An advanced question - sampling an oscillator's signal for analysis - Page 1
Forum section: electronics / general

author: dnessett
author_rank: Regular Contributor
timestamp: June 08, 2018, 09:26:53 pm
content: I have an advanced question that I decided to post here in case there are some who contribute to this forum who have expertise in signal measurement. I am developing a test procedure for characterizing the stability of some hobbyiest 10 MHz oscillators. This is in preparation for a study of a couple of 10 MHz distribution amplifiers. (For the record, I intend to make the results of this study available under the creative commons attribution-share alike license and I get no financial gain from the project - I am doing it to satisfy my curiosity.) While researching background information for this project, a question arose that I have been unable to answer through Googling appropriate words and phrases.An oscillator is mathematically characterized as:v(t) = [V0 + e(t)] * cos[w0*t + phi(t)], where V0 is the base oscillator amplitide, w0 is the base oscillator frequency (in radians/sec), and both e(t) and phi(t) are stochasitic processes that respecitively add amplitude noise and phase noise to the oscillator's output.For any practical oscillator, the stochastic processes e(t) and phi(t) are cyclostationary, which means their moments (e.g., mean and variance) are normally not constant (which would be true for a stationary process), but periodic. That means over time they change in value, but are periodic over some timeframe.My problem is how to properly sample cyclostationary processes such as e(t) and phi(t). My uneducated gut feeling is that if I am attempting to characterize short term oscillator stability, I would want the time during which multiple samples are drawn (one sample being, for example, the number of zero crossings during an interval) to be defined so the moments of the probability density functions of e(t) and phi(t) vary only slightly. Otherwise, the samples at the beginning of the sampling period (i.e., the total time during which samples are drawn) would be influenced by one set of moment values and the samples drawn later would be influenced by another significantly different set of moment values.To characterize long-term stability, my gut feeling is to use a sampling interval during which the moments of e(t) and phi(t) "cycle" several times. This would allow the calculation of an "average" of these moments.Of course, even if my gut feelings are correct, it isn't clear how to determine an appropriate sampling period. Without getting into a lot of experimental work attempting to characterize the cyclostationary process associated with each oscillator (which is probably beyond the reach of my equipment and skill), I was hoping some general rules of thumb have been developed for common oscillators.In addition, I was wondering what parameters might control the cyclostationary processes. The ones I could come up with after googling a bit are (with no distinction between short-term and long-term): temperature, humidity, power supply ripple, crystal and electrical component aging, mechanical vibrations, variations in loading. Some of these can be controlled in the short-term (e.g., temperature, humidity, mechanical vibrations), while others are probably only long-term factors (e.g., crystal and electrical component aging).Given this background, my questions are: is my gut feeling about short-term and long-term sampling intervals correct, and if so, are there any general guidelines that would help me to develop an experimental design in regards to this question? Are there other parameters that would contribute to variation in the cyclostationary processes?

author: tomato
author_rank: Regular Contributor
timestamp: June 09, 2018, 01:05:34 am
content: NBS Monograph 140 (Time and Frequency: Theory and Fundamentals)

author: tautech
author_rank: Super Contributor
timestamp: June 09, 2018, 01:31:31 am
content: Might be interesting to see if a narrow Mask could detect drift and small amplitude variations on a DSO.I might have a play with this and pop up some screenshots of results.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 09, 2018, 04:13:22 am
content: If I understand correctly, you want to measure deviations in amplitude and phase for a nominally ideal 10MHz sinusoid?If you have a stable (enough) 10MHz reference, why not just multiply the two signals together which will give you the sum and difference of the two (acting as a demodulator). The difference component contains information about the amplitude and phase differences. This concept is used for phase-sensitive detection (such as for lock-in amplifiers).I'm not sure it is necessary to delve into stochastic processes etc.

author: ap
author_rank: Frequent Contributor
timestamp: June 09, 2018, 04:45:23 am
content: The variability of the phase is called phase noise and related to this is what is called Allen variance. You will find a lot of information on technics how to measure phase noise in older HP documents.

author: tomato
author_rank: Regular Contributor
timestamp: June 09, 2018, 05:29:00 am
content: Quote from: ap on June 09, 2018, 04:45:23 amAllanVariance

author: dnessett
author_rank: Regular Contributor
timestamp: June 09, 2018, 05:32:22 am
content: Quote from: JohnnyMalaria on June 09, 2018, 04:13:22 amThanks for your comment. However, you are describing a particular technique to make a measurement. I have read quite a bit about that topic and have a good handle on how to do it. However, in order to obtain statistically valid results you need to make multiple measurements and then process them. My question is about the interval over which these multiple measurements are made.Quote from: ap on June 09, 2018, 04:45:23 amYes, I understand that. In fact there are more modern versions of the Allan variance (e.g., the modified Allan variance, the Hadamard variance) that provide better confidence intervals than the Allan variance. I have read quite a few NBS/NIST technical reports about processing the sample data of an oscillator once you have obtained it, but none of them (except perhaps the one referenced by Tomato above - I haven't completely read its relevant sections) discuss how to select the sample interval during which you make N measurements.

author: tomato
author_rank: Regular Contributor
timestamp: June 09, 2018, 05:56:44 am
content: Quote from: dnessett on June 09, 2018, 05:32:22 amYou want to characterize "hobbyist 10 MHz oscillators". The good 'ole vanilla (2-pt.) Allan variance will give you all the information you need. There's no need to mess with modified Allan Variance.Quote from: dnessettYou choose your sampling interval based on the shortest time period you are interested in characterizing your oscillator. You choose the number (N) of data points based on the longest time period you are interested in characterizing your oscillator.

author: awallin
author_rank: Frequent Contributor
timestamp: June 09, 2018, 07:30:23 am
content: Quotedepends on the quality of the clock I guess.FWIW with active hydrogen masers that start out at 1e-13 @ 1s it usually makes sense to look at only one phase-measurement per day. A typical time-interval counter has white phase-noise of around 2e-11/tau(s), so by measuring more often you only see the noise of the counter, not the maser.The masers usually have linear frequency drift and it takes at least 30 days to get a reliable number for the drift, usually something like 1e-15/day.With Cs-clocks it could make sense to measure a bit more often, since the cs-clocks are noisier wrt. the counter.AFAIK most timing labs take phase-measurements every 6/10/12 minutes or so - but as mentioned above for a good clock one point per day has the useful information.On the other hand when characterizing poor oscillators or e.g. AC-mains feedthru at 50/60 Hz it is useful to have a phase-meter (like microsemi 3120A) that outputs 1000 phase-measurements per second so you easily catch e.g. 50Hz spurs as oscillations in the ADEV.for poorer clocks you can guess at what causes instability - and match the measurement to that. For example AC-mains oscillations or poor voltage regulation or DC-DC switchers, GNSS constellation diurnals, temperature/air-conditioning effects, ambient pressure variation (Rb-clocks!), and so on.

author: dnessett
author_rank: Regular Contributor
timestamp: June 09, 2018, 03:56:15 pm
content: There seems to be some confusion about the questions I asked in my first post. Both Tomato and awallin understood it and I thank them for their help. However, for the benefit of others, I will briefly elaborate.An ideal oscillator is mathematically characterized as:v(t) = V0 * cos[w0*t], where V0 and w0 are defined as in the original post. One characteristic of an ideal oscillator is its signal has exactly the same value at t and t+(2*PI).However, ideal oscillators exist only in the minds of mathematicians. The signal generated by a real physical oscillator obeys the equation given in the first post, i.e., v(t) = [V0 + e(t)] * cos[w0*t + phi(t)]. The quantities e(t) and phi(t) are not deterministic functions. Rather, for a given value of t, say t=10, they are random variables. That is, e(10) and phi(10) supply a value controlled by a probability distribution function (pdf). The symbols e(t) and phi(t) represent (in this case) an uncountably infinite number of random variables, indexed by the variable t representing time. We say e(t) and phi(t) are stochasitic processes.If two random variables have the same pdf, they are said to be independent and identically distributed (often abreviated as "i.i.d."). If the random variables comprising a stochastic process are all i.i.d., then that process is said to be stationary. Stationary processes lend themselves to the experimental determination of the moments of their pdfs (e.g., their mean and variance). Since all random variables associated with the stochasitic process are i.i.d., sampling their values a different times and computing statistics corresponding to their mean and variance is mathematically justified. All samples are from the same pdf, so such computations are valid.However, the stochastic processes e(t) and phi(t) are not stationary, so you can't blindly use samples from different times to compute the underlying moments of their pdfs. Fortunately, these processes normally have a weaker property known as cyclostationarity. This means that periodically the random variables associated with them are i.i.d., i.e., for some value p, e(t) and phi(t) are the same random variable as e(t+p) and phi(t+p). This periodicity is normally not represented by a sine wave, so p is not a constant value for all values t; the periodicity is controlled by quite a few physical variables and generally its shape is unknown.Characterizing the frequency stability of an oscillator consists of using sample data generated by the oscillator signal to estimate the variance of phi(t). But, since phi(t) is cyclostationary, the expermenter must take into account the change of its random varaible pdfs. Normally, it is assumed: 1) over very short time periods the pdfs change only slightly, and 2) over very long time periods, the pdfs cycle. In the first case, samples taken over a short time period approximate samples from i.i.d. random variables. In the second case, a large number of samples taken over a long period approximate those of a random variable that is a complex combination of the underlying stochastic process random variables. Thus, computing a variance estimate using these samples is a kiind of averaging of the underlying pdf variances. (Don't ask me about the mathematics of this "averaging" - I imagine it is pretty complicated).The questions in my first post basically sought guidance on how to determine the appropriate values for short and long sampling periods; and in addition wondered what factors control the cyclostationarity of e(t) and phi(t).

author: tomato
author_rank: Regular Contributor
timestamp: June 09, 2018, 05:20:29 pm
content: Quote from: dnessett on June 09, 2018, 03:56:15 pmYou're going to have to convince me of the validity of this as a general statement. The only non-stationary noise I've ever observed in an oscillator involved failing components or an improper test setup, and I've never observed cyclo-stationary noise in an oscillator.Can you give an example of a cycle-stationary noise process in an oscillator?

author: dnessett
author_rank: Regular Contributor
timestamp: June 09, 2018, 09:08:54 pm
content: Quote from: tomato on June 09, 2018, 05:20:29 pmI'm just quoting what I have readhere(see slide 4),here,here(2nd paragraph in section 1), andhere(1st partial paragraph under figure 3). Intuitively, it makes sense. Consider just one parameter - temperature - that controls oscillator noise and for argument sake, ignore all others. For a given temperature, the noise should be pretty much identical each time the environment cycles through that value.

author: tomato
author_rank: Regular Contributor
timestamp: June 10, 2018, 01:45:10 am
content: Quote from: dnessett on June 09, 2018, 09:08:54 pmThe second and fourth links are discussing noise that is cyclic at the period of the oscillator, which would be 100 ns for a 10 MHz oscillator. I assume you will be making measurements on time scales many orders of magnitude larger than this, so the cyclo-stationary aspect is not important.QuoteI don't think temperature dependent noise would be considered cyclo-stationary. Regardless, I've never heard of phase noise being a strong function of temperature variations with any well designed oscillator.

author: dnessett
author_rank: Regular Contributor
timestamp: June 10, 2018, 02:46:47 am
content: Quote from: tomato on June 10, 2018, 01:45:10 amOK. It makes it much easier to design a sampling experiment if I can assume phase noise is a stationary process. That is the type of advice I am looking for. Thanks.Following up, let me ask your advice on averaging and sampling times for short-term stability. To define short-term, I was thinking that most hobbyists use a time standard (e.g., ocxo or rubidium oscillator) to synchronize test equipment like frequency counters, oscilloscopes, spectrum analyzers, ... when conducting measurement experiments. So, my first guess is they would be interested in short-term stability on the order of several minutes to several hours. So, following your advice in a previous post, I should make the averaging interval on the order of a minute and the sampling interval on the order of several hours. Have I understood you correctly?

author: tomato
author_rank: Regular Contributor
timestamp: June 10, 2018, 03:12:31 am
content: Quote from: dnessett on June 10, 2018, 02:46:47 amAre you asking what time frames are of interest to users of a "hobbyist" oscillator? I don't know the answer to that question.

author: rhb
author_rank: Super Contributor
timestamp: June 10, 2018, 01:45:07 pm
content: Get a copy of "Random Data" by Bendat and Piersol. They treat the data analysis very thoroughly including how to deal with non-stationary series. That's been my go to for weird questions that walked into my office for 30 years and 3 editions. The 4th is the final one as Piersol passed away.Fundamentally you take long samples, window them and average. The details depend upon what you want to characterize. In reflection seismology one is usually doing this to characterize attentuation so one is averaging amplitude spectra.

author: tomato
author_rank: Regular Contributor
timestamp: June 10, 2018, 06:59:53 pm
content: Quote from: rhb on June 10, 2018, 01:45:07 pmThis is not seismology. There are specific analysis techniques (i.e. Allan Variance) that have been developed for characterizing clocks and oscillators. NBS Monograph 140 is the correct reference for this problem.

author: dnessett
author_rank: Regular Contributor
timestamp: June 10, 2018, 07:02:40 pm
content: Quote from: rhb on June 10, 2018, 01:45:07 pmThanks. I have ordered a copy. When I get some data (I am building the test setup right now), I can analyze it to see if it represents a stationary or non-stationary process.

author: KE5FX
author_rank: Super Contributor
timestamp: June 11, 2018, 04:07:51 am
content: The book you're looking for may bethis oneby Rubiola.

author: dnessett
author_rank: Regular Contributor
timestamp: June 11, 2018, 01:25:13 pm
content: Quote from: KE5FX on June 11, 2018, 04:07:51 amLooks like a good book, but its expensive ($62.75 in paperback). I looked through the table of contents and there seems not to be an in depth treatment of sampling oscillator signals to derive stability characteristics. In the index, measurement of random processes is given a single page right at the beginning of the book (13), which suggests only a superficial treatment. However, if I am wrong and sampling is given a thorough treatment, let me know and I will consider buying it.

author: rhb
author_rank: Super Contributor
timestamp: June 11, 2018, 02:12:28 pm
content: Having spent my career in signal analysis and having a long standing hobby interest in all aspects of electronics, I'm quite intrigued by your question. So I'll be contemplating the measurement problem in the context of the applicable system errors.One approach that occurs to me is to interpolate the times of the zero crossings relative to a high precision clock. Then look at the variance from the mean as a function of time (aka Allan variance). If you do a sparse L1 pursuit to obtain the frequency and phase over a cycle or two of a sine wave and then solve that for the central zero crossing you should avoid problems with quantization and mismatch between the sampling period and the frequency.I'll need to study the oscillator model you posited to say more.

author: GerryBags
author_rank: Frequent Contributor
timestamp: June 11, 2018, 03:47:44 pm
content: A few docs that may be of interest, if you haven't read them already:http://tycho.usno.navy.mil/ptti/1985papers/Vol%2017_05.pdf"Characterization, Optimum Estimation, and Time Predictionof Precision Clocks"https://fenix.tecnico.ulisboa.pt/downloadFile/3779572188799/Tn296.pdf"Characterization of Clocks & Oscillators" Covers portions of Monograph 140 mentioned above by Tomato. Co-authored by Allan.http://www.photonics.umbc.edu/Menyuk/Phase-Noise/rutman_ProcIEEE_910601.pdf"Characterization of Frequency StabilityIn Precision Frequency Sources" By J. Rutman & F. A. Wall

author: dnessett
author_rank: Regular Contributor
timestamp: June 11, 2018, 04:18:17 pm
content: Quote from: tomato on June 09, 2018, 01:05:34 amI finished reading section 8 of the Technical Report, which is the material germane to this thread. It is a good clear explanation of the problem/approaches and I found it very useful.However, there is something missing from it and parenthetically from all of the material I have read so far. Specially, how do you use the Allan variance (or its square root, the Allan deviation) once you have computed it. I imagine someone setting up a system might want to know if a particular oscillator is suitable for use in that system. For example, a hobbyiest may wish to measure signal characteristics of some radio transmission system he is building. He wants to use a 10 MHz reference clock passed through a distribution amplifier to synchronize the instruments he is using to test his system.I understand from the reading that I have done that computing the traditional variance of fractional frequency data doesn't work because it doesn't converge as the sample size increases. That is one of the reasons Allan created his variance measure. But, with the traditional variance (actually its square root, the standard deviation), if you assume a gaussian distribution of the fractional frequency process, 99.7% of the values lie within a 3 sigma band around the mean. So, if the designer had a traditional variance to work with, he could look at the range of frequencies within the 3 sigma band and decide whether that sort of jitter was acceptible for testing his system.So far, I have found nothing like this for the Allan variance. How do you use it in a practical situation?

author: dnessett
author_rank: Regular Contributor
timestamp: June 11, 2018, 04:41:27 pm
content: Quote from: GerryBags on June 11, 2018, 03:47:44 pmThanks for the references. Comments below.Quote from: GerryBags on June 11, 2018, 03:47:44 pmI have read several reports by Allan, although I don't think I have read this particular one. I briefly looked it over and I think it doesn't contain anything I haven't read before.Quote from: GerryBags on June 11, 2018, 03:47:44 pmLooks interesting and it is more recent than Monograph 140. I will take a look at it.Quote from: GerryBags on June 11, 2018, 03:47:44 pmThis one also looks interesting.

author: rhb
author_rank: Super Contributor
timestamp: June 11, 2018, 05:04:40 pm
content: My "I read it on the internet" understanding of the Allan variance is it simply is treating the variance as a random variable. So one has then the mean and variance of the variance. One can take the variance and compute the FFT to look for periodicities in the variance. I *think* that would be the cyclostationarity, but I've never encountered that term before. So I'm just guessing.I rather suspect that this is a lexical minefield where different specialties define slightly different meaning and scaling conventions to the same words.

author: tomato
author_rank: Regular Contributor
timestamp: June 11, 2018, 08:27:31 pm
content: Quote from: dnessett on June 11, 2018, 04:18:17 pmFor the sake of convenience, let's refer to the paper by Rutman & Walls (linked by GerryBags) instead of the NBS Monograph, since it contains everything we need and everybody has access to it.There are (generally) two ways to view the stability of an oscillator -- in the frequency domain and in the time domain. In the frequency domain, one is concerned with the spectral densities of phase and frequency fluctuations and the resulting spectral density of the oscillator itself. In the time domain, one is concerned with variances, i.e. standard deviations. The utility of the Allan Variance is that it provides a link between these two domains. (See Table 1 of the cited paper.) In brief, the Allan Variance allows one to determine the dominant noise process of an oscillator on any given time scale. For example, if the (root) Allan Variance of an oscillator has 1/root(Tau) dependence over some time scale, it can be concluded that the dominant noise source on that time scale is white phase noise. If the (root) Alllan Variance of this same oscillator flattens out at longer times, it can be concluded that the dominant noise source is flicker frequency at longer times.QuoteYou cannot make the assumption that the distribution is Gaussian and, therefore, you can't conclude much from the standard deviation of the frequency of an oscillator. In general, a traditional variance provides very little information about the underlying behavior of an oscillator. As an example, consider two 10 MHz oscillators monitored over some long time period. Oscillator 1 might have very low "jitter" but it drifts linearly about 10 Hz during the monitoring period. Oscillator 2 might not have any linear drift, but it has about 10 Hz of random jitter. Despite having very different characteristics, these oscillators will have nearly the same traditional variance. Their Allan Variances, however, will be very different.QuoteI'm guessing a lot of people on this forum are familiar with GPS-disciplined oscillators, where a local oscillator is locked to a signal extracted from GPS satellites. The big advantage of these devices is the ability to impose the long term stability of the GPS (Cesium) clocks onto a less expensive, local clock. But, how does one marry the local clock to the GPS signal? In other words, how quickly or how tightly does one lock the local oscillator onto the GPS signal? The answer to that question depends on the characteristics of both the local oscillator and the GPS signal, and the Allan Variance gives you those characteristics. For instance, the Allan Variance of a simple TXCO might indicate it should be locked onto the GPS signal with a short time constant, whereas the Allan Variance of a Rb oscillator might indicate that it should be locked onto the GPS signal with a relatively long time constant.

author: tomato
author_rank: Regular Contributor
timestamp: June 11, 2018, 08:30:27 pm
content: Quote from: rhb on June 11, 2018, 05:04:40 pmNo, you missed the mark on this one.

author: dnessett
author_rank: Regular Contributor
timestamp: June 11, 2018, 09:10:57 pm
content: Quote from: GerryBags on June 11, 2018, 03:47:44 pmWhen I looked at this, I only examined the table of contents to see if it might be interesting (which I thought it was). However, the URL suppliedonlythe table of contents. The full report is here:"Characterization of Clocks & Oscillators"

author: dnessett
author_rank: Regular Contributor
timestamp: June 11, 2018, 09:35:09 pm
content: Quote from: tomato on June 11, 2018, 08:27:31 pmThis is all very reasonable, but doesn't solve the problem I posed. Let me try again.I am a hobbyist who is building some circuit or system. I want to test that system using different pieces of equipment (e.g., oscilloscope, spectrum analyzer, frequency counter) simultaneously. I have two oscillators I can use to synchronize the equipment (through a distribution amp), say a rubidium oscillator and an ocxo. Which one do I use? From just playing around with my own rubidium and ocxo oscillators, it appears to me that the rubidium has good long-term stability, but not so good short-term stability. On the other hand, the ocxo has good short-term stability and not as good long-term stability. This intuition is born out by at least one study I have looked at (e.g., see slide 16 ofthispresentation)What I need is information on the stability of these two oscillators that will help me choose which one to use. I am not designing oscillators, I am using them. Perhaps naively, I presumed that the stability measures now in use would provide information so I can make an informed choice. Did I presume incorrectly?

author: tomato
author_rank: Regular Contributor
timestamp: June 11, 2018, 09:54:53 pm
content: Quote from: dnessett on June 11, 2018, 09:35:09 pmYouhavethe information. Does your system require better short-term or long-term stability? Only you can answer that question.

author: tautech
author_rank: Super Contributor
timestamp: June 11, 2018, 09:55:24 pm
content: Exactly why do you need to go down this rabbit hole ?Why do you need such good drift accuracy ?

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 11, 2018, 10:20:40 pm
content: @OPWhat do you mean by stability? Amplitude, frequency or both?What do you mean by short-term vs. long-term? ms vs s, min vs hours?What's your metric for stability? Hz/s, standard deviation of frequency?If understand it, you have a choice of two oscillators that you actually have and want to select the most stable for your application.If you are looking for changes of a few kHz over seconds vs. over hours (I have no realistic idea) then I'd do something along these lines:1. If you can interrogate your frequency counter a high enough rates (a few time a second) then just record an hour or two of the readings then use something like Excel to calculate standard deviations over some suitable statistic over blocks of say 1s, 2s, 5s, 10s, 20s, 50s, 100s etc etc and, of course, just plot the frequency.2. Use another oscillator as a reference and then do demodulation (multiply) for both your oscs at the same time (to allow for reference drift). It would be a straightforward matter to compare the two demodulated signals statistically to see which is more stable according to your definition of it. I think a Fourier transform of each would help since the osc with the least line broadening would be your best bet.I said earlier that I think digging into the whole stochastic process yada stuff is unnecessary. You can afford to be semi-quantitative about this and not purist. I stand by that

author: rhb
author_rank: Super Contributor
timestamp: June 11, 2018, 11:46:27 pm
content: This strikes me as an interesting application for a sparse L1 pursuit.Construct a dictionary/wavelet basis which consists of windowed sinusoids which vary in phase, frequency and amplitude as a function of time. This amounts to constructing an A matrix with mostly zero elements which has at any window in time a set of possible solutions to be considered and then solving Ax=y using an L1 solver such as linear programming. If the solution vector x is sparse, then you have the optimal decomposition of the signal into the basis. If it's not sparse then you will grow old and die before you get an answer. While that can happen, it's quite rare. David Donoho and Emmanuel Candes have done a lot of work in this area. Mallat gives a brief review of the some applications in "A Wavelet Tour of Signal Processing", 3rd ed.In the context of oscillator performance, you can separate a sine wave which is phase shifted, from a sine wave whose frequency changes, from a sine wave whose amplitude changes and all combinations and permutations of those. That problem is NP-hard, and was considered unsolvable. But in 2004 Donoho proved that if a sparse L1 solution existed, it was the optimal L0 solution.This is the major paper:http://statweb.stanford.edu/~donoho/Reports/2004/l1l0EquivCorrected.pdfThe first 2 pages present the matter very clearly and succinctly. The math is the ugliest I've ever read. One of Donoho's proofs is 15 pages for a single theorem!There is another aspect of it which I can't say how it fits in at the moment, compressive sensing by sampling at random intervals. This is an active area of research and the mathematics are rather painful to read. The gist of it is that if your samples are collected randomly aliasing does not take place and you only need about 10-20% of the number of samples required to meet the Nyquist criterion to achieve the same resolution. The ultimate example being the single pixel camera which substitutes a series of samples over time for spatial pixels. The monograph that I have is "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut which appeared in 2013. Since then there have been others, but Focuart and Rauhut appeared just at the time I stumbled into the subject of sparse L1 pursuits.http://statweb.stanford.edu/~donoho/Reports/2004/CompressedSensing091604.pdfIt's rather mind boggling.

author: tomato
author_rank: Regular Contributor
timestamp: June 11, 2018, 11:54:59 pm
content: Quote from: rhb on June 11, 2018, 11:46:27 pmTo a man with a hammer, everything looks like a nail ...

author: rhb
author_rank: Super Contributor
timestamp: June 12, 2018, 12:27:18 am
content: Quote from: tomato on June 11, 2018, 08:30:27 pmWhich part? Perhaps you would be so kind as to explain in more detail. I looked at the referenced slide that introduces "cyclostationarity" though I'm not convinced that the cited deviations from stationarity are in any way cyclical. I should think that requires additional proof. But an oscillation modulated by other oscillations does not seem implausible. I can list many potential causes. Not the least of which is device heating due to the changing current.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 12:39:00 am
content: Quote from: tomato on June 11, 2018, 09:54:53 pmYou seem to follow the "just try it and see what happens" school of design. That's fair. A lot of engineering, perhaps most, is done that way and I won't criticize it. But I am curious about the precise differences between various hobbyist oscillators; specifically their stability. That is why I am doing this project.In order to understand those differences I want to understand how established measures of oscillator stability relate to practical questions, such as "if I use this oscillator, what are the probable bounds of its jitter? Is it likely that the frequency of this particular oscillator will vary by 10 Hz, 100 Hz, 1 KHz over a 2 hour period (given some parameters such as temperature, power line ripple, ...)?" Without understanding how Allan variance relates to this question, why should I be interested in it?

author: KE5FX
author_rank: Super Contributor
timestamp: June 12, 2018, 12:48:40 am
content: Quote from: dnessett on June 11, 2018, 04:18:17 pmThink of the ADEV plot the way you would a phase noise plot, if you're more familiar with traditional PLL theory. To determine the best loop bandwidth for a given PLL, one common approach is to overlay the frequency-normalized phase noise plots of the reference source and the VCO being controlled. The point where they cross is usually the best choice of loop bandwidth, in the absence of any further constraints on the problem. ADEV works in the time domain rather than the frequency domain, but the same basic principle still applies.E.g., if you were looking to discipline a crystal oscillator with a rubidium standard, you might end up with a plot like this one. At taus below one second, the rubidium standard is noisier than the crystal oscillator. If you used a loop bandwidth much higher than 1 Hz, you would stabilize the crystal oscillator adequately but you would also lose its superior short-term noise performance. If you used a time constant much slower than that, though, there would be a big hump in the plot where the oscillator wanders around over intervals of a few seconds before being stabilized at longer taus. It will never be perfect, so your goal is to avoid corrupting the short-term performance while minimizing the hump. (You can see this optimization process at work in the plot of the rubidium standard by itself, in fact, since that's the exact problem its designers were faced with.)One of the points Rubiola raises in his book is that the reason we use ADEV is because true frequency-domain analysis was computationally difficult back in the 1960s. You can go from an FFT to an ADEV plot, at least in theory, but not vice-versa. Ideally, the problem outlined abovewouldbe solved in the traditional phase-noise crossover sense.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 12, 2018, 12:52:27 am
content: Quote from: dnessett on June 12, 2018, 12:39:00 amIt seems to me you are getting two distinct types of advice. One is to get heavily into the theory etc and the other is to just try it. In an earlier post you say:QuoteSo, the pragmatic approach seems a fair one. But, I can see that the phrase "I need...information on the stability of these two oscillators" can be taken one of two ways. Either "I need to find a way to differentiate between two oscillators so I can choose one" vs. "I'd like to understand *why* one oscillator is better and how to measure the particular parameters the explain it mathematically."Given all this and the fact that you have two oscillators to choose from (at least that's what seems to be the case), I'd do the pragmatic approach and the more rigorous/theoretical approach. It can be a valuable exercise since you can find surrogate measurements that are much simpler to make than the ones that strict adherence to the model would suggest.

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 01:10:42 am
content: Quote from: rhb on June 12, 2018, 12:27:18 amQuoteYou're missing the point. Your statement doesn't even scratch the surface.QuoteWhile (sort of) technically correct, this is not something that anyone would ever do. It would not yield useful information.QuoteThis is incorrect.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 01:39:45 am
content: Quote from: KE5FX on June 12, 2018, 12:48:40 amYou make many good points in this post, but you are focusing on oscillator design, not oscillator use. I wouldn't even think of designing an oscillator (other than, perhaps, a simple colpitts oscillator for some throw away project) because I am not an experienced oscillator designer and, more importantly, you can buy simple oscillator modules very cheaply (I just bought 7 10 MHz oscillator modules from Jameco for $10). My interest is using existing oscillators. So, as an example, I have both a 10 MHz Rubidium oscillator (an FEI FE-5650) and two 10 MHz ocxos (one using a Bliley module and the other an Isotemp module). I built the enclosures for them and for one designed a simple filter to turn the square wave into a sine wave (which doesn't work very well). However, the core oscillators are off-the-shelf.I bought the core oscillators on eBay. All were rescued from obsolete equipment and are probably 20 years old. That means they have aged. I would like to know how they compare to new core modules. Do they conform to the aging parameters in their data sheets? Has their performance degraded in a way that dramatically affects their jitter characteristics? I would imagine others might like to know this as well, since hobbyists rarely buy new rubidium or ocxo modules. Most, I would imagine, got them from eBay as I did.

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 01:43:08 am
content: Quote from: dnessett on June 12, 2018, 12:39:00 amAt this point, I have no idea what you're asking. Maybe you can be more specific about what you want to do and what you want to know.

author: KE5FX
author_rank: Super Contributor
timestamp: June 12, 2018, 01:54:47 am
content: Quote from: dnessett on June 12, 2018, 01:39:45 amWithout continuous monitoring you can't say much about the aging process, but you can certainly characterize the oscillators'currentperformance at both short- and long-term intervals. PN and ADEV are the core metrics needed for this.Ideally, the manufacturers of your used/surplus oscillators will have specified the performance in terms of Allan deviation, phase noise, or both. So all you need is a reference with known performance to compare them to, and the necessary instrumentation to make the measurements. Now you have the classic man-with-two-clocks problem, of course. There is a reason why my forum avatar is a rabbit seen in infrared light, as might be encountered by a well-equipped explorer in the twisty passages of a deep, dark hole.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:05:11 am
content: Quote from: tomato on June 12, 2018, 01:43:08 amSee my post to KE5FXhere.

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:26:38 am
content: Quote from: dnessett on June 12, 2018, 05:05:11 amKE5FX gave you the answer ... measure the Allan Variance.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:30:47 am
content: Quote from: KE5FX on June 12, 2018, 01:54:47 amTheFEI FE-5650spec does give information about phase noise and the Allan variance, but if I run tests on my aged unit and get a different Allan variance value, what does that tell me from a practical standpoint? That is, how would I use that information to make decisions?TheISOTEMP module specgives some information about phase noise, but nothing about Allan variance.I can't find the data sheet for the BLILEY module, although I thought I had found it once upon a time.Correcting the record: I got the BLILEY module from eBay, but the ISOTEMP module came with the AnalysIR OCXO board that I purchased on Tindie.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:32:43 am
content: Quote from: tomato on June 12, 2018, 05:26:38 amWe are going in circles. How does the Allan Variance tell me anything practical about jitter?

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:39:31 am
content: Quote from: dnessett on June 12, 2018, 05:32:43 amThat is whatit does.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 05:48:36 am
content: Quote from: tomato on June 12, 2018, 05:39:31 amLet's use a concrete example. The FEI FE-5650 spec gives an Allan Variance of 1.4*10-11/sqrt(t) when the unit is new. Using that number (if you need other information, the URL to the spec is in my post to KE5FX), tell me how to determine that the frequency of the unit will not vary by more than x% (you choose x) over a two hour period with a probability of p (you choose p).

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 06:02:53 am
content: Quote from: dnessett on June 12, 2018, 05:48:36 amIt can't be determined from their specifications, because they do not state the range over which 1.4*10-11/sqrt(t) is valid.

author: RoGeorge
author_rank: Super Contributor
timestamp: June 12, 2018, 08:01:16 am
content: Quote from: dnessett on June 08, 2018, 09:26:53 pmThose are very broad statements, especially when the time frame can be from ms to years. Also, there are some assumptions that might be irrelevant, or simply wrong, depending on the situation.You mentioned surplus oscillators, synchronize multiple instruments, square to sin conversion of 10 MHz, rubidium clock, and so on.What are you after? What exactly are you trying to do, or to achieve?What is your measuring setup? What exactly do you plan to measure with the given setup?

