Confessions Of A Reformed Frequency Standard Nut

Do you remember your first instrument, the first device you used to measure something? Perhaps it was a ruler at primary school, and you were taught to see distance in terms of centimetres or inches. Before too long you learned that these units are only useful for the roughest of jobs, and graduated to millimetres, or sixteenths of an inch. Eventually as you grew older you would have been introduced to the Vernier caliper and the micrometer screw gauge, and suddenly fractions of a millimetre, or thousandths of an inch became your currency.  There is a seduction to measurement, something that draws you in until it becomes an obsession.

Every field has its obsessives, and maybe there are bakers seeking the perfect cup of flour somewhere out there, but those in our community will probably focus on quantities like time and frequency. You will know them by their benches surrounded by frequency standards and atomic clocks, and their constant talk of parts per billion, and of calibration. I can speak with authority on this matter, for I used to be one of them in a small way; I am a reformed frequency standard nut.

That Annoying Final Counter Digit

Tuned circuits in a radio IF transformer. Chetvorno [CC0].
Tuned circuits in a radio IF transformer. Chetvorno [CC0].
You might ask how such an obsession might develop. After all, who needs a frequency standard accurate to an extremely tiny fraction of a Hz on their bench? The answer is that, unless your job depends upon it, you don’t. If you are a radio amateur, you really only need a standard good enough to ensure that you are within the band you are licensed to transmit upon, and able to stay on the frequency you choose without drifting away. But of course such sensible considerations don’t matter. If you’ve bought a frequency counter, you have an instrument with nagging seventh and eighth digits that show you how fast that crystal oscillator you thought was pretty stable is drifting. And there you are, teetering on the edge of that slippery slope.

The first electronic radio frequency oscillators used turned circuits, combinations of inductors and capacitors, to provide their frequency stability. A tuned circuit oscillator can be surprisingly stable once it has settled down, but it is still at the mercy of the thermal properties of the materials used in that tuned circuit. If the temperature goes up, the wire in the inductor expands, and its inductance changes. Older broadcast radios sometimes required constant manual retuning because of this, and very few radio transmitters rely on these circuits for their stability.

The answer to tuned circuit instability came in the form of piezoelectric quartz crystals. These will form a resonator with similar electrical properties to a tuned circuit, but with a much lower susceptibility to temperature-induced drift. They are stable enough that they have become the ubiquitous frequency standard behind most of today’s electronics: almost every microprocessor, microcontroller, or other synchronous circuit you will use is likely to derive its clock from a quartz crystal. Your 1957 FM radio might have needed a bit of tuning to stay on station, but its 2017 equivalent is rock-stable thanks to a crystal providing the reference for its tuning synthesiser.

A crystal oven installed in a Hewlett-Packard frequency counter. Yngvarr [CC BY-SA 3.0].
A crystal oven installed in a Hewlett-Packard frequency counter. Yngvarr [CC BY-SA 3.0].
Crystals are good — good enough for most everyday frequency reference purposes — but they are not without their problems. They may be less susceptible than a tuned circuit to temperature-induced drift but they still exhibit some. And while they are factory-tuned to a particular frequency they do not in reality oscillate at exactly that frequency. Crystal oscillators seeking that extra bit of accuracy will therefore reduce drift by placing the crystal in a temperature-regulated oven, and will often provide some means of making a minor adjustment to the frequency of oscillation in the form of a small variable capacitor.

If you have a crystal oscillator in an oven, you’re doing pretty well. You’ve reduced drift as far as you can, and you’ve adjusted it to the frequency you want. But of course, you can’t truly satisfy the last part of that sentence, because you lack the ability to measure frequency accurately enough. Your trusty frequency counter isn’t as trusty once you remember that its internal reference is simply another quartz crystal, so in essence you are just comparing two crystals of equivalent stability. How can you trust your counter?

At this point, we’re done with frequency standards based on physical dimensions of materials, and have to move up a level into the realm of atomic physics. All elements exhibit resonant frequencies that are fundamentals of the energy levels in their atomic structure, and these represent the most stable reference frequencies available: those against which our standard definitions of time and frequency are measured. There are a variety of atomic standards at the disposal of metrologists with large budgets, but the ones we will most commonly encounter use either caesium, or rubidium atoms. The caesium standard forms the basis of the international definition of time and frequency, while rubidium standards are a more affordable and accessible form of atomic standard.

Raise Your Own Standard

My trusty Heathkit crystal calibrator.
My trusty Heathkit crystal calibrator.

One of the oldest and simplest ways to calibrate an oscillator to a standard frequency is to perform the task against that of a broadcast radio transmitter. You will hear an audible beat tone in the speaker of a receiver when the frequency of the oscillator or one of its harmonics is close enough to the station for their difference to be in the audible range, so it is a simple task to adjust the oscillator to the point at which the beat frequency stops. The lower frequency limit of human hearing allows a match to within a few tens of hertz, and a closer match can be achieved with the help of an oscilloscope.

A 100 kHz crystal calibration oscillator used to be a standard part of a radio amateur’s arsenal, and it could be matched to any suitable broadcast frequency standard worldwide. For a Brit like me back in the day it was convenient to use the caesium standard BBC Radio 4 long wave transmitter on 200 kHz to calibrate my 100 kHz oscillator, but sadly for me in 1988 when the ink was barely dry on my licence they reorganised long wave frequencies and moved it to 198 kHz.

When I was at the height of my quest for a pure frequency standard, the next most accessible source was to take a broadcast standard and use that as the reference source to discipline a crystal oscillator by means of a phase-locked loop. You could buy off-air frequency standard receivers as laboratory instruments, but as an impoverished student I opted to build my own.

Here in the UK, I had the choice of the aforementioned 198 kHz Radio 4 transmitter or the 60 kHz British MSF time signal, and I chose the former as I could cannibalise a long wave broadcast receiver for a suitable ready-wound ferrite rod antenna. This fed an FET front-end, which in turn fed a limiter and filter that provided a Schmitt trigger with what it needed to create a 198 kHz logic level square wave. Then with a combination of 74-series logic dividers and the ever-versatile 4046 PLL chip I was able to lock a 1 MHz crystal oscillator to it, and be happy that I’d created the ultimate in frequency standards. Except I hadn’t really. Despite learning a lot about PLLs and choosing a long time constant for my loop filter, I must have had an unacceptably high phase noise. Not the only time my youthful belief in my own work exceeded the reality.

A handy GPS module from Adafruit. Oomlout [CC BY-SA 2.0]
A handy GPS module from Adafruit. Oomlout [CC BY-SA 2.0]
Off-air standards are still an accessible option for the would-be frequency afficionado, but it is rather improbable that you would build one in 2017 because a far better option now exists. The network of GPS and similar navigation satellites is an accessible source of high-accuracy timing for everybody, with a multitude of affordable GPS hardware for all purposes. Thus it is simpler by far to opt for a GPS-disciplined crystal oscillator, and indeed we have seen them from time to time being used in the projects featured here.

GPS is very good, and the only way to get fancier is to go atomic. The once-impossible dream of having your own atomic standard is now surprisingly affordable, as the proliferation of mobile phone networks led to a large number of rubidium standards being deployed in their towers. As earlier generations of cell towers have been decommissioned, these components have found their way onto the second-hand market, and can be had from the usual sources without the requirement to mortgage your children.

The modules you can easily buy contain a crystal oscillator disciplined by reference to the rubidium standard itself. The standard monitors the intensity of monochromatic light from a rubidium lamp through a chamber of rubidium gas exposed to radio frequency matching the resonant frequency of the transition between ground states of the rubidium atom, and locks the radio frequency to the resonance observed as a dip in that intensity.

Seekers of the ultimate in standard frequency accuracy now have several options when it comes to calibration sources. Making an off-air standard is more trouble than a GPS-based one, and the more adventurous among you can find a rubidium-disciplined source. Or perhaps you already have. There’s no shame in excess precision, but we’re curious: do you really need such an accurate source of timing information? Or are you chasing that last digit just because it’s there?

57 thoughts on “Confessions Of A Reformed Frequency Standard Nut

  1. *Or are you chasing that last digit just because it’s there?*

    YES. And here I sit drawing out plans to build a gps reference to replace the crystal and feed the serial port on the embedded board for my NTP/PTP server…
    Because why just settle for accurate time in the lab when you can use ESP8266’s to have all of your appliances set their own time corrections from your NTP server automatically…
    Sometimes I think I may be developing a problem, but then I think about how much I hate setting clocks, and I feel way better about it.

    1. Once you go for that level of precision, don’t you have to start worrying about the stability of the recipient device?

      CPU clocks are often pretty good by quartz timekeeping standards; but you don’t get absurdly cheap, small, and low power by caring more about frequency stability than you have to. Depending on implementation details, serial and other busses may not help matters: vendors tend to avoid timing issues bad enough to cause visible failures and data loss; but that’s a markedly lower standard.

      1. But if you are using NTP and a drift-calculator/corrector like chronyd, then the NTP server will probably be the weakest link. At least for anti-drift. The second to second precision isn’t that great on a regular PC, but it is well under 1/100th of second.

    1. Duty ratio? That just makes phase noise. You need a linear oven controller. In the oven of course (to keep external thermal effects from messing with your control loop gains). Then you’ve just got the problem of ensuring clean power and low vibration.

    2. Wouldn’t crystals get more stability and less noise if kept on a constant low temperature in a Peltier freezer, rather then in an oven? I understand that the latter was easier to maintain, but today it wouldn’t be too expensive to make the former either.

  2. I bought a used rubidium atomic oscillator on ebay as a reference, and for a while was convinced I could measure frequencies exactly. Then I bought another, and now I’m not so sure :-)

    1. Clearly you need a third. Or a cesium (that’s ceasium to you Jenny :) ) beam standard.

      The truly nuts go to hydrogen masers of course.

      I don’t think there are any atomic fountain clocks in private hands. Yet.

    2. My big problem is that I spent a boatload of cash to get a measurement uncertainty in the low 10^-11 range… but now I am building GPSDOs theoretically with low tau stability in the low -12s. But I can’t really prove it with what I have.

    3. Moe wonders what time it is, and Curly pulls up his sleeve revealing three wristwatches. Moe asking what’s the idea of the three watches. Curly say it’s to tell the time and explain s first watch’s ten minute’s fast, it would be two hours; a second watch’s twenty minutes slow, would be four hours. The one in the middle’s broken and stopped at two o’ clock. Moe asking again how Curly tell the time and Curly say he take the ten minutes on a first watch, and subtract it from the twenty minutes on a second watch, then He divide by the two in the middle. When Moe say what time is it now, Curly pulls out a pocketwatch and say this time is about ten minutes to four.

  3. Rubidium clocks are secondary standards, i.e. you need to calibrate them against another clock, preferably a primary standard (Cesium clock). They have great short-term performance, but drift long-term.

    GPSDO are technically drift-free while disciplined, because the satellite clocks are corrected every orbit. However, GPSDO rely on GPS reception, so they are extremely noisy in the short-term. GPS system is at best limited to around “better than 1 meter” (supposedly about 0.5 m in practice), or roughly 3 ns uncertainty, and the GPDSO will add about 3~6 ns of uncertainty to that.

    High precision timing is a requirement at microwave frequencies, because a small frequency error can get hugely multiplied. Hence, there are also a supply of Rb clocks available from decomissioned military communications and Friend-or-Foe systems, etc.

    1. GPSs intended for time keeping have something called a position hold mode. So if your antenna is stationary you just take a ton of samples (say a weeks worth of seconds), average that to a long/lat/altitude, then put your GPS in hold mode. That way you get a very accurate time source.

  4. I’m not sure about the “because it’s there” rationalization, but the first time that I put a rubidium oscillator into my best frequency counter, seeing all those zeros stabilize at 10.000004 MHz as the counter’s ovenized oscillator warmed up was cool in a way that is hard to describe.

  5. The Frequency Electronics Rubidium standards you can get on eBay are synthesizers. This, unfortunately, means that their low tau Allan performance is rather pedestrian. You can do better from a short term perspective with a GPSDO based on an OCXO. Where the Rubidium modules really shine is holdover stability. You can use a GPS PLL to calibrate them, then they’ll have much less wander than an OCXO would without discipline.

  6. It is an affliction. There is even a mailing list for time/frequency addicts.

    For dedicated insanity, see Tom Van Baak’s trip up a mountain with several cesium standards and his kids in tow to prove relativity. Not quite as nuts as the HP guys who flew one across the country on an airplane, but they were Paid Professionals time nuts.

    Metrology in general gets to be an affliction. There is a volt-nuts mailing list too, for those who are interested in getting the last digit of their 8.5 digit DVM locked in.

    For me, not only was watching my frequency counter stabilize at 10.000004, but feeding my 10Mhz standard in to that and all the other gear on the bench (signal generators, spectrum analyzer, oscilloscope all have fequency standard inputs) and see it all line up exactly to as many decimal points as I had. Was very very cool. Now if I could only get the voltage based gear to do the same…Gah! Insanity!

    1. There is a box that was put out by Data Precision in the 1970’s that is an amazingly accurate voltage reference. Hooking one up to an HP34401 is entertaining, an HP3458 is more so. They still bring serious money after all these years. Unfortunately, they use funky mechanical encoders for each digit, and they are failing. They still have a GPIB interface on the back that works though, so if you can find one with bad encoders, it will only cost you an arm and you can keep your legs.

  7. A while back I tore apart a GPS (SatNav -Jenny) that had a bad display and battery. I kept the RF board, but haