do not plan to use either a DSO or SA in the data acquisition system.

[rhb]

In the above quote, you address the data analysis problem. Once the type of signal (e.g., phase difference, zero-crossing count per unit time), the sample rate, error bounds, and precision of the data are known (there may be other factors, but these are the major ones), the data analysis problem need not consider how the data was captured.

I'm afraid I've never visited that planet.  Every problem I've ever worked on was highly constrained by the data acquisition.  That completely controlled what I could or could not do in the analysis.  If you collect data which do not contain the information you seek it is completely useless.  Other than as a lesson in what not to do.

Seismic surveys cost many millions to acquire and still more to process.  The acquisition requirements occupy many pages in  a survey contract and there is a company observer present to verify that those requirements are met.  Those requirements are based in large part on the purpose of the survey and in some cases the purpose completely dominates all other requirements.

Before you build your cart, you should find out what a horse looks like.

[rhb]

As I recall, you have a Siglent SSA3021X.  Did you connect the 10 MHz ref in to the GPSDO or any of your other  reference oscillators?

No matter how you acquire data, you are always going to have the convolution of a reference oscillator and the DUT to deal with.

[dnessett]

As I recall, you have a Siglent SSA3021X.  Did you connect the 10 MHz ref in to the GPSDO or any of your other  reference oscillators?

No matter how you acquire data, you are always going to have the convolution of a reference oscillator and the DUT to deal with.

I'm not sure what you are getting at. I have never connected the GPSDO to my SA as an external 10 MHz reference. I once connected the Rubidium oscillator to it, but that was some time ago.

Is this in relation to the phase noise measurements? If so, Borghese's post correctly pointed out that the phase noise of the Siglent is worse than the phase noise of the Rubidium oscillator, so what I was seeing was the phase noise of the SA, not of the oscillator.

If this is in regard to something else, it would help me to respond if you would set the context.

By the way, I plan to start out with a one oscillator test set up (using the delay line approach), to get an estimate of phase noise of each oscillator so when I move to the reference versus DUT test set up, I will have an idea how much (in a rough sense) phase noise observed comes from the reference and how much from the DUT

[rhb]

Why don't you connect one of the reference oscillators to the ref in and set the instrument to use that?  Then examine the other oscillators with that as the reference.  You're attempting to evaluate reference oscillators without using them.  If you're not going to use one, why bother having one?

I'm afraid I don't see how you can measure the phase noise of a 10 MHz oscillator with a delay line.  I think I understand how to do it at several GHz, but it seems physically impractical at HF.  And I'm not entirely sure you can measure phase noise with a delay line at any frequency.  I sort of *think* it might be possible with a variable delay line at several GHz, but I've not convinced myself it's true.

But if you can do it, why would you do anything else?

Whether you sample with a DSO or heterodyne in an SA, you are doing a multiplication in time.  So the spectra of the two oscillators are convolved with each other.  While it was not stated in those terms, that was the point of the comment that you were observing the phase noise of the SA, not the oscillators.

[dnessett]

Why don't you connect one of the reference oscillators to the ref in and set the instrument to use that?  Then examine the other oscillators with that as the reference.  You're attempting to evaluate reference oscillators without using them.  If you're not going to use one, why bother having one?

Because the phase noise of the SA is greater than the phase noise of the DUTs (see this previous post). It doesn't matter whether an external or internal oscillator is used to clock the SA.

I'm afraid I don't see how you can measure the phase noise of a 10 MHz oscillator with a delay line.  I think I understand how to do it at several GHz, but it seems physically impractical at HF.  And I'm not entirely sure you can measure phase noise with a delay line at any frequency.  I sort of *think* it might be possible with a variable delay line at several GHz, but I've not convinced myself it's true.

But if you can do it, why would you do anything else?

I am not sure why you think you cannot use the delay line technique on a 10 MHz signal. The wavelength of 10 MHz in RG-58 coax is 64.9 feet (see this post). I have 83 feet of coax and have just received another 100 feet. That is a total of 183 feet. That is ~2.8 wavelengths. I am in the process of building a selectable delay device that will give me between 1 and 50 100 ns (i.e., up to another 1/2 wavelength) of delay. So, with this equipment, I can get the delayed signal 3.3 3.8 wavelengths away. I will use the selectable delay to put the original and delayed signal in or close to quadrature to get the most precise measurement from the AD8302.

In regards to measuring phase noise with a delay line, read section IV of Phase Noise and AM noise measurement in the Frequency Domain. The disadvantage of this technique is it has a higher noise floor than the two oscillator technique. But, it should provide sufficient accuracy to estimate the phase noise contributed by the GPSDO when I get to the two oscillator technique (at least, that is my hope).

Whether you sample with a DSO or heterodyne in an SA, you are doing a multiplication in time.  So the spectra of the two oscillators are convolved with each other.  While it was not stated in those terms, that was the point of the comment that you were observing the phase noise of the SA, not the oscillators.

Ultimately, I am not going to use either a DSO or SA for data capture. I am going to build a data capture device out of a Arduino Due (as you have suggested previously). However, I will initially use my DSO for short interval data capture to get some experience with the other parts of the system.

[rhb]

I suggest you review the formula for sin(a) - sin(b).  That's what you *can* measure with a delay line.  In particular, I call to your attention that you are implicitly heterodyning the oscillator with harmonics of itself.

Any way you sample the DUT you are going to be performing a multiplication in the time domain.   I very much doubt that an Arduino has better phase noise than a Siglent SA or a Rigol DSO .  Look at the EEVblog review of the SSA3021X vs the  Rigol DSA815.  If and *only* if you clock the Arduino with a good reference oscillator will you be able to make meaningful measurements.

[tomato]

I am not sure why you think you cannot use the delay line technique on a 10 MHz signal. The wavelength of 10 MHz in RG-58 coax is 64.9 feet (see this post). I have 83 feet of coax and have just received another 100 feet. That is a total of 183 feet. That is ~2.8 wavelengths. I am in the process of building a selectable delay device that will give me between 1 and 50 100 ns (i.e., up to another 1/2 wavelength) of delay. So, with this equipment, I can get the delayed signal 3.3 3.8 wavelengths away. I will use the selectable delay to put the original and delayed signal in or close to quadrature to get the most precise measurement from the AD8302.

The delay line method is a perfectly good way to make measurements, but you will want to buy a giant spool of coax if you want to do it.  Your (relatively) short delay line will only allow you to see higher frequency phase noise. A much longer delay line is needed if you want to measure phase noise near the carrier.

[dnessett]

The delay line method is a perfectly good way to make measurements, but you will want to buy a giant spool of coax if you want to do it.  Your (relatively) short delay line will only allow you to see higher frequency phase noise. A much longer delay line is needed if you want to measure phase noise near the carrier.

Good point. According to Phase Noise and AM noise measurement in the Frequency Domain page TN-222 in the paragraph following equation 85, in a power limited system (which is true for my setup, i.e., the power of the Oscillator under test is fixed), the optimal coax length occurs when the attenuation it induces is 8.686 dB. The attenuation for RG-58 is 1.4 dB/100 feet (see this coax attenuation chart for 10 MHz), which means the maximum length of coax I need is 8.686/1.4=~620 feet. I already have 183 feet, so I need another 440 feet. Actually, I will be using RG-174 to implement the selectable delay device and it has an attenuation of 3.3 dB per 100 feet, so I can probably get away with another 400 feet of RG-58. That will cost about $56.

[tomato]

Good point. According to Phase Noise and AM noise measurement in the Frequency Domain page TN-222 in the paragraph following equation 85, in a power limited system (which is true for my setup, i.e., the power of the Oscillator under test is fixed), the optimal coax length occurs when the attenuation it induces is 8.686 dB. The attenuation for RG-58 is 1.4 dB/100 feet (see this coax attenuation chart for 10 MHz), which means the maximum length of coax I need is 8.686/1.4=~620 feet. I already have 183 feet, so I need another 440 feet. Actually, I will be using RG-174 to implement the selectable delay device and it has an attenuation of 3.3 dB per 100 feet, so I can probably get away with another 400 feet of RG-58. That will cost about $56.

Keep in mind, that calculation is about keeping cable losses under control. If you use the "optimum" cable length, you still will not be able to measure phase noise near the carrier.  That can be a serious limitation of the delay line method. You will have to decide if it is a deal-breaker.

[dnessett]

Good point. According to Phase Noise and AM noise measurement in the Frequency Domain page TN-222 in the paragraph following equation 85, in a power limited system (which is true for my setup, i.e., the power of the Oscillator under test is fixed), the optimal coax length occurs when the attenuation it induces is 8.686 dB. The attenuation for RG-58 is 1.4 dB/100 feet (see this coax attenuation chart for 10 MHz), which means the maximum length of coax I need is 8.686/1.4=~620 feet. I already have 183 feet, so I need another 440 feet. Actually, I will be using RG-174 to implement the selectable delay device and it has an attenuation of 3.3 dB per 100 feet, so I can probably get away with another 400 feet of RG-58. That will cost about $56.

Keep in mind, that calculation is about keeping cable losses under control. If you use the "optimum" cable length, you still will not be able to measure phase noise near the carrier.  That can be a serious limitation of the delay line method. You will have to decide if it is a deal-breaker.

Understood. The objective of the delay line approach is to get an estimate of phase noise and phase noise bandwidth for each oscillator. I need to know if the short-term phase noise of the GPSDO (for which I have no specification) is sufficiently smaller than the other oscillators in order to use it as the reference in a two oscillator configuration. While I may not get phase noise close to the carrier for each oscillator, I should get enough information to reasonably conjecture that the GPSDO has (or does not have) sufficiently lower phase noise than the other oscillators to use it as a reference. The reason I am worried about this (at least for short-term stability characterization) is the GPSDO has an OCXO as the base oscillator that is corrected by the GPS signal periodically. Short-term its stability may be no better than the other OCXOs I have.

I need the phase noise bandwidth estimate to design the data acquisition system that will replace my DSO. I need to know the sampling rate it must support, which is driven by the bandwidth of the signal it must capture.