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 03:40:31 pm
content: Quote from: tomato on June 12, 2018, 06:02:53 amMake an assumption and specify how to do the computation. Right now the process is more important than the answer.

author: dnessett
author_rank: Regular Contributor
timestamp: June 12, 2018, 03:46:08 pm
content: Quote from: RoGeorge on June 12, 2018, 08:01:16 amThere are several messages in this thread that specify what I am trying to achieve. In summary I am trying to characterize the stability of several hobbyist oscillators in a way that is useful to an amateur.Quote from: RoGeorge on June 12, 2018, 08:01:16 amI am in the process of building the measuring setup at the moment. Right now I am waiting on some parts to arrive. I have a GPS disciplined 10 MHz oscillator that will serve as the reference clock coming to me from China, which will probably arrive at the end of the month or perhaps the beginning of next month.Added Later: I plan to start with a zero crossing detector feeding one of the analog pins of an Arduino development board. The Arduino will be used for interrupt processing and data accumulation. It will be controlled by a Raspberry PI that will act as the archiving system. I plan to use Octave (an open source MatLab clone) as the analysis engine. I have the Arduino (actually a Vellman VMA100 clone), the Raspberry Pi and the USB cables to connect them, but haven't integrated them together yet (I got the Vellman yesterday). I will communicate with the Raspberry Pi over ethernet to access the archived data for analysis.

author: tomato
author_rank: Regular Contributor
timestamp: June 12, 2018, 04:27:06 pm
content: Quote from: dnessett on June 12, 2018, 03:40:31 pmIt's probably safe toassumethat the Allan Variance is no worse than 1*10-11at 2 hours.

author: KE5FX
author_rank: Super Contributor
timestamp: June 12, 2018, 10:02:47 pm
content: When you see a sqrt(tau) expression in a specification for a long-term reference like an Rb or Cs standard, you can usually assume that it's valid between t=1s and the flicker floor. Essentially, they are giving you a limit mask in the form of a diagonal line with slope -0.5 on a log-log plot, suggesting that they expect the instability to be dominated by white-noise frequency variations.In that regard, the FE-56x0 models will resemble most other small telecom-grade rubidium standards:That sort of spec leaves out a few details -- for one thing, whereisthe flicker floor? In the blue trace above, the line bottoms out at what might be the flicker floor, but could also simply represent the onset of drift due to insufficient warmup time. However, the rudimentary ADEV spec would have met customer requirements at the time, and it may also reflect the limitations of the measurement setup the manufacturer had available.The plot above actually came from an eBay'ed FE-5680 with a ton of hours on it, so you can probably expect yours to perform about the same. As far as the error bars on "probably," that would be left as an exercise for the reader.Edit: FEI'sbrochureis actually pretty informative, check it out if you haven't already.

author: dnessett
author_rank: Regular Contributor
timestamp: June 13, 2018, 02:04:07 am
content: Quote from: KE5FX on June 12, 2018, 10:02:47 pmVery informative post, but I am still trying to figure out how to go from ADEV to something practical; specifically how much the frequency will vary over a specified time period according to some statement of probability. "Exercise left for the reader" presumes the reader knows how to execute the exercise. So far, no one has provided an algorithm (or process, if "algorithm" is too restrictive) to convert ADEV to such a quantity.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 02:24:55 am
content: My understanding re. ADEV is that it calculates the standard deviation of the oscillator's signal over different time intervals and plots those deviations as a function of the time interval. Why not just digitize the signal in the time domain and calculate the standard deviation over different time intervals, of, say, the interval between cross-over points? It's a trivial exercise to do that. Then generate the log-log plot from which you can fit straight lines to the pertinent parts of the plot and find the break points, too. There's a very powerful statistical method for the latter - CUSUM.Another option is cross-correlation, particularly multidecade. It basically achieves the same end result.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 03:08:02 am
content: Quote from: JohnnyMalaria on June 13, 2018, 02:24:55 amNo, it's not calculating standard deviations.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 03:32:14 am
content: Quote from: tomato on June 13, 2018, 03:08:02 amvariance = standard deviation squaredAllan -> measuring it as a function of time intervals. This is also how correlation functions are constructed except instead of calculating the expectation value of the square difference, correlation calculates the expectation value of the product C(tau) = <y(t).y(t+tau)> (auto- or cross-correlation).Even the man himselfsays it:Quote

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 03:47:04 am
content: Quote from: JohnnyMalaria on June 13, 2018, 03:32:14 amRead the sentence in bold. The Allan Variance is not calculating standard deviations.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 04:03:45 am
content: Look at the equation. LHS is sigma squared.The angle brackets are all important. You can't just do the 2-point difference once. It has to be done many times (hundreds or more) to reach the expectation value that Allan says. If you perform the calculation enough times then you'll get sigma2or sigma (which he calls the deviation). i.e., you are calculating variance/standard deviation. The only difference between the two is that there'll be a factor 2 difference in the gradient on the log-log plot.The reason you have to perform the calculation over many t (i.e., (y(t+tau)-y(t))2is because of the pseudo cyclostochastic nature of the signal (noise).It terms of practical calculation, it is so simple especially with a matrix-based language like Matlab or Python with Numpy. I perform autocorrelation of pseudo cyclostochastic photodetector signals. The only difference is calculating the product y(t+tau).y(t) instead of the square of the difference.In Python/Numpy, it takes just 8 lines of code.

author: dnessett
author_rank: Regular Contributor
timestamp: June 13, 2018, 04:29:34 am
content: Quote from: tomato on June 13, 2018, 03:08:02 amOne reason Allan came up with the Allan Variation is the traditional standard deviation of real oscillators diverges as the sample size increases.I began thinking about how to convert an Allan Variance/Deviation into a probabilistic bounds on frequency during a particular interval. However, it quickly became apparent that this is not a simple problem.The Allan Variance uses the average frequency, fi(measured in radians/sec), over an averaging interval tau. These are normalized by the nominal frequency to ensure the Allan Variances of oscillators with different frequencies, w0, are comparable. This normalization produces what is called fractional frequency data ffi= fi/w0. Suppose these samples are generated by a stationary process. Then the standard variance is simple to compute.However, the Allan Variance is a function of the differenced fractional frequency data: ai= ffi+1-ffi. It sums the square of these values and averages the sum (dividing by 2). The time series aiis autocorrelated. Now, it is possible for a stationary process to produce an autocorrelated series, but this is generally not the case. So, it is possible (likely) that airepresents samples from a non-stationary process. (Someone who is more knowledgable than I can correct me on this.) If so, the Allan Variance will not have the same properties as a standard variance. In particular, you can't use the Allan Deviation as you would a standard deviation from some pdf, defining probabilistic bounds based on it.However, I am not an expert on Allan Variance/Deviation, so maybe there is some way to use it to compute the desired bounds. This is what I have been asking for someone to explain in recent posts.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 04:39:15 am
content: Quote from: JohnnyMalaria on June 13, 2018, 04:03:45 amThere is no other way to say this -- you are wrong. The Allan Variance is not standard deviations calculated at different times. In simple terms, the standard deviation is calculated from the differences between data points and the mean of the data, whereas the Allan Variance is calculated from differences between data points separated in time. Those calculations are very different. Read one of the cited papers.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 04:45:28 am
content: Quote from: dnessett on June 13, 2018, 04:29:34 amYou're starting to get it. You just need to abandon the idea of computing probabilistic bounds ...

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 04:50:44 am
content: Oddly enough, I was just thinking about autocorrelation in the context of Allan variance. Iwasgoing to suggest that measuring the variance function and the correlation function could be very useful especially given the trivial algorithm required (also another driver for Allan since computing power wasn't powerful enough for anything more complicated).Specifically, the cyclic part of the process could be estimated by autocorrelation readily in the absence of noise but in the presence of noise it depends on the physical basis for the noise. If the noise is truly random (e.g., shot noise) then the calculated autocorrelation function will decay to zero within the first tau interval since there can be no temporal correlation for a truly random process. However, if the noise is due to a process akin to a random walk (e.g., Brownian motion) then useful information can be obtained by autocorrelation. The autocorrelation function will oscillate due to the periodic process and decay with a time constant related to the characteristic correlation time of the random process. e.g., large particles diffuse more slowly than for smaller ones and, hence, the characteristic correlation time (the decay constant) is longer for large particles. Indeed, autocorrelation is used extensively in light scattering techniques to measure the size of nanoparticles diffusing in liquids. Unlike the autocorrelation method, the Allan variance (or standard deviation) approach is appropriate for a truly random process.

author: dnessett
author_rank: Regular Contributor
timestamp: June 13, 2018, 05:01:55 am
content: Quote from: tomato on June 13, 2018, 04:45:28 amSo far all I get is that the Allan Variance/Deviation is for oscillator designers not oscillator users.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 05:03:29 am
content: Quote from: tomato on June 13, 2018, 04:39:15 amThat's EXACTLY the point I'm making and is born out in the equations I included and my emphasis about expectation values. I CLEARLY state that you calculate the difference between two points in time (y(t+tau)-y(t))2. Certainly not the standard deviation of the all the data points between t and t+tau. I also state that you have to do this many times. That's what the < > expressly mean.The algorithm to achieve this is trivial and actually faster than having to calculate standard deviations across many data points. It's identical to autocorrelation except that the latter uses the product of two points instead of the difference.What I am really struggling with is the OP says (I think - it's not clear) that they want to use whatever the standard way is to compare the stability of two oscillators and understand why they are different. Allan variance is that way, isn't it? Well, I know how to construct the Allan variance function from raw data in an extremely efficient way (I've been doing it for a long time for autocorrelation which uses the same basic algorithm).

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 05:43:45 am
content: Quote from: dnessett on June 13, 2018, 05:01:55 amIt's a general tool for characterizing oscillators. It's every bit as useful to users as it is to designers.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 06:05:00 am
content: Quote from: JohnnyMalaria on June 13, 2018, 05:03:29 amYou really need to read the cited papers. In particular, read section VI part D of the Rutman and Walls paper, and embrace Equation 10.QuoteThe standard algorithm for computing Allan Variances is actually very efficient.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 12:42:36 pm
content: I fail to see how my description is inconsistent with the equation Allan presents:How are these statements inconsistent with the equation?QuoteQuoteEither the equation he put in his own article is wrong or we are talking about two different things.

author: rhb
author_rank: Super Contributor
timestamp: June 13, 2018, 01:47:05 pm
content: I'd like to suggest a data acquisition arrangement amenable to simple equipment.On the 4 oscillators to be compared, attach 10 fast comparators (e.g ADCMP581), four to the zero reference and 6 pair wise among all the pairings. Multiply the GPSDO 10 MHz output to clock a fast ARM processor. The pair wise comparators will need to have the gain adjusted so that the amplitudes are as closely matched as possible. If matching proves problematic use two comparators per pair referencing the average of the two signals.At each sampling clock tick read the comparators and use those as the address of a counter in memory and increment that counter. At the i PPS tick increment the base address of the array of 64 counters.A potentially useful embellishment would be to add a comparator tracking a noise source and collect a second set of counts when the sample clock tick value of the noise source comparator is positive. That has the virtue that the random sampling precludes aliasing of harmonics produced by the oscillators but without requiring an antialias filter.Bendat & Piersol and Octave will take care of things from there with ease.After looking at the papers on cyclostationarity, I got the impression that's more a model for synthesizing noise in Spice than a model for analyzing clock data.

author: dnessett
author_rank: Regular Contributor
timestamp: June 13, 2018, 03:13:15 pm
content: Quote from: rhb on June 13, 2018, 01:47:05 pmI plan to do something simpler that what you propose. Use a zero-crossing detector on the oscillator output. Differentiate the zero-crossing detector output and clip the negative going pulse. That will give a pulse each time the oscillator has a positive going zero-crossing. Feed the output of the clipped differentiator into an analog port on the Arduino clone. Use code in the Arduino to count the positive zero-crossings. Set up that code to send the count to a Raspberry Pi when the averaging interval expires. Use the Raspberry Pi to store the data on flash memory. After the experiment is over, download the file of sample data to an analysis computer and process it using Octave (I could do the analysis on the Raspberry Pi, but using my main desktop machine is more convenient).

author: In Vacuo Veritas
author_rank: Frequent Contributor
timestamp: June 13, 2018, 03:26:10 pm
content: This hypothetical hobbyist would have more stringent demands than the folks at CERN or ITER...

author: dnessett
author_rank: Regular Contributor
timestamp: June 13, 2018, 03:35:44 pm
content: Quote from: tomato on June 13, 2018, 05:43:45 amYou keep making generalized statements without any supporting evidence.Here is a concrete example of oscillator use that illustrates why Allan Variance is probably not very interesting to, at least some, oscillator users. This example focuses on doppler radar.An amateur use of dopplar radar might be to track model drones in a drone air race. Doppler radar sends out signals at a specific frequency and receives reflected signals in which that frequency is shifted. The frequency shifts are processed and turned into estimates of the drones' velocity. It is important that the frequency source is stable, otherwise the velocity estimates will be erroneous. More to the point, the designer of the dopplar radar system wants to know the bounds on the frequency jitter of the source oscillator. From those bounds (which are probabilistic in nature, e.g., 99.7% of the oscillator frequency variation is between w0-b0and w0+b1), he can produce error bounds on the computed velocities.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.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 05:49:34 pm
content: Quote from: dnessett on June 13, 2018, 03:35:44 pmWhat would you consider supporting evidence? The fact that Allan Variance is used byeverynational standards lab in the world?QuoteYoucanderive "jitter bounds" from the Allan Variance. As per your previous post:QuoteThe reason it is not a simple problem is because the behavior of an oscillator is (in general) not simple. The non-simple behavior of oscillators is why the Allan Variance was developed. Stating that Allan Variance has no value in the above application is ludicrous -- abandoning it will not simplify the behavior of the oscillator. You can use a different analysis technique that more easily produces "jitter bounds", but those jitter bounds will be of limited usefulness. If you want meaningful results, you have to use the correct tools.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 05:54:24 pm
content: Quote from: JohnnyMalaria on June 13, 2018, 12:42:36 pmYou haven't read section VI, part D of the and Rutman and Walls paper, have you?I'm also guessing you have never worked with Allan Variances before?

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 07:01:28 pm
content: 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.

author: tomato
author_rank: Regular Contributor
timestamp: June 13, 2018, 07:11:14 pm
content: Quote from: JohnnyMalaria on June 13, 2018, 07:01:28 pmThe link was in an earlier post (#21?) by GerryBags.

author: DimitriP
author_rank: Super Contributor
timestamp: June 13, 2018, 07:30:08 pm
content: 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 1x10-6stable oscillator will be "off" 10Hz @10 MHz and 100KHz "off" @ 10GHz ;is that what you are looking for ?

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 13, 2018, 09:23:10 pm
content: Quote from: tomato on June 13, 2018, 07:11:14 pmThank 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 totoday's multichannel multiple tau USB single photon digital correlators.

author: rhb
author_rank: Super Contributor
timestamp: June 14, 2018, 12:06:30 am
content: This was a reference in one of the previous links. It's HP AN1289:http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdfI 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.

author: dnessett
author_rank: Regular Contributor
timestamp: June 14, 2018, 12:26:01 am
content: Quote from: DimitriP on June 13, 2018, 07:30:08 pmThe "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 1x10-6will 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).

author: rhb
author_rank: Super Contributor
timestamp: June 14, 2018, 12:58:57 am
content: 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.

author: KE5FX
author_rank: Super Contributor
timestamp: June 14, 2018, 02:27:56 am
content: Quote from: dnessett on June 14, 2018, 12:26:01 amHave 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.)

author: awallin
author_rank: Frequent Contributor
timestamp: June 14, 2018, 04:25:51 am
content: 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/colorednoisethe 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 welcomehttps://github.com/jleute/colorednoise/blob/master/example_noise_slopes.pySome 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 TICChttps://www.tapr.org/kits_ticc.htmlan alternative could be the digilent analog discovery which was used in a recent "sine-wave fitting ADEV" paperhttps://arxiv.org/abs/1711.07917cheerio,A

author: dnessett
author_rank: Regular Contributor
timestamp: June 14, 2018, 04:51:24 am
content: Quote from: KE5FX on June 14, 2018, 02:27:56 amI 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 ishere.

author: dnessett
author_rank: Regular Contributor
timestamp: June 14, 2018, 04:57:14 am
content: Quote from: awallin on June 14, 2018, 04:25:51 amEven though I am unconvinced of the practical usefulness of Allan Variance and its derivatives, I appreciate the links.

author: rhb
author_rank: Super Contributor
timestamp: June 14, 2018, 08:36:59 pm
content: 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

author: dnessett
author_rank: Regular Contributor
timestamp: June 14, 2018, 10:58:15 pm
content: Quote from: rhb on June 14, 2018, 08:36:59 pmEven more reading to do. Nevertheless, thanks for the link.

author: tomato
author_rank: Regular Contributor
timestamp: June 14, 2018, 11:09:59 pm
content: Quote from: dnessett on June 14, 2018, 04:57:14 amAll 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.

author: rhb
author_rank: Super Contributor
timestamp: June 14, 2018, 11:27:06 pm
content: Quote from: dnessett on June 14, 2018, 10:58:15 pmI 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.

author: KE5FX
author_rank: Super Contributor
timestamp: June 14, 2018, 11:57:47 pm
content: Also:Quote from: dnessett on June 13, 2018, 03:35:44 pmRadar 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.

author: dnessett
author_rank: Regular Contributor
timestamp: June 15, 2018, 12:41:25 am
content: Quote from: KE5FX on June 14, 2018, 11:57:47 pmAt 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).Quote from: KE5FX on June 14, 2018, 11:57:47 pmHere'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

author: KE5FX
author_rank: Super Contributor
timestamp: June 15, 2018, 01:12:56 am
content: Quote from: dnessett on June 15, 2018, 12:41:25 amIt 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 wasxmicroseconds 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 atthis articlefor 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.QuoteUnfortunately 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.

author: dnessett
author_rank: Regular Contributor
timestamp: June 15, 2018, 02:42:33 am
content: Quote from: KE5FX on June 15, 2018, 01:12:56 amI freely admitIdon'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.

author: dnessett
author_rank: Regular Contributor
timestamp: June 15, 2018, 02:54:49 am
content: Quote from: KE5FX on June 15, 2018, 01:12:56 amThe 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!

author: rhb
author_rank: Super Contributor
timestamp: June 15, 2018, 12:02:18 pm
content: 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.

author: dnessett
author_rank: Regular Contributor
timestamp: June 15, 2018, 03:18:52 pm
content: Quote from: rhb on June 15, 2018, 12:02:18 pmThe 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.

author: rhb
author_rank: Super Contributor
timestamp: June 15, 2018, 04:55:33 pm
content: 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://www.keysight.com/upload/cmc_upload/All/PhaseNoise_webcast_19Jul12.pdfhttps://publications.npl.co.uk/npl_web/pdf/mgpg68.pdfhttps://tf.nist.gov/general/tn1337/Tn190.pdfMeasuring phase noise is an interesting problem. I noticed in the NIST update to 140 that improvements in practice must await better phase measurements.

author: dnessett
author_rank: Regular Contributor
timestamp: June 16, 2018, 01:38:37 am
content: Quote from: rhb on June 15, 2018, 04:55:33 pmI 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 inradians2/Hz (corrected 6/16/180), not watts/Hz. It is aspectral density, but not apower 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.

author: Kleinstein
author_rank: Super Contributor
timestamp: June 16, 2018, 11:09:24 am
content: 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.

author: rhb
author_rank: Super Contributor
timestamp: June 16, 2018, 12:06:25 pm
content: I fixed the npl link. Sorry about that.Using the analytic signal (aka I/Q) is the way to go. And very easy to implement. A Tayloe detector is an obvious choice and will allow using a sound card for the ADC step. Input to the Tayloe mixer is the signal of interest and a square wave clock at 4x the frequency. Output is I & Q streams at baseband. Because the mixer harmonics are so far above the baseband, it's easy to suppress them.http://www.wparc.us/presentations/SDR-2-19-2013/Tayloe_mixer_x3a.pdfOr you could opt for an HPAK E4406A which provides I/Q complex plane displays. They're relatively cheap.http://literature.cdn.keysight.com/litweb/pdf/E4406-90304.pdfLook at the polar I/Q displays (e.g. p 122). However, you can do the same thing with any scope in XY mode and any quadrature mixer that produces I/Q output.A probability density plot of the I/Q plane collected using a DSO with deep memory would probably give you the information you're seeking.

author: dnessett
author_rank: Regular Contributor
timestamp: June 16, 2018, 04:46:15 pm
content: Quote from: Kleinstein on June 16, 2018, 11:09:24 amA simple way to obtain fractional frequency data is to count the number of zero-crossings in an averaging interval measured by a reference clock. This is one technique used early in measuring oscillator stability and it is the first thing I plan to do. However, thinking about this last night has raised some issues that I think may prevent the use of this data to determine phase noise. Since some reading this thread are not familiar with stochastic processes, I am going to do this slowly with some tutorial information. Those familiar with stochastic process can skip over the next 5 paragraphs.Restating the basic equation for a real oscillator:v(t) = [V0+ e(t)] * cos[w0*t + phi(t)]Both e(t) and phi(t) are stochastic processes (see this post). Assume for the moment that these are stationary processes (if not, things get worse) and concentrate on phi(t). The mathematical framework for stochastic processes presumes that for any constant value of t, say t=ti, phi() is a random variable. Its pdf has moments, such as its mean and variance. In order to estimate these (we are speaking about phi(t=ti) here), you would have to sample the random variable several times and compute the estimate according to its defintion. For example, to compute the mean of phi(t=ti), you would sample it N times, summing the values and dividing by N.But, that isn't possibile in reality. You can only sample this random variable once, since it only is accessible at t=ti. To sample it more than once, you would have to travel to N parallel universes in which the random variable exists and obtain N samples that way (something that is obviously impossible according to currently validated physical theories). The standard terminology for the moments of phi(t=ti) is its ensemble moments (e.g., ensemble mean, ensemble variance).Instead of sampling the same random variable over and over again, you can sample phi(t) at different times, e.g., sample phi(t=ti), then phi(t=ti+1), .... If you obtain N such samples you can treat them as if they came from the same random variable and compute moments. So, you can compute the mean by adding the values returned and dividing by N. These moments are called time moments (e.g., time mean, time variance).But, what can you do with these moments? It turns out if the stochastic process is ergodic, then the time moments equal the ensemble moments. All ergodic processes are stationary, but not all stationary processes are ergodic. So, in order to use this technique to estimate ensemble moments, you have to show the stochastic process is ergodic.OK, enough tutorial material. The first question is: do practical oscillators represent erodic processes? I have seen it stated in several places that their associated processes are stationary, but I have not seen anywhere that they are ergodic.The second question centers on the relationship between instantaneous frequency and instantaneous phase, f(t)=d/dt[phi(t)]. What does this mean when phi(t=ti) is a random variable? Not clear. In order to compute the derivative, you have to take the limit as h->0 of [phi(t+h)-phi(t)]/h. But this usually presumes phi(t) is a continuous function in the vincinity of t. Random variables are not functions in this sense. They return different values each time they are "accessed", so I don't know how to compute this derivative.The third question relates to the averaging of(corrected 6-16-18) instantaneousfrequency during the zero-crossing counting process. The result is an average of the instantaneous frequency over the averaging interval. I don't know how to use this to get the average phase angle during the same interval. Someone more knowledgable(corrected 6-16-18) thanI will have to provide an argument (either for or against) that the derivative of a random variable average equals the average of the random variable derivative (what ever that means). Specifically, (using <> to indicate the mean of a random variable): d/dt[<phi(t)>] = <d/dt[phi(t)]> = <f(t)>.The fourth question is, even if the last equation is true, how is phi(t) obtained? Normally, you would integrate d/dt[<phi(t)>] to get <phi(t)>. But, d/dt[<phi(t)>] = <f(t)> is a single number, not a function or even a set of values that you can sum to derive an estimate of the integral.In summary, it seems to me you can't derive the average phase angle over a sample interval when you have measured the average frequency over that same interval. However, I would be happy to be disabused of this opinion.

author: Kleinstein
author_rank: Super Contributor
timestamp: June 16, 2018, 05:16:58 pm
content: Calculating the derivative is a linear operation. So one can interchange the averaging and derivative. So d/dt[<phi(t)>] = <d/dt[phi(t)]> = <f(t)> should be OK.If phi(t) is a random variable this means, there is a kind of random part added (that is at least the easiest assumption - a factor does not make much sense with a phase angle) to it. However in close to reality model the random part can not be arbitrary but would be assumed to be a well behaved function too, so there can be derivative of the random part too. So one it likely in a case where e(t) and the similar random phase error will not the pure white noise, and thus no independent numbers for different times.Anyway the phase is not sampled at infinite fine time steps, but at a much slower sampling rate. So the process is more like a discrete time series more than a continuous stochastic process.

author: JohnnyMalaria
author_rank: Super Contributor
timestamp: June 16, 2018, 06:05:09 pm
content: If the period of the phase noise is sufficiently "stable" over a 100+ periods of the oscillator (or less if other random noise is sufficiently small) and you obtain the IQ pair from multiplication then you can use can construct thephase structure function. It will tell you the mean amplitude of the phase oscillation and its frequency.Milleret al, J. Coll. Int. Sci., 143(2), May 1991, Pages 532-554

author: rhb
author_rank: Super Contributor
timestamp: June 16, 2018, 06:30:06 pm
content: QuoteIn general, oscillators are not ergodic. They *are* if and only if they are constant amplitude. c.f. Bendat & Piersol example 5.11 pp 144-145 3rd ed.QuoteRandom processes are continuous except perhaps for some pathological examples."the periods of the communications engineer are always more or less periods, never precise periods and therefor have absolutely continuous spectra" c.f. "Extrapolation, Interpolation and Smoothing of Stationary Time Series", N. Wiener, p 59. This appeared in public in 1949, but was written in 1941 and is famously known as "the yellow peril" because of the density of mathematical exposition and the yellow covers to denote that it was classified.I'm still pondering question 3.QuoteConsider a perfect sine wave in analytic form in the I/Q plane. This traces a circle. The instantaneous phase error is the deviation of the physical trace from circularity.c.f. "The Fourier Transform and Its Applications", R. Bracewell, 2nd ed 1978, pp 267-272Edit: Edit 2: c.f.https://www.markimicrowave.com/blog/top-7-ways-to-create-a-quadrature-90-phase-shift/Edit 3: Brain fart correction. Two sine waves at 90 degrees form a circle.Edit 4: Cyclostationarity can be evaluated by examining the PDF of the sine wave and itself shifted 45 degrees.In sum, the best way to evaluate the short to medium term behavior of an oscillator appears to be with a pair of delay lines cut to 45 and 90 degrees of 10 MHz using a DSO to acquire data and then render the data as a probability density function over different time intervals.

author: dnessett
author_rank: Regular Contributor
timestamp: June 16, 2018, 08:49:03 pm
content: Quote from: Kleinstein on June 16, 2018, 11:09:24 amOriginally I thought it would be simple to count zero-crossings for a 10 MHz signal using an Arduino Uno clone. However, I didn't spend enough time thinking it through. My plan was to generate an interrupt on the Arduino each time the signal crossed-zero in a positive direction. However, the Arduino Uno has only a 20 MIPS processor, which means between two positive zero-crossings it could only execute 2 instructions. Obviously, this is insufficient to service the interrupt train that would be generated by my simple design. So, now I have to enhance the simple design I envisioned with an 8-bit counter (to increase the interrupt servicing period from 100 ns to 25.6 us), a 4x frequency multiplier (to generate the clock required to dump the processor into a register for later reading by the Arduino), logic to dump the counter without interrupting the zero-crossing processing, logic to allow the Arduino to command the device to dump the counter, read the dump register, etc. This will be fun project, but it will take some time.Before getting deeply into Allan Variance, I bought an evaluation board for a AD8302, which compares two signals and returns the phase difference between them encoded as a voltage between 0 and 1.8v. It is sitting on my workbench. Perhaps I will start playing with it while I design the zero-crossing logic in order to get a feel for the phase noise side of the problem.

author: dnessett
author_rank: Regular Contributor
timestamp: June 16, 2018, 09:37:04 pm
content: Quote from: rhb on June 16, 2018, 06:30:06 pmIf oscillators are not ergodic, then how is it valid to characterize them with time moments such as the Allan Variance?Quote from: rhb on June 16, 2018, 06:30:06 pmI just looked at Wikipedia's article on continuous stochastic processes (I know - Wikipedia isn't normative. But it generally provides the correct idea about a subject, unless its politics). There are several definitions of stochastic process continuity, all of which utilize the notion of "continuity in probability". This is not the sort of continuity that is used when defining a derivative such as d/dt[phi(t)].It seems that the calculus of stochastic processes is very different than the normal calculus, utilizing something called theIto Stochastic Integral. I think it would be very dangerous to suppose the ideas of normal calculus transparently transfer to this new type of calculus.

author: rhb
author_rank: Super Contributor
timestamp: June 16, 2018, 10:55:30 pm
content: If over a sampling period, the variation is rapid and random, then *over a period at least as long* it may be considered ergodic. One can, however, get into trouble if the sampling interval is correlated with the amplitude variations. That's why I have repeatedly suggested sampling randomly.I'm not a time nut. I am a general data analyst which is rather broader. I have never had justification for digging into the details of Allan variance. I have less than a metrology lab technician knowledge of the subject. And no real inclination to go farther in that direction at present. The transfer functions of AVAR, MVAR and TVAR, make clear what those do to allow making an assumption of ergodicity. This is why they implement bandpass filters over the frequency spectrum for which that is not applicable. There are better methods, but they were to compute intensive to employ when Allan derived his metric. It continues in use because it serves horological purposes as is generally well understood in that community.Reality is continuous above the quantum level. I was taught everything in the context of a Wiener process. The rest is just mathematicians trying to clean up the theoretical details to match experience. In practice I have never encountered an instance where ordinary calculus was not sufficient. Yes, it is true that the conditions of ordinary calculus may not be met, but it doesn't matter. So far as I can see, all the exotic integrals are of necessity backward compatible with the traditional integral of Newton and Liebniz. At a quantum level I suspect that it gets a bit tricky in places.FWIW I have a book which consists entirely of theorems related to the Fourier transform. Almost always they do not matter. But sometimes they do, and for that reason, I have the book on my shelf. I can't actually recall ever using but once. As I recall it did not help. My problem was the result of failing to recognize that the discrete Fourier transform is defined over the semi-closed interval [a,b). I was being OCD and performing arbitrary resampling via FFT and encountered a phase error I could not understand. It was a *very* long couple of weeks figuring that out and fix my code. I have subsequently examined a number of texts in that regard, and cannot recall any that mentions it directly. It is implied by the periodic nature of the discrete transform. If the interval were not semi-closed, an end value would repeat once a cycle.I've attached the reference from B & P.

author: dnessett
author_rank: Regular Contributor
timestamp: June 17, 2018, 12:15:21 am
content: Quote from: rhb on June 16, 2018, 10:55:30 pmThanks for the B & P extract. I should receive my copy sometime this week.

author: rhb
author_rank: Super Contributor
timestamp: June 17, 2018, 02:53:23 am
content: I'm afraid you have made me rather unhappy. As a consequence of this thread I set up my Keysight 33622A and 3104T to plot Lissajous figures. Along the way I discovered some rather mind boggling faults with the 3104T, such as not being able to set cursors except by using the touch screen arrows and waiting while the cursor crawls across the screen a pixel at a time or direct entry of the cursor location. If I knew that I wouldn't need the cursor!The 33622A claims a <1 pS jitter for square waves, but with CH1 & 2 coupled and producing a 20 MHz sine wave, there is a 1.2 degree phase offset and the narrowest line I can get on the screen looks as if it were drawn with a magic marker. At 10 MHz the phase offset is 0.7 degrees. I plan to have a conversation or two with Keysight on Monday.

author: dnessett
author_rank: Regular Contributor
timestamp: June 17, 2018, 04:14:32 am
content: Not being an expert in stochastic theory, I could not figure out how to define the derivative of a stachostic process. After poking around a bit, I found this defintion (seehere, slide 7):Suppose <[(phi(t+h)-phi(t)/h)-phi'(t)]2> -> 0 when h->0, , where <> is the expected value of the complicated stochastic process [(phi(t+h)-phi(t)/h)-phi'(t)]2. Then the stochastic process phi'(t) is said to be the derivative of phi(t).Note the significant differences between this definition and the definition from the traditional calculus. Two features stand out: 1) first the difference between (phi(t+h)-phi(t)/h) and phi'(t) is squared, and 2) instead of the expression (phi(t+h)-phi(t)/h) converging to phi'(t) as h -> 0, the expected value (first order moment) of the(corrected 6-17-18) squareddifference goes to zero.Applying this to the equation d/dt[phi(t)] = f(t), where phi(t) is the instantaneous phase angle and f(t) is the instantaneous frequency, it must be the case that:<[(phi(t+h)-phi(t)/h)-f(t)]2> -> 0 when h->0However, there is nothing in this definition that suggests how to compute phi(t) given f(t). As far as I know (and I freely admit my knowledge of this topic is rudimentary), there are no differentiation rules like d/dt[sin(t)] = cos(t). So, even if f(t) was known exactly for all values t, there would be no obvious way to integrate f(t) to derive phi(t).More prominently, if I have an estimate of the averaged instantaneous frequency over some averaging interval, this definition doesn't provide a way to integrate f(t) to get phi(t). The basic problem is I have <f(t)> over the averaging interval, not f(t).

author: rhb
author_rank: Super Contributor
timestamp: June 17, 2018, 06:38:18 pm
content: Quantum mechanics was developed by physicists, not mathematicians. The physicists used the mathematical tools with which they were familiar. I'm certain some recognized that they were violating the requisites of traditional mathematics, but physical experiment proved that doing so was valid. This forced the mathematicians to develop the theory to match reality.It took about 100 years to develop mathematically rigorous proof of the Fourier transform. They managed Heaviside operational mathematics a bit quicker; it only took about 40-50 years to dot all the i's and cross all the t's for that.This has proven to be a very interesting thread, especially having disposed of Allan variances from the discussion. The ideal solution to the measurement of phase noise is an analog correlator, but that is at best awkward as it requires a large number of delay lines.My intuition leads me to expect that there exists a sampling technique which will solve the problem, but a proper statement still eludes me. I can merely note that the interchange of order of addition is a very powerful tool.

author: dnessett
author_rank: Regular Contributor
timestamp: June 17, 2018, 07:26:27 pm
content: Quote from: rhb on June 16, 2018, 10:55:30 pmTo understand what your saying I need to make sure we are using the same terminology. From what I have read the sampling process for oscillators is driven by 3 variables, tau, T and N. tau is the averaging period for a single datum. So, for example, if I count zero-crossings for 1 second and divide that count by the oscillator nominal frequency, I get a fractional frequency datum. T is the time between the start of one averaging period and the next. If the next averaging interval does not start immediately after the present one, then there is dead time in the sampling process and the duration of that dead time is T-tau. Finally, the signal is sampled N times to get the data for analysis. N*T is the sampling interval.So, when you say "the sampling interval is correlated with the amplitude variations" do you mean the averaging interval, the T interval or the sampling interval as specified in the previous paragraph?In any case, I want to restate in more detail your comment to ensure I understand it correctly. Basically, if the average/sample interval (whichever is the correct one) is "short enough" so that variations are approximately random, then people assume the underlying process is ergodic. Is this correct? How do you determine what interval is "short enough"? Are there tests that might be applied to sample data that indicated whether the variations of import are random enough?Once you have indicated which interval you mean by "sampling period", would you elaborate your recommendation to "sampling randomly"? How randomly? Should I introduce dead time into the sampling process (note, this is generally disparaged by what I have read so far) and if so, how would you characterize the length of the dead time? Also, would this tactic apply to both frequency measurements and phase angle measurements?Quote from: rhb on June 16, 2018, 10:55:30 pmOK. But, we are dealing with random variables, not deterministic functions, so the traditional calculus doesn't really make any sense. That said, after reading more about stochastic derivatives, this stuff gets real complicated real fast, so I don't think I am interested in going down that route. I think the equation d/dt[phi(t)] = f(t) is valid (using normal calculus) when phi() and f() are deterministic functions. However, I am now convinced that it makes no sense when d/dt represents a stochastic derivative. Perhaps there is a way of translating the deterministic differential equation into a stochastic differential equation, but I think continuing to explore this avenue of investigation would take too much time and effort. From a measurement point of view, I will just measure both and not try to convert frequency data into phase noise data.

author: RoGeorge
author_rank: Super Contributor
timestamp: June 17, 2018, 09:00:11 pm
content: Judging by the radar problem and the time sampling/counting approach mentioned before, I think you need to lookupthe random walk problem, like in: We have 10MHz osc with its (white) phase noise, and want to know the random distribution of the 10th's million rising edge.How would it be the 10th million rising edge probability distributed around the ideal 1 second mark?Is this what you are looking for?

author: rhb
author_rank: Super Contributor
timestamp: June 17, 2018, 09:58:21 pm
content: This is one of those things which is a lot easier to discuss in the office drawing on the white board.You wrote "short" for where I wrote "long".Let's take a concrete example using thermal noise and current noise in a resistor produced by a 60 Hz AC current. We shall assume the resistor is at ambient temperature before the current is applied.The current noise will rise and fall exactly in phase with the current. The thermal noise will will increase and decrease at the same frequency, but with a lag related to the magnitude of the current and the thermal mass of the resistor. The thermal noise will also show an increase related to the ratio of the heating and the radiation and conduction fluxes.If we sample the noise at regular intervals of say 600 samples per second, the series will *not* be ergodic. The amplitude of the noise will rise and fall at 120 Hz and in addition there will be a lower frequency component related to the change in thermal noise as the device warms up. Once the resistor reaches a thermal equilibrium state, there will be a constant level of thermal noise upon which is an additive 120 Hz current noise. If we take an ensemble average at the zero crossings, it will *not* be the same as an ensemble average taken at the peak. It will be stationary, but not ergodic.However, if we calculate the mean and deviation over many cycles, then we will obtain the same result when we compare an ensemble and a single record. The requirement is that the contribution from any fraction of a cycle in the be small relative to the variance of the noise.Or put differently, if we use a small ensemble and compare the result to a time series of similar length the data will not be ergodic. But if we take a large ensemble of millions of instances all of random phase and compare that to a time series of equivalent length they will be ergodic.I'd supply an example using Octave at this point but I'd have to start up a VM and remember how to use it. In the last 5-10 years it has become less Octave like and more MATLAB like. The syntax changes are small and subtle, hence quite frustrating when encountered. Moreover, it's a tool I rarely use now. But create a sinusoid and a Gaussian random process and analyze the product of the two. That's the current noise term in the preceding exposition. Examine the Fourier transform of the full series. Then compute mean and variance for windows of increasing length starting with 3 samples. The mean and variance of the short consecutive windows will vary over time. As the windows get longer, the variance of the mean and variance will decrease and will reach a constant value.I just took a look at B & P to see if I could find a succinct quote, but it's rather densely mathematical. Your questions are treated in exquisite detail in some of the best mathematical prose I have ever read. While it will be tempting to just dive in, read the part of particular interest and go on, I urge you to take the time to give the entire text a quick read. Don't labor over it or work problems. Just read it through. If you have questions post or send me a PM. I feel confident that you will discover by the end that most of the book is quite familiar and that the only real difference between what you know already and "stochastic" processes is lexical.Returning to the question of how to characterize a set of precision oscillators, how to determine which is "best" and what the proper criteria for "best" is for a frequency reference is quite interesting. My adventures in the mathematics of sparse L1 pursuits taught me a number of new stratagems for solving problems using sampled data.I've attached a few more pages from B & P which should keep you entertained for at least a day or two. It's the part on derivatives and level crossings. I've not read it thoroughly, especially the zero crossing part. I took two semesters of integral transforms under Bill Guy and one semester of linear systems under Clark Wilson at Austin before I ever encountered B & P, so I've never actually read it straight through. It simply superceded several other texts I had been using. I never took courses in either linear algebra nor probability, so I had to learn those on my own.

author: dnessett
author_rank: Regular Contributor
timestamp: June 17, 2018, 11:00:10 pm
content: Quote from: RoGeorge on June 17, 2018, 09:00:11 pmThis may sound a little (or very) stupid, but I don't know what I am looking for. Or to be more precise, I am looking for guidance from those who use oscillators in applications to specify the characterizing parameters that are important to them. If I am going to spend a good deal of time and effort analyzing some oscillators, the last thing I want to hear when I publish the results is: "who cares about the parameters you measured. You should have measured these things."I have thought of another application, the engineers of which might be interested in the stability of a component oscillator. Frequency hopping spread spectrum radios need to control the power emitted in bands not occupied by their frequency channels. This is likely true for direct sequence spread spectrum as well, but it is obvious for frequency hopping. Leaking signal power into bands outside their assigned channels both reduces their efficiency and increases the potential for interference.If they use a base oscillator to drive frequency synthesizing modules to generate the channel frequencies, it would seem to me they would be interested in how clean is its output in regard to phase noise and frequency fluctuations. So, for any out there who have designed spread spectrum radios (or those who are familiar with this technology), what oscillator parameters are important when considering the selection of such an oscillator?

author: DimitriP
author_rank: Super Contributor
timestamp: June 18, 2018, 09:56:47 am
content: QuoteYou might just have to contact the guy at match.com. They claim to be experts at doing this exact thing.To asnwer your question: Best stability and phase noise for a given working voltage and power consumption in a size that fits and doesn't cost an arm a a leg. Depending on what you are building and who is paying for it.

author: rhb
author_rank: Super Contributor
timestamp: June 18, 2018, 01:27:11 pm
content: QuoteThere are 4 unknowns in this equation. If one compares the voltages of 8 oscillators in a pair wise fashion for all 32 permutations one has an even determined system of equations. I *think* that by counting the number of times each permutation exists at random times over periods of several cycles one can solve for all the variables without having to assume the availability of a perfect reference.The random sampling is important as it precludes aliasing taking place. Mathematically this is rather exotic, at least for me, so there may be complications I've not spotted yet. It would be *very* interesting to know if there is anything in the professional literature related to this. I only became aware of the anti-aliasing properties of random sampling recently. In many applications one still needs a precise reference clock to record the time of the samples. But in this case, I think simply counting states will suffice.

author: dnessett
author_rank: Regular Contributor
timestamp: June 18, 2018, 04:05:47 pm
content: Quote from: rhb on June 18, 2018, 01:27:11 pmSeeA method for estimating the frequency stability of an individual oscillator. This technique uses triads, not pairs. It is the basis for the so-called "three corned hat" oscillator stability measurement technique described in section 10.14 ofThe Handbook of Frequency Stability Analysisput out by NIST.

author: dnessett
author_rank: Regular Contributor
timestamp: June 18, 2018, 11:01:03 pm
content: I decided to get some experience measuring phase delay between two oscillator signals. The oscillators I chose were my FEI FE-5650 and Rigol DG1022 set to 10 MHz. I connected these two oscillators to the AD8302 evaluation board I purchased and looked at the VPHS signal it generates. This output ranges from 0 to 1.8V and is interpreted as follows: 1) phase difference of 180 degrees - 30 mV; 2) phase difference of +/- 90 degrees - 900 mV; 3) phase difference of 0 degrees - 1.8V. VPHS tracks the phase differences with an advertised bandwidth of 30 MHz.I am posting these results in this thread because they relate to the questions I have been asking. However, I would understand if some felt this is off-topic (the thread started out as an advanced question related to cyclostationarty - asking questions about measurement techniques and results isn't implied by that subject. I will move it to new thread if people want me to.)Figure 1 shows an oscilloscope trace of the raw VPHS signal. There is a prominent crossing point at ~900 mv, which suggests the two signals are frequently in quadrature alignment. However, there is also a lot of fuzz in the envelope between 0 and 1.8V, so it is hard to tell how much time is spent in this state.Figure 1 -Figure 2 shows the signal over a ~25 us interval. If you look closely there are prominent crossings about 1/4 from the left of the trace and about 7/8 from the right of the trace. These appear to be the regular appearance of the quadrature alignment points shown in detail in Figure 1.Figure 2 -Figure 3 shows the same signal with cursor measurement data. The time difference between the two quadrature points is ~16.2 us, which corresponds to ~61.7 KHz. The voltage difference between top and bottom is 1.95V, which seems reasonable assuming some overshoot due to impedance mismatching between the coax and the input to the AD8302 (coax is terminated by 50 Ohms and AD8302 inputs are roughly 3 Kohms input impedance).Figure 3 -Figure 4shows the power spectrum of the VPHS signal. I have a SIGLENT 3021X with its input connected to a 10 dB pad. Furthermore, I was using a high impedance scope probe to tap the VPHS output and the SIGLENT input impedance is 50 Ohm, so the dBm values are not faithful. The important informaton from the SA plot is the shape of the spectrum and the fact that it reaches the noise floor at around(corrected later:) 80 Hz.(added 6-19-18) I disconnected the scope probe from the SA and discovered that the spectrum remained unchanged. So, figure 4 seems to display an a SA noise floor plot for frequencies between 0-100 Hz. In my enthusiasm I forgot that the SIGLENT is speced for frequencies between 9 KHz and 2.1GHZ. It isn't intended for frequencies in the audio and sub-audio range. I'll leave the image as a reminder that one shouldn't get all excited and forget to do basic things, such as checking the noise floor of a SA or using it for purposes for which it was not designed.Figure 4 -So, why am I posting these results - easy, to get some input on interpreting them. It isn't clear why the two oscillators would have a prominent quadrature alignment at 61.7 KHz. I looked at the phase difference power spectrum out to 100 KHz and found nothing prominent at 61.7 KHz or at any other frequency greater than(corrected later:) 80 Hz.I am not sure whether it is valid to use results such as these to compute a phase noise plot. Eventually, when it arrives, I will have a GPS disciplined reference clock to use as the standard against which to analyze the other oscillators (using the Rubidium now is just a way to get some experience, it is not what will be used when I start characterizing the oscillators in earnest). So, I don't expect to produce a valid phase noise plot from this data. However, I would be interested in ideas suggesting how to turn the power spectrum of the phase difference signal into a phase noise plot, if that makes sense.I was hoping to develop the procedure I will eventually use to produce phase noise plots by playing around in this way. (NB: I plan on using the VPHS signal as the input to an Arduino analog pin and then using the onboard Arduino ADC to convert the signal level to digital data. The internal ADC can produce data at about a 10 KHz rate. In this way I will have a digital record of the VPHS signal that I can use for analysis.).Any constructive comments are welcome.Added later:I had an epiphany about the 61.7 KHz signal embedded within the phase difference data. When I bought the FEI FE-5650, I built an enclosure for it, with leds indicating power and oscillator lock. I couldn't get the oscillator to lock, so I contacted the vendor from whom I bought the device. After a bit of back and forth, I finally noticed a 60 KHz pulse train superimposed on the power supply voltage coming from the cheap power brick I had bought. I put an appropriate bypass capacitor on it and the FEI FE-5650 successfully locked. My guess is that while the bypass decreased the amplitude of the power supply ripple, it did not eliminate it completely, and somehow it is leaking into the phase difference data.Here is a nice example how oscillator implementation can create problems when using them in applications.

author: rhb
author_rank: Super Contributor
timestamp: June 19, 2018, 12:25:46 am
content: For a sanity check, put a scope in XY mode and display the Lissajous figure. I was doing that at 10 MHz with an 8648C with the OXCO option and a 33622A yesterday. Also measure both frequencies with the same counter.As for the paper you referenced earlier, that only addresses FM noise. It's using the Allan variance, so low frequency phase noise is being excluded by design.I don't think one can say that an oscillator is *best* without stating an application.

author: dnessett
author_rank: Regular Contributor
timestamp: June 19, 2018, 12:44:49 am
content: Quote from: rhb on June 19, 2018, 12:25:46 amI tried this, but the Lissajous figure wouldn't slow to a point that it was recognizable.Quote from: rhb on June 19, 2018, 12:25:46 amNo argument from me. However, it should be possible to come up with a list of characteristics (e.g., phase noise, some measure of short term stability (not Allan Variance), ...) that when measured would provide the necessary information for an application engineer to choose one.

author: rhb
author_rank: Super Contributor
timestamp: June 19, 2018, 02:05:22 am
content: Quote from: dnessett on June 19, 2018, 12:44:49 amThat *should* have told you something. It took a lot of fiddling with the frequency of the 33622A to get a slowly (360 degrees in 5-20 seconds) Lissajous figure. It proved very difficult to get the frequencies matched, but I did not resort to warming up the counter and using that to set them both. I'll try that next time.

author: tomato
author_rank: Regular Contributor
timestamp: June 19, 2018, 02:06:01 am
content: Quote from: dnessett on June 18, 2018, 11:01:03 pmThe method you're experimenting with will rarely produce useful results with low performance oscillators unless they are phase locked together (or frequency divided) so they do not slip cycles.

author: dnessett
author_rank: Regular Contributor
timestamp: June 19, 2018, 02:34:56 am
content: Quote from: DimitriP on June 18, 2018, 09:56:47 amBest stability measured by what metric?

author: DimitriP
author_rank: Super Contributor
timestamp: June 19, 2018, 05:35:28 am
content: Quote from: dnessett on June 19, 2018, 02:34:56 amWhen going window shopping I look at published specs.This one is 0.1ppb and it's just under $1800 (so just an arm, you get to keep the leg ), and if you need more that three, you gotta wait 17 weekshttps://www.digikey.com/product-detail/en/abracon-llc/AOCJY6-10.000MHZ-1/535-11919-ND/3641391

author: rhb
author_rank: Super Contributor
timestamp: June 19, 2018, 03:26:08 pm
content: I've got my 8648C and 33622A within 0.01Hz which as close as I can adjust the 33622A. So it takes a minute or two to go through a complete cycle. I can see the Lissajous figure "breathe" as it rotates slowly. So phase noise close in is clearly visible. The "breathing" is at 0.1-1 Hz. However, I have no way of knowing if it's real or an artifact of the DSO timebase.I'm going to look into setting up my GPSDO. The first task is to decide where to mount the antenna and how to bring the coax into the house. The 8648C has the high stability timebase option, but the 33622A does not.If the GPS antenna installation proves troublesome, I'll reference the 33622A to the 8648C for a few tests.

author: dnessett
author_rank: Regular Contributor
timestamp: June 19, 2018, 07:40:02 pm
content: Quote from: DimitriP on June 19, 2018, 05:35:28 amI looked at the detailed spec and a frequency stability of +/- 0.1ppb seems to be an aging factor; specifically, +/- 0.1ppb per day. (There is no frequency stability figure given in the detailed spec.) Also, phase noise values are given for 1, 10, 100, 1K, 10K and 100K Hz. You didn't mention them. So for the application you had in mind, are you saying the phase noise data isn't a factor and frequency stability means for you the upper limit on frequency drift per day?What application did you have in mind when responding?

author: dnessett
author_rank: Regular Contributor
timestamp: June 19, 2018, 08:10:08 pm
content: Quote from: rhb on June 19, 2018, 03:26:08 pmI looked at the specs for the 8648C and 33622A. The former gives a frequency stability of 3*10^-6 * carrier frequency and an aging factor of +/- 2 ppm/year and +/- .0005/day. The latter specifies a combined stability/aging value of +/- (1ppm + 15 pHz) * carrier frequency over a year period.These are very precise units with a concomitant price tag. On eBay, a used 8648C is advertised for $2,555 and a 33622A for $3,373. If people want to invest in this class of equipment, that's great. Either of these units could be used to generate the reference signal against which DUT oscillators are measured.But, I am more interested in getting as much information as possible from more affordable gear. So, I will use a $89 GPS disciplined 10 MHz oscillator as the reference signal and the other oscillators will be measured against it. Both the reference and DUT oscillators will be fixed frequency units (with the exception of the Rigol 1022, which will be one of the DUT oscillators); there is no way to adjust their frequency to get a Lissajous figure.My objective is to develop or use already developed techniques to measure phase noise and fluctuations with fixed frequency oscillators. I'm not saying your approach is wrong; it may be better. But, it is not a path available to me.

author: rhb
author_rank: Super Contributor
timestamp: June 19, 2018, 10:12:19 pm
content: I got my 8648C for under $1k, but I paid Keysight's eBay store about what you quoted for the 33622A.I'm *not* interested in measurement methods that require that level of equipment. I'm interested in what can be done on the cheap. I only used them because *I* don't have two OXCOs and a Rb reference to use as signal sources. ;-)Besides which, I'm measuring them with a cheap Chinese DSO. I happen to have my $1700 MSO-2204EA hooked up at present, but I was using my $244 GDS-2072E yesterday.I did a little preliminary work today for mounting the GPSDO antenna and hopefully I'll be able to finish in the morning before it gets hot.As I know that there are issues in setting up the GPSDO, I'll probably reference the 33622A to the 8648C before I reference the two of them to the GPSDO.A side note on the cost of gear. I just turned 65. I'm "retired" only because no one in the oil industry will employ anyone my age. All my life I have squeezed every penny with a pair of vice grips. Despite a tremendous desire for a good electronics lab, I went without because of the cost. In recent years I've had two friends die of cancer and two of a heart attack. Another friend is currently undergoing chemo. But the biggest impact has been watching my brother in-law deteriorate from Parkinson's over the last 9 months. That has made me an old man in a hurry. And loosened my purse strings. I still have the one new vehicle I ever bought for myself in 1993, a base model Toyota pickup for which I paid $7800 with A/C. So I'm allowing myself the cost of a new midrange car for my lab. I've never bought a boat, RV, motorcycle, taken a $3000 vacation or any of the other things most people do.My primary interest is low cost test gear. My major project is writing FOSS FW for Zynq based scopes. Unfortunately for that project, I am easily side tracked by good problems such as the one you presented. For which I am grateful. Not quite as much fun as a similar class problem in my specialty, but still a great pleasure.

author: dnessett
author_rank: Regular Contributor
timestamp: June 19, 2018, 11:31:49 pm
content: Given the fiasco with figure 4 ina recent post of mine, I thought I should provide a more useful image of the phase noise between the FEI FE-5650 and Rigol DG1022. I finally got my scope to synch both signals by increasing the sample size to its maximum for 3 active channels (3Mpoints). The resulting image shows the FEI in yellow, the Rigol in blue and the phase difference signal in purple.There is an obvious conclusion from this trace (concentrate on the purple plot). There is significant linear drift between the two oscillators (not something that will astonish anyone), specifically 74.63 Hz. Surrounding this is a bunch of fuzz representing the phase noise. So, the trick will be to get the numerical data, analyze it for linear drift, subtract the linear drift, and then subject the resulting signal to phase noise analysis. Again, this is somewhat obvious, but since the object of the current exercise is to develop a technique for analyzing the phase difference data, stating the obvious once shouldn't be too annoying.

author: rhb
author_rank: Super Contributor
timestamp: June 20, 2018, 12:00:34 am
content: Looks pretty good. But where's the Lissajous?I don't think stating the obvious in a project like this is bad. I think it needs to be repeated regularly. Otherwise there is a great tendency to run off into the ditch.

author: dnessett
author_rank: Regular Contributor
timestamp: June 20, 2018, 12:03:00 am
content: Quote from: rhb on June 20, 2018, 12:00:34 amI finally got the Lissajous to work, but on my scope it was basically useless. I could get it to almost stop, but the lines defining it were so thick that you couldn't really see any "breathing".

author: rhb
author_rank: Super Contributor
timestamp: June 20, 2018, 12:54:32 pm
content: Quote from: dnessett on June 20, 2018, 12:03:00 amThe width of the Lissajous figure should be the phase noise from cycle to cycle.I saw that on the MSOX3104T. I *think* it's caused by a waveform update rate which exceeds the response time of the LCD. That was a factor in my decision to return it. I've been considering getting a fast analog scope. I found a nice refurbished 485, but to my horror they are socketed semiconductors throughout. While that's fine in a dry climate like southern California, it's a nightmare in a humid climate such as Houston or central Arkansas.I'd like to return to the equation from your original post:v(t) = V0 + A(t)*(cos( wt + phi(t))That seems to me an adequate formulation. I can't think of any real oscillator behavior that can't be shoved into either A(t) or phi(t). The linear drift can be accommodated by writing phi(t) = a + b*t + c*rand(t). Once we have phi(t) we can pick it apart as needed. So the first order problem is to separate the variables.As a perfect reference does not exist, the only way to do that is to set up a system of equations with as many equations as there are unknowns. We can do that with 8 oscillators by comparing phase pair wise for all pairs. However that leads to 32 equations.The A(t) term is the harmonic content. So there is the potential to simplify the problem by low pass filtering the oscillator outputs. That would reduce the problem to 18 equations in 3 variables. But 120 dB filters are not easy and require very careful shielding to be effective. To get 120 dB down by the 2nd harmonic requires a 20 pole filter. I rather fear trying to build even one of those.So on balance, from a physical implementation perspective I think the easiest way to proceed is with 8 oscillators and 32 comparators. However, this is 4 bytes per comparison. With a 10 MHz oscillator frequency, a single comparison per cycle would produce 40 MB/S. So even this is not easy.However, the quantities of interest are the expectations of random processes. So if we can guarantee that the samples are not correlated with any oscillator a few samples per cycle should suffice.The preceding is a national lab level measurement. We need to determine if it has been tried or studied and found to have a fatal flaw other than the problem of output data volume. I don't think it sensible to move on implementing it without having completed a thorough analysis.While not adequate for absolute measurements, mixing the oscillator ouput with the 10 MHz output of a GPSDO and using that to produce a baseband IQ stream seems an appropriate first step. The STM32F4 series have three 2.4 MSa/S 12 bit ADCs. They can be interleaved to get 7.2 MSa/S which allows for a fairly simple anti-alias filter. Another option would be an LPC4370 which offers an 80 MSa/S single channel ADC and is available on a $20 eval board from Digikey.A NOTE TO OTHER READERS: I shall ignore all comments which do not include carefully stated, mathematically sound proof of any assertions made. So if you can't do the math, don't bother to comment. And I should like to caution that any use of the word "clock" is not in the sense of time keeping. This is not a discussion of time keeping. It is a discussion of the physics and metrology of electrical oscillators.

author: tomato
author_rank: Regular Contributor
timestamp: June 20, 2018, 11:16:55 pm
content: Quote from: rhb on June 20, 2018, 12:54:32 pmShouldn't that give you 28 equations? n(n-1)/2?QuoteYou're in luck -- this has not been done before. You will pioneer the field.

author: rhb
author_rank: Super Contributor
timestamp: June 21, 2018, 02:42:50 am
content: Thank you for calling attention to my blunder.The correct equation is (N-1)*(N/2) = 4*N. So one needs 9 oscillators to produce 36 equations with 36 unknowns.I am rather surprised by your assertion that this has not been investigated. While the problem was for a long time computationally difficult, modern computers can handle it with ease.Do you know the name of anyone at NIST who works on such things?

author: tomato
author_rank: Regular Contributor
timestamp: June 21, 2018, 03:00:05 am
content: Quote from: rhb on June 21, 2018, 02:42:50 amIt has nothing to do with the computational difficulty.QuoteYes, but I'm not dragging them into this, because they are my customers. Check the NIST personnel directory.

author: awallin
author_rank: Frequent Contributor
timestamp: June 22, 2018, 11:03:59 am
content: Quote from: rhb on June 21, 2018, 02:42:50 amThe conventional N-cornered hat and N-clock ensemble time-scale papers make N-1 independent measurements between the oscillators. This leaves the 'absolute' frequency of all oscillators unknown (N unknowns, N-1 measurements) but you can estimate and predict the frequency/phase differences between oscillators.I think I lost track of what you're trying to achieve, and your oscillator model with 4? unknowns per oscillator....

author: rhb
author_rank: Super Contributor
timestamp: June 22, 2018, 01:16:03 pm
content: From the first post in the thread:QuoteIt's not my project, I just got interested in the problem. Making the separation above is the first step. Then the real fun begins dissecting phi(t) into the sum of multiple noise sources. The latter is what interests me as it seems an excellent application of a sparse L1 pursuit. In particular, a basis pursuit with a large dictionary of possible models.Curiously for someone with a BA in English lit and an MS in geology, as I have gotten older I have become increasingly interested in mathematics and the analysis of random data in particular. I think it's because I now see so many parallels to familiar problems from 30 years of reflection seismic signal processing in the oil industry.I ran what I jokingly call "the orphan home for lost problems". Lots of strange, arcane questions would come to my office door. It was lots of fun solving them.

author: rhb
author_rank: Super Contributor
timestamp: June 22, 2018, 10:07:26 pm
content: R&S sent me a link to a primer on spectrum analyzers. It's actually quite well written and provides references relevant to this topic.http://www.rohde-schwarz-usa.com/rs/324-UVH-477/images/SpecAnFundamentalsPrimer.pdf

author: dnessett
author_rank: Regular Contributor
timestamp: June 22, 2018, 11:28:22 pm
content: RoGeorge provided a very nice explanation why the traditional variance of time-keeping devices diverges as sample sizes increase. However, it is in another thread (here). I responded in that thread and asked several questions. One specifically relates to Figure 3 in Rutman and Wall's paperCharacterization of Frequency Stability In Precision Frequency Sourcesthat shows a knee in a plot of log(sqrt(<y2(t)>)) against log(tau). RoGeorge couldn't comment on the question, since he was unfamiliar with the paper and had other things he needed to focus on rather than reading it.I don't want to continue the discussion of this question within that other thread, because that would be hijacking it for a purpose other than that which it was created. So, I am raising the question in this post and suggesting why I think that knee may be important.After following the discussion in the other thread, it seems now clear (at least to me) that time-keeping has very different requirements for oscillators than other applications, such as doppler radar and spread spectrum communications. This can be discussed subsequently, but I would like to focus on time-keeping and suggest that Allan Variance/Deviation may be important for long-term time-keeping applications, such as national clock references, but may not be critical for short- to medium-term time-keeping applications.To illustrate, suppose there is an application that needs to time the flight of frisbees in some frisbee sport competition. Frissbee flight times are relatively short, so the clocks used likely need not be designed/selected with their Allan Variance/Deviation in mind. Similarly, suppose there is a need to time the growth of fungus on moist leather. Again, the Allan Variance/Deviation of these clocks is probably not a selection parameter when considering which to use.So, when does it become necessary to consider the Allan Variance/Deviation of a clock for a particular application? I hypothesize in order to start discussion that it has something to do with the knee shown in Figure 3 of the paper referenced above. As long as the local variance and Allan variance are for all practical purposes equal, then traditional oscillator stability measures (e.g., parts-per-whatever/(minute, hour, day) frequency error rates, phase noise values/plots in rad2/Hz) are sufficient. Applications needing clocks to operate for sufficiently long periods of time (that period being related to the knee in Figure 3), on the other hand, probably should consider the Allan Variance/Deviation of the clocks they select for use.

author: tomato
author_rank: Regular Contributor
timestamp: June 23, 2018, 02:51:15 am
content: Quote from: dnessett on June 22, 2018, 11:28:22 pmQuestion: How do you know where the knee is?Answer: Allan VarianceGeneral:1. There is nothing about the Allan Variance that restricts it's use to the "long term."2. There is no information that can be derived from the standard deviation that cannot be derived in a more unambiguous way from the Allan Variance.3. The Allan Variance tells you when the standard deviation is a useful parameter.

author: rhb
author_rank: Super Contributor
timestamp: June 23, 2018, 03:03:32 am
content: Quote from: tomato on June 23, 2018, 02:51:15 amPerhaps you would be so good as to produce a concrete mathematical example. So far all you have done is thump your chest claiming great authority and expertise. Anyone who actually understands anything can explain it to a 12 year old. So how about explaining it to PhDs. That should be even easier.Someone providing janitorial services to NIST has NIST as a customer. But they're still just a janitor.

author: tomato
author_rank: Regular Contributor
timestamp: June 23, 2018, 03:29:23 am
content: Quote from: rhb on June 23, 2018, 03:03:32 amRegurgitating mathematics to correct a general misstatement isn't a very good use of anyone's time.QuoteI didn't realize correcting mistakes or misinterpretations fell under the category of "thumping one's chest." And I certainly have not claimed great authority in any of my posts. In fact, I have been careful not to list my credentials.QuoteExplaining things to 12 year olds is often easier.QuoteI do not provide janitorial services to NIST.

author: dnessett
author_rank: Regular Contributor
timestamp: June 23, 2018, 01:12:15 pm
content: Recently,herein a different thread, thermistor-guy responded to a comment I made about Allan Variance in that thread. Specifically, I stated that I had not seen mentioned anywhere how someone is supposed to use Allan Variance in practice (other than as an abstract measure of "goodness"). He pointed me to theInterpretation of value section of the Wikipedia article on Allan Variance. I am responding in this thread to that post so that I do not hijack the other thread in order to discuss this issue, which is really not related to the other thread's topic. I invite thermistor-guy to reply here, rather than in the other thread.I will provide the quote from the Wikipedia article to which I believe thermistor-guy is referring to save people the trouble of finding it. It is short, so I think this is appropriate."An Allan deviation of 1.3×10−9at observation time 1 s (i.e. tau = 1 s) should be interpreted as there being an instability in frequency between two observations 1 second apart with a relative root mean square (RMS) value of 1.3×10−9. For a 10 MHz clock, this would be equivalent to 13 mHz RMS movement. If the phase stability of an oscillator is needed, then the time deviation variants should be consulted and used."It is not entirely clear, at least to me, what this means. Variance is a measure related to a probability distribution function (pdf), specifically that distribution's second moment. The statement in the above quote seems to suggest a deterministic "movement" in the signal's frequency. This is more apparent in the example, where it is suggested that for a 10 MHz clock, the movement would be equivalent to "13 mHz RMS movement". I think the problem is the idea of "movement" is left undefined. Given that Allan Variance is a variance, I would have expected an interpretation that referenced a probability bounds on the signal's frequency at the end of the 1 s period.I would like to make one other point. When the article states, "If the phase stability of an oscillator is needed, then the time deviation variants should be consulted and used.", does this mean that the traditional variance of frequency fluctuations is the appropriate measure to use when computing phase stability? If someone knows the answer to this question, would they respond?In order to forestall any misinterpretation of my response, I am grateful to thermistor-guy for pointing me to this information, so this post is not intended as a snotty rebuke. Rather, I just don't understand the explanation given in the Wikipedia article.

author: awallin
author_rank: Frequent Contributor
timestamp: June 23, 2018, 02:30:49 pm
content: Quote from: dnessett on June 23, 2018, 01:12:15 pmThat's a reasonable explanation, although note that conventional RMS is 'global' i.e. you compare each data-point to the mean of all data and compute the root-mean-square, while ADEV is 'local' in the sense that you only take consecutive frequency-points/pairs from the time series in order to build the sum.Quotemaybe the wikipedia use of 'movement' is not the best here - I don't think any deterministic movement should be understood.In the example if you take a time-series of frequency-points, each averaged for 1s, and histogram the difference between consecutive points, you should get some (not necessarily known..) distribution with a width of 1.3e-9 in relative units (13 mHz if the time-series in in Hz).QuoteTVAR is just MVAR scaled with the averaging-time (usually 'tau'), and thus TDEV has units of time (seconds). It predicts how much variance in phase (in units of time) to expect (in an RMS-sense) from one phase point to the next (where the spacing between points is tau).In practice there are technical problems with measuring a (gap-free!) frequency time-series and then predicting (integrating) phase from that - not recommended. For timekeeping measure phase with a time-interval counter.

author: rhb
author_rank: Super Contributor
timestamp: June 23, 2018, 02:45:32 pm
content: I just came across this by way of a mailing list. A little surprised it had not been mentioned before.http://www.ke5fx.com/gpib/pn.htm

author: dnessett
author_rank: Regular Contributor
timestamp: June 24, 2018, 05:04:09 am
content: Quote from: awallin on June 23, 2018, 02:30:49 pmThanks for the replies, but my question remains unanswered. I think I need some time to try to work it out myself, which seems silly because I am sure someone has already done so. Oh well, I suppose the attempt will have the benefit of clarifying the concepts in my mind even further.

author: rhb
author_rank: Super Contributor
timestamp: June 24, 2018, 01:04:45 pm
content: I don't know why I didn't realize it earlier, but hands down the best way to make the measurements is to get an SDRplay RSP2 and a GPSDO that provides the reference frequency required by the RSP2. Leo Bodnar sells one which is why I bought it. That combination will provide 12 bit data limited only by the available disk space.Record the IQ stream to a stereo WAV file and import into Octave.I'll try to get my GPSDO setup and collect some data from several sources later today.Edit: Probably won't happen today. I got the GPSDO installed and producing 10 & 24 MHz, but the SDRplay RSP2 is not cooperating. Windows says it is there, but SDRUno and SDR Console say it isn't :-(

author: dnessett
author_rank: Regular Contributor
timestamp: June 24, 2018, 11:04:24 pm
content: For me clarity about Allan Variance was greatly increased when RoGeorge posted his explanations (hereandhere) of the conceptual reasoning behind the increase of traditional variance as tau increases. I have thought about this and think I can supply a more mathematically inclined argument for this property. The concepts behind the argument are only roughly accurate, as should become apparent during their presentation, but it does have the advantage of a bit more rigour than RoGeorge's metaphorical description. It also supports a result that I have not yet seen mentioned.Before presenting the mathematics, it is prudent to make sure everyone is on the same page in regards to terminology. I have read a lot of papers about Allan Variance and have noted the terminology is not quite consistent.Figure 1 shows a sine wave generated by an oscillator. Periods of this sine wave are measured from one rising edge to the next. For the purposes of this presentation, at each rising edge the preceding period is determined to be either longer or shorter than the nominal period of an ideal oscillator. So, period 1 may be shorter than the nominal period (and hence averaged over the period, the oscillator has a greater frequency than the nominal ideal frequency). Or period 1 may be longer than the nominal period (and therefore when averaged over the period, the oscillator has a smaller frequency than the ideal oscillator). While it would be more accurate to include a third possibility, i.e., period 1 has the same frequency as the nominal oscillator, that would overly complicate the model and would not provide any significant clarity to the narrative.Figure 1 -Figure 2 shows mulitple periods of the oscillator. An averaging interval defined by the value tau measures whether the oscillator is of higher or lower frequency than a nominal ideal oscillator. For the purposes of the following mathematics, tau is always a multiple of the nominal ideal oscillator period. The averaging measurement (conceptually) occurs by noting the "polarity" of each oscillator period. Here "polarity" means whether for that period the oscillator was of greater frequency (G) or lower frequency (L) than the nominal ideal oscillator. There are m oscillator periods in each averaging interval.Figure 2 -Figure 3 shows how each averaging interval is utilized to create a total measurement. In particular n intervals of length tau are statistically analyzed to produce the measurement. The sample time (ST) is the value tau times n.Figure 3 -Consider the situation in Figure 1. Each period produces a result - either G or L. These results are analyzed over the averaging interval. If the probability of obtaining G is p, then the probability of obtaining anL is 1-p. For simplicity it is assumed that p=1-p=.5.For measuring oscillator stability the statistic of interest is not how many Gs or Ls appear in an averaging interval, but the difference between these values. The process represented by an averaging interval is well-known and is called a bernoulli trial. The expected value of the difference between the number of Gs and Ls is presentedhere, specifically: 2mp - m = m(2p-1) = 0. [Note: the referenced web page uses n as the number of trials, whereas here that value is m. The value n is used here to represent the number of averaging intervals. Also, the problem solved there is stated in terms of successes and failures. The logic is exactly the same. Simply substitute L for success and G for failure.]The variance of the difference between the two random variables in a Bernoulli trial (see above reference) is: 4mp2= m. Notice (!) that the variance depends on m. So, as the value of tau increases, so does the variance.This has an interesting side-effect. The sample time equals tau * n. So, the traditional variance does not diverge as sample time increases. It diverges as the averaging time increases. Given the capabilities of computers in the 1960s and 1970s, when Allan Variance was developed, it was necessary to increase tau in order to obtain long-term measures of clock stability. Today, computers are much more powerful. So, it would be interesting to determine the sample_time/tau ratio above which an analyst would be forced to increase tau in order to obtain practical clock evaluation results. This would, of course, depend on the computer available. However, I would guess most desktop systems these days could analyze a very long data set in a practical amount of time.

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: June 25, 2018, 02:41:41 am
content: Quote from: awallin on June 23, 2018, 02:30:49 pmwhich is consistent with the Wikipedia article, in the section on Time Stability estimators:https://en.wikipedia.org/wiki/Allan_varianceI found the Research History section also informative:QuoteAs a time-nut novice, I'd say this is not an easy article, and not an easy topic.

author: tomato
author_rank: Regular Contributor
timestamp: June 25, 2018, 02:45:16 am
content: Quote from: awallin on June 23, 2018, 02:30:49 pmThe parenthetical remark was probably missed by most, but it is very important.

author: tomato
author_rank: Regular Contributor
timestamp: June 25, 2018, 03:53:22 am
content: Quote from: dnessett on June 24, 2018, 11:04:24 pmYour picture of an oscillator has evolved from a Gaussian distribution (in earlier posts) to a binomial distribution, but the distribution for any real oscillator is not purely one or the other. Oscillator noise is complicated -- it cannot (generally) be reduced to a simple Gaussian process with it's "jitter" described by a single parameter, i.e. by a standard deviation.QuoteAllan Variance calculations are very simple calculations. They do not require much computational power, even when measuring long term stability. Tau is often increased for long term measurements because there are hardware advantages (reduced dead time, higher counter resolution, etc.) and it is computationallyconvenientto simply increase tau instead of increasing the number of data points. There are no serious disadvantages to increasing tau instead of increasing the number of data points.An example: Let's say you want to measure the Allan Variance from tau = 1 s to tau = 105s. To get a reliable Allan Variance at 105s, you will need 106s of data.Method 1) Collect 106counter readings with a gate time of 1 s. Total number of data points is 106, and the total acquisition time is about 278 hours.Method 2) Collect 103counter readings with a gate time of 1 s, then collect 104counter readings with a gate time of 100 s. The total number of data points is about 100x less than method 1, the dead time is about 100x less than method 1, counter resolution is improved, but the total acquisition time is only about 17 minutes longer. Resulting Allan Variance will be consistent with that attained by method 1.

author: dnessett
author_rank: Regular Contributor
timestamp: June 27, 2018, 01:04:12 am
content: OK, I tried to sharpen the result given in my recent post on the variance of average clock (not oscillator) frequency over an interval tau (i.e., that it increases with increasing tau). But, the result I now have suggests just the opposite - variance should decrease with increasing tau. Here is the argument.The oscillator model presented in most of the papers I have read about Allan Variance proposes that at each time t the oscillator signal has an associated instantaneous frequency, say if(t). The average frequency over the interval tau is then the intergral of if(t) over that interval. While conceptually clean, this model is not amenable to a simple mathematical treatment. In particular, it leads to the formulation of a generalized Wiener process with continuous time and continuous variable. Believe me, this is not something an amatuer wants to get anywhere near.So, it is prudent to formulate a different oscillator model using some simplifying, but realistic assumptions. In particular, discard the idea of instantaneous frequency. Conceptually, one can observe the length of each period of the oscillator signal. This defines an average frequency over that period. The average frequency over a tau interval is then the average of these averages. Also, assume the average frequencies observed over each period are i.i.d. (seethe material in this post. Also see the discussion below).The advantage of this model is it is easy to analyze. The disadvantage is it presumes measurements begin and end at the same place in a period (e.g., at the rising edge). Since tau is measured using an ideal oscillator (or in a practical measurement setup, by a reference oscillator), it is virtually certain the beginning and end of the tau interval will not fall at the same place in the period of the oscillator implementing the clock under test. However, if the number of periods in the tau interval is very large, the errors introduced by this inaccuracy will be very small, so from a practical perspective, this is not an issue.One problem with the model is the assumption that the period average distributions are i.i.d. This implies the oscillator has no drift, which is not realistic. So, in order to apply this model, the collected data must be first analyzed using regression and any non-random effects removed.Given this background, the confusing result is immediate. The tau interval frequency is the sum of the average period frequencies divided by the number of periods (m, where tau = m * oscillator period length). The central limit theorem (seeCentral Limit Theorem) stipulates that the average of the sum of any set of i.i.d. random variables, independent of their underlying probability distribution, converges to a random variable with a normal distribution with mean mu (the expected value of each period distribution) and variance sigma2/m (where sigma2is the variance of the period distribution). Consequently, the tau interval frequency shoulddecreasewith increasing tau, since when tau increases, so does m.Can anyone figure out where have I gone wrong? Might it be that I have assumed non-random effects are first removed before analyzing the data? If so, then Allan Variance has little attraction, since regression analysis has improved considerably since the 1960s and 1970s. The sample time average is the average of the tau averages, so the central limit theorem applies to the sample average as well. One could utilize the 3 sigma rule on the standard variance of the sample time distribution to compute a probability bounds on clock jitter.Added 6-28-18: I figured out my mistake. By modeling the oscillator as a signal source with a RV per period that when sampled specifies its length, I decreased tau to equal one oscillator period. Thus, there is no accumulation of period length errors, which is why variance increases with increasing tau in the traditional model.

author: rhb
author_rank: Super Contributor
timestamp: June 27, 2018, 01:50:16 am
content: QuoteI don't think it's all that bad, but then I've been doing it for 30 years. But, yes, they had good reason to call the classified version of "Extrapolation, Interpolation and Smoothing of Stationary Time Series" the "yellow peril" in reference to the yellow covers indicating a classified document.I'll comment further later, but I did an interesting experiment today. Using a Rohde & Schwarz RTM3104 I measured the period of my GPSDO at an output frequency of 10 MHz. I also measured the output of my 33622A at 10 MHz. I don't know the jitter spec for Leo Bodnar's dual output GPSDO, but Keysight claims less than 1 pS for the 33622A and less than 0.5 pS with the OXCO option which I don't think I have. The statistics function of the RTM3K gave a standard deviation of ~26 pS for both sources. At present I have to attribute that to the RTM3K time base.The RTM3K provides a 10 MHz reference out which I'll analyze when I get my SDRplay RSP2 working again with the GPSDO reference input. Right now it's not getting along with Windows 7 on a VBox VM.

author: dnessett
author_rank: Regular Contributor
timestamp: June 27, 2018, 03:00:19 am
content: Quote from: rhb on June 27, 2018, 01:50:16 amHere is my logic. Modeling a process that changes at every value of t, where t is a subset of the real line, requires continuous time. The change at each value of t is not discrete, but rather a sample from the Real line, which (I am less sure about this) requires a continuous random variable for each value t. From what I have read so far, normal weiner processes do not support random variables that produce results from the reals, for that you need a generalized wiener process.Quote from: rhb on June 27, 2018, 01:50:16 amI agree. The culprit is probably the RTM3K time base.

author: tomato
author_rank: Regular Contributor
timestamp: June 27, 2018, 03:43:52 am
content: Quote from: dnessett on June 27, 2018, 01:04:12 amYou're making this far too complicated. Forget about making m measurements of the oscillator period and the Central Limit Theorem -- it's a red herring. Consider the simple case of frequency measurements of duration (gate time) equal to tau = m * period. If you take N frequency measurements and plot the distribution, what will you see? For any real oscillator, the distribution of frequency values willnot, in general, be Gaussian and the standard deviation may not be independent of the number of samples, N. In fact, the distribution can take different forms depending on the value of tau and/or the number of samples, N. This arises because there can be several physical processes driving the instability of the oscillator, and these processes can have very different signatures. Some will dominate at short times, while others may dominate at long times. Some can actually produce a nice Gaussian distribution of frequency values but, generally, only for a certain range of tau values.QuoteYou seem to have concluded long ago that the Allan Variance has no practical value, and keep trying to find ways to support your conclusion. It is an extremely powerful tool. Ignoring it is your loss.

author: rhb
author_rank: Super Contributor
timestamp: June 27, 2018, 01:00:17 pm
content: I'm attaching a relevant section from:Probability, Random Variables and Stochastic ProcessesA. PapoulisMcGraw-Hill 1965This is by far the best reference I have on probability theory. While not a complete treatment of the oscillator noise problem, it does cover several important cases and provides exact results.I'll have a look later at some other references, but this what I usually start with. However, I have many books for the sole reason that they treat some particular case which no one else does.I should have mentioned earlier that if you have a DSO, you can collect simultaneous traces from as many oscillators as you have inputs and then run cross spectral analyses. If one of those is a GPSDO, you should get splendid results. B & P should provide sufficient details. You'll need to handle ADC channel skew and various other sampling artifacts bit it's pretty straight forward stuff.

author: dnessett
author_rank: Regular Contributor
timestamp: July 03, 2018, 01:15:43 am
content: I finally got my GPSDO working and ran a test on my Rubidium oscillator. I used the GPSDO as the reference clock and (among other things) measured how long it took the Rubidium to slip a period (it was loosing time). It took about 52 minutes. This means it slips ~1.15 cycles per hour or ~27.7 cycles per day. At 100 ns per cycle, this means it is slipping 2.77 msec per day (27.7 cycles*(100 ns/cycle)). Comparing that to the FEI FE-5650 spec of 2*10e-11/day for drift, my oscillator is over 1000 times worse. For example, seethis listwhere it also specifies a drift figure of 2*10e-11/day and equates this to gaining/losing +/- 1.1 usec per day.Now I realize this measured drift occurred over only 1 hour and the Rubidium oscillator might gain back some time over a full day. However, I periodically looked at my scope over a period of 3 hours and it always appeared that the Rubidium was loosing time. Also, it is possible that some of this error is attributable to the GPSDO, but I imagine not much of it.The vendor who sold me the Rubidium oscillator provided a data sheet. If I am reading it correctly, the oscillator was built in Nov, 2003 - which means it is ~15 years old. I couldn't find any aging data in the spec, so I don't know if such a degradation of performance is within the unit's specs.Of course, it is possible that my result arises from an operator error. I didn't sit at the scope looking at the drift for 52 minutes. It is possible the drift reversed while I was out of the room and I read a cycle shift when in fact the drift reversed and no slippage occurred. I would be interested whether any one else has tested an old ebay Rubidium oscillator for drift to see if my result is typical.

author: tautech
author_rank: Super Contributor
timestamp: July 03, 2018, 01:43:51 am
content: Could the quality/strength of the GPSDO reception be causing this ?

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: July 03, 2018, 03:14:51 am
content: Quote from: dnessett on July 03, 2018, 01:15:43 am27.7 * 100E-9 s per day = 2.77E-6 s per dayrelative error = 2.77E-6 s per day / 8.64E4 s per day = 0.32 * 1E-6 * 1E-4 = 3.2E-11So your Rubidium reference is a little out of spec., but not way out. May I suggest leaving it powered, uninterrupted, for a week, and checking the drift once per day. You might find it comes back into spec. The good news is that the servo loop that drives the Rb resonance cell seems to be working.Usually, Rb references come with a C-field adjustment that you can fine-tune, once you are satisfied the drift rate is stable. See for example the C-field section in:http://www.wriley.com/Rubidium%20Frequency%20Standard%20Primer%20102211.pdf

author: dnessett
author_rank: Regular Contributor
timestamp: July 03, 2018, 05:26:03 am
content: Quote from: thermistor-guy on July 03, 2018, 03:14:51 amI didn't realize the drift figure was relative error. Thanks.However, that gives rise to another mystery. How is it that the list I quoted specifies 2*10e-11/day relative accuracy, but the time accuracy figure is 1.1 usec/day?Quote from: thermistor-guy on July 03, 2018, 03:14:51 amThanks for the reference. It is very helpful.

author: dnessett
author_rank: Regular Contributor
timestamp: July 03, 2018, 05:27:53 am
content: Quote from: tautech on July 03, 2018, 01:43:51 amThe GPSDO indicates both a lock with the GPS satellites and error less than 0.1Hz. So, I think the reception is OK.

author: tautech
author_rank: Super Contributor
timestamp: July 04, 2018, 10:26:40 am
content: A post and screenshot from the clever old master rf-loop might be of interest:https://www.eevblog.com/forum/testgear/is-bandwidthmemory-depth-a-waste-of-money-in-oscilloscopes/msg1648538/#msg1648538

author: dnessett
author_rank: Regular Contributor
timestamp: July 07, 2018, 01:04:59 am
content: I ran a test that recorded the phase difference between my Rubidium oscillator (FEI FE-5650A) and a cheap GPSDO I bought on ebay, which is described in the discussion withinthis thread. Internally, it is identical to the unit shownhere. The phase difference data described below was collected after both the Rubidium oscillator achieved Lock and the GPSDO showed satellite acquistion and oscillator integrity whereby the accumulated frequency error was less than 100 mHz (the latter condition occurs when the ALM LED goes off, seethe ebay listing). After that condition arose, I waited an extra hour for complete oscillator warm-up before viewing signals and collecting data. For the purposes of this micro-study, I assumed the GPSDO was the reference clock and the Rubidium oscillator was the DUT. To minimize noise in the scope probe measurements, I didn't use the normal ground wire configuration. Instead, I used the spring on the probe tip technique, which meant the distance between the probe tip and grounding site was on the order of a few mm.I obtained the phase difference data using an ebay board hosting an AD8302 chip (data sheet here). Characteristics of this chip important to this discussion are: 1) it provides both an amplitude and phase difference signal. The phase difference signal is free from oscillator AM modulation noise.The AD8302 phase difference signal encodes the phase difference as a voltage, where the phase difference runs from 0 - 180 degrees (180 - 360 degrees is mapped onto that interval withdecreasingincreasingvoltage). 180 degrees of separation is represented by 30 mV; 90 degrees of separation is represented by 900 mV; and 0 degrees of separation is represented by 1.8V. Therefore, 10 mV excursion represents 1 degree of change. There are dead zones near 180 and 0 degrees.The AD8302 uses a multiplier circuit to detect phase changes. It turns out that when comparing 2 10MHz signals, the sum of these frequencies leaks through (i.e., there is a 20MHz component). The AD8302 provides for lowering the output bandwidth by adding an external capacitor. For the tests described below, I used a 68pf capacitor, which is insufficient to suppress all of the 20 MHz (and, it turns out 40 MHz) signal.Figure 1 shows the spectral power density of the phase difference signal from 1 - 100 MHz.Figure 1 -Figure 2 shows the spectral power density from 9 KHz-1 MHz. As is evident, most of the spectral power density exists between 0 Hz and 400 KHz. The power below 9 KHz is not analyzable by my SA (a SIGLENT SSA3021X).Figure 2 -Figure 3 shows the oscilloscope display (Rigol DS 1104Z) of a typical phase difference signal.Figure 3 -Figure 4 shows a zoomed-in display of the 20 MHz signal modulated on the phase difference signal.Figure 4 -I ran a one-shot capture of the phase difference signal and moved it to a USB stick. Important parameters for the data series are: 500 Msa/s and 6 Mpoints captured - implying 2 ns between each data point and a 12 msec (2ns * 6E6) capture period. After importing the data into Octave, I ran a 5th order Butterworth 10 MHz low pass software filter on it to eliminate the 20 MHz modulation. Figure 5 shows 100,000 points of the filtered data (in black) superimposed over the unfiltered data (in yellow).Figure 5 -The data set exported by the Rigol has two columns: 1) the index of the row (i.e., 0, 1, 2, 3, ....) and the voltage for that data point. I converted the index column into a time value by multiplying it by 2*10e-9 and converted the voltage value to radians by multiplying each value by ((2*pi)/360)/.01. Figure 6 shows the resulting data set.Figure 6 -Corrected Figure 6, which didn't have full x-axis label.It is apparent from this figure that the data set contains significant white noise. I used the dftmag2 Octave (and MATLAB) function described in the (excellent) articleReal spectrum analysis with Octave and MATLABto create a spectral density plot of the software filtered phase difference data. This function eliminates the DC (first bin) and last bin values, since (as explained in the article) they must be normalized differently than the other data and there is no normalization procedure that works well. Figure 7 shows the result (using a loglog plot).Figure 7 -Several features are notable. First, comparing the plot with Figure d on pg. 75 of the reportHandbook of Frequency Analysis by W. J. Riley, it appears that the signal is composed of white noise at frequencies greater than 1000 Hz. However, between 10Hz and 1000Hz, the loglog plot has an average slope of zero. From 1Hz to 10 Hz the slope is very steep. I am insufficiently schooled in phase fluctuation analysis to interpret the last two characteristics.There is one other interesting result. I wanted some sense of the variation of phase differences over the 12 msec interval. The max and min of the raw data are 0.74100 and 0.55700 respectively. Converting this to degrees (which are easier to visualize than radians) yields 74.1 and 55.7, which is a difference of 18.4 degrees. This is an enormous variation of phase between the DUT and Reference Clock for such a short interval of time, which took me by complete surprise. This may indicate a problem with my test setup or may suggest that the very short-term stability of the Rubidium and GPSDO oscillators are horrible. Recall that both utilize a crystal oscillator in a frequency locked loop. It may be that the feedback loop frequency is significantly greater than 12 msec, which allows the crystal oscillator to display significant jitter during short intervals. However, this result completely mystifies me.I am new to oscillator evaluation and freely acknowledge that my test setup and analysis may have significant flaws. I welcome any constructive criticism that others might give. I also have made the data I collected available for others to inspect or analyze. The zipped cvs file is availablehere. At the beginning of the file is a Creative Commons Share-alike/Attribution license as well as some comments, which means effectively you can do anything you want with it. Each line of text has the "%" character in the first position, so the file can be loaded by Octave or MATLAB without change. For other analysis engines, it is up to the user to convert the file to the appropriate format.

author: tomato
author_rank: Regular Contributor
timestamp: July 07, 2018, 02:13:11 am
content: There's a host of simple sanity checks youcanshould do. The first is to connect one oscillator to both inputs, with one arm delayed by a long (20-50 ft.) piece of coax.

author: dnessett
author_rank: Regular Contributor
timestamp: July 07, 2018, 02:44:15 am
content: Quote from: tomato on July 07, 2018, 02:13:11 amGood thought. Anything else?

author: tomato
author_rank: Regular Contributor
timestamp: July 07, 2018, 03:31:36 am
content: Quote from: dnessett on July 07, 2018, 02:44:15 amStep 2 depends on the results of step 1, and digesting the results of step 1 could take longer than you think.

author: dnessett
author_rank: Regular Contributor
timestamp: July 07, 2018, 11:34:43 pm
content: Quote from: tomato on July 07, 2018, 02:13:11 amThe only long piece of coax I have lying around is ~83 feet. Since it is RG-58 (which has a delay characteristic of 1.541 ns/foot), this will push the delayed signal into the next period (I have measured signal peak to delayed signal peak delay of 29.2 ns, which implies 129.2 ns). Is there any reason why this will not work?

author: dnessett
author_rank: Regular Contributor
timestamp: July 08, 2018, 10:34:55 pm
content: Quote from: tomato on July 07, 2018, 02:13:11 amFollowing this suggestion, I performed the indicated delay check on both the Rubidium and GSPDO oscillators. Instead of using a 20-50 foot coax, I used an 83 foot RG-58 coax I had lying around. The delay for this coax (using the established signal delay for RG-58 of 1.541 ns/foot) is ~ 128 ns. When I eye-balled the cursors to the peaks of the signal and its delayed twin, I measured 29.2 ns. So, the delayed signal slipped a period and represented 129.2 ns of delay.I won't show the plots, since they look pretty much like the noise plot previously posted. However, here are the max/min values for each experiment:GPSDO delayed: max=0.90900;min=0.49300Rubidium delayed: max=0.85600;min=0.68400In degrees this represents a difference of:GPSDO delayed: 41.6 degreesRubidium delayed: 17.2 degreesBoth of these seem to be very large for the 12 msec measurement period, as was the case for the GPSDO/Rubidium phase difference measurement.To see if there was a problem with the AD8302 or its setup, I used a dataset that I had previously captured comprising the simultaneous values for the GPSDO and Rubidium oscillators displayed on the Rigol scope. This data set has only 3 Mpts, representing 6 msec of capture, since my Rigol only has 12 Mpts of storage and I was probing the phase difference signal at the same time as the two input signals.Once I loaded the data set into an Octave variable "randg"", I performed the following software analysis (seethis discussion/first answer/section on Hilbert Transform):Code:r=randg(:,2);g=randg(:,3);r_h=hilbert(r);g_h=hilbert(g);phase_rad = angle(r_h ./ g_h);The Hilbert transform enables access to the phase data associated with the two signals. The variable "phase_rad" is the software equivalent of the AD8302 phase difference signal. The max and min of phase_rad were (in radians):max=2.3345min=1.8933Converting to degrees (i.e., multiplying by 360/(2*PI)=57.3), yields:max=133.7min=108.5Which represents a phase difference interval of 25.2 degrees.This suggests that the AD8302 is not causing the high variation of phase differences during the interval.So, either the signalsaredisplaying these large values of phase fluctuation, or there is something wrong with the Rigol or its setup.In order to investigate the latter possibility, I used a TEK 2465 scope to display the GPSDO delayed phase difference signal from the AD8302. Figure 1 shows the result.Figure 1 -The phase difference signal is at the top with the input and delayed signals at the bottom. I used a probe set to 1X to measure the phase difference signal and the cursors show the extent of the voltage excursion visible on the scope. While the cursor readout indicates 1.6V, the cursor logic assumes the use of a 10X probe, so in fact the voltage variation is 160mV. This represents 16 degrees of variation. While this is significantly less than the 41.6 degrees obtained from the Rigol data, that is most probably due to the max and min of the phase difference data not occuring often enough to display on the 2465.At this point, I am beginning to believe the large phase difference result as an actual phenomenon, rather than a measurement blunder. However, I am not confident of this conclusion and think it is now time to ask others (in the spirit of scientific enquiry) who have a Rubidium oscillator or GPSDO oscillator (of the same kind I have) if they would run tests on their units to see if they confirm or repudiate these results. It is unnecessary to use an AD8302 in this process. Any method that indicates the phase differences of a delayed GPSDO, delayed Rubidium or Rubidium versus a GPSDO would suffice.

author: tomato
author_rank: Regular Contributor
timestamp: July 09, 2018, 03:06:35 am
content: Quote from: dnessett on July 08, 2018, 10:34:55 pmHere's the sanity check: You are seeing phase measurements that range from 16 degrees to 41 degrees,when you measure from one cycle of an oscillator to the next cycle... does that seem reasonable?If you really want to make this unambiguous, cut your cable down to 20' and repeat the measurement.QuoteI did a quick measurement (with a long cable delay in one arm) using a time interval counter. I could see 0.01 deg variations using a good oscillator, which is likely limited by the 4ps resolution of the counter. A lower quality oscillator gave variations of about 0.1 deg. The only way I could get the variations to approach 1 deg was by attenuating the oscillator amplitude, thereby decreasing the rise time and introducing discriminator errors.

author: dnessett
author_rank: Regular Contributor
timestamp: July 09, 2018, 04:29:54 am
content: Quote from: tomato on July 09, 2018, 03:06:35 amI do not understand your point. What do you mean by "when you measure from one cycle of an oscillator to the next cycle"? The total variation is observed over 120,000 cycles. I specifically asked you whether delaying by more than one period would be important. You did not answer. If you think this is an important point, would you answer it now and explain why it is important?Also, the total variation is not a per period statistic. It represents the maximum phase difference minus the minimum phase difference over the whole interval of 120,000 cycles. For example, taking the GPSDO delayed case, one period during the interval had a phase shift of 90.9 degrees, while another, probably distant from the first period, had a phase shift of 49.3 degrees. It is extremely unlikely that the change from maximum to minimum phase shift occurred over a single period.Nevertheless, I agree the result is counterintuitive and am open to an alternative explanation that identifies how these measurements arise?Quote from: tomato on July 09, 2018, 03:06:35 amWould you identify the oscillators you tested? My observations were for specific oscillator types (specifically, a cheap eBay GPSDO and a FEI FE-5650A Rubidium oscillator). I am not claiming the results apply to all oscillators.But more importantly, I don't understand your test set-up. Would you elaborate? Does your statistic of 0.1 degree variation represent the maximum phase fluctuation over a large number of cycles?Updated later, since I inadvertantly pressed "Post" before finishing the response.

author: dnessett
author_rank: Regular Contributor
timestamp: July 09, 2018, 04:44:40 am
content: Quote from: tomato on July 09, 2018, 03:06:35 amThinking about this, it is possible there is non-random drift in the data. If you observed 0.1 degree variation between consecutive periods, then if this was completely non-deterministic drift in one direction, over 120,000 cycles, the phase difference would have changed by 12,000 degrees (obviously, this is an extreme example, which I make only to suggest how your results and mine might be harmonized). I will look to see if there are any non-deterministic factors in the data.But, even if there are, the changes I reported seem large considering the measurement interval was only 12 msec long. If these results stand-up, I would say using either of these oscillators as the distribution signal to synchronize instruments in a lab would be problematic for most (or at lease many) tests.

author: tomato
author_rank: Regular Contributor
timestamp: July 09, 2018, 05:00:01 am
content: Quote from: dnessett on July 09, 2018, 04:29:54 amWhat does the output of your AD chip represent? It represents the relative phase of the two inputsright now. It doesn't know anything about the phase of the signal 120,000 cycles later.QuoteYou made your measurement with the longer cable without waiting for an answer. There's nothing wrong with that, so I tried to apply a sanity test to what you observed.QuoteBoth the 90.9 deg phase shift and the 49.3 deg phase shift represent the time delay that occurs from the start of one oscillator cycle to the start of the next cycle. The only way to get that big of a (real) change is if the frequency of the oscillator changed by about 1 MHz.The whole point of this test is to remove phase fluctuations of the oscillator from the problem. Cut your cable down to 20' and see what you get. Any "phase fluctuations" you measure will be due to your acquisition system, not the oscillator.QuoteI used a couple of Stanford Research clock generators (CG635). One has a Rb timebase, the other has a standard time base, but the oscillator doesn't really matter if you use a shorter cable for the measurement.The issue is not whether the results apply to other oscillators; the issue is whether the results are reasonable.QuoteEach measurement is the the relative phase of the oscillator and the oscillator delayed by roughly 1-1/2 cycles. The time interval counter can do some simply statistics on the measurements, nothing fancy.

author: tomato
author_rank: Regular Contributor
timestamp: July 09, 2018, 05:03:14 am
content: Quote from: dnessett on July 09, 2018, 04:44:40 amCut your cable. It's easy and it will remove any issues about the stability of your oscillator and instantly tell you if your acquisition system is measuring anything real.

author: tautech
author_rank: Super Contributor
timestamp: July 09, 2018, 05:07:51 am
content: FFS there's an easy way to quantify this.Did you not follow my link in reply #163 or not understand its content ?

author: dnessett
author_rank: Regular Contributor
timestamp: July 09, 2018, 09:59:25 pm
content: Quote from: tautech on July 09, 2018, 05:07:51 amI had a lot of trouble understanding it, since the poster doesn't seem to be a native English speaker.

author: dnessett
author_rank: Regular Contributor
timestamp: July 09, 2018, 10:09:55 pm
content: Not that I think it important, but to get this red herring off the table, I found two 10' coax patch cables and attached them to each other to create a 20' length. I then ran the GPSDO delayed test. The results are not suprising. Here are the maximum and minimum phase differences.max=57.6 degreesmin=35.4 degreesvariation = 22.2 degreesConsequently, reducing the length of the delaying coax provides no insight into the problem.So, I return to more interesting issues. I ran a 1st difference of the GPSDO 83' delayed data (picking every 20th data point, since the raw data has a data point each 5 ns) to see what phase differences occurred at each period of the signal. Figure 1 shows the results for the 1st 1000 periods. The Rigol has a lower bound of 1mV vertical resolution, so the data it captures has 1 mV resolution. This makes the phase difference signal appear as a step function, which is actually an artifact of the Rigol capture.Figure 1 -The plot shows a maximum of around 2.6 degrees phase difference on the top side and -2 degrees on the bottom side, so the bounds in the first 1000 periods is 0 -> 2.6 degrees. The max and min for the complete difference data vector are:max = 3.6 degreesmin = -2.6 degreesSo, for the complete data set the bounds are 0 -> 3.6 degrees phase difference per period.It doesn't appear there is much in the way of deterministic drift, although I am not a regression specialist. I continue to work on this question.Added later: It may be of some interest to convert the phase difference in degrees to ns. Using the formula 100/360 (=.27777...) ns/degree, the 0 -> 3.6 degrees of per period deviation represents a maximum of 1ns jitter (= 1%) per period.

author: tautech
author_rank: Super Contributor
timestamp: July 09, 2018, 10:15:39 pm
content: Quote from: dnessett on July 09, 2018, 09:59:25 pmAll the info and clues you need to perform the same measurement are contained in the screenshot.Please study it again in depth......every little snippet of info.Clue, look at the Stats box and the # count =1000s, so with infinite persistence the jitter (ch4) WRT 1pps (ch1) is under 4ns for a 1000s of a 10 MHz ref signal !Very clever use of standard features in a DSO.Linked again below for simplicity:https://www.eevblog.com/forum/testgear/is-bandwidthmemory-depth-a-waste-of-money-in-oscilloscopes/msg1648538/#msg1648538

author: tautech
author_rank: Super Contributor
timestamp: July 09, 2018, 10:26:44 pm
content: So with what you're trying to achieve (big picture) is the most accurate 10 MHz ref you can so no doubt it'll be GPS disciplined, therefore using a similar method you can get some real #'s on how your system performs.Hope that helps.

author: dnessett
author_rank: Regular Contributor
timestamp: July 09, 2018, 11:39:18 pm
content: Quote from: tautech on July 09, 2018, 10:15:39 pmI looked at the Rigol 1104Z manual, but could find no way to measure the skew between channels. So, I don't think I can perform the procedure suggested by the screen shot.However, it is interesting that the test shown displayed 3.9 ns of jitter in the 1pps signal from a GPSDO. For a 10 MHz signal there are 100/360 (=.27777...) ns/degree. Applying this to the phase difference data I collected, the corresponding(maximum)jitter result is:GPSDO delayed: 41.6 degrees = 41.6*.27777 = 11.555 nsRubidium delayed: 17.2 degrees = 17.2*.27777 = 4.7777 nsGPSDO versus Rubidium = 18.4 degrees = 18.4*.27777 = 5.1111 nsOf course, there are differences in the measurements. The 1 pps measurement was over 1001 seconds. The 10 MHz measurements are over 12 msec. Compared to the 1001 cycles for the pps measurement, the 10 MHz measurements are over 120,000 cycles.The percentage jitter for the 1 pps signal is 3.9*10E-7%. For the 10 MHz measurements the are respectively (GPSDO delayed) 11.5%, (Rubidium delayed) 4.77% and (Rubidium versus GPSDO) 5.11%, a much more serious deviation.

author: tautech
author_rank: Super Contributor
timestamp: July 10, 2018, 12:48:09 am
content: Quote from: dnessett on July 09, 2018, 11:39:18 pmYou've got infinite persistence, cursors and a stopwatch haven't you ?

author: tomato
author_rank: Regular Contributor
timestamp: July 10, 2018, 03:07:34 am
content: Quote from: dnessett on July 09, 2018, 10:09:55 pmNothing could be further from the truth. The measurement made with the 20' delay line is extremely revealing. You need to think about what you're measuring, and why the above numbers are alarming.Hint 1: the above numbers have nothing to do with the stability of the oscillator.Hint 2: 12 ms is the red herring.

author: rhb
author_rank: Super Contributor
timestamp: July 10, 2018, 08:09:11 pm
content: If the phase difference between the signal from the same source traveling down two pieces of coax is not constant, then the experimental setup is flawed.Most sources are 50 ohms. Many cheap scopes don't have a 50 ohm input, in which case you need a 50 ohm thru terminator at each scope input. If you drive the two lengths of coax using a T rather than a splitter transformer you will get ringing from the mismatch at the T. Very likely a 75 ohm cable TV splitter will do a better job than a T. The T will have a reflection coefficient of 1/3. The 75 ohm splitter an RC of 0.2, more than 50% lower.Be wary of cheap Chinese thru terminators. I bought some that seemed OK, but recently discovered that some of them are not. So I need to test them all and discard the ones which are NG.

author: dnessett
author_rank: Regular Contributor
timestamp: July 10, 2018, 10:22:40 pm
content: Quote from: rhb on July 10, 2018, 08:09:11 pmThat is what I thought. But, when I studied the data, another possibility arose, which I think is the real answer. (And it has nothing to do with the length of coax used for the delayed signal)I couldn't figure out how the phase difference between a signal and its constantly delayed image could vary as much as the data indicated. Then I noticed an artifact. (see Figure 1)Figure 1 -Figure 1 is an image produced by plotting the (1st 20000 data points in the) result of the following Octave code (where "p" holds the GPSDO delayed phase difference data).Code:Fc=10000000;Fsam=500000000;Fnyq=Fsam/2;[b,a]=butter(6, Fc/Fnyq);output=filter(b,a,p);pf=output;pfn=pf(:,2);pfn=pfn.-mean(pfn);This code normalizes the data by first applying a 5th order 10 MHz low pass Butterworth filter to it (to eliminate the 20 MHz superimposed signal) and then normalizing it by subtracting the mean from each element. I have marked with red lines prominent spikes in the data.A free running oscillator would not have such spikes, but neither the Rubidium oscillator nor the GPSDO are free running oscillators. They are disciplined oscillators comprising a crystal oscillator that is periodically corrected by a reference signal. The periodicity of this correction (technically, its reciprocal) is commonly referred to as the servo loop bandwidth. My current hypothesis is the spikes represent periodic corrections to the frequency/phase of the crystal oscillator.The effect of this is the crystal oscillator free runs for a while and then experiences a movement in frequency/phase. Sometimes this movement is significant, which appears as a large change in the phase difference between the signal and its delayed image.One question that presented itself is how could the free running oscillator drift so far in frequency as to require a significant correction? One possibility is a previous change overcorrected the error, which then requires a significant movement in the opposite direction. That is speculation, but it is at least plausible.I eye-balled the distance between two spikes and it was about 1200 points apart. At 2 ns between data points, this represents about 2.4 usec separation. That would imply a servo loop bandwidth of ~417 KHz.Since I do not have access to the circuit diagrams and design information for the GPSDO, this is still a working hypothesis. However, it is a plausible explanation for the significant differences in the phase difference data. I don't know any engineers who have designed either a GPSDO or a Rubidium oscillator, so I cannot ask them whether this hypothesis makes sense. If anyone reading this thread is such an engineer or knows someone with such experience, comments from them would be appreciated.Added later: By the way, using the phase differences between a signal and its constantly delayed image is a good way to characterize the short-term stability of an oscillator. It eliminates the need for a reference oscillator, the use of which introduces errors in the measurements.

author: tomato
author_rank: Regular Contributor
timestamp: July 10, 2018, 11:01:03 pm
content: Quote from: dnessett on July 10, 2018, 10:22:40 pmNo. Go back and re-read the above statement from rhb. There is no way a correction to the phase of the oscillator will produce those spikes.QuoteLoop bandwidths for GPSDO are orders of magnitude slower than this. Regardless, those spikes aren't due to any servo correction.QuoteSee previous.

author: rhb
author_rank: Super Contributor
timestamp: July 11, 2018, 01:48:44 pm
content: Feed the signals from the two different lengths of coax to your DSO. Place cursors at the zero crossings. Let it run for as long as you like. The phase relationship should not change unless the coax is bad or you have a reflection problem. Until you can get a reliable signal to the instrument there is no point in speculating about possible causes of artifacts in the phase measurements.You will get apparent jitter in a stable signal because the scope is interpolating the trigger point and the measurement points. The 40 pS pulser is far less stable than the 33622A or GPSDO, but it *appears* to have less jitter because it has a very fast edge. I don't know the jitter spec for Leo's GPSDO, but the 33622A is specified at less than 1 pS but the RTM3K indicated ~24 pS standard deviation for the time period. That's not real. It's a DSO artifact.7042 shows the 33622A hooked up with what should be a good piece of coax, but there is an obvious mismatch. There is not 30 pS of jitter in the 33622A. The GPSDO has a faster rise time so the step is more pronounced as seen in 7037, but when I connected the GPSDO directly the step went away. So my "To Do" list got testing and culling BNC cables added.Tomato is absolutely correct, though not very clear. The first requirement is to verify that you can get accurate signals to the test device. There is no reason to assume that the inputs to the AD board are actually 50 ohms. Or that anything else is 50 ohms. 10 MHz is not all that high, but it is still RF and can be confusing because of the speed. I makde the mistake of buying 10 Chinese BNC cables. They make great 50 MHz notch filters, but are useless for anything else.I suggest you start by sweeping your cables on the spectrum analyzer. If at all possible do the cal with a known high quality N cable. My "To Do" list already has testing a bunch of Chinese adaptors of which I know at least one is bad and I suspect there are others.

author: dnessett
author_rank: Regular Contributor
timestamp: July 11, 2018, 11:31:26 pm
content: Quote from: rhb on July 11, 2018, 01:48:44 pmThanks for the useful suggestions.I checked all of the coax cables using the TG on my SA and they were fine. I also checked the BNC Ts and 30 dB pads (see below) and they were fine as well. However, in the process of disassembling and reassembling the set up, I noticed some of the BNC to SMA adapters were loose. I tightened them up and that cleaned up the signal. I performed the input signal cursor test you suggested and it remained stable for an hour.I think it is best at this point to document the test setup and seek constructive criticism of it. Figure 1 shows it in wide angle. The delaying coax and the GPSDO are off-camera to the left.Figure 1 -Figure 2 shows the connections to my Rigol DS1104Z. The input from the DUT comes into channel 2, which is T'ed to the cable carrying the signal to the AD8302 PC board (see Figure 3). The input signal arrives at a T connecting it to one of the AD8302 board inputs through a 30 dB pad and moves past it to one side of the delaying coax. The delaying coax returns to the AD8302 board to another T connected to the board's other input through another 30 dB pad. It then moves past it to channel 1 on the Rigol, which is T'd between the channel and a 50 ohm terminator. Channel 3 of the Rigol is connected to the probe that is shown in Figure 3 connected to pin 5 of the header and grounded at pin 6.Figure 2 -Figure 3 -Figure 4 shows a close up of the AD8302 on its PC board. Pins 1-7 are on the left side. Pins 1 and 7 are ground and pin 4 is +5V. Pins 2 and 6 are the AD8302 inputs, which are fronted by capacitors. It is not apparent what value these are, but one of the test setups described in the spec suggests using 1nF. The impedance for both inputs is spec'd at 3K Ohms/2 pf. Pin 8 (lower right corner) has the 68 pf capacitor I soldered to it. It is a messy solder job because I tried several other capacitor values before settling on the one shown. I stopped trying new values because I was worried the pads on the board would lift.Figure 4 -Figure 5 shows the layout of the chip taken from the spec.Figure 5 -I am in the process of analyzing the new data and will provide the results in a new post.

author: tomato
author_rank: Regular Contributor
timestamp: July 12, 2018, 05:09:44 am
content: Quote from: dnessett on July 11, 2018, 11:31:26 pm1) You've got some termination issues. You can't just connect your signal to the AD chip with BNC tees, because the AD inputs are terminated with 51Ω resistors. You need to connect via splitters or directional couplers.2) Why in the world do you have 30dB attenuators on the inputs of the AD chip?

author: rhb
author_rank: Super Contributor
timestamp: July 12, 2018, 12:29:36 pm
content: Quote from: tomato on July 12, 2018, 05:09:44 amA mild understatement.1) Tee + terminator != thru terminator. That little stub rings like mad, but because it's short you can't see it on the Rigol. Can't see it on my 200 MHz Instek either. But it's there.#6 40 pS pulser to 50 ohm thru#7 same but Tee + terminator#8 Tee+terminator but with a short BNC cable between the Tee and the terminatorThe white reference trace in #7 & #8 is the trace in #6#9 pulser feeding a Tee and BNCs w/ thru terminators. One cable is a couple of inches longer. Again, the reference trace is #6. Note the apparent increase in gain as we now have approximately 25 ohms terminating the pulser rather than the 50 it needs.To summarize: You cannot make meaningful measurements with things connected the way you have them. I suggest a quick review of transmission lines.I also suggest being *very* wary of cheap Chinese RF connectors. I bought a bunch and am finding that there are lots of flaky units waiting to confuse things.

author: dnessett
author_rank: Regular Contributor
timestamp: July 12, 2018, 11:42:55 pm
content: Thank you for your comments and question. I will address them in reverse order.Quote from: tomato on July 12, 2018, 05:09:44 amSince you are asking about attenuators on the AD8302 inputs, I presume you have read the device data sheet. If that presumption is correct, then you know the input power range is 0 dBm to -60 dBm (with respect to a 50 ohm load).I have several oscillators I want to characterize using the test set-up. There are (among a larger set) the GPSDO, which outputs 1.25V P-P sine wave, the Rubidium, which outputs a 1 V P-P sine wave, and an OCXO, which outputs a 50% duty cycle square wave from 0 to 3.5V. The RMS voltage of a 50% duty cycle non-negative square wave is VP-P/sqrt(2). So, the RMS voltage of the OCXO output is ~2.47V. Looking into a 50 ohm load its power is Vrms2/R ~= 6.1/50 = .122 watt =~20.6 dBm. So, a 20 dBm attentuator just misses the mark, which implies the next common attenuator value of 30 dB. That is why I put them in front of the AD8302 inputs.I wanted to address the pad issue first, since its existence complicates the analysis of the termination problem. I designed the input circuit to the AD8302 board with the idea of comparing two signals, a reference oscillator signal and a device (oscillator) under test signal. I didn't design it for comparing a signal with its delayed image; a situation I was forced into when the Rubidium/GPSDO comparison test yielded counter-intuitive results. I will admit, I didn't give the delayed coax configuration enough thought. In my defense I only will say that I was hunting down a bug and in the heat of the chase was more interested in getting some hints about what was going on than engineering interface circuits. And it worked, so it had that advantage.In any case, now is a good time to investigate how the input circuit might affect the results I seek. Figure 1 illustrates the termination topology for both cases.Figure 1 -In the original setup, both inputs had the same configuration, which is shown in the Figure. I measured the through resistance and to-ground resistance of the pad with the following results: 1) through resistance = 94 ohms; 2) to-ground resistance = 50 ohms. The AD8302 has a 51 ohm resistor to-ground in front of each signal input. So, the effective resistance from the coax to ground is 25 ohms in series with 94 ohms = 119 ohms.The length of each coax cable is 3'. The wavelength of a 10 MHz signal isCorrected 7-13-18:98.4 feet64.9 feet (velocity factor of RG-58=.66 and wavelength in vacuum of 10 MHz~=98.4 feet => wavelength in RG-58 is 98.4*.66=64.9 feet). So, each coax is much less than even a quarter wavelength and in practicecan be ignored as a source of standing wavesneed not be treated as a transmission line. This greatly simplifies the computation of termination resistances, since the resistor network at the AD8302 input is effectively directly connected to the terminating resistance at the scope. If you do the math, I should have an 86 ohm terminating resistor at the scope to achieve an effective to-ground resistance of 50 ohms to the coax. I don't have a BNC terminator with an 86 ohm resistor and I really didn't want to build one; but I may reconsider if turns out to be important. In any case I used a standard 50 ohm terminator, which gives an effective coax termination of 35 ohms. Given the short distances of the coax, I think this is probably OK.The delay coax setup is significantly different. The total coax length between the oscillator and scope is about 89', which is very near the full wavelength of the 10 MHz signal. Consequently, it is likely that a standing wave will occur due to the mismatched terminations. Since analyzing complex termination toplogies on coax is a skill gained from experience and since I don't have that experience, I will leave the math to others. Instead, I decided to simply measure some factors and see the results, rather than compute them.One thing to keep in mind: the AD8302 separates the amplitude and phase data. So, a standing wave (which generates a DC bias as a function of position along the coax) should not affect the measurement I am making. There may perhaps be other effects that do, but if so I don't know of them.Figure 2 shows the spectrum of the signal presented to input 1 of the AD8302. This is after it comes from the oscillator and moves through the BNC T and 30 dB pad. As is evident, there are no significant spectral anomolies present. Figure 3 shows the spectrum of the signal presented to input 2 (after it travels through the 83' of coax and then the BNC T and pad). Again, there are no significant spectral features that suggest a problem.Figure 2 -Figure 3 -This leads me to believe the phase difference data should be uneffected by the termination issues you raise. I am, of course, open to clear arguments that suggest otherwise.

author: dnessett
author_rank: Regular Contributor
timestamp: July 13, 2018, 12:20:58 am
content: Quote from: rhb on July 12, 2018, 12:29:36 pmThe figures you posted show the effects of various input hardware on square waves. Right now I am working with fairly pure sine waves. When I get around to measuring a square wave, I may need to revisit some of the issues you raise, but I don't think they are germane at the moment.Also, it is beneficial to remember that, presently, I am measuring phase difference data, not baseband data. Changes in amplitude are filtered out by the AD8302, so at least the amplitude component of the ringing you illustrate will not have an affect on the measurement. In addition, the ringing displayed is of significantly higher frequency than the fundamental frequency. I apply a 10 MHz low pass filter to the data gathered, which means the effects of such ringing will fail to survive the post processing phase.

author: tomato
author_rank: Regular Contributor
timestamp: July 13, 2018, 01:08:01 am
content: Quote from: dnessett on July 12, 2018, 11:42:55 pmYes, I looked at the data sheet. Although the input range is -60 to 0 dBm, the noise in the phase output increases significantly as the amplitude of the input signal decreases. Your GPSDO is +6 dBm and your Rb is +4 dBm. Aren't those the oscillators you've been using in all your tests? You're throwing away signal and compromising your S/N for no reason. Save the 30 dB attenuator for when you are using the OXCO.QuoteYou're making things too complicated again. A properly designed attenuator terminated by 50Ω will appear as 50Ω at it's input.The problem is that your signal sees 25Ω at the BNC tee, because it is split into two paths that are both 50Ω. You need a splitter or directional coupler instead of the BNC tee.QuoteYour goal is to measure phase changes that correspond to time delays measured in ps. Proper termination is electronics 101; good luck if you choose to ignore it.

author: dnessett
author_rank: Regular Contributor
timestamp: July 13, 2018, 01:32:48 am
content: Quote from: tomato on July 13, 2018, 01:08:01 amOK. I need some help finding a splitter that satisfies the requirements you think important. Willthis onework?

author: rhb
author_rank: Super Contributor
timestamp: July 13, 2018, 01:43:14 am
content: It doesn't matter what the signal is. A transmission line is a transmission line. The advantage of the square wave it that it makes the effect of reflections more obvious. With a pure sine wave, all you get are phase shifts.I made up that example because it highlighted the salient issue. You cannot collect valid data with your test setup. To make it work you'll have to get an exemption from God on the laws of physics. Not a likely event. Get some 50 ohm splitters.You do not have a pure sine wave. Sit down and do the algebra for a sine wave and a 2nd and 3rd harmonic reflected at the end of a cable. Then consider the effect of a fundamental frequency shift on the harmonics and what that phase effect will be.I'll let tomato answer this:Is there any reason to expect that the amplitude of the harmonics of a physical oscillator will be constant over time? What is the consequence of the harmonics not being constant amplitude relative to the fundamental. Both of you should be able to quote chapter and verse. This is basic day to day math in a laboratory setting.

author: tomato
author_rank: Regular Contributor
timestamp: July 13, 2018, 02:04:32 am
content: Quote from: dnessett on July 13, 2018, 01:32:48 amYou're woking at 10 MHz, so I'd look for a splitter with lower minimum frequency than that one.Pick up a few attenuators (10dB, 6dB, 3dB).You're trying to monitor the signals with both the oscilloscope and AD chip at the same time? Use the splitter to split the output of your source. Connect the two signals to the scope inputs (hi-Z) with BNC tees, then continue on and terminate at the AD chip. Use as little attenuation as possible at the AD chip. (Ultimately, you'll get rid of either the scope or the AD chip when you want to make serious measurements.)

author: dnessett
author_rank: Regular Contributor
timestamp: July 21, 2018, 12:33:45 am
content: While waiting for power splitters and directional couplers to arrive (hopefully sometime next week), I did some reading about test setups for measuring oscillator stability. One of the calibration steps described requires the measurment of phase noise bandwidth. Since I had time on my hands, I did a quick check of this for the GPSDO, Rubidium and Rigol DG1022. One thing surprised me, so I thought I would forward the results to this thread for comment.I am sure to get blasted unless I state the following. My intention was to explore the phase noise bandwidth issue, not to obtain definitive measurement values. That is a later goal So, the following information is best viewed as exploratory.Figures 1 shows the noise floor of the spectrum analyzer for a band from 9 MHz to 11 MHz using a RBW of 30 Hz.Figure 1 -Using noise markers, I measured the phase noise bandwidth of the oscillators (Figures 2 (GSPDO), 3 (Rubidium), and 4 (Rigol)) from 9 MHz to 11 MHz.Figure 2 -Figure 3 -Figure 4 -Pay no attention to the dBm values, I did not setup the SA to obtain valid power values (for example, the internal attenuator is set to -20 dB). My interest was in the bandwidth of the phase noise, not its power. Here is a tabulation of the pertinent data.OscillatorLowerUpperBandwidthGSPDO9.58910.402813 KHzRubidium9.66910.328659 KHzRigol9.68810.309621 KHzI found it surprising that the GPSDO had the largest phase noise bandwidth. While the difference in bandwidth between the Rubidium and Rigol is probably insignificant, it is still a bit surprising that the Rigol had the lowest value.

author: borghese
author_rank: Regular Contributor
timestamp: July 21, 2018, 07:19:47 pm
content: I think you're measuring the phase noise of the spectrum analyzer; a good oscillator has> 150 dBc at 1 kHz offset.

author: dnessett
author_rank: Regular Contributor
timestamp: July 21, 2018, 09:05:14 pm
content: Quote from: borghese on July 21, 2018, 07:19:47 pmI don't have phase noise specs for the GPSDO, since it is an ebay special. But, for the others:FEI FE5650-100 dBc @ 10Hz-125 dBc @ 100 Hz-145 dBc @ 1 KHzThe spec doesn't indicate, but the dBc figures are almost certainly dBc/Hz.Rigol DG1022-108 dBc/Hz @ 10 KHz.The FEI FE5650 spec comes closest to your suggestion that a good oscillator displays a phase noise of ~150 dBc/Hz at 1 KHz. On the other hand, I bought it on ebay and it is 20 years old, so it may not meet its original specifications.Nevertheless, the kernel of your comment is correct. I have a Siglent SSA3021X, which has a phase noise figure of < -95 dBc/Hz @ 10 KHz, <96 dBc/Hz @100 KHz, and , < -115 dBc/Hz @ 1 MHz. From what I have read, the phase noise figure of a spectrum analyzer measuring phase noise of a device should be at least 10 dB less than that of the device. So, using it to determine the phase noise bandwidth of the oscillators is not going to work out.Any suggestions how to achieve this measurement in some other way?

author: borghese
author_rank: Regular Contributor
timestamp: July 21, 2018, 09:31:47 pm
content: You can read "Choosing a Phase Noise Measurement Technique" from HP or Agilent.

author: tomato
author_rank: Regular Contributor
timestamp: July 22, 2018, 02:14:36 am
content: Quote from: dnessett on July 21, 2018, 12:33:45 amSetting 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 22, 2018, 02:32:53 am
content: Quote from: tomato on July 22, 2018, 02:14:36 amAs 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 22, 2018, 02:57:56 am
content: Quote from: borghese on July 21, 2018, 09:31:47 pmThanks for the references. In prepping for specing a data acquisition system other than my oscilloscope, I readPhase Noise and AM noise measurement in the Frequency DomainandFrequency 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.

author: rhb
author_rank: Super Contributor
timestamp: July 22, 2018, 03:08:24 am
content: Quote from: dnessett on July 22, 2018, 02:57:56 amA 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 22, 2018, 03:32:52 am
content: Quote from: dnessett on July 22, 2018, 02:57:56 amAre you sure about that? It's impossible to believe any scope would be that hamstrung.

author: dnessett
author_rank: Regular Contributor
timestamp: July 22, 2018, 05:45:52 am
content: Quote from: tomato on July 22, 2018, 03:32:52 amYour 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 22, 2018, 09:38:21 pm
content: Quote from: tomato on July 22, 2018, 03:32:52 amIn 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.

author: rhb
author_rank: Super Contributor
timestamp: July 22, 2018, 10:47:32 pm
content: 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 23, 2018, 12:55:37 am
content: Quote from: dnessett on July 22, 2018, 09:38:21 pmWhy do you think it is necessary to sample the phase noise for ~minutes to determine the bandwidth of the phase noise?

author: dnessett
author_rank: Regular Contributor
timestamp: July 23, 2018, 01:44:02 am
content: Quote from: rhb on July 22, 2018, 10:47:32 pmI 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 23, 2018, 02:16:49 am
content: Quote from: tomato on July 23, 2018, 12:55:37 amRight 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 (seeCyclostationary 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 23, 2018, 03:08:12 am
content: Quote from: dnessett on July 23, 2018, 02:16:49 amYou 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 23, 2018, 05:38:51 am
content: Quote from: tomato on July 23, 2018, 03:08:12 amYou 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.

author: rhb
author_rank: Super Contributor
timestamp: July 23, 2018, 01:49:57 pm
content: Quote from: dnessett on July 23, 2018, 01:44:02 amUntil 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 23, 2018, 08:12:39 pm
content: Quote from: rhb on July 23, 2018, 01:49:57 pmWe 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.

author: rhb
author_rank: Super Contributor
timestamp: July 23, 2018, 11:36:14 pm
content: Quote from: dnessett on July 23, 2018, 08:12:39 pmI'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.

author: rhb
author_rank: Super Contributor
timestamp: July 25, 2018, 05:20:26 pm
content: 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 25, 2018, 07:54:26 pm
content: Quote from: rhb on July 25, 2018, 05:20:26 pmI'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 postcorrectly 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

author: rhb
author_rank: Super Contributor
timestamp: July 26, 2018, 12:06:34 am
content: 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 26, 2018, 03:40:54 pm
content: Quote from: rhb on July 26, 2018, 12:06:34 amBecause the phase noise of the SA is greater than the phase noise of the DUTs (seethis previous post). It doesn't matter whether an external or internal oscillator is used to clock the SA.QuoteI 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 (seethis 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 and50100ns (i.e., up to another1/2wavelength) of delay. So, with this equipment, I can get the delayed signal3.33.8wavelengths 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 ofPhase 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).QuoteUltimately, 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.

author: rhb
author_rank: Super Contributor
timestamp: July 26, 2018, 05:32:14 pm
content: 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 26, 2018, 05:44:12 pm
content: Quote from: dnessett on July 26, 2018, 03:40:54 pmThe 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 26, 2018, 09:28:58 pm
content: Quote from: tomato on July 26, 2018, 05:44:12 pmGood point. According toPhase Noise and AM noise measurement in the Frequency Domainpage 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 26, 2018, 10:14:38 pm
content: Quote from: dnessett on July 26, 2018, 09:28:58 pmKeep 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.

author: dnessett
author_rank: Regular Contributor
timestamp: July 26, 2018, 10:44:15 pm
content: Quote from: tomato on July 26, 2018, 10:14:38 pmUnderstood. 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.

author: tomato
author_rank: Regular Contributor
timestamp: July 26, 2018, 11:03:59 pm
content: Quote from: dnessett on July 26, 2018, 10:44:15 pmYou're using the phrase "short term" a lot, yet it has different meanings in different contexts. Short term as it relates to a GPS disciplined oscillator is orders of magnitude longer than short term as it relates to delay line measurements.I think you may find that none of the phase noise of the OCXO is "short term", as defined by the delay line. In other words, all the phase noise is close to the carrier and, therefore, not readily measured by the delay line method.

author: dnessett
author_rank: Regular Contributor
timestamp: July 26, 2018, 11:46:29 pm
content: Quote from: tomato on July 26, 2018, 11:03:59 pmLet me clarify. I am concerned that when measuring the stability of the GSPDO over a few seconds, its phase noise will be that of an OCXO. If so, using it as the reference for short-term (in this context, a few seconds) experiments may not be valid. It may work fine in the medium term (say minutes, but less than an hour) and the long-term (hours), but if the GPSDO over a few seconds displays phase noise equal to that of a OCXO, I will need to figure out how measure the phase noise of another OCXO (and perhaps the Rubidium oscillator) using a different reference than the GPSDO (say, by buying a low phase noise oscillator).In regards to the delay line measurements, it is not my objective to establish the complete phase noise characterization of each oscillator using this technique. I just want to see if the GPSDO can be used as a reference in each type of experiment (i.e., short-term (seconds), medium-term (minutes) and long-term (hours)). While I may not be able to measure phase noise close the carrier using the delay line approach for any oscillator, if the GPSDO has less phase noise than another oscillator away from the carrier, then I can conjecture it will have less phase noise near the carrier than the other oscillator.For example, suppose I measure the phase noise for the GPSDO using the delay line technique and come up with -100 dBc @ 10 Hz, -125 dBc @ 100 Hz and -145 dBc @ 1 KHz. I then measure another oscillator using the delay line technique and come up with -90 dBc @ 10 Hz, -110 dBc @100 Hz, and -120 dBc@ 1 KHz. It is then likely that the phase noise of the GPSDO will be better than the other oscillator for Fourier frequencies nearer to the carrier. This will give me confidence that I can use the GPSDO as the reference oscillator in the two oscillator test setup.

author: tomato
author_rank: Regular Contributor
timestamp: July 27, 2018, 12:03:04 am
content: Quote from: dnessett on July 26, 2018, 11:46:29 pmIn the context of delay line measurements, 10 Hz - 10kHz from the carrierisnear the carrier. You will not be able to measure this with a delay line that is a few hundred feet long.

author: dnessett
author_rank: Regular Contributor
timestamp: July 27, 2018, 12:40:56 am
content: Quote from: tomato on July 27, 2018, 12:03:04 amThe delay line will be almost 600 feet long.

author: tomato
author_rank: Regular Contributor
timestamp: July 27, 2018, 12:58:31 am
content: Quote from: dnessett on July 27, 2018, 12:40:56 amYes, I know. You might want to do a quick calculation of how much the amplitude of a 10 Hz sideband is attenuated when measured with a 600' delay line.Here's another quick sanity check: Add 1 kHz sidebands to a 10MHz oscillator. Make a direct measurement of the modulation index with your spectrum analyzer. Then set up a delay line measurement and measure the apparent modulation index at various delay line lengths. Repeat the experiment with 10 kHz, 100 kHz, and 1 MHz sidebands and look for a trend.

author: dnessett
author_rank: Regular Contributor
timestamp: July 27, 2018, 03:15:32 am
content: Quote from: tomato on July 27, 2018, 12:58:31 amFor the first calculation, do you mean add a 10 Hz sideband in the frequency domain? This isn't what we are talking about and it would be hard to predict, sincethis coax attenuation chartonly goes down to 1 MHz. However, the attenuation per 100 feet decreases with decreasing frequency, so the ratio of sideband to carrier power would be greater in the delayed signal, making it easier to detect.However, I presume you mean a 10 Hz signal FM modulating a 10 MHz signal (which is what 10 Hz of phase noise represents). FM modulation produces more than one sideband for a modulating pure tone, so to make things simple, focus on the sidebands nearest to the carrier. They manifest themselves at 9,999,990 Hz and 10,000,010 Hz. These are so close to 10 MHz that they should attenuate at effectively the same rate as the carrier (1.4 dB per 100 feet of RG-58), so the dBc value should remain constant.The real problem is phase noise for a good oscillator is generally much weaker than the carrier. Detecting these modulating signals is difficult, a problem that has nothing to do with delay lines. For example, the Rubidium spec for 10 Hz is -100 dBc, whereas for 100 Hz it is -125 dBc. This suggests that for a typical oscillator with a Christmas tree shaped spectrum around the carrier (where the phase noise resides) it is easier to detect phase noise closer to the carrier than such noise farther away.In regards to your second sanity check, I again presume you mean modulate a 10 MHz signal with 1 KHz, 10 KHz, 100 KHz and 1 Mhz. It would be an interesting experiment, but you have left off one parameter, the amplitude of the modulating signal.

author: pigrew
author_rank: Frequent Contributor
timestamp: July 27, 2018, 03:34:00 am
content: What is the observed phase noise of a rubidium oscillator? I can't find any specs online... Does any equipment directly use the 6.835... GHz signal? Is it less noisy than a quartz oscillator (OCXO)?I should have read a few more minutes before posting. The RF is synthesized from the 10 MHz signal... so the 10 MHz would be better quality than the 6.8 GHz.

author: tomato
author_rank: Regular Contributor
timestamp: July 27, 2018, 04:23:22 am
content: Quote from: dnessett on July 27, 2018, 03:15:32 amSorry, my choice of of the term attenuation was unfortunate, as it led to confusion. I was referring to attenuation of the signal due to the measurement technique, not due to cable losses.1) Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line. (You can ignore cable losses for the calculation.) You don't actually have to do an exact calculation; a "back of the envelope" calculation will still be enlightening.2) The sanity check is to actually measure some sidebands using both the spectrum analyzer and a delay line setup. For convenience, modulate the 10 MHz carrier at 1 kHz, 10 kHz, 100 kHz, and 1 MHz. The spectrum analyzer will easily resolve these sidebands and give you a confirmation of the modulation amplitude. Compare these results to those measured with the delay line.

author: dnessett
author_rank: Regular Contributor
timestamp: July 27, 2018, 10:52:09 pm
content: Quote from: tomato on July 27, 2018, 04:23:22 amI spent yesterday evening and this morning thinking about this and for the life of me, I cannot understand what you are getting at. For a while I thought you were referencing possible non-linearities in the coax for large distances, but that would not entail a "back of the envelope" calculation. In addition, the cable TV services run thousands of feet of coax to distribute TV channels, so I don't think 600' of coax will have significant non-linearities.If the coax is treated as a linear transmission line and we are to ignore attenuation due to cable losses, then I'm not sure what else to consider. The wavelength of 10 MHz in RG-58 coax is 64.9 feet (seethis post), so 584.1 feet will provide a delay of 9 wavelengths. That is, the original and delayed signals will be in phase after the signal traverses a coax of that length. The only attenuation I can think of is that caused by cable losses. If there is some other attenuating mechanism, you will have to mention it explicitlly.QuoteMy function generator can only FM modulate signals up to 20 KHz, so I set it up to modulate a 1 KHz signal on a 10 MHz carrier. Figure 1 shows the spectrum produced by that experiment. Markers 1 and 3 give the amplitude of the two nearest sidebands for this modulated signal. At the bottom is a marker table that shows the amplitude for the carrier (marker 2) and the two sidebands. The amplitude of markers 1 and 3 are relative to the carrier (i.e., they are in units of dBc).Figure 1 -Figure 2 shows the spectrum produced when that signal is delayed by 183 feet of RG-58 (I have ordered, but not yet received the extra 400 feet I need for the complete delay line). This spectrum shows that the carrier power has decreased by about -3dB. However, the two sidebands have maintained their relative power with respect to the carrier (their relative power actually has slightly increased).Figure 2 -So, this suggests that the delay line will maintain or even slightly improve the relative power of the sidebands with respect to the carrier.

author: tomato
author_rank: Regular Contributor
timestamp: July 28, 2018, 01:45:29 am
content: Quote from: dnessett on July 27, 2018, 10:52:09 pmWe're discussing your latest proposal for measuring the phase noise of on oscillator, using the "delay line" approach. Follow the ball ...Quote from: dnessettQuote

author: dnessett
author_rank: Regular Contributor
timestamp: July 28, 2018, 02:20:40 am
content: Quote from: tomato on July 28, 2018, 01:45:29 amI think the ball you have launched bounces all over the place and I am having trouble following it. You write:Quote from: tomato on July 27, 2018, 04:23:22 amYou suggest calculating the strength of a 10 Hz signal that modulates a 10 MHz carrier after transiting a 600 foot coax, but I am to ignore cable losses. What property of the coax am I to use to carry out this calculation? What effects the diminution of modulating signal strength over a coax other than attenuation due to its lumped elements (fundamentally, its resistance per unit length)?I measured the diminution of a 1 KHz modulating signal on a 10 MHz carrier over 183 feet of coax and found that it looses strength at the same rate as the carrier. What makes 10 Hz modulating 10 MHz over 600 feet different?What are you trying to get at in your proposal:Quote from: tomato on July 27, 2018, 04:23:22 amIf you mean the delayed signal amplitude will be lower than the non-delayed signal, that is pretty obvious (and is a result of cable losses you suggest I ignore). However, the AD8302 uses logarithmic amplifiers to ensure the two signals are at roughly the same amplitude before presenting them to the phase detector circuit. If you mean something else, just state it. Stop trying to mimicAristotleSocrates (identified the wrong ancient Greek philosopher).So far, I am unconvinced that the delay line approach has any problem that the two oscillator approach doesn't have, other than a higher noise floor. In addition, I think digging the noise signal out of the modulated oscillator signal is by far the hardest problem to solve. This is true whether one uses the one or two oscillator setup.

author: tomato
author_rank: Regular Contributor
timestamp: July 28, 2018, 03:13:09 am
content: Quote from: dnessett on July 28, 2018, 02:20:40 amThe delay line method has one serious limitation. I stated what it was five times in my previous post. I can't state any more plainly.The issue is not the properties of the cable. It is about the measurement method, i.e how does a delay line allow an oscillator to serve as its own phase reference, and what are the consequences?One more time:"If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will beif you measure phase with a delay line setupand a 600' delay line. (You can ignore cable losses for the calculation.)"You can approach the problem from another angle, by considering these three questions:1. What do you see with the delay line method if the delay line has zero length?2. What do you see with the delay line method if the delay line is infinitely long?3. What do you see with the delay line method if the delay line has a non-zero, finite length?

author: rhb
author_rank: Super Contributor
timestamp: July 28, 2018, 06:48:19 pm
content: Not to put too sharp a point on it, but:sin(w*t) - sin(w*(t+dt)) = 2*cos(w*(2*t+dt)/2)*sin(w*dt/2)So the result is a cosine wave at over twice the frequency and the maximum amplitude goes to *zero* at certain delays.You can use a delay line if one of two conditions is true:you can vary the frequency of the oscillator over a sufficiently large rangeyou can vary the delay over a sufficiently large rangeThe required delay and frequency relationship is controlled by the sin(w*dt) term.Fundamentally you are trying to apply a technique more suited to UHF and above to HF without bothering to make actual calculations. Rather like when I handed you the solution from Papoulis for a problem and you complained that the upper limit of integration was not infinity.Would you *please* do the brain dead obvious experiment of try each oscillator as the reference for the SA and post the spectra for the other oscillators? That's 12 plots. You just might learn something in the process.

author: dnessett
author_rank: Regular Contributor
timestamp: July 28, 2018, 11:41:53 pm
content: Quote from: rhb on July 28, 2018, 06:48:19 pmYour formulation is incorrect:When you combine the generated and delayed signals at the mixer to get the phase difference, the result is not:sin(w*t) - sin(w*(t+dt)), it is:sin(w*t)*sin(w*(t+dt))= 1/2 [cos((w*t)-w*(t+dt)) - cos((w*t)+w*(t+dt))]= 1/2 [cos(-w*dt) - cos((w*(2t+dt))].This will be zero when:cos(-w*dt) = cos(w*(2t+dt)) or when:-w*dt = w*(2t+dt) + 2*n*PI or equivalently when:(-w*dt)-w*(2t+dt) = 2*n*PI, for some integer n.This occurs when w*(t+dt) = -n*PI. Without loss of generality, we can dispense with the negative sign, since n can be either a positive or negative integer and eliding the minus sign has no effect on the equation.Solving for dt,dt = (n*PI/w)-tThe mixed signal will be zero only at those points in time that satisfy this equation. This is checked by substituting the value of dt into the mixer equation:sin(w*t)*sin(w*(t+dt)) = sin(w*t)*sin(w*(t+[(n*PI/w)-t]))= sin(w*t)*sin(n*PI) = 0Note that we could have solved for t:t = (n*PI/w)-dtSubstituting this into the mixer equation yields:sin(w*t)*sin(w*(t+dt)) = sin(w*[(n*PI/w)-dt])*sin(w*([(n*PI/w)-dt]+dt))= sin(n*PI-w*dt)*sin(n*PI-w*dt+w*dt) = sin(n*PI-w*dt)*sin(n*PI) = 0Either approach yields the same result. There is no value of dt for which the mixer equation is zero for all values of t.

author: dnessett
author_rank: Regular Contributor
timestamp: July 29, 2018, 02:08:59 am
content: Quote from: tomato on July 27, 2018, 12:03:04 amI am going to go out on a limb and say you are wrong. There is no structural reason why the delay line (aka one oscillator) set up cannot measure phase noise arbitrarily close to the carrier. According toPhase Noise and AM noise measurement in the Frequency Domain, the noise floor of the one oscillator set up is reduced compared to the two oscillator approach. The graph given in support of this shows the noise floor rising as the the Fourier frequency of the phase noise approaches that of the carrier. Unfortunately, the justification for this graph is another paper that I have not been able to acquire. So, there is no way to check the argument that led to that graph. However, the text makes no mention of a "structural problem" that leads to the result.There are plenty of practical problems with measuring phase noise close to the carrier. However, these are not specific to the one oscillator set up. They apply equally to the two oscillator set up. I will describe them in a separate post.So, on to the argument that the delay line/one oscillator measurement set up is not structurally deficient as a measurement technique. This argument follows your lead in assuming transmission lines are perfect (not lossy and linear) and it assumes all electronic circuits are perfect (e.g., filters have cutoff frequencies that are exact - they do not drop off over a range of frequencies). In this regard, the argument assumes a bandpass filter that passes only the carrier frequency and the carrier frequency plus 1 Hz. This filter is placed on the oscillator output before the signal enters one side of the mixer and the delay line. So, the signal presented to the double balanced mixer on both sides comprises a 2 Hz band limited to the carrier frequency and the carrier frequency plus 1 Hz. Since the delay line is perfect, the amplitudes of the generated and delayed signal are exactly equal.To keep the argument simple, it is assumed that the generated signal is either at the carrier frequency or at the carrier frequency plus 1. No frequencies between these two are possible. Also, it is assumed that we are interested in SSB measurements. That is why the filter does not admit a band comprising the carrier frequency plus or minus 1.Consider the output of the mixer. Represent the carrier frequency by fc. There are 3 situations to consider:1) Both the generated and delayed signal are at fc. The mixer/phase detector will indicate in-phase.2) Either the generated or delayed signal is at the carrier frequency and the other is at the fc+1. The mixer/phase detector will indicate out-of-phase.3) Both the generated and delayed signal are at fc+1. The mixer/phase detector will indicate in-phase.The spectral density associated with the 1 Hz phase noise will be proportional to the fraction of time the mixer is(Changed 7-29-28)in situation 2 divided by the fraction of time the mixer is in either situation 1 or 3(I thought about this later and now think the formula should be:) in either situation 2 or 3 divided by the fraction of time the mixer is in situation 1. (The exact constant of proportionality requires further thought - but I probably won't spend any time on it, since this is a conceptual argument, not a proposal for an actual measurement setup)I am completely aware that this setup framework is impossible to achieve in practice. However, it demonstrates that the one oscillator set up isstructurallycapable of measuring phase noise as close to the carrier as one may wish.If you disagree or find fault with this argument, I welcome you to provide a counter-argument or refutation. However, I am not interested in playing 20 questions with you. So, if you follow your recent habit of patronizating discourse, I probably will not respond.

author: dnessett
author_rank: Regular Contributor
timestamp: July 29, 2018, 02:13:43 am
content: There has been a lot of discussion recently on this thread about measuring phase noise close to the carrier. I have thought about this a bit and have concluded some of the implied objectives in those posts are unrealistic for a hobbiest, such as I. This post documents the rationale behind that conclusion.Some have proposed that the one oscillator (delay line) set up will have difficulty measuring phase noise close to the carrier due to structural reasons. I have provided an argument against this view and await comment. However, in those posts it is suggested that the one oscillator setup would not be able to measure 1 Hz phase noise associated with a 10 MHz oscillator. While I don't believe there are structural reasons why the single oscillator setup could not achieve this, there are plenty of practical reasons why this objective is outside the capabilities of a hobbiest whether the one or two oscillator set up is used.1 Hz phase noise is that which occurs when an oscillator's instantaneous frequency is at the carrier frequency plus/minus 1 Hz. In the case of a 10 MHz oscillator, this frequency is either 10,000,001 Hz or 9,999,999 Hz. Consider the latter case. The period of a 10 MHz oscillator is 100 ns. The period of an oscillator vibrating at 9,999,999 Hz is 1/9,999,999 = 100.00001 ns. The difference between the 10 MHz and 9,999,999 Hz periods is 10 femto-seconds. Just to get a feel for the realm in which this period resides, visible light has a period roughly in the 2 femto-second range.What phase difference exists when comparing a 10 MHz signal with a 9,999,999 Hz signal? One degree of phase difference for a 10 MHz signal corresponds to roughly 278 pico-seconds. One degree is about .0088 radians. So, for a 10 MHz signal 1 milli-radian in phase difference corresponds to roughly 31.8 pico-seconds. In order to discriminate between a 10 MHz signal and a 9,999,999 Hz signal would require a phase detector capable of resolving phase differences on the order of 36 micro-degrees (.000036 degrees) or .000036*.0088 = 317 nano-radians.This is obviously well outside the capabilities of a typical hobbiest. It may be something that a national laboratory would be equipped to handle, but not an amateur.This raises the question of the limits inherent to the AD8302 in measuring phase noise. The spec gives a figure of 1 degree per 10mV of output voltage by the phase detector on the AD8302. I could find nowhere in the spec where it is indicated that 1 degree is the limit of its phase difference precision. Phase difference precision is not given.So, I have to assume it cannot provide better precision than 1 degree. Given this, what is the lower bound of phase noise frequency it is capable of measuring for a 10 MHz oscillator. As stated previously, one degree for 10 MHz corresponds to about 278 ps. Since the period of a 10 MHz oscillator is 100 ns, the frequency of a signal with a period one degree less is 1/((100-.278)*10e-9) = 10,027,877 MHz. So, the AD8302 can only discrimiate phase noise at about 28 Khz and above.Given the oscillators I wish to characterize, this isn't very good. So, my plan is to get some experience measuring phase noise with the AD8302 and then acquire a more precise phase detector, perhaps one attached to a high-precision PLL. To get into the tens of Hz I would need a phase detector able to discriminate differences at least as low as .001 degrees for two signals in the neighborhood of 10 MHz.Anyone have any suggestions of ICs that might meet those requirements?

author: tomato
author_rank: Regular Contributor
timestamp: July 29, 2018, 04:37:47 am
content: Quote from: dnessett on July 29, 2018, 02:08:59 amSee equation 84. It tells you why the delay line method has limitations. (But I won't ask you any questions about it.)QuoteI apologize if you feel I've been patronizing. A few posts back you wrote the following:QuoteI stated what the limitations of the delay line method are, but you don't seem to want to simply be told the answers. I have posed questions designed to make you think critically about what you're doing, with the goal of leading you to the answers, but you have now rejected that approach. I don't know any other way to convey the information to you.

author: awallin
author_rank: Frequent Contributor
timestamp: July 29, 2018, 07:36:45 am
content: Quote from: dnessett on July 29, 2018, 02:13:43 amdepends on the level of hobbyist...software defined radio, digitizes two 10MHz signals REF and DUT, downcoversion, low-pass filtering, and decimation on FPGA:https://arxiv.org/abs/1605.03505around -140dBc/Hz for 10MHz signals, or 7e-14 @ 1s ADEV in 1 Hz BW.this is with an Ettus/NI N210 which is about 1800eur new or about 800eur on e-bay.Andrew Holme has some impressive stuff here:http://www.aholme.co.uk/PhaseNoise/Main.htmto me it looks like a xilinx dev-board, then an ADC-dev board on the FMC-connector, and some home-made front-ends on that.Probably a bit more $$/eur but still within reach of advanced hobbyist.Looks like he is using the cross-spectrum method (4 ADCs, two for REF, two for DUT) which overcomes the ADC-noise floor - given enough averaging time.YMMV with cheaper two-channel SDRs (like red-pitaya or similar). Noise floor should scale with bit-depth, so if you are just into frequency comparisons of Rb-clocks/GPSDOs an 8-bit two-channel SDR might be enough. If H-masers is more of a thing for you then look at 14-bit or 16-bit SDRs. It would be good to come up with common gnu-radio and UI software for this, so that time-nuts worldwide could evaluate and compare the bang-for-buck of different SDR setups.AW

author: dnessett
author_rank: Regular Contributor
timestamp: July 29, 2018, 08:37:13 pm
content: Quote from: awallin on July 29, 2018, 07:36:45 amThe red-pitaya looks intriguing. From what I have read so far, it appears that it is not open hardware, so when you say "similar", I presume you do not mean a clone. Can you point me anywhere that might reveal what systems are considered "similar" or mention them yourself?Added later: One thing the red-pitaya doesn't have is a high precision phase difference detector, which was what my original query sought. Anyone have information on such a device (preferably an IC with ~ .001 degree precision).

author: dnessett
author_rank: Regular Contributor
timestamp: July 30, 2018, 09:53:00 pm
content: Quote from: awallin on July 29, 2018, 07:36:45 amAn alternative to measuring phase differences between a reference and DUT using hardware would be to utilize the two inputs on the red-pitaya and attempt to do this in software after the signals are captured. The red-pitaya supports 125 Msa/s so each sample is 8 ns apart. So, one approach would be to observe when a signal transitions from negative to positive and extrapolate from the two voltages (the first at the negative sample and the second at the positive sample) to obtain the time when the signal crossed zero. Doing so for both the reference and DUT signals would allow the computation of an estimate of their phase difference. However, in thinking about this, there seems to be at least one problem.At 10 MHz, phase noise of 100 Hz represents a difference in zero crossing time between the ref and DUT of ~ 1 ps (after subtracting any constant phase differences due to things like the signal propagation through the test setup). But, an ADC doesn't provide an instantaneous quantization of its input. In particular there is settling time involved. This indicates two issues. First, the variance of the settling time of one ADC is going to be non-zero, the voltage value for the negative sample and positive sample will have errors. Note, this is not due to quantization error, it is due to variance in the settling time.More importantly, the two ADCs will not be perfectly synchronized, so the difference between the time one produces a negative/positive sample pair and the time the other produces such a pair would have some uncertainty. If the two were not controled by the same sampling clock, this uncertainty could be as much as almost 8 ns. Even if they are controlled by the same sampling clock, the uncertainty is unlikely to be on the order of 1 ps.(Added later to clarify: It is likely to be greater)I could find nowhere in the specs where sampling synchronization between the two ADCs is described or where time bounds on the sampling time between them is given. If this information exists somewhere and someone knows where it is, would they provide a pointer to it?

author: tautech
author_rank: Super Contributor
timestamp: August 03, 2018, 10:36:31 am
content: Stumbled on this thread about a Fluke counter that just might give to the info you need for oscillator analysis:https://www.eevblog.com/forum/testgear/fluke-pm6690-12-digits-frequency-counter/Lots of examples of what it can do later in the thread.

author: dnessett
author_rank: Regular Contributor
timestamp: August 09, 2018, 01:22:52 am
content: Quote from: tautech on August 03, 2018, 10:36:31 amThanks. I'll give the thread a look-over.

author: dnessett
author_rank: Regular Contributor
timestamp: August 09, 2018, 11:43:09 pm
content: Quote from: tautech on August 03, 2018, 10:36:31 amI didn't find the discussion in the thread over-exciting, but I downloaded the PM6690 operator's manual and read sections. The material I found most interesting was the phase function, which measures phase differences between input signals A and B. I then went to the back of the manual, which gives the instrument's specifications.The material on the phase function is a bit disappointing. First, in regards to phase measurement uncertainties, the spec states the following: "NOTE. Phase is an auxiliary measurement function, intended to give an indication, with no guaranteed specification." So, it seems phase measurements are not reliable.Second, when I read the specification on phase resolution, it is 0.1 degree between 1 MHz and 10 MHz. This is somewhat better than the AD8302 (<1 degree), but given that a used PM6690 will set me back at least $300 (probably more), I am reluctant to invest that much for only a small increase in precision. I am thinking of experiments that would provide measurements of the AD8302's phase measurement precision, since the data sheet doesn't really give a figure.Anyway, thanks for thinking of this project and forwarding the information you did. I am happy to look at material that might provide a solution to the problems I face. In the future if you run into something else you think might help, please don't hesitate to mention it.

author: Vgkid
author_rank: Super Contributor
timestamp: August 09, 2018, 11:57:54 pm
content: The HP 5335a has 0.1deg phase resolution. It is 30Hz - 1MHz , though.

author: dnessett
author_rank: Regular Contributor
timestamp: August 10, 2018, 12:16:16 am
content: Quote from: Vgkid on August 09, 2018, 11:57:54 pmThanks. However, I need something that will measure phase differences for a 10 MHz signal. I am looking for anything (instrument, IC) that has a precision of .001 degree, although given the lack of success I have experienced, I am now willing to consider something that provides .01 degree precision.

author: Vgkid
author_rank: Super Contributor
timestamp: August 11, 2018, 05:01:25 am
content: Thinking about this , couldn't you measure the difference in time between the 2 sources , doing this at 1pps will be a lot easier.I need to go to bed , I will edit / reply when rested.

author: dnessett
author_rank: Regular Contributor
timestamp: September 11, 2018, 12:31:39 am
content: I have been inactive on this thread for a while because I found the phase noise measurement device that I was looking for. I purchased an HP11729c carrier noise test set unit from ebay for $299 + $69 shipping. It supports phase noise measurements down to 1 Hz, although I probably won't push it that close to the carrier for the foreseeable future. I have spent most of my hobby time in the past several weeks reading its documentation and some supporting application notes gearing up to use it. It arrived three weeks ago and I have been familiarizing myself with its operation in preparation for testing.I document the test setup to support two objectives: 1) to get some constructive feedback, and 2) to make it visible so when I publish test results those reading them are aware of how they were made. For those uninterested in how the tests are made and wish only to see the results, skip this and the next two of my posts.During my reading, it became clear that much of the test setup and procedures required to determine phase noise are applicable to both the HP11729c and the AD8302. At some point I may compare measurements made with the AD8302 to those made with the HP11729c in order to see how accurate the AD8302 is in measuring phase noise.Figure 1(a) shows the configuration of a generic Heterodyne Phase Detector. The Reference and DUT outputs both feed a mixer. The output of the mixer is passed through a low pass filter, which produces the phase difference signal.Figure 1The AD8302 (Figure 1(b)) uses log amplifiers before the mixer. However, the AD8302 does not itself provide a low pass filter for the mixer output. That must be provided externally.The HP11729C is configured to provide two phase difference signals. Figure 1(c) presents a simplified view of how the first of these signals is created. This signal has a bandwidth of 10 Hz to 10 MHz and varies between 1 and -1 Volt. The mixed signal is first processed by a 15 MHz low pass filter, which feeds a 40 dB low noise amplifier. The result is presented at a connector on the unit, which has an output impedance of 50 ohms.The second phase difference signal (Figure 1(d)) provided by the HP11720C has a bandwidth of 1 Hz to 1 MHz. Its signal path has the mixer and 15 MHz filter in common with the 10 Hz to 10 Mhz signal. However, it is not amplified before output. Instead, it is filtered a second time by a 1.5 MHz filter. The result is then presented at a second connector on the unit's body with an output impedance of 600 ohms. It varies between +10 and - 10 Volts.Figure 2 shows a generic version of the test setup architecture. A concrete version of this architecture may contain other components and may elide some of those shown. Also, the signals feeding the phase detector may be sourced through the coupled port of the directional coupler, rather than the out port, in which case the out port is connected to the oscilloscope. Finally, the inputs to the phase detector may in some cases require the insertion of an attenuating pad to ensure the phase detector is not over-driven.Figure 2Figure 2 also illustrates how the phase detector signal is analyzed. Two (not necessarily exclusive) options are shown. The first is to display the spectrum of the phase detector signal on a low frequency spectrum analyzer in order to read the phase noise spectrum directly. This option is useful for measuring short-term oscillator stability. Normally, the spectrum analyser output is captured in a file in csv format and transfered to a machine for subsequent analysis. The output of the phase detector may also be connected to a data acquisition system that archives a digitized record of the phase detector signal for processing at a later time. This option is necessary for characterizing medium- to long-term oscillator stability.The generic architecture of the oscillator test setup is presented to provide context for the plan to characterize oscillators for short-, medium- and long-term stability. The next post presents the first instance of the generic architecture, which is used to measure short-term oscillator stability. Specifically, it presents the details of a test setup using the HP 11729C as a frequency discriminator (delay line or one oscillator) phase noise test harness. A subsequent post describes the procedures used to turn the spectrum data into a phase noise plot.It is unlikely that the casual reader will deep dive into the details of the next two posts. I provide these details only for those who are interested and to concretely document the measurement techniques used to characterize the phase noise information that I will publish on the EEVblog subsequently.

author: dnessett
author_rank: Regular Contributor
timestamp: September 11, 2018, 12:34:27 am
content: Documented in this and the next post is a detailed description of the test setup and procedures used for measuring phase noise using the HP11729C as a frequency discriminator (one oscillator configuration). This post describes the test setup and the next post the procedures used to obtain phase noise characteristics for several hobbyiest oscillators.I am providing this information with two objectives in mind. First, I invite constructive criticism of these details in order to improve the accuracy of the measurements I will make and publish. Second, putting these details on record allows those who read the phase noise measurements to know how those measurements were made.Figure 1 shows the general architecture of the test setup. The box labeled "Phase Detector" is the HP11729C. This architecture follows the instructions given inthe HP11729C operation manual. I will provide the set up information in stages, described by the headings prior to the textual description.Figure 1HP11729C Mechanical ConfigurationFor this test setup, the HP11729C has the following mechanical configuration:50 ohm terminator on the 640 MHz output. Since the oscillators tested are all 10 MHz, the 640 MHz signal (which generates down converting frequencies to put the oscillator signal into the 10-1028 MHz range) is unused.50 ohm terminator on the unused noise spectrum output. Sometimes this is the 1Hz-1MHz output and other times it is the 10Hz-10Mhz output.The Mode selector is set to phi(phase), CW and the Local selector is on.Device Under testThe Device Under Test (DUT) must output a signal having power within the range of the HP11729C input limits. For 10 MHz signals this range equals -5 dBm to +10 dBm. All the oscillators tested have power greater than - 5 dBm (0.3556 Vp-p). Some however exceed 10 dBm (1 Vp-p). In this case a suitable attenuator pad (not shown in Figure 1) is placed between the DUT and the HP11729C signal input.Directional CouplersThe HP11729C inputs terminate the coaxes that are connected to them. However, to monitor the signals during a test, two directional couplers are used to tap the oscillator and delay line inputs. The signals from these taps are displayed on an oscilloscope (Rigol 1104Z), which allows the use of the Delay Device to bring the two signals into rough quadrature. The Phase Lock indicator on the HP11729C is then used to bring the signals into tight quadrature. The insertion loss of a coupler, if necessary, is considered when determining which attenuation pad to use between the DUT and the directional coupler. Unless otherwise noted, the directional couplers used are MiniCircuit ZDC-10-1 devices.Delay Line and Delay DeviceThe Delay Line is 400'+2*25'+2x50' = 550' of RG-58 coax. The total delay of the signal between the IF output and the mixer input varies depending on the delay value selected for the Delay Device. The Delay Device is described inthis EEVBlog topic. Normally, the signal is delayed about 875 ns (8 full periods plus an extra 75 degrees) by the combined Delay Line and Delay Device (the Delay Complex).Figure 2 shows a Tracking Generator trace of the Delay Complex (with a typical setting to bring two 10 MHz signals into quadrature) from 1 MHz to 20 MHz. As is apparent, the delay characteristic is linear in this frequency region.Figure 2Figure 3 shows an oscilloscope display of the input and output of the Delay Complex with a 10 MHz/1 Vp-pinput generated by a Rigol DG1022. The measurement cursors show the amplitude of the input signal.Figure 3Figure 4 shows the same display with the cursors measuring the amplitude of the output.Figure 4The data in these two images shows that the Delay Complex reduces the power of the input by 8.268 dB. The calculation is:Input: 1.088Vp-p= 4.712 dBmOutput: 420 mVp-p= -3.556 dBmDifference: 8.268 dBAs stated in the next post on procedures, the maximum sensitivity of the frequency discriminator occurs when the delay complex attenuates the input signal by 8.7 dB. While the 8.268 dB value provided by the Delay Complex is somewhat less than this optimal value, the need to put the two signals into quadrature and to utilize coaxes that were available necessitated the use of this slightly non-optimal value.Low Frequency Spectrum AnalyzerThe output of the HP11729C is the output of the mixer after it is passed through a 15 MHz filter and low noise amplifier. This signal carries the phase noise information of the oscillator under test (DUT). The bandwidth of the signal used for the foreseeable future is 10 Hz - 10 Mhz. Some of the most interesting information is at very low frequencies, specifically those less than 9 KHz. The spectrum analyzer used in these tests is a Siglent SSA3021X (hacked to elevate it to the capabilities of a SSA3032X). This spectrum analyzer has a lower frequency bound of 9 KHz, which means much of the interesting information in the phase noise signal is inaccessible.I am currently investigating ways to capture the spectral phase noise data below 9 KHz. For the present, however, this is the lower bound for phase noise measurements using the test setup documented here.

author: dnessett
author_rank: Regular Contributor
timestamp: September 11, 2018, 12:37:24 am
content: Given the test setup architecture documented in my last post, here are presented the procedures used to measure phase noise with a HP11729C in a frequency discriminator configuration for the hobbyiest oscillators targeted by the project. The procedures themselves are derived from theHP11729C operators manualand suitably modified. Mathematical support for these procedures are documented in the appendices of that document as well as in two HP application notes (especially their appendices), specifically,Phase Noise Characterization of Microwave oscillators - Frequency Discriminator MethodandPhase Noise Characterization of Microwave oscillators - Phase Detector Method Method.Warning: This post contains more than a normal amount of mathematics and is probably of no interest to the casual reader. I provide it only to document and justify the procedures I use to derive the phase noise data for various hobbyiest oscillators. Unless you like mathematics and are interested in these procedures, I suggest you stop reading at this point and move on to the next post.Critical to understanding the mathematical justification of the procedures sketched below is the derivation of the phase discriminator equation, which applies to both the Phase Detector (two oscillator) Method and the Frequency Discriminator (one oscillator) Method. This derivation defines two key constants, the phase discriminator constant (\$K_{d}\$) and the phase detector constant (\$K_{\varphi}\$) that control the output of the Phase Detector.The phase discriminator constant depends on the phase detector constant, which is, in fact, the mixer conversion gain/loss constant (in the HP11729C case it is a loss). These two constants are related according to the equation:\$\nu(t)=K_{d}\varphi(t)\$, where \$K_{d}=\frac{K_{\varphi}V_{R-AMP}V_{DUT-AMP}}{2}\$, \$\nu(t)\$ is the voltage output of the Phase Detector after low-pass filtering, \$V_{R-AMP}\$ is the amplitude of the reference oscillator (or the Delay Complex output in the case of the Frequency Discriminator Method), and \$V_{DUT-AMP}\$ is the amplitude of the DUT. To get the units right (seethis discussion(12-2-18 - corrected the missing URL)), \$K_{\varphi}\$ is specified in units of Volts-1.This equation is dervied in appendix B ofPhase Noise Characterization of Microwave oscillators - Frequency Discriminator Method. However, it is not particularly well argued. I have attached a pdf file to this post that presents a more general deriviation. It loosely follows the material in section 8.9.1 ofTime and Frequency: Theory and Fundamentals. I decided not to include this math inline because: 1) there are probably few who are interested in it, and 2) this post is alreadyverylong.The output of an HP11729C when in a Frequency Discriminator (single oscillator) configuration is a signal having the following time dependent voltage (see appendix A ofPhase Noise Characterization of Microwave oscillators - Frequency Discriminator Methodfor the mathematical justification):\$\nu(t)=K_{\varphi}2\frac{\Delta f}{f_{m}}\sin(\pi f_{m}\tau_{d})\sin(2\pi f_{m}(t-\tau_{d}/2))\$where \$f_{m}\$ is the modulation frequency; \$\Delta f\$ is the peak modulation deviation; \$\frac{\Delta f}{f_{m}}\$ is the modulation index; and \$\tau_{d}\$ is the total time delay of the Delay Complex.(Note to the fastidious: Appendix A cited above is generally a good derivation. However, the author gets sloppy when dealing with \$K_{\varphi}\$. In particular, the two input signals are specified as VR(t) and VL(t) where each is defined as v*cos(angle stuff). When the mixer output is displayed, it is given as Vm(t)=\$K_{\varphi}\$*(lots of sinusoids). That would imply \$K_{\varphi}\$ = v2/2, which has units Volts2. But this isn't compatible with the eventually derived equation, which has units V/Hz, not V2/Hz. For those interested in this question, I again suggest readingthis discussion(12-2-18 - corrected the missing URL).)The second sine on the right hand side of the equal sign in the above expression is a time varying signal, while the expression preceding it is the time-independent amplitude of that signal. Thus, the change of amplitude as a function of a change of (Fourier) frequency is expressed as (see above referenced appendix A):\$\Delta V=2\pi K_{\varphi}\tau_{d}\Delta f\frac{\sin(\pi f_{m}\tau_{d})}{\pi f_{m}\tau_{d}}\$For \$f_{m}<\frac{1}{2\pi\tau_{d}}\$ the approximation \$\frac{\sin(\pi f_{m}\tau_{d})}{\pi f_{m}\tau_{d}}\backsimeq1\$ holds, in which case we can use the approximation: \$\Delta V\backsimeq K_{d}\Delta f\$, where \$K_{d}=2\pi K_{\varphi}\tau_{d}\$. \$K_{d}\$ has units Volts/Hz.The condition \$f_{m}<\frac{1}{2\pi\tau_{d}}\$ controls the maximum phase noise frequency this method can measure. As specified in the test setup architecture post, the delay created by the Delay Complex is approximatley 875 ns. Using this value in the above expression yields a maximum phase noise frequency of about 180 KHz. Attempting to resolve phase noise frequencies above this value will yield erroneous results.The lower bound of phase noise frequency resolvable by the test setup depends on both the HP11729C and the spectrum analyzer. The 10Hz - 10 MHz output of the HP11729C resolves phase noise down to 10 Hz, whereas the 1Hz - 1 Mhz output resolves phase noise down to 1 Hz. However, the Siglent SSA3000X has a lower Fourier frequency bound of 9 KHz. Until I figure out how to implement a data recording low frequency spectrum analyzer (or buy one), that is the lower limit of phase noise measurements this setup supports.Calibration and MeasurementThe procedures documented here yield the function: \$\mathscr{L(\mathcal{\mathrm{f}})}\$, where\$\mathscr{L(\mathcal{\mathrm{f}})=\frac{\mathcal{P_{SSB}}(\mathrm{f})}{\mathcal{P_{\mathrm{Carrier}}}}}\$\$\mathcal{P_{\mathrm{Carrier}}}\$ is the power of the (oscillator) carrier signal. \$\mathcal{P_{SSB}}(\mathrm{f})\$ is the power of the frequency discriminator output at the Fourier frequency f. The spectrum analyzer captures \$\mathcal{P_{SSB}}(\mathrm{f})\$ for the phase noise frequencies within the bound alluded to above. However, the mixer output does not include the carrier frequency power. In fact, the carrier frequency power is never directly measured. Instead, \$\mathcal{P_{SSB}}(\mathrm{f})\$ is expressed logrithmically and the log value of \$\mathcal{P_{\mathrm{Carrier}}}\$ set during calibration is subtracted from it. The first procedure (documented in theHP11729C operators manualstarting at pg 3-22) is the calibration used to accomplish this.In brief, a signal generator (in my case a Rigol DG1022) capable of producing FM modulated signals is first connected to the spectrum analyzer. The signal produced is a 10 MHz carrier at -10 dBm modulated by a 10 KHz sinewave. The frequency deviation is set to 200 Hz. This results in sidebands at 10 MHz +/- 10 Khz. The difference between the power of the 10 MHz carrier and the positive 10 KHz sideband is recorded in dB. The signal generator is then connected to the HP11729C input and the Delay Complex is used to interconnect the HP11729C IF output to its 5-1280 MHz input (the other input to the HP11729C mixer). The HP11729C 1Hz-10MHz output is connected to the spectrum analyzer. The Delay Device is then set so that the signal generator input and Delay Complex input are in quadrature. The power of the 10 KHz sideband is noted.The signal generator is disconnected from the HP11729C. The oscillator DUT output is attenuated so that it is in the range -3dBm - 2 dBm. This is then connected to the input port of the HP11729C. The resulting spectrum is recorded (in csv file format) and saved to a USB stick.CorrectionsThe values of the noise spectrum generated using the procedures sketched above need correction in order to produce the correct value of \$\mathscr{L(\mathcal{\mathrm{f}})}\$. This is accomplised using Octave. The csv file is moved to a suitable computer.Corrections are made by applying to every point in the spectrum representing \$\mathscr{L(\mathcal{\mathrm{f}})}\$ the following adjustments (see Appendix A of theHP11729C operators manual):Convert the data from 10 Hz RBW to 1 Hz equivalent noise bandwidth. The Siglent SSA3000X datasheet shows a RBW to noise bandwidth correction factor of -10 dB for frequencies between 1 MHz and 3.2 GHz whether the preamp is on or off. Consequently, 10 dBm must be subtracted from each data point in the spectrum.The phase noise data need correction according to the values used and observed during calibration. First, the carrier power used during calibration (-10 dBm) is added to each phase noise datum, effectively reducing its value by 10 dBm. Then the observed carrier to sideband separation in dB is subtracted from each data point. This converts the data units to dBc/Hz.The phase noise data does not yet represent the values of \$\mathscr{L(\mathcal{\mathrm{f}})}\$. Converting them to \$\mathscr{L(\mathcal{\mathrm{f}})}\$ requires a correction factor that depends on the phase noise Fourier frequency Specifically: \$-20\log\left(\frac{f_{off}}{f_{cal}}\right)\$ is added to each phase noise datum, where \$f_{off}\$ is the Fourier frequency corresponding to the phase noise datum (offset from the carrier) and \$f_{cal}\$ is the calibration frequency (10 KHz). The justification for this correction is given in Appendix A ofHP11729C operators manualstarting on page A-3 in the section titled, "Frequency Discriminator Correction Factor". Notice that for the phase noise datum corresponding to 10 KHz, this results in a log(1)=0 correction factor, i.e., the value of the 10 KHz datum does not change.The Siglent, as do most modern spectrum analyzers, uses logrithmic averaging, which introduces errors when measuring noise. This is explained inKeysight Technologies Application Note: Spectrum and Signal Analyzer Measurements and Noise(see pages 6-8). This requires adding 2.51 dBm to each data point.

author: dnessett
author_rank: Regular Contributor
timestamp: September 11, 2018, 12:39:36 am
content: In order to test the HP 11729C Phase Noise measurement procedures for correctness, I analyzed an FEI FE-5650A. The raw (uncorrected) results from the Siglent SSA3032X spectrum analyzer are shown in Figure 1.Figure 1This data is provided only to show that it remained above the noise floor of the Siglent.Figure 2 is a graph of the corrected data.Figure 2Three data points are of interest:10 KHz : -124 dBc/Hz100 KHz: -169 dBc/Hz180 KHz: -178 dBc/HzThe 10 KHz figure is in rough agreement with theFE-5680A phase noise measurementsposted on John Miles's KE5FX website. (Thanks to Skip Withrow of RDR-Electronics for pointing me to this result.) The 5680A and 5650A are virtually the same device, where the latter is repackaged in a smaller enclosure. However, the figures for 100 KHz are different. I measured -169 dBc/Hz and the graph on the web page shows around -133 dBc/Hz. It isn't clear (at least to me) whether this is a difference between the FE-5680A and FE-5650A or is an artifact of the HP11729C measurement discipline. In regards to the latter, it is interesting to note that as the frequency offset gets larger, the correction factor of \$-20\log\left(\frac{f_{off}}{f_{cal}}\right)\$ drives the corrected phase noise value lower and lower. So, it may be that there is a limit to the separation between the calibration frequency and the offset frequency, since one would expect the noise plot to stablize and become non-decreasing once it becomes pure white noise. As far as I can tell, this is not mentioned in the operator manual or application notes.

author: hendorog
author_rank: Super Contributor
timestamp: September 12, 2018, 10:29:40 pm
content: Great job documenting all of that.I'm unclear on how you can tell that your measurement is above the _phase noise_ floor of the SSA?I thought that you need a low frequency SA which itself has better phase noise performance than the DUT to do a PN measurement using a delay line.The only way I know of to measure below the PN floor of the SA is to use NFE to subtract a pre-measured PN floor. I'm not an expert by any means so correct me if I'm wrong.

author: dnessett
author_rank: Regular Contributor
timestamp: September 12, 2018, 11:46:31 pm
content: Quote from: hendorog on September 12, 2018, 10:29:40 pmThanks.Quote from: hendorog on September 12, 2018, 10:29:40 pmThe noise floor of the Siglent is documented in its data sheet as -126 dBm at 10 MHz with a RBW of 10 Hz with the preamp off and -144 dBm at 10 MHz with a RBW of 10 Hz with the preamp on (which I used for the measurements). The raw data (Figure 1) I obtained from the SA is higher than -100 dBm, so the data is not corrupted by the noise floor of the SA.You are right, I need a low frequency SA to get to most of the interesting data. I am working on that right now. Also, I am trying to understand why at 100 KHz and 180 KHz the corrected data is obviously wrong. I have put a question out to a group that specializes in old HP/Agilent/Keysight equipment to see if they can help.Quote from: hendorog on September 12, 2018, 10:29:40 pmI don't want to measure below the noise floor of the SA (the PN floor of the SA isn't relevant, since the signal from the HP11729C is a voltage that the phase discriminator equation maps to frequency fluctuations). I just wanted to check that the data wasn't being corrupted by the SA's noise floor.

author: hendorog
author_rank: Super Contributor
timestamp: September 13, 2018, 12:03:55 am
content: Thanks!Reading up about it in the pdf you linked - note there is a extra character at the start and end of your link to this pdf.http://hpmemoryproject.org/an/pdf/pn11729C-2.pdf

author: dnessett
author_rank: Regular Contributor
timestamp: September 13, 2018, 12:34:32 am
content: Quote from: hendorog on September 13, 2018, 12:03:55 amThanks for the heads-up on the bad hyperlinks. I usually test all of the links before posting, but I obviously didn't for those. I have fixed them (there were three).

author: dnessett
author_rank: Regular Contributor
timestamp: September 26, 2018, 08:18:09 pm
content: I asked theHP/Agilent/Keysight interest community on groups.ioabout the suspcious results I obtained for the phase noise of an FE-5650A using a HP11729C. There were several suggestions why the HP11729C might not provide the correct values, but John Miles (KE5FX), who also contributes to this forum, provided the correct analysis. To ensure this post is self-contained, I repeat the phase noise measurements I obtained:10 KHz : -124 dBc/Hz100 KHz: -169 dBc/Hz180 KHz: -178 dBc/HzWhile the 10 KHz value was in the range of values shown for the FE-5680A (which is supposedly the same electrical device in a different physical package), the value for 100 KHz was much lower than that shown on John Miles's website (seethe phase noise plot). The phase noise graph did not display a value for 180 KHz.John had used the HP11729C in the past and remembered that for frequencies near the low end of its input range, the input signal sum component in the output of the mixer/LPF drives the LNA into saturation. This means the amplifier cannot properly produce the correct phase noise output.In the case under consideration, the mixer produces a 20 MHz output component of considerable power, which represents the sum of the two inputs into the mixer (10 MHz). The 15 MHz LPF doesn't sufficiently suppress this sum. In addition, looking at the input to the LNA (which is available as the aux noise output), an even stronger 10 MHz component exists in the mixer output. This component will not be suppressed by the 15 MHz LPF. So, both the 10 MHz and attenuated 20 MHz components drive the LNA into saturation. It isn't clear why the mixer is producing a 10 MHz component, since classically only sum and difference products should appear.Figure 1 shows the signal output of the 15 MHz LPF (the aux noise output). Notice the significant 10 MHz and 20 MHz frequency components.Figure 1Figure 2 shows the output of the LNA. There are significant extraneous spurs visible, which is evidence of LNA saturation. Note: the power of the 10 MHz and 20 MHz components is about 50 dB higher than the aux noise output. The LNA is spec'd at 40 dB gain, so this is additional evidence of the LNA going into compression.Figure 2I thank John for this analysis. To be honest, it is not something that would have occurred to me.To work around this problem, I decided to use the 1Hz-1MHz output of the HP11729C. This output does not use the LNA and has an extra 1.5 MHz LPF that will eliminate the 10 MHz and 20 MHz outputs of the mixer.The 1Hz-1MHz output has an output impedance of 600 ohm and a voltage range of +/- 10V. Fortunately, I had bought a 600-50 ohm impedance matching pad in case I had to use this output. This pad has an advertised insertion loss of 16.6 dB. Consequently, when processing the raw output, I included a correction that added 16.6 dB to each data point (in addition to the other corrections specified ina previous post). Since a voltage swing of +/- 10V represents a signal with maximum power of 30 dBm, with the 600-50 ohm matching pad in place, the maximum power of this signal would be 13.4 dBm. On the other hand, since the two inputs are in quadrature, it is likely the actual voltage swing of the output will be much less.I ran the phase noise experiment. The processed spectrum (10Hz-200Hz) is shown in figure 3.Figure 3This yielded better results for 100Khz. Specifically,10 KHz : -96 dBc/Hz100 KHz: -122 dBc/HzComparing these results with those on John Miles website reveals some puzzles. In particular, the published results are:10 KHz: lower bound of around -125 dBc/Hz and upper bound of around -100 dBc/Hz (the data is in a graph and not presented numerically)100 KHz: lower bound of around -133 dbc/Hz and upper bound of around -113 dBc/HzThe 100 KHz result from the HP11729C is within the bounds of the published results, but the HP11729C 10 KHz result is about 4 dB higher than the upper bound of the published result.I decided to back out the 16.6 dB correction for the impedance matching pad and see what happened. Figure 4 shows the result.Figure 4Numerically, the offsets of interest are:10 KHz : -112 dBc/Hz100 KHz: -138 dBc/HzNow the 10 KHz value is within the range of the published result, while the 100 KHz result is about 5 dB lower than the published result's lower bound.What to do? After stewing on this for a while, I had an idea. Suppose the published figure for the impedance matching pad insertion loss was too high? If it was somewhat lower, both the 10 KHz and 100 KHz experimental results might conform to the published result.So, I measured the insertion loss of the impedance matching pad. This was a bit tricky, since the only device I have with connectors at 600 ohm output impedance is the HP11729C. Furthermore, I couldn't use an input signal that would be filtered by the 1.5 MHz LPF in front of the 1Hz-1MHz output.To begin with, I purchased a 600 ohm BNC terminator, which arrived last weeked. Needing only some signal of sufficient power coming from the 1Hz-1MHz output, I did the following. I input a 1 MHz/200 mV signal from my DG1022 to the 5-1028 MHz input (one of the mixer inputs) of the HP11729C. I then input a second 1 MHz/200 mV signal phase shifted by 90 degrees into the Microwave test signal input (the other mixer input). I connected the 1Hz-1MHz output to my scope using a 3' coax (which at 1 MHz should not have transmission line characteristics), first through a BNC-T terminated with the 600 ohm terminator and then through the impedance matching pad to the BNC-T terminated with a 50 ohm terminator.Figure 5 shows the result without the impedance matching pad and Figure 6 shows the result with the pad.Figure 5Figure 6The (rough) peak-to-peak voltages are 9 mV or -36.9 dBm and 1.1 mV or -55.19 dBm. This is a difference of 18.29 dB. The measurements on my scope (a Rigol 1104Z) using a crude cursor set up at the lower limit of the scope's voltage range are not definitive. Nevertheless, it doesn't seem like the insertion loss is less than 16.6 dB. So, this eliminated the hypothesis I was considering.I then considered the possibility that the phase noise data published on John Miles's website was averaged over a significant interval of time. This seems reasonable, since the FE-5650A is intended as a component in a time-keeping device.The sweep interval selected by my SA for 10KHz-200KHz at 10 Hz RBW was about 17 seconds. So, I decided to lengthen this interval to see if that brought the experimental data into line with the published results.Unfortunately, the Siglent SSA3032X would not let me increase the sweep interval when the RBW is 10 Hz. I had to increase RBW to 1 KHz to execute this experiment.Figure 7 shows the results from a 6 second sweep, whereas Figure 8 shows the results from a 300 second sweep.Figure 7Figure 8A cursory examination of the plots shows that increasing the sweep interval actually increased the measured phase noise. For example, the (raw and uncorrected) value for 10 KHz from the 6 second sweep is ~ -49 dBm, whereas the (raw and uncorrected) value for 10 KHz from the 300 second sweep is ~ -44 dBm. In other words measured phase noise gets worse for longer averging times.At this point, I decided to present the results I have so far obtained and ask for comments. As things stand now, I can think of 4 possibilities for the discrepancies between the experimental results I obtained and those published on John Miles's website:• There is a problem with my measurement methodolgoy or its execution.• There is a problem with the published results.• The FE-5680A and FE-5650A are not identical except for packaging. The published results do not apply to the FE-5650A.• The published results are for a freshly minted FE-5680A, whereas my experimental results are for a 15 year-old FE-5650A. Aging has deteriorated the phase noise performance of the latter.I would be interested in comments addressing these possible explanations or other explanations for the discrepencies between the results I have obtained and the published results.

author: KE5FX
author_rank: Super Contributor
timestamp: September 27, 2018, 04:06:18 am
content: Maybe try a phase-locked measurement instead of a frequency discriminator measurement. The calibration process for that should rule out any gain/loss problems in your test signal path.

author: dnessett
author_rank: Regular Contributor
timestamp: September 27, 2018, 05:04:59 am
content: Quote from: KE5FX on September 27, 2018, 04:06:18 amThanks, John, for the suggestion. However, there are some problems with that approach.First, the phase-locked method requires an tunable reference oscillator to keep it and the DUT in quadrature. One of the advantages of the frequency discriminator setup is once you obtain quadrature (by adjusting the delay complex), the inputs stay in quadrature. I have thought about this and have bought a couple of BLILEY 10 MHz sine wave OCXOs that can be adjusted in the vicinity of +/- 4 Hz. Somewhere down the road I plan on trying this out, but I have to think through the interface between the HP11729C and the adjustable OCXO. Of course, I could buy a used HP8662A with option 3 tunable source. However, on ebay, the cheapest used HP8662A with option 3 I could find goes for $2,700. Right now that is outside my hobby budget.Second, at present I am limited to phase noise measurements greater than 10 KHz because that is the lower limit of my SA. So, I am trying to figure out a way to implement a low frequency recording spectrum analyzer and investing a lot of my time on that. I can't say I am near solving this problem, but I don't want to go through all the learning it would take implement the phase-locked approach at the present by putting the low frequency spectrum analyzer on the back burner. I intend to do this sometime in the future, but right now I want to figure out how to measure phase noise less than 10 KHz using the frequency discriminator approach.Third, I am new to phase noise measurement and one of the attractions of this project is to learn. If I just give up on the frequency discriminator approach without understanding what is going on, I have failed to meet this objective. In addition, while I won't say I never give up, when I do it leaves a bad taste in my mouth.Dan

author: dnessett
author_rank: Regular Contributor
timestamp: November 27, 2018, 12:20:15 am
content: I have been searching for a low frequency recording spectrum analyser in order to measure the phase noise spectrum of various hobbiest oscillators. This has taken a very long time and significant effort, but eventually paid off. Here I describe the unsuccesful part of my search in order to document some approaches that do not work. I have started a new thread to describe the approach that was successful. I use a different thread for this becausea low frequency recording spectrum analyzeris an instrument that has many uses, not just the measurement of oscillator phase noise.I needed an SA that measures signal spectra from 1 Hz to at least 200 KHz. I have a Siglent SSA3021X hacked to SSA3032X. However, this SA is limited to frequencies above 9KHz. My first attempt at creating a low frequence SA involved a Spyverter upconverter that shifted low frequencies to a band in the 120 - 180 MHz range. The marketing blather for the Spyverter indicated that it shifted "almost DC" to 60 MHz into this range. My plan was to upconvert the low frequencies and then analyze the spectra on my Siglent.This did not work because the marketing information was (like most marketing drivel) dead wrong. Below about 1 KHz the Spyverter introduced significant insertion loss, which meant I would have to correct the value for each frequency bin in order to obtain correct spectrum data. (seethis post). To be fair, the technical information I could find on the Spyverter (there wasn't much) indicated a lower bound of 1 KHz. While it would be possible to calibrate the Spyverter and correct the spectrum accordingly, it is likely the correction factior would depend not only on the fourier frequency, but also on the total signal power. Furthermore, there is no evidence that two Spyverters would generate the same correction data. So, I abandoned this approach.My next attempt was to see if there was a low frequency spectrum analyzer on Ebay. The best deal was a used HP3580A, which typically costs about $750. However, this scope is not a recording instrument, so I couldn't postprocess the data I measured (which was a requirement for my application). Furthermore, it measures only 5Hz to 50 KHz. I needed an instrument that was capable of computing spectra from 1Hz - 200 KHz. So, I gave up on used instruments from Ebay.I then read a post that suggested PicoScope USB products had a good FFT spectrum analyzer built in. After investigating its capabilities, I bought a PicoScope 4262 (I originally purchased a 4224, but its 12-bit ADC was insufficient, so I returned it and got the 4262, which is 16-bit). This approach worked, but there are some problems that require workarounds. Thelow frequency recording spectrum analyzerpost describes them. The PicoScope 4262 costs more than I originally budgeted for a low frequency recording spectrum analyzer (it lists at $1235). Fortunately, TEquipment had one on sale for $915.51 (I got the last one).Now that the capture of low frequency spectra is solved, the next step in using the frequency discriminator configuration of the HP11729C is calculating its noise floor. I will make the necessary measurements and calculations and report the results. I also need to change some of the post-processing calculations, as the original ones assumed the use of an analog spectrum analyzer, not an FFT-based instrument. I will publish the modified calculations after figuring out how to obtain the noise floor information.

author: dnessett
author_rank: Regular Contributor
timestamp: January 12, 2019, 12:42:46 am
content: I have finally obtained the last piece of infrastructure necessary to analyze the phase noise of hobbiest oscillators. To ensure that phase noise measurements with the frequency discriminator configuration of the HP11729C are not simply displaying the phase noise of this instrument, I need to measure its noise floor. The approach I decided to take was to obtain a low phase noise oscillator and apply it to the frequency discriminator. The result would either be the phase noise floor of the oscillator or the phase noise floor of the frequency discriminator (or some piecewise composition of both). In any case, the result would be an upper bound on the phase noise of the frequency discriminator. As long as phase noise measurements stay above this floor, they should be accurate.My search for an ultra low phase-noise oscillator took longer than I expected. I first tried to purchase a new OX-204 oscillator from Microsemi. This was a frustrating exercise, since they do not provide this product through a distributer. So, I had to contact the manufacturer and after several weeks of email conversations, it became apparent they were not set up to deal with sales to individuals.So, I looked around for a used ultra-low phase noise oscillator. I found one - the Morion MV89. It had at least two advantages over the OX-204. First, its phase noise specs were significantlly better (those given below are for 5 MHz, but the literature leads one to believe that the 10 MHz version has similar characteristics):Frequency OffsetdBc/Hz1 Hz-10510 Hz-130100 Hz-1451 Khz-15010 KHz-155Table 1 - Phase noise of the Morion MV89This is significantly better than the advertised phase noise of a new FE-5650, which is:Frequency OffsetdBc/Hz10 Hz-100100 Hz-1251 Khz-145Table 2 - Phase noise of the FE-5650The GPSDO I intend to test has no published specs, so it is impossible to say whether the Morion MV89 specs are better or worse.The second advantage of the MV89 is cost. The OX-204 has a new cost of $480 (in the configuration I attempted to buy). The used MV89 cost me $40 on ebay.One disadvantage of the MV89 is its reputation for poor manufacturing quality control. A number of purchasers have reported its failure after ~30 days. However, they have also reported that if a unit last longer than this interval, it generally is reliable. Since the device costs so little, I bought 3 of them to ensure I had at least one that I could rely on.Each unit I purchased is about 14 years old. So, it is likely they will not deliver their advertised new phase noise specifications. However, as long as the noise floor produced using them in the frequency discriminator configuration of the HP11729C is lower than the measured phase noise of the test units, they will have done their job.One advantage of the MV89 is it has an electronically controlled frequency adjust input. The range of carrier frequencies produced by this adjustment is 10Mhz +/- 4 Hz. This means I should be able to use them to configure the HP11729C as a phase detector instrument. One problem is the frequency adjust voltage of the HP11729C is +/-5V, whereas the frequency adjust voltage that the MV89 expects is +/- 2.5V. I will have to design a simple resistor divider circuit to bring these two into compliance.The next step is to obtain a noise floor measurement of the frequency discriminator configuration of the HP11729C and then start testing 10 MHz oscillators.

author: jpb
author_rank: Super Contributor
timestamp: January 12, 2019, 02:51:43 pm
content: I have an MV89 I got from China years ago and it seems to work fine (though I don't have anything that will measure its phase noise though.The main issue with them I seem to remember for Time Nuts postings is that the 10MHz devices are frequency doubled 5MHz devices:https://www.mail-archive.com/time-nuts@febo.com/msg58269.htmlThe reliability issue is to do with a capacitor going bad but that shows up as a low level output I think.It will be interesting to see what your measurements show.

author: dnessett
author_rank: Regular Contributor
timestamp: January 14, 2019, 10:12:12 pm
content: Quote from: jpb on January 12, 2019, 02:51:43 pmThanks for the info, jpb.Given your experience with the MV89, I have a question. When I ran one of the MV89s for an hour or so, I noticed it became quite hot. I am still able to pick it up and hold it my hand, but it is on the borderline of that. When you were working with yours, did you have a heatsink on it? If so, how did you attach it (as there are no screw holes for this purpose on the top)?

author: FriedLogic
author_rank: Regular Contributor
timestamp: January 19, 2019, 10:23:40 pm
content: The reason that the case of an MV89 is quite hot is that it has a large outer oven very close to the case. There's a picture of one opened up with the outer oven top removed on this page:http://www.rbarrios.com/projects/MV89A/So definitely no heatsink required.The temperature control on an oven oscillator can fail, and then it can get really hot. That's one of the reasons that you have to be careful if you ever cover them.

author: dnessett
author_rank: Regular Contributor
timestamp: January 30, 2019, 01:32:50 pm
content: Quote from: jpb on January 12, 2019, 02:51:43 pmQuote from: FriedLogic on January 19, 2019, 10:23:40 pmSince both of you seem to have experience with the MV89, I have a question about its operation. I have been beating my head against a wall for the past 2 weeks trying to get the adjust function to work. I have designed 3 circuits of increasing sophistication that translate -/+ 10 V to 0-5 V and then connected the output of these circuits to the adjust pin of the oscillator. With the latest circuit, I could only get the voltage on the adjust pin to move from 5 volts to about 4.1 volts.My frustration then led me to do what I should have done in the first place, I used a resistor between the ref pin and the adjust pin to see if I could get the voltage to swing between 0 and 5 volts. I first started with 10 Kohm, then increased to 100 Kohm, 1 Mohm and then 10 Mohm. As the resistance increased, the available swing between the two pins increased.Finally, I just tested the voltage with a short between the adjust and ref pins and leaving the ref pin open (effectively, infinite resistance). In the latter case, the adjust pin would only go down to ~2.5v. With the pins shorted, the voltage at the adjust pin is 5v.The spec states that the adjust pin should be capable of a swing of 0-5v. But, I can't figure out how to get it below 2.5v. The information on frequency adjust is almost nil.Even when I bring the adjust pin up to 5v, I see no effect on the output frequency. When I first turn on the oscillator, my frequency counter shows 9,999,995Hz or thereabouts. As the oscillator warms up it reaches 9,999,999.5Hz. So, my counter is able to see changes in Hz. (It is a very old discrete transistor piece of equipment built by a company called Kay Elemetrics Corp, called a Count-a-Marker, model 8323A. The date on the drawings is 2-6-1970, so we are taking about something almost 50 years old).Even if the counter isn't accurate in regards to the absolute frequency, it should show changes as I change the voltage on the adjust pin. But, so far I cannot see any change whatsoever.Any help you or others can provide on how to use the adjust pin would be greatly appreciated.

author: FriedLogic
author_rank: Regular Contributor
timestamp: February 01, 2019, 01:48:26 am
content: Hi,The frequency control pin - 'Uin' in the data sheet - on the MV89A the I have is biased to half the reference voltage 'Uref'. In this case it's 4.96V for Uref and 2.48V on the Uin pin if nothing is connected to it.Connecting Uin to 0V with a 1K resistor pulled the voltage on it down to 64mV (so 64uA current), and connecting it to Uref with the 1K takes it up to Uref less 63mV. Like most frequency control inputs on oscillators, it's quite high resistance so is not hard to drive.The frequency change was -3.53Hz and +3.47Hz. Data sheet spec is >+/-2.5Hz, so most counters should see it fine.

author: dnessett
author_rank: Regular Contributor
timestamp: February 07, 2019, 09:01:25 pm
content: Quote from: FriedLogic on February 01, 2019, 01:48:26 amSorry about the late reply. I have notifications turned on, but for some reason did not receive an email when your post appeared.I will respond in a day or two. I have had a family medical emergency that I am dealing with right now.

author: dnessett
author_rank: Regular Contributor
timestamp: February 12, 2019, 12:08:37 am
content: Quote from: FriedLogic on February 01, 2019, 01:48:26 amI have had a bit of time to work on experimenting with the Adjust pin of the MV89. Here are the results.I measured the output impedance of the Ref Pin and the input impedance of the Adjust pin. Figure 1a shows the test setup for the former.Figure 1I first measured the voltage when R_out_test was open and then for the values 200 ohms and 400 ohms. The open voltage was 5.09V. The output impedance of the Reference pin is then:Output Impedance = ((5.09/V_out_test)-1)*R_out_testHere are the results:R_out_testV_out_testOutput Impedance200.553.35104.16399.94.02106.44So, it appears the Output impedance of the Reference Pin is approximately 100 ohms.Figure 1b shows the test setup for measuring the input impedance of the Adjust pin. Varying R_Input_Test and measuring the voltages V1 and V2 gives the current flowing through R_Input_Test, which then is used to estimate the input impedance of the Adjust pin.Iin=(V2-V1)/R_Input_TestZin=V1/IinI performed the test for three different values of R_Input_Test. Here are the results:R_Input_TestV2V1IinZin1.0001K3.00952.994515uA19963310.255K3.00952.94796.024uA489320100.39K3.00952.72252.856uA952305This suggests the Adjust pin is approximately a current sink without a fixed input impedance.I then tried the suggestion by FriedLogic of connecting a 1K resistor to a voltage source and connecting the output of the resistor to the Adjust pin. Here are the results:Voltage SourceFrequency5V9999999.612.5V9999999.580V9999999.53Unless I am reading the frequency counter incorrectly, I am only getting a fraction of a Hz variation in the output frequency for the full range of the Adjust pin specified input.Anyone have an idea what might be happening (including an operator error on my part)?

author: FriedLogic
author_rank: Regular Contributor
timestamp: February 13, 2019, 08:58:22 pm
content: The generic data sheet specification is that for a 0-5V change in the control voltage you should get at least 5Hz change in the output frequency. You're not getting close to that, so the oscillator looks like it might be faulty. It would also be worth checking the connections and power supply, just in case.The frequency control input on my one looks like the 2.48V on it is a voltage divider made up from two resistors of around 75K to divide the reference voltage by 2. Maybe somebody has opened up the ovens and knows what the circuit actually is.

author: SoundTech-LG
author_rank: Frequent Contributor
timestamp: February 14, 2019, 04:13:00 pm
content: These MV89s seem of poor reliability in general. While they do perform well within spec, the failure rate seems high. I have one that I burned in for a couple of years. I then installed it, and within a few weeks it died. It seems the heater is no longer working. Maybe I'll heat it up with a blow torch and pop the guts out...

author: dnessett
author_rank: Regular Contributor
timestamp: February 15, 2019, 12:28:40 am
content: Since others were getting frequency variation when the adjust pin was set to voltages between 0 and 5V and I was not and since this was true for all three MV89s that I had purchased, I began to suspect my frequency counter was faulty. Therefore I bought a used HP5335A from ebay. This was the quickest delivery of an ebay item that I have ever experienced. I ordered it on Feb 12 and it arrived in the evening of Feb 13. This certainly had something to do with the fact that the seller was located only 50 miles from my residence, but still I was completely amazed that purchase through shipment preparation and then shipment transport (by Fedex) took only 2 days.Anyway, varying the voltage on the adjust pin of each MV89 yielded the following data on the HP 5335A:Table 1 - MV89 - 1Adjust Pin VoltageFrequencyopen10,000,1510V10,000,1472.5V10,000,1515V10,000,154Table 2 - MV89 - 2Adjust Pin VoltageFrequencyopen10,000,1530V10,000,1492.5V10,000,1535V10,000,156Table 3 - MV89 - 3Adjust Pin VoltageFrequencyopen10,000,1530V10,000,1502.5V10,000,1535V10,000,157This confirms that there is nothing wrong with the MV89s I bought. Frequency variation is approximately 7 Hz for each (I have left off the fractional hertz part of the measurement). This variation agrees with what FriedLogic specified in his post (-3.53 to +3.47Hz).Now I have to figure out why the HP5335A is measuring ~150Hz greater than 10MHz for each oscillator. The fact that each oscillator is showing this suggests that the frequency counter is out of calibration. I confirmed this by measuring the output of an ebay 10 MHz GPSDO and observed its frequency to be 10,000,151 Hz.The HP5335A was advertized to have option 10, which is the OCXO equipped version, but I haven't looked inside yet to confirm this. I also looked at the manual and could not find a way to trim the frequency of the instrument's internal frequency standard to correct this apparent anomaly. However, I can always use an external oscillator and bypass the internal oscillator.Now that it is confirmed the MV89s can be adjusted properly, the next step is to build enclosures for each of them that takes the frequency adjust signal from the HP11729C and adjusts the frequency of the oscillator so I can use the HP11729C in a phase detector configuration.

author: FriedLogic
author_rank: Regular Contributor
timestamp: February 16, 2019, 11:37:55 pm
content: Quote from: dnessett on January 30, 2019, 01:32:50 pmOops, I didn't pay enough attention to what you said there. The frequency change during warm up should be in the hundreds of hertz (it's 310Hz low when cold at 20°C ambient on my one), so that was a giveaway.The HP5335A frequency error sounds like a fault rather than a calibration issue.As you mentioned, the first thing to try would be an external reference.I think that the HP5335A normally used a 10811 OCXO, which has a hole on the top for the frequency adjustment trimmer capacitor in it, but this will not adjust it by 150Hz.The 10811 that I have is about 210Hz low when cold at 20°C ambient, so if your one is 150Hz low it might be worth checking if the oven is heating up - if it's there at all!

author: dnessett
author_rank: Regular Contributor
timestamp: February 18, 2019, 01:32:15 am
content: Quote from: FriedLogic on February 16, 2019, 11:37:55 pmI took off the cover of the HP5335A and powered it up. It does indeed have a 10811 OCXO. After 1/2 hour there was no noticeable warmth coming from the exterior of the 10811. So, either it is busted, or something else is wrong (e.g., power not getting to it).Right now fixing it will have to take a backdoorseatto building the MV89 enclosures. Did you happen to replace the fan in your HP5335A? If so, which model did you use? Mine is using a DC version of the original Pabst fan, which sounds like a small refrigerator.

author: FriedLogic
author_rank: Regular Contributor
timestamp: February 20, 2019, 12:40:25 am
content: I don't have that counter, just the oscillator - this thread has some info if you've not already seen it:https://www.eevblog.com/forum/testgear/hp-5335a-timer-counter-anything-i-should-know/If you get to looking at the oscillator, there are various versions of the manual and other info online, such as:http://ftb.ko4bb.com/getsimple/index.php?id=manuals&dir=HP_Agilent/HP_10811_Crystal_Oven_OscillatorThe thermal fuse and its connections often cause problems, so if the power is getting to it that might be a good place to start.

author: Gerhard_dk4xp
author_rank: Frequent Contributor
timestamp: February 24, 2019, 08:21:32 pm
content: The MV89A that I have on my table definitely needs a +/- 5V tuning voltage.I also have one that stops oscillating when Vtune > 0.5V. It seems theydrift down over time.I had about 50% loss with my Chinese MV89As.They have all a 20 year hot life behind them and are removed from theirboards in a most cruel way. There are lots of scars to prove that.The MTI-260 also seem to have a lot of subtypes.I'm just doing a PLL to lock all of them to an incoming reference frequency.

author: dnessett
author_rank: Regular Contributor
timestamp: February 28, 2019, 01:10:08 am
content: One piece of design I need for the enclosure is an interface between the HP11729C Freq-Cont X-Osc output and the MV89A adjust input. This interface must convert the +/- 10 V swing of the Freq-Cont X-Osc output to the 0-5 V swing required by the adjust pin on the MV89A.I came up with a simple divider network to achieve this conversion, shown in Figure 1Figure 1 -The 470 resistor divider pair converts +/- 10 V to +/- 5V. Using the 5V reference provided by the MV89A, the 10K resistor divider pair converts this swing to 0-5 V (in theory). I breadboarded this circuit and found that the actual swing is 1.06V - 4.3V. This reduced breadth is due to the actual voltage produced by the Freq-Cont X-Osc circuit when driving the interface. Instead of +/- 10 V, the range observed on the Freq-Cont X-Osc input was: -6.1V -> +7.2V. Since the output impedance of Freq-Cont X-Osc is specified as 100 ohms and it is driving ~940 ohms, this is a little surprising.However, the circuit is not a simple passive network, because the MV89 Ref connection to the 10K resistor divider has an output impedance of 100 ohms (see previous message). I decided not to pursue a network analysis of the circuit, since the measured swing is sufficient to drive the MV89A adjust pin.The SPDT switch allows the adjust pin to be driven either by the Freq-Cont X-Osc line or by a 2.5V constant voltage derived from the Ref pin. This means the MV89A can be used either as a reference oscillator in an HP11729C phase detector configuration or as a DUT analyzed by the HP11729C in a frequency discriminator configuration.I would welcome thoughts about how to test this circuit with the HP11729C to insure it can keep the MV89A in quadrature with another oscillator over long time intervals when using a phase detection configuration.

author: dnessett
author_rank: Regular Contributor
timestamp: March 10, 2019, 03:23:29 pm
content: Quote from: FriedLogic on February 20, 2019, 12:40:25 amThanks for the pointers to the manuals for the 10811. Now that I have an enclosure built for one of the MV89s, I need to get the HP5335A repaired. I started with recalibrating the two adjustable power supply voltages. The 3.1 supply was off, but I was able to get it back into range. However, the 15.7 power supply was at 15V and I could not get it to 15.7 V by adjusting the controlling pot. I suspect the HP11811 might be causing the problem, so I plan to take it out of the 5335A and troubleshoot it.However, the power supply is connected to it by an edge connector. I thought about using a alligator clip to attach power by clipping it to the pad for that purpose, but am concerned that it will slip and put 20V onto some other pad, thereby damaging the device.Do you have any suggestions? Is there a way to test the thermal fuse and connections without applying power to the 10811? If not, are mating connectors for the edge connector widely available (eBay or perhaps an electronic parts distributer)? How do you power your 10811?

author: Gerhard_dk4xp
author_rank: Frequent Contributor
timestamp: March 10, 2019, 06:33:50 pm
content: The mating plug isEDAC 305-030-520-202That's what is printed on it. I can't find where I have ordered them, at least not quickly.Probably Mouser or Digi Key.I'm just doing version 2 of my OCXO support board. It hosts one of 10811A, MV89, MTI260or CVHD-950 or ECOC2522, KVG O-30-ULPN-100M, KVG O-40-ULPN-100M for 100 MHz.There is a Xilinx Coolrunner2 that creates a 1pps out and that has a dual Flipflop PFD.The Oven can be synchronized to an incoming reference frequency or an incoming 1pps.There is also a doubler for 5 -> 10 MHz if needed.This is V1:<https://www.flickr.com/photos/137684711@N07/30952252115/in/album-72157662535945536/><https://www.flickr.com/photos/137684711@N07/30952263115/in/album-72157662535945536/>It used a ring mixer as phase detector. That could not work for 1pps.But this is still work in progress.regards, Gerhard

author: dnessett
author_rank: Regular Contributor
timestamp: March 18, 2019, 12:51:31 am
content: Quote from: FriedLogic on February 20, 2019, 12:40:25 amInstead of trying to fix the HP10811, I decided to buy one from eBay and replace the one that came with the instrument. This fixed the problem. By tweeking the frequency adjust screw on the new 10811, I got the HP5335A to measure one MV89A oscillator frequency to within .01Hz of 10 MHz. Also, the new 10811 is warm to the touch after 10-15 minutes, whereas the old one did not warm up at all.Of course, in effect I am using the MV89A as a calibration oscillator, so there is no guarantee that the HP5335A is actually calibrated properly. But at least it should be possible to get within 1-2 Hz of an accurate measurement.In regards to the HP10811, I did buy a connector, so at some future point I could attempt to fix it. However, I was already sidetracked by trying to get the HP5335A to work properly. I didn't want to get sidetracked on a sidetrack. My goal is measuring phase noise, which now, after building enclosures for the other 2 MV89As, is within reach.

author: jpb
author_rank: Super Contributor
timestamp: April 19, 2019, 12:55:19 pm
content: Quote from: dnessett on January 14, 2019, 10:12:12 pmSorry, I've only just seen this and now it is rather too late to reply!Just for the record, my MV89 did not have a heat sink and it did get warm but almost all OCXOs do - in fact some get quite hot. This is not that surprising as the temperature of the crystal is around 70C or more, an OCXO that is specced to operate up to 70C must keep the crystal at some temperature above that as it has no means of cooling only heating.On the subject of the 10811 - I had one which was broken, (weird waveform). I managed to mend it using the repair manual which is very good but then I was doing one last probe of all the voltages and managed to blow up one of the transistors. I replaced it with one I had but it was not the right specs. The original type is unobtainable but recently I got round to ordering a similar part but it has been a couple of years and one house move since I last worked on it so I'm going to have to start over when I have time.I'm looking forward to seeing how your phase noise measurements go dnessett.I am thinking of getting a 16bit picoscope myself but I'm torn between this and an audio interface with word clock. Are you still happy with the picoscope?I wish it had 4 inputs instead of 2. I want to use it for ADEV measurements but for three-cornered-hat measurements I really need 3 or 4 inputs.Also it would be nice to have an external clock reference option - I can't work out if this matters or not if one input is used for a reference.

author: dnessett
author_rank: Regular Contributor
timestamp: April 19, 2019, 10:06:50 pm
content: Quote from: jpb on January 12, 2019, 02:51:43 pmI only use my Picoscope as a spectrum analyzer. It has the advantage of analyzing down to 1 Hz, whereas my Siglent 3032X only goes down to 9 KHz. For phase noise measurements, the Picoscope is crucial. Also, the 16 bits of the 4262 is necessary to get enough precision to capture low power phase noise values.My mother broke her hip and I have had to dial back my work on this project in order to interact with doctors and help her with her rehabilitation. However, I hope to have some results in the next week or two.

author: jpb
author_rank: Super Contributor
timestamp: April 20, 2019, 06:59:52 pm
content: Quote from: dnessett on April 19, 2019, 10:06:50 pmI'm sorry to hear about your mother. I wish her a speedy recovery.I look forward to reading the outcome of your measurements.I've been having fun making ADEV measurements but at present I'm using my counter and despite best efforts with mixers to provide some heterodyne gain (if that is the right term) the measurements are buried in noise (particularly quantisation noise)below about 20 or 30 seconds. I'd like to get down to about a second. There are lots of approaches to take, but most of them require acquisition of more equipment!

author: dnessett
author_rank: Regular Contributor
timestamp: May 27, 2019, 10:51:47 pm
content: It has been a long, hard and onerous journey of about a year, but I am now in the position to run some experiments. The test setup is in place and working. There have been changes since I originally described this setup, which I now document.HP11729C Based Frequency Discriminator ConfigurationFigure 1HP11729C Mechanical ConfigurationFor this test setup, the HP11729C has the following mechanical configuration:50 ohm terminator on the 640 MHz output. Since the oscillators tested are all 10 MHz, the 640 MHz signal (which generates down converting frequencies to put the oscillator signal into the 10-1028 MHz range) is unused.50 ohm terminator on the 10Hz-10Mhz (unused) noise spectrum output.The Mode selector is set to phi(phase), CW and the Local selector is on.Device Under testThe Device (oscillator) Under Test (DUT) must output a signal having power within the range of the HP11729C input limits. The output of the directional coupler (see below) between the DUT and HP11729C is connected to a variable attentuation pad (shown in the figure) to ensure the input to the HP11729C does not exceed 3.5 dBm. This constraint is necessary because exceeding this input power drives the HP11729C into compression.Directional CouplersThe HP11729C inputs terminate the coaxes that are connected to them. However, to monitor the signals during a test, two directional couplers are used to tap the oscillator and Delay Complex (see below) inputs. The signals from these taps are displayed on an oscilloscope (Rigol 1104Z), which allows the use of the Delay Device to bring the two signals into rough quadrature. The Phase Lock indicator on the HP11729C is then used to bring the signals into tight quadrature. The directional couplers are MiniCircuit ZDC-10-1 devices.Delay Line and Delay DeviceThe Delay Line is 400'+2*25'+2x50' = 550' of RG-58 coax. The total delay of the signal between the IF output and the mixer input varies depending on the delay value selected for the Delay Device. The Delay Device is described inthis EEVBlog topic. Normally, the signal is delayed about 875 ns (8 full periods plus an extra 275 degrees) by the combined Delay Line and Delay Device (the Delay Complex). The Delay Complex reduces the power of the IF output by 8.268 dB.The maximum sensitivity of the frequency discriminator occurs when the Delay Complex attenuates the IF output by 8.7 dB. While the value provided by the Delay Complex is somewhat less than this optimal value (around 8.268 dB), the need to put the two signals into quadrature and to utilize coaxes that were available necessitated use of this slightly non-optimal value.Low Frequency Spectrum AnalyzerThe Low Frequency Spectrum Analyzer used in these experiments is a PicoScope 4262. This is an FFT SA, the use of which results in some differences in the measurement procedures specified in theHP11729C Operating and Service Manual. These changes are documented in the next message that I will post to this topic.The 1Hz-1MHz output of the HP11729C feeds the PicoScope through a Tee. One end of the Tee connects to the PicoScope while the other end is terminated by a 600 ohm terminator. 600 ohm termination is necessary, since the 1Hz - 1MHz output has a source impedance of 600 ohms. (The coax connecting the 1Hz-1MHz output to the Tee is 50 ohm RG-58. However, it is only about 5 feet long and at 10 Mz should not behave as a transmission line, so this impedance mismatch can be safely ignored.)

author: dnessett
author_rank: Regular Contributor
timestamp: May 27, 2019, 10:53:51 pm
content: The measurement procedures for an HP11729C operating in Frequency Discriminator mode are somewhat complicated and require documentation and comment. In addition, the procedures as described in theHP11729C Operating and Service Manualare predicated on the use of a swept-tuned spectrum analyzer. However, the test setup utilizes an FFT spectrum analyzer (a PicoScope 4262), which has some significant differences to a swept-input SA. These differences create changes in the computations required to characterize phase noise in oscillators.In regards to the use of a PicoScope in the test setup, I gratefully acknowledge the help given me by Gerry, a tech specialist active on thePicoScope forum, navigating through several issues that affect such use.Corrected on 10/21/2019.Below is presented the procedure used to compute phase noise using the test setup described in the previous message. This procedure is presented in some detail so that others may evaluate it and, if desired, use it to conduct their own experiments. It should be noted that this procedure is general and, with suitable minor modifications (e.g. elimination of step 1), should apply to any double balanced mixer implementing a frequency discriminator based phase noise analyzer.Procedure to Test An Oscillator with the HP11729C in Frequency Discriminator Mode1. Make sure the 640 MHz output and the 10 Hz-10MHz output are terminated by 50Ω.2. Connect a signal generator to a swept-tuned spectrum analyzer (to make these instructions concrete, it is assumed here that the signal generator is a Rigol DG1022 and the swept-tuned spectrum analyzer is a Siglent SSA3032X. The latter is used since the Picoscope 4262 has a maximum input frequency of 5 MHz, which is insufficient to execute the next steps.). Set the output frequency of the DG1022 to 10 MHz and the amplitude to 200 mVp-p (-10 dBm).3. Select the FM modulation function on the DG1022; set the modulation frequency to 1 KHz and the frequency deviation to 100 Hz.4. Using the SSA3032X, measure the difference in dB between the 10 MHz and 10.001 MHz lines and note the value (call itDelta_SB-cal). This value is the sideband power minus the carrier power. For example, if the carrier power is -10 dBm and the sideband power is -30 dBm, thenDelta_SB-calwould equal -20 dBm.5. Disconnect the DG1022 from the SSA3032X. Connect the DG1022 to the Microwave Test Signal input of the HP11729C and the IF output of the HP11729C to the PicoScope 4262. Measure and note the output power of the 10 KHz line on the PicoScope. (call itP-cal).Corrected on 10/21/2019.6. Connect the oscillator to the input of a directional coupler. Connect the output of the directional coupler to the SSA3032X, adding enough 50Ω attenuation padding so the output from the directional coupler is less than or equal to 3.5dBm. (It is convenient if the pad is adjustable in 1 dB increments.)7. Disconnect the padded directional coupler output from the SSA3032X and connect it to the Microwave Test Signal input of the HP11729C.8. Connect the IF output of the HP11729C to the input of the Delay Complex. Connect the output of the Delay Complex to the input of a second directional coupler. Connect the output of that coupler to the SSA3032X and measure the output power. The difference between the IF output and Delay Complex output power should be close to 8.7 dBm, if the coax cable length is properly chosen.9. Connect the Delay Complex output to the 5-1280 MHz input of the HP11729C.10. Connect the 1 Hz-1MHz output of the HP11729C to a Tee at the PicoScope 4262 input. Connect the other end of the Tee to a 600Ω terminator.11. Set up the PicoScope to use Blackman-Harris windowing, dBm@50 ohm scale and select an appropriate number of bins for the FFT. (Assuming the use of a PicoScope 4262, in the channel setup menu, choose 200 KHz hardware low pass filtering.) Choose display mode as "Average" and select an appropriate number of segments over which to compute the average (using the “Statistics Captures” box on the General tab of the Tools->Preferences window). Set the Frequency Span of the PicoScope to an appropriate value. If desired, set the primary view of the PicoScope to “Scope Mode” and the secondary view to “Spectrum Mode”. This allows the adjustment of spectrum properties so that bin width can be adjusted precisely (seethis discussion on the PicoScope Fourm)12. Connect the coupler ports of the directional couplers to two channels of the oscilloscope with the output of the oscillator directional coupler Tee'd at the oscilloscope input. Connect the Tee'd output of the oscilloscope input to a Frequency Counter (e.g. HP5335A), so that the frequency of the oscillator can be monitored. Connect the Tee'd output of the Delay Complex coupler port to a 50 ohm terminator. Adjust the Delay Device so the two signals are roughly in quadrature.13. Using the quadrature LEDs on the HP11729C, fine tune the Delay Device so that the green LED is lit.14. After the chosen number of segments have been averaged (as indicated when the capture count equals this value), copy the PicoScope spectrum in CSV format to a file and move it to the analysis computer.15. Using Octave, convert to mW by first applying 10^(dBm-value/10). If necessary sum the bins so the spectrum is presented in 1 Hz increments (or as close to that as is possible). That is, if necessary, sum the bins between x±.5, x=1…(upper range of spectrum) to yield bins 1 Hz wide. Ignore the bins with offset freqencies less than .5 Hz.Corrected on 10/21/2019.16. To convert the measurements to phase noise, add 10 dB and the value ofDelta_SB-calnoted in step 4 to each data point. (NB: there is a mistake in step 22 of theHP11729C Operating and Service Manual. This step, which appears on page 3-24, stipulates that theDelta_SB-calvalue should be subtracted, not added to each data point. However, in the example given at the end of step 22, it is added. The error is also apparent when the mathematics behind the corrections are derived. Seethe mathematical justification for Phase Noise corrections.) Adding 10 dB normalizes each data point value to a carrier power level of 0 dBm (recall that the calibration uses a carrier of -10 dBm). Subtract P-cal from each data point. Subtract 20 log(f-off/1 Khz), where f-off is the offset frequency of a bin, from the bin power value (to compensate for differences between the calibration Fourier frequency (1 KHz) and the offset frequency).17. The result of the adjustments is the phase noise spectrum of the oscillator.DiscussionWhen I first worked my way through the procedure described in theHP11729C Operating and Service Manual, it seemed like voodoo. There was very little justification for its prescriptions and even that (found mostly in the appendices) was vague and puzzling. Fortunately, I found an HP product note that went into much more detail on the theory behind the practice (i.e.,HP product note 11729C-2: Phase Noise Characteristics of Microwave Oscillators - Frequency Discriminator Method). However, even that very helpful document contained many inscrutable passages and I had to work hard to extract a working understanding of what was going on.I thought it would be useful to present my current understanding of several issues, in order to relieve others from the onerous work necessary to dig this understanding out of the product note.Steps 1-5The basic goal of these steps is to measure the values required to compute the discriminator constant.Delta_SB-calis required to convert dBm measurements to dBc units.P-calis the system response to a known sideband value. Both are used in the corrections described in step 16.Step 6Setting the padded input from the oscillator under test (DUT) to a level equal to or less than 3.5 dBm is required to ensure the HP11729C doesn't go into compression, thereby invalidating the frequency discriminator calibration procedure.Steps 7-10Keeping the difference between the IF output power and Delay Complex output power as close to, but not exceeding 8.7 dBm yields the optimum system sensitivity, as described in Appendix C ofProduct note 11729C-2.Steps 11-15The selection of a Blackman-Harris window was somewhat arbitrary, but did have support fromthis article. The Blackman-Harris window used by the PicoScope is 4-termSee this post. After some experiments, a different choice of FFT window may recommend itself.Serendipitously, the PicoScope 4262 makes available a 200 KHz hardware low-pass filter. This has to be enabled in the Channel setup menu and provides significant anti-aliasing protection for the signal coming out of the HP11729C. I chose to sum those sub-Hertz bins that were +/- .5 Hz on either side of the integral Hz value. Bins associated with Hz values less than or equal to .5 Hz were dropped.Corrected on 10/21/2019.Step 16The motivation for these corrections is not self-evident and requires some explanation. As mentioned previously, at first they seemed to me to be something like voodoo. The justification is mathematical and while not particularly difficult (only algebra is involved), it is somewhat long. Consequently, I decided to make it the subject of aseparate message. This will allow those not interested to simply skip it and accept the correctness of the corrections made in step 16 as given.

author: dnessett
author_rank: Regular Contributor
timestamp: May 27, 2019, 10:54:51 pm
content: The corrections made to the measurements described in step 16 of theFrequency Discriminator test setup procedureare somewhat inscrutable. For those who wish to understand the rationale behind them, I provide the mathematical justification in this message. Those who don't like or can't be bothered with math are encouraged to skip the remainder of this message.Warning: Algebra aheadHP product note 11729C-2provides the mathematical justification for the corrections specified in step 16. However, this justification is not isolated to a single section of the product note; although most of the material is found on pgs 16, 24-27 and 40. One complication that arises is the product note includes some corrections required when using a swept-tuned spectrum analyzer, corrections that are not applicable to an FFT spectrum analyzer. Specifically, the Noise Bandwidth of analog HP spectrum analyzers is used for one correction; whereas the Effective Noise Bandwidth correction of the FFT windowing function is already applied by the PicoScope 6 software and requires no further correction. In addition, a correction factor for the "log-shaping and detection circuitry of an analog spectrum analyzer" is applied. Again, this is not applicable to FFT spectrum analyzers. Consequently, the correction procedure given in the test setup description elides these steps and the mathematics justifying their use is modified to eliminate terms corresponding to them.Inthe derivation of the equation for the frequency discriminator constantthe final result is: \$\nu(t)=K_{d}\varphi(t)\$, where \$\nu(t)\$ is the voltage output of the Phase Detector after low-pass filtering, \$K_{d}\$ is the (frequency) discriminator constant, and \$\varphi(t)\$ is the instantaneous frequency corresponding to the output voltage.In the HP product note, this is presented in a slightly different form: \$\Delta V = K_{d}\Delta f\$, where \$\Delta V\$ is the change in output voltage and \$\Delta f\$ is the change in instantaneous frequency. These are mathematically equivalent formulations.The equations above are time domain descriptions, whereas the spectrum measurements are in the frequency domain. Consequently, additional notation is necessary to identify these measurements. (Subsequent page references are citations to theHP product note).On page 6, two symbols are defined to identify the relevant spectral data. First, \$S_{v}(f_{m})\$ identifies the "power spectral density of the voltage fluctuations out of the detection system" at the offset frequency \$f_{m}\$. \$S_{\Delta f}(f_{m})\$ is the spectral density of the frequency fluctuations at the offset frequency \$f_{m}\$ . Thus, \$S_{v}(f_{m})\$ represents the power spectral density of the signal \$\nu(t)\$ (this is what is measured by the low frequency spectrum analyzer during an experiment) and \$S_{\Delta f}(f_{m})\$ represents the frequency spectral density of the signal \$\varphi(t)\$.While discussing symbols representing spectral densities, it is convenient to mention another quantity that plays an important role in the characterization of phase noise, \$\mathscr{L(\mathcal{\mathrm{f_{m}}})=\frac{\mathcal{P_{SSB}}(\mathrm{f_{m}})}{\mathcal{P_{\mathrm{Carrier}}}}}\$. \$\mathcal{P_{\mathrm{Carrier}}}\$ is the power of the (oscillator) carrier signal. \$\mathcal{P_{SSB}}(\mathrm{f_{m}})\$ is the single side-band power of a phase modulation sideband at the offset frequency \$f_{m}\$. When discussing phase noise, most specifications provide values of \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$, so there is a requirement to convert the spectra measured by the frequency discriminator into the form \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$. On page 6 is derived the relationship between \$S_{\Delta f}(f_{m})\$ and \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$:\$\mathscr{L(\mathcal{\mathrm{f_{m}})}} = \mathcal{\frac{S_{\Delta f}(f_{m})}{{2f_{m}}^2}}\$.Spectral densities are continuous functions of frequency. When the set of frequencies associated with a power measurement is countable, this is not true and the result is referred to as a spectrum. Since the measurements by a frequency discriminator test setup quantize frequency, phase noise characterizations based on measurement deal with spectra rather than spectral densities. We continue to use the notation \$S_{v}(f_{m})\$, \$S_{\Delta f}(f_{m})\$, and \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$ to identify the spectra arising from quantization of the identically named spectral densities.Phase noise is canonically described as arising from FM modulations of the carrier signal by stochastic (noise) processes within the oscillator. The products of these processes add linearly to create the total phase noise spectrum or spectral density.Consider the value associated with \$S_{v}(f_{m})\$, for a particular offset frequency \$f_{m}\$. This is the power of the \$f_{m}\$ component of the spectrum and the total phase noise spectrum is mathematcially equivalent to a sum of spectra, where each comprises a single tone spectrum for the frequency \$f_{m}\$ (m ranging over all values for \$S_{v}(f_{m})\$). To be clear, the single tone spectra arenotthose produced by the noise processes, which generally create multi-tone spectra. The single tone spectra are a mathematical decomposition useful when considering how to measure the discriminator constant. In particular, measurement of the system response to a single tone input contains all the information needed to compute the discriminator constant. This is the objective of the calibration steps described in the test setup procedure presented previously, specifically in steps 3-5.The mathematical justification for the corrections specified in step 16 is found on page 40. It begins with the casual assertion that for m<0.2rad, where m is the modulation index of the modulation:\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4}\$I searched for hours on the internet to find a justification for this result without success (it may be that it exists in some textbook, of which I do not have a copy). Finally, I found enough information to dervive it. Onthis web page, it is noted that for sufficiently small FM modulation indices (which on other web pages is given as m<0.2), the Bessel J coeffients are: \$J_{0} = 1\$, \$J_{1} = \frac{m}{2}\$, and \$J_{n} = 0, n>1\$. As an aside, the correct constraint on the modulation index is m<.2, not m<0.2rad, since the modulation index is defined as: \$ m = \frac{\Delta f_{peak}}{f_{m}}\$, where \$\Delta f_{peak}\$ is the peak frequency deviation of the FM modulation and \$f_{m}\$ is the FM rate. This is a unitless ratio. The constraint m<0.2rad is appropriate for Phase Modulation and I found several references on the internet where it is erroneously cited for FM modulation.In the calibration procedure (step 3), the FM rate is set to 1 KHz and the frequency deviation to 100 Hz. This yields a modulation index of .1, which satisfies the given constraint.In aslide presentationavailable on the internet (on slide "Angle and Pulse Modulation - 7"), the total power \$P_{T}\$ of an FM modulated signal with carrier \$P_{C}\$ is given as:\$P_{T} = P_{C}({J_{0}}^2 + 2({J_{1}}^2+{J_{2}}^2+ ...))\$Noting the values of \$J_{i}\$ when the constraint m<.2 holds and substituing into this equation:\$P_{T} = P_{C}(1 + 2(\frac{m^2}{4})) = P_{C} + P_{C}\frac{m^2}{2}\$In the last expression to the right of the equal sign, the first term represents the carrier power and the second term represents the power of the double sideband. The single sideband power is 1/2 of this, i.e., \$P_{ssb} = P_{C}\frac{m^2}{4}\$. Dividing this expression by \$P_{C}\$ (aka \$P_{Carrier}\$) yields the assertion made at the beginning of page 40.Given \$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4}\$, we can substitute the values measured during calibration in steps 3-5 and develop an expression for the single-sideband to carrier power ratio in terms of these values. First, to ensure clarity, the derivation on page 40 identifies the calibration values as \$\Delta f_{peak_{cal}}\$ and \$f_{m_{cal}}\$ and uses them to express the modulation index, \$m = \frac{{\Delta f_{peak_{cal}}}}{f_{m_{cal}}}\$, so:\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4} = \frac{1}{4}\frac{{(\Delta f_{peak_{cal}})}^2}{(f_{m_{cal}})^2}\$At this point it is useful to mention that, so far, we have not been dealing with values expressed in logrithmic units. Rather, the values used in the expressions are in linear units. This is important in the next step of the derivation. The measurement ofP-calandDelta_SB-calon the spectrum analyzer generally will be made in logrithmic units (e.g. dBm). To use these values in the derivation, we must express them in linear units. To retain clarity, the distinction between these values in linear and logrithmic units is made by appending them with either  or . Thus, from this point,P-calin linear units (e.g. milliwatts) is represented by the symbol \$P_{cal}\$ and in logrithmic units by the symbol \$P_{cal}\$. SimlarlyDelta_SB-calin linear units is represented by \$\Delta SB_{cal}\$ and in logrithmic units by \$\Delta SB_{cal}\$. The  and  notation applies to the other symbols as well.In step 4 of the test setup procedure, the difference between the carrier and sideband power is measured by subtracting the former from the latter (this assumes the SSA3032X is displaying results in dBm). In other words, \$P_{ssb} - P_{carrier} = \Delta SB_{cal}\$. In linear units the subtraction becomes division and therefore:\$\frac{P_{ssb}}{P_{carrier}} = \Delta SB_{cal}\$.Consequently, we can write:\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4} = \frac{1}{4}\frac{{(\Delta f_{peak_{cal}})}^2}{(f_{m_{cal}})^2} = \Delta SB_{cal}\$The last equality can be re-expressed as:\$\Delta {f}^2_{peak_{cal}} = 4 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}}{10}}}\$, since \$10^{{\frac{\Delta SB_{cal}}{10}}} = \Delta SB_{cal}\$Thederivation of the equation for the frequency discriminator constantspecifies voltage amplitudes for the oscillator (DUT),\$V_{DUT-AMP}\$ and the referenced signal, \$V_{R-AMP}\$. However, it fails to indicate whether these amplitudes are peak-to-peak values or RMS values. This follows the formuation in Appendix A (page 34), on which the derivation is based, which also does not indicate whether peak-to-peak or RMS voltages are meant. On page 40, however, the discriminator constant is defined implicitly as:\$K_{d} = \frac{\Delta V_{rms}}{\Delta f_{rms}}\$So far, we have derived the equivalent expression for \$\Delta {f}^2_{peak_{cal}}\$, not \$\Delta {f}^2_{rms_{cal}}\$. This is easily fixed, since \$\Delta {f}_{peak_{cal}} = \sqrt{2} \Delta {f}_{rms_{cal}}\$ and therefore:\$\Delta {f}^2_{rms_{cal}} = 2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}}{10}}}\$Substituting this expression into the definition of \$K_{d}\$ yields:\$K^2_{d} = \frac{\Delta V^2_{rms}}{2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}}{10}}}} = \frac{P_{cal}}{2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}}{10}}}}\$, since \$P_{cal}\$ is the response expressed as power (\$\Delta V^2_{rms}\$) to the calibration input.Applying \$10 log_{10}()\$ to both sides of the equation re-expresses it in terms of dB:\$2K_{d} = P_{cal} - (\Delta SB_{cal} + 20 log_{10}(f_{m_{cal}})+3dB)\$Note: There is a mistake on page 40, which is corrected in the equation given above. On page 40, the left hand side of the equals sign is given as \$K_{d}\$, rather than \$2K_{d}\$. It turns out that this mistake is cancelled out by an error in the equation given for \$S_{\Delta f}(f_{m})\$ on page 16, which should be:\$S_{\Delta f}(f_{m}) = S_{v}(f_{m}) - 2K_{d}\$I am deliberately leaving off the units in this equation, since as stated on page 16, \$S_{\Delta f}(f_{m})\$ is in units of [dBHz/Hz], whereas both \$S_{v}(f_{m})\$ and \$K_{d}\$ are given in units of . How one gets a quantity in [dBHz/Hz] by subtracting two quantities in  is beyond my comprehension. In fact the whole document is riddled with equations that combine units in such a way as to be completely baffling.Anyway, the desired final result is \$\mathscr{L(\mathcal{f_{m}})}\$ and this is expressed in terms of \$S_{\Delta f}(f_{m})\$ on page 7:\$\mathscr{L(\mathcal{f_{m}})} = S_{\Delta f}(f_{m}) - 20 log_{10}(\frac{f_{m}}{1 Hz}) - 3 dB\$\$\;\;\;\;\;\;\;\;\;= S_{\Delta f}(f_{m}) - 20 log_{10}(f_{m}) - 3 dB\$,where \$20 log_{10}(f_{m})\$ in the last expression to the right of the equal sign is written without the explicit reference to its units.Substituing the equation for \$S_{\Delta f}(f_{m})\$ and in that the equation for \$2K_{d}\$ gives:\$\mathscr{L(\mathcal{f_{m}})} = S_{v}(f_{m}) - (P_{cal} - (\Delta SB_{cal}\$\$\;\;\;\;\;\;\;\;\;\;\;\;\; + 20 log_{10}(f_{m_{cal}})+3dB)) - 20 log_{10}(f_{m}) - 3 dB\$\$\;\;\;\;\;\;\;\;\;= S_{v}(f_{m}) - P_{cal} + \Delta SB_{cal} - 20 log_{10}(\frac{f_{m}}{f_{m_{cal}}})\$Recalling that \$S_{v}(f_{m})\$ is what is measured by the low frequency spectrum analyzer during an experiment, the last equation to the right of the equal sign justifies the corrections made in step 16 (except adding 10 dBm, which is already justified in the description of the step).

author: dnessett
author_rank: Regular Contributor
timestamp: May 27, 2019, 11:11:22 pm
content: 6/01/2019: While working on the writeup for the MV89A oscillator tests, I discovered a bug in my Octave code that removes processing gain and sums frequency bins to 1 Hz width. Specifically, I did these things in the wrong order. I first summed the bins and then corrected the result by adding 10 * log10(rows(summed spectrum)/2) to each bin. I should have corrected each bin in the original data and then summed the bins. I have corrected this, but the plots in the original version of this post were incorrect. I have replaced them with corrected plots and also added a comment (shown in red) focused on why the noise floor shown in the plots doesn't seem to agree with the noise floor implied by the PicoScope 4262 spec.Note that the conclusions about the PicoScope 4262 noise floor with respect to the MV89A data output by the Frequency Discriminator haven't changed. The corrected plots show these two signals in the same relationship as before. However, the absolute power values have changed.Prior to testing oscillators using the frequency discriminator mode of the HP11729C, it was necessary to ascertain whether its output is above the PicoScope 4262's noise floor. To explore this question, I analyzed one of the MV89A oscillators I obtained. This device is an ultra low phase-noise double oven oscillator and I reasoned that if the output of the HP11729C in frequency discriminator mode with the MV89A as DUT is above the noise floor of the PicoScope, then the PicoScope should be suitable for the analysis of most oscillators.Figure 1 compares the noise floor of the PicoScope with the output of the HP11729C in frequency discriminator mode with the MV89A as DUT. The PicoScope noise floor is in red and the HP11729C output is in blue.Figure 1(Corrected on 6/01/2019)It is important to understand that the blue plot isnotthe phase noise of the MV89A. It represents the output of the HP11729C before the corrections indicated in step 16 of the test setup procedure are applied. Specifically, both red and blue plots are normalized according to the instructions in step 15 in order to correct for processing gain, and sum bins to normalize the spectra to 1 Hz bin width. Only these corrections are made, since it would make no sense to apply the phase noise corrections given in step 16 to the PicoScope noise floor data. This comparison only determines whether the signal from the HP11729C is hitting the PicoScope noise floor, which would invalidate the measurement.Figure 1 clearly shows the PicoScope noise floor being below the signal output by the HP11729C. However, as the offset frequencies near 0, the two approach each other. Figure 2 shows the two plots in the range 1-100 Hz.Figure 2(Corrected on 6/01/2019)It is clear that the two approach each other at the low end of the spectrum. This introduces some uncertainty in the measurements. Keep this in mind when evaluating the results of oscillator tests. At just what offset the output of the HP11729C are corrupted by the PicoScope noise floor is a judgement call.One prominent feature of the MV89A noise plot are the significant spurs occuring at the low end of the spectrum. It turns out most of these are due to 60 Hz frequency modulations of the oscillator carrier. These will be discussed in more detail when the test results of various oscillators are published.One issue requires comment. In thePicoScope 4262 spec, the maximum sensitivity of the device is give as 8.5 uV. At 50 ohms, this corresponds to -99 dBm. However, the noise floor shown in figure one is only about -82 or -83 dBm. How is this difference reconciled?Figure 3 shows a plot of the PicoScope 4262 before bin summing, but after processing gain elimination. Clearly the noise floor is roughly -99 dBm, which corresponds to the quoted maximum sensitivity.Figure 3(Added on 6/01/2019)As of this writing I have tested two oscillators and am in the process of writing up the results. I have decided to publish these results in a new forum topic, since this topic is focused on how to measure phase noise. I assume many will be interested in the test results who have no interest in the details of phase noise measurement. When I create the new topic, I will fill inthis link(which at present is deadwhich is now active) so those who have followed the discussions here are directed to the results.

author: dnessett
author_rank: Regular Contributor
timestamp: November 07, 2019, 11:33:10 pm
content: The Frequency Discriminator configuration of the HP111729C presented a great way to learn about the device and also to get some experience in the subtleties of measuring phase noise. However, as many mentioned before I started, this configuration isn't suited for measuring phase noise at offsets close to the oscillator fundamental frequency (aka the carrier). Nevertheless, one interesting result from the experiments was the appearance of 60 Hz harmonic spurs in the phase noise plots. While several articles I read warned that power supply leakage might introduce such spurs in the phase noise, it was interesting to see it first hand and to see how prevelant these spurs were for offset frequencies far away from the carrier.Given that the applicability of the Frequency Discriminator configuration has reached a limit, it is time to use the HP11729C in its phase detector configuration. This requires understanding the mechanical configuration, the measurement procedures and corrections, and the math behind the latter. This post documents the mechanical configuration.HP11729C Mechanical ConfigurationFigure 1 - Phase Detector Test SetupHP11729C Mechanical Configuration for the Phase Detector configurationThe relevant information for using the HP11729C in its phase detector configuraiton is found in theHP11729C Operating and Service Manualand inHP product note 11729B-1.For this test setup, the HP11729C has the following mechanical configuration:50 ohm terminator on the 640 MHz output. Since the oscillators tested are all 10 MHz, the 640 MHz signal (which generates down converting frequencies to put the oscillator signal into the 5-1028 MHz range) is unused.50 ohm terminator on the 10Hz-10Mhz (unused) noise spectrum output.The Mode selector is set to phi(phase), CW and the Local selector is on.Device Under testThe Device (oscillator) Under Test (DUT) connects to the Microwave Test Signal input (through a directional coupler and attenuation pad). The input level must be less than or equal to 3 dBm (.8934 VP-P). The attenuation pad is adjusted to ensure this constraint.Reference OscillatorThe Reference Oscillator is connected to the 5-1280 MHz input of the HP11729C (also through a directional coupler and attenuation pad). Calibration of the Phase Detector configuration requires setting the input level of the Reference Oscillator as close to 0 dBm as possible. The instructions for calibration presume the use of an analog low-frequency spectrum analyzer to measure the power level of a beat signal in order to determine the phase detector constant of the instrument. Consequently, the instructions direct the operator to keep the Reference Oscillator input level at the same value it was set during calibration.The Phase Detector configuration of the HP1729C uses a Phase Lock Loop (PLL) within the HP11729C to keep the Reference Oscillator and DUT in quadrature during the measurement period. This requires the ability for the Reference Oscillator to act as a VCO and thus be dynamically tuned during the measurement. The Reference Oscillator chosen for experiments is a Wenzel HF-ONYX-IV low-phase-noise 10 MHz oscillator (part 501-22578-04), which has a Electronic Frequency Control (EFC) pin.The HP11729C uses its Freq-Cont X-Osc signal to control the Reference Oscillator when implementing the PLL. However, the Freq-Cont X-Osc signal ranges in value from -10V to +10V, whereas the Reference Oscillator EFC pin takes a 0 - 10V input. A simple resistor divider network is used to convert the -10V to 10V signal to the range required by the Reference Oscillator.In order to monitor the VCO control voltage (Freq-Cont X-Osc) from the HP11729C a Tee is placed in-line between it and the EFC port of the Reference Oscillator. One output of this Tee connects to the EFC port, while the other output is connected to a DVM (e.g, HP34401A).Directional CouplersThe HP11729C inputs terminate the coaxes that are connected to them. However, to monitor the signals during a test, two directional couplers are used to tap the Reference Oscillator and DUT inputs. The signals from these taps are displayed on an oscilloscope (Rigol 1104Z). The directional couplers are MiniCircuit ZDC-10-1 devices.Low Frequency - Low Noise Amplifier (LF-LNA)The Low Frequency - Low Noise Amplifier boosts the HP11729C 1Hz-10MHz output signal level so it remains above the noise floor of the Low Frequency Spectrum Analyzer. The LF-LNA used in the experiments is a AlphaLab LNA-10, which has an effective bandwidth of DC-1MHz and voltage gain settings of 10X, 100X and 1000X.Low Frequency Spectrum AnalyzerThe Low Frequency Spectrum Analyzer (LF-SA) used in the experiments is a PicoScope 4262. This is an FFT SA, the use of which results in some differences in the measurement procedures specified in theHP11729C Operating and Service Manual. These changes are documented in the next message in this topic.The 1Hz-1MHz output of the HP11729C feeds the the LF-LNA, which output is connected to the LF-SA. The coax connecting the 1Hz-1MHz output to the LF-LNA and the LF-LNA to the LF-SA is 50 ohm RG-58. Both are only about 5 feet long and at 10 Mz should not behave as a transmission line, so this impedance mismatch can be safely ignored.

author: dnessett
author_rank: Regular Contributor
timestamp: November 07, 2019, 11:37:04 pm
content: The measurement procedures for an HP11729C operating in Phase Detector mode are documented here. The procedures described in theHP11729C Operating and Service Manualare predicated on the use of a swept-tuned spectrum analyzer. However, the test setup on which these instructions are based employs an FFT spectrum analyzer (a PicoScope 4262), which has some significant differences to a swept-input SA. These differences create changes in the computations required to characterize phase noise in oscillators.In regards to the use of a PicoScope in the test setup, I gratefully acknowledge the help given me by Gerry, a tech specialist active on thePicoScope forum, navigating through several issues that affect such use.Below is presented the steps used to compute phase noise using the test setup described in the previous message. These steps are presented in some detail so that others may evaluate them and, if desired, use them to conduct their own experiments. It should be noted that the procedure documented in this message is general and, with suitable minor modifications (e.g. elimination of step 1), should apply to any double balanced mixer with quadrature maintaining phase lock loop implementing a phase detection phase noise analyzer. To make the instructions concrete, it is assumed that the signal generator is a Rigol DG1022 and the swept-tuned spectrum analyzer is a Siglent SSA3032X. The latter is used since the Picoscope 4262 has a maximum input frequency of 5 MHz, which is insufficient to execute steps 3, 4, and 5. The oscilloscope used to monitor the two inputs to the HP11729C is a Rigol DS1104Z. The Low Frequency Low Noise Amplifier (LF-LNA) is an AlphaLab LNA 10.Procedure to Test An Oscillator with the HP11729C in Phase Detection Mode1. Make sure the 640 MHz output and the 10 Hz-10MHz output of the HP11729C are terminated by 50Ω. Allow both the DUT and Reference Oscillator to warm up (for at least an hour).2. Connect the coupler ports of the directional couplers to two channels of the oscilloscope with the output of the Reference Oscillator coupler port Tee'd at the oscilloscope input. Connect the Tee'd output of the Reference Oscillator oscilloscope input to a Frequency Counter (e.g. HP5335A), so that the frequency of the Reference Oscillator can be monitored. (NB: Some steps below require the use of the Frequency Counter for other purposes. When so, disconnect the Reference Oscillator at its TEE from the Frequency Counter, execute the required measurements and then reconnect the Reference Oscillator to the Frequency Counter before measuring the specturm of the HP11729C output.)3. Connect the Reference Oscillator directional coupler through its attenuation pad to the swept-tuned spectrum analyzer. Adjust the Reference Oscillator attenuation pad so the input to the spectrum analyzer is as close to 0 dBm as possible. Note the power level for use in step 5 and then disconnect the Reference Oscillator directional coupler and attenuation pad from the spectrum analyzer.4. Connect the DUT directional coupler through its attenuation pad to the swept-tuned spectrum analyzer. Adjust the DUT attenuation pad so the input to the spectrum analyzer is as close to but no greater than 3 dBm. Disconnect the DUT coupler and attenuation pad from the spectrum analyzer. Connect the DUT through its directional coupler and attenuation pad to the Microwave Test Signal input of the HP11729C.5. Connect the DG1022 to the Frequency Counter. Connect a 10 MHz Disciplined Oscillator (e.g., a GPSDO) to the external 10 MHz input of the DG1022. Enable the external 10 MHz clock signal (by selecting Utility->System->Timer->External). Allow the Disciplined Oscillator and DG1022 to warm up and frequency stablize before making measurements. Set the amplitude of the DG1022 to 0 dBm. Using the Frequency Counter, adjust the Frequency setting on the DG1022 so a reading of 10.01 MHz is obtained. Disconnect the signal generator from the Frequency Counter. Measure the output level of the DG1022 by connecting it to the swept-tuned spectrum analyzer. Set the amplitude of the 10.01 MHz signal as close as possible to the value measured in step 3, minus 40 dBm. Call the difference between the value measured in step 3 and the input amplitude of the 10.01 MHz signalDelta_SB-cal. For example, if the Reference Oscillator input to the spectrum analyzer in step 3 measured 0.61 dBm, then set the amplitude of the DG1022 signal measured by the swept-tuned spectrum analyzer as close to -39.39 dBm as possible. Disconnect the DG1022 from the swept-tuned spectrum analyzer and connect it to the 5-1280 MHz input of the HP11729C.6. Set up the PicoScope to use Blackman-Harris windowing, dBm@50 ohm scale and select the number of bins for the FFT so the bin width is approximately 1 Hz. Choose display mode as "Average" and select an appropriate number of segments over which to compute the average (using the “Statistics Captures” box on the General tab of the Tools->Preferences window). Set the Frequency Span of the PicoScope to 20 KHz.7. Connect the 1 Hz-1MHz output of the HP11729C to the PicoScope 4262 input. Using the PicoScope in spectrum mode, measure the power of the 10 KHz spectral line and note its value (call itP-cal).8. Disconnect the DG1022 from the HP11729C and connect the Reference Oscillator directional coupler through its attenuation pad to the 5-1280 MHz input of the HP11729C. Connect the 1Hz - 1 MHz output of the HP11729C to the LF-LNA In+input port. Make sure the In-input port is shorted to ground. Set the gain to 1000X, 100X or 10X as appropriate. Set the input switch to In+- In-and connect the output port of the LF-LNA to the PicoScope input. Connect the Freq-Cont X-Osc port of the HP11729C through a TEE to the EFC control port of the Reference Oscillator. Connect the TEE to a DVM (e.g. an HP34401A) to monitor the EFC signal.9. Set up the PicoScope to use Blackman-Harris windowing, dBm@50 ohm scale and select an appropriate number of bins for the FFT. (Assuming the use of a PicoScope 4262, in the channel setup menu, choose 200 KHz hardware low pass filtering.) Choose display mode as "Average" and select an appropriate number of segments over which to compute the average (using the “Statistics Captures” box on the General tab of the Tools->Preferences window). Set the Frequency Span of the PicoScope to an appropriate value (but no greater than 100 KHz).10. Set the Lock Bandwidth factor of the HP11729C to 100. On the front panel of the HP11729C, press then release Capture. If phase lock is acquired, the green LED will light on the HP11729C indicating quadrature. If phase lock is not acquired, set the Lock Bandwidth factor to 1 K and try again.11. Start the PicoScope measurement process. After the chosen number of segments have been averaged (as indicated when the capture count equals this value), save the PicoScope spectrum in CSV format to a file and (optionally) move it to an analysis computer.12. Using Octave, convert to mW by applying 10^(dBm_value/10). If necessary sum the bins so the spectrum is presented in 1 Hz bin increments (or as close to that as possible). That is, if necessary, sum the bins between x±.5, x=1…(upper range of spectrum) to yield bins 1 Hz wide. Ignore the bins with offset freqencies less than .5 Hz. Convert the millwatt values back to dBm.13. To convert the measurements to phase noise, subtractP-calfrom each measured value. Then subtract the value ofDelta_SB-cal. Subtract 6 dB from each data point and subtract the equivalent dB value corresponding to the LF-LNA gain setting (i.e., 1000X -> 60 dB, 100X -> 40 dB and 10X -> 20 dB). If necessary, make a correction for any offset frequencies inside the loop bandwidth (see the Discussion section.)14. The result of the adjustments is the phase noise value of the oscillator at the given offset frequency. For example, suppose the measurement at 10 Hz is -78 dBm,P-calequals -46 dBm,Delta_SB-calequals 40 dBm, the LF-LNA is set at 1000X gain and the Lock Bandwidth factor used to obtain phase lock was 100. Assuming no offset frequencies were inside the loop bandwidth, the phase noise value at 10 Hz would be: -78 dBm - (-46) - 40 dB - 6 dB - 60 dB = -138 dBm.DiscussionThere are several points to make in regards to the measurement procedure.Steps 1-6On page 21 ofHP product note 11729B-1, it states that the CW microwave input level must be between 7 and 18 dBm. However, on page 15 ofHP product note 11729C-2, it states the mixer inputs reach compression at 3 dBm. There is no guidance for the input level of signals attached to the Microwave Test signal input in theHP11729C Operating and Service Manual. So, I needed to figure out what is the right power level for the DUT input.I ran a test varying the input power to the Microwave Test Signal input of the HP11729C. I connected the DUT directional coupler and attenuation pad to the swept-input SA input and set the input power to 10.85 dBm. I then reattached it to the Microwave Test Signal input of the HP11729C. Figure 1 shows the resultant signal shape displayed on the oscilliscope.Figure 1 - Microwave Test Signal at 10.85 dBmIt is obvious that some of the power of the signal at 10.85 dBm is reflecting back through the directional coupler and corrupting the coupler port signal. Specifically, harmonics of 10 MHz seem to distort the coupled signal.I then set the input power to 2.86 dBm and connected it to the Microwave Test Signal input. The result is shown in Figure 2Figure 2 - Microwave Test Signal at 2.86 dBmThe oscillator trace of the input signal is nice and clean, indicating that very little (if any) reflected power is getting to the coupler port.The best explanation of the seemingly inconsistent guidance in the HP11729C literature for input power levels was provided byJohn Miles in this post. There are two mixers inside the HP11729C - one in the downconverter logic and one used to phase detect the reference/DUT combined signal (see figure 4.4 on page 21 of the HP11729C-2 product note). John suggests the 7-18 dBm recommendation probably refers to the DUT input when using downconversion (and thereby using the downconverter mixer), whereas the 3 dBm compression spec refers to the phase detector mixer. Since analyzing a 10 MHz signal for phase noise does not use the downconverter logic, keeping it less than or equal to 3 dBm is probably the right thing to do.Allowing the DG1022 sufficient time to warm up is critical. My DG1022 drifted over 81 Hz before roughly settling after 2 hours (even then, it continued to drift slowly down in frequency). This motivated the use of an external 10 MHz Disciplined Oscillator to keep the DG1022 output frequency stable.Step 13The subtraction ofDelta_SB-calandP-calfrom the power value corresponding to each frequency offset in the PicoScope output was a bit of mystery at first. It turns out the math deriving these corrections and the argument justifying them is trivial. However, development of the argument took some time. I thought it worthwhile to go through the logic to save others the effort in case they were interested.Figure 3 illustrates the transformation of signal levels at the input of the HP11729C to those at the output.Figure 3 - The logic for the corrections usingDelta_SB-calandP-cal.The HP11729C attenuates the signal levels at its inputs, which for the frequencies of interest is constant for a given setup. This attentuation value is represented asRetardin the figure.On the left side of the figure is shown 3 signal levels that play a role in the correction mathematics. These are the Carrier input (Carrierin), the sideband value for the calibration signal (SBCal-in) and the sideband value for a particular frequency offset (SBoffset-in). Each of these signals is attenuated in amplitude at the output side of the HP11729C. While the Carrier output (Carrierout) is shown in the figure, its value is not measureable, since the double balanced mixer in the HP11729C executes carrier suppression.The calibration levels (SBCal-inandSBCal-out) are both available, but the offset levelSBoffset-inis not. OnlySBoffset-outis measured. The goal is to useCarrierin,SBCal-in,SBCal-outandSBoffset-outto computeSBoffset-in.The strategy is to computeRetardand subtract it fromSBoffset-outto getSBoffset-in.Delta_SB-calequalsCarrierinminusSBCal-inandP-calequalsSBCal-out. As derived in the figure,RetardequalsDelta_SB-calplusP-cal. Therefore,SBoffset-inequalsSBoffset-outminusDelta_SB-calminusP-cal, which is the computation carried out in step 13 .The subtraction of 6 dB from the measured phase noise power levels is justified in Appendix A (pg. 35) ofHP product note 11729B-1. The derivation there is straight forward and so is not duplicated here.Both the corrections section of theHP11729C Operating and Service Manual: pg. 3-21andHP product note 11729B-1: pg. 25note that for offset frequencies inside the loop bandwidth, a correction is necessary to the corresponding power levels, since they are attenuated. This is discussed on page 11 of the 11729B-1 product note in the second and third paragraphs. The attenuation is illustrated by an example shown in Figure 3.10.The product note provides a formula for computing loop bandwidth when the HP11729C is used with an HP8662A. However, the test setup described here does not use an HP8662A; it uses a Wenzel HF-ONYX-IV, which has different characteristics than the HP8662A. So, it is necessary to derive the correct formula for loop bandwidth when using a Wenzel HF-ONYX-IV with the HP11729C.Fortunately, Appendix B of the product note provides the necessary algebra to derive this quantity (pp. 37-38). The derivation uses 6 defined quantities:Kd= Phase slope or phase detector gain factor of the mixer (volts/rad).Ko= VCO (EFC) slope (Hz/volt)F = HP11729C Lock Bandwidth FactorKa(s) = loop amplifier gainN = multiplication factor when a frequency band other than 5-1280 MHz is used. For this test setup, N =1.s = 2*PI*j*f (Hz), where f=offset frequency.On page 38, it states that Kd* Ka* Ko= 10-3. Whereas the values of Kdand Kaare not given, on page 3-21 of theHP11729C Operating and Service Manual(under NOTE in the first paragraph), the value of Ko(HP8662A) is given as 10-1Hz/Volt. TheWenzel HF-ONYX-IV specificationindicates a tuning range over 0-10V of +/- 10-6, which for a 10 MHz oscillator translates to a range of +/- 10 Hz. Since the HP11729C EFC tuning signal bounds are +/- 10V, this means the Wenzel slope, Ko(Wenzel), when used with an HP11729C is 20Hz/20Volts = 1Hz/V (NB: a resistor divider network changes the Wenzel EFC range from 0-10V to +/- 10V). This is 10 times the value of Ko(HP8662A). Therefore, when using the Wenzel as Reference Oscillator, Kd* Ka* Ko= 10-2.This means the loop bandwidth of the HP11729C/Wenzel phase detector configuration equals F/102]. For example, when using a Lock Bandwidth Factor of 100, the loop bandwidth equals 1 Hz.The corrections for offsets inside the loop bandwidth are derived according to the instructions given on page 26 of the product note. However, if quadrature lock is obtained using a Lock Bandwidth Factor of 100 or less, no "inside the loop bandwidth" corrections are necessary.

author: dnessett
author_rank: Regular Contributor
timestamp: March 02, 2020, 02:52:22 am
content: I have spent the last 2 months attempting to eliminate the 60Hz harmonic spurs apppearing in the output of my HP11729C. Those interested in the details can read the message thread that begins on Jan 11 (message #101757) on the HP-Agilent-Keysight-equipment@groups.io mail list (the whole thread can be accessed using the following link60 Hz harmonic spurs on the HP11729C). Be forwarned, this is a long conversation, but there is useful information in it.The conclusion of this discussion was the 60Hz and harmonic spurs were caused by the fan on the 11729C. After much discussion, I replaced the fan with a modern one (see the complete description of how to do this in thismessage). Unfortunately, while the fan replacement reduced the 60 Hz spur by about 12-13 dB, it increased the power of the 120 Hz and 240 Hz spurs by about 16 dB (see complete analysishere). So, replacing the fan did not solve the original problem.Nevertheless, in the process of attacking it, I changed the procedure I use to measure phase noise using the phase detection mode of the 11720C. To ensure there is clairity in the interpretation of future results of my phase noise measurements, I document these changes here.First, I now use a makeshift faraday cage to isolate the Oscillator under test from stray EMI. Followinga suggestion by Leo Bodnar, I built the faraday cage out of a biscuit tin (Note: for those unfamiliar with non-US english, biscuit in UK english = cookie in US english. However, you will rarely if ever find cookies in the US packaged in a tin. I had to purchase some ginger snaps from Sweden at Cost Plus World Market to obtain the necessary hardware.)Figure 1 shows the faraday cage opened to display how the oscillator fits into it. Note the use of plastic wrap to protect the electronics from shorting against the biscuit tin.Figure 1 - Faraday cage openedFigure 2 shows the faraday cage with the lid in place. At the top of the biscut tin are the connecting cables that feed the oscillator power and route the oscillator signal from it.Figure 2 - Faraday cage closedSecond, in order to eliminate the possibility that the power source of either the oscillator under test or the reference oscillator is leaking 60 Hz + harmonics into the oscillators, I now power both using a battery. For 5 V oscillators, I use a10000mAh ROMOSS Universal Power Bank. For 12 V oscillators I use aTalentcell Rechargeable 6000mAh Li-Ion Battery Pack.Third, since my attempt to clean up 60 Hz + harmonic spurs by fixing the 11729C hardware failed, I now use software to remove non-stochastic spurs from phase noise plots. Fortunatley, Octave has a ready made routine for this in the signal pkg - medfilt1. Documentation ishere. This routine uses a moving average replacement algorithm that replaces a data point by the median (not the mean) of the points in a window of size n around this point. It is eminently suited for spur removal in spectrum plots.For example, figure 3 shows the 60 Hz and harmonic spurs in a plot of the output of the 11729C analyzing a Connor-Winfield HO100-61005SV low phase noise oscillator. (Recall that the output of the 11729C isnotthe phase noise of the device. Several corrections are required to this data to produce the phase noise of the oscillator.) Note the prominent 60 Hz and harmonics spurs in the spectrum plot.Figure 3 - Plot of 11729C output for a Connor-Winfield HO100-61005SV low phase noise oscillatorFigure 4 shows the same output plot with the output of medfilt1 superimposed in red.Figure 4 - Plot of 11729C output for a Connor-Winfield HO100-61005SV low phase noise oscillator with the output of medfilt1 superimposed in redFor reference, the data produced by the PicoScope 4262 uses ~20 mHz bins. So, each Hz bin comprises about 50 of these smaller bins. Therefore, I used a window of 100 to average the raw data over about 2 Hz.One thing to note is the filtered data (i.e., the medfilt1 output) doesn't work well at very low Hz values. The reason for this is the window gets cut off at the left edge. There are two ways to implement this cut off in medfilt1. You can artifically zero fill the window out on the left to restore a window of 100 points. Alternatively, you can truncate the window and reduce the number of points in it.Of these two options, truncate is the most appropriate for this application, since zero filling the window effectively makes the data to the left of 0 Hz equal to 0 dBc/Hz (technically 0 dBc/20mHz). This biases the result and raises the average above the expected value for low Hz power.On the other hand, truncate also produces biased results. At very low frequencies the power is rising very fast. As you reduce the number of points in the window, the median no longer represents a unbiased estimate of the actual power at a particular Hz value. As is seen in the figure, the lower power values tend to dominate the median computation and the output artifically displays a value lower than what would be expected.So, the filtered output is acceptiable down to 2 Hz, but below this value is not a true representation of the output. Imposing a conservative saftey margin, the filtered results probably should not be used for Hz values between 1-10 Hz.There is a problem with simply showing the filtered phase noise, eliminating the spurs. For the Connor-Windfield oscillator, 60 HZ + harmonic spurs are the only ones with significant power. However, other oscillators have spurs unrelated to 60 Hz. For example, The Bliley NV47A1282 phase noise spectrum is cluttered with spurs unrelated to 60 Hz (see Figure 5).Figure 5 - Plot of phase noise for a used Bliley NV47A1282 oscillatorIt isn't clear what causes these spurs, but obviously eliminating them obscures the potential problems that might occur when employing such a used oscillator in an application. I plan on retaining the information these spurs convey by using the following two point strategy. First, I will rerun the Bliley oscillator phase noise tests using my 11729C with its upgraded fan and also using batteries to power the oscillators. Second, when displaying a phase noise plot, I will always superimpose the spur removed plot over the plot of the raw phase noise data. This will show where the spurs were removed and afford the observer an opportunity to interpret the causes of the spectrum spurs.Finally, I am using one other modification to my prior described test setup. My Rigol DG1022 went belly up and so I have purchased a Siglent 40 MHz SDG 2042X function generator. I will not update the instructions how to use this new function generator to calibrate the 11729C when using a particular oscillator, since these effectively do not change. There might be one or two minor differences (e.g., how to connect an external 10 MHz signal to the function generator), but the translation from one function generator to the other should be obvious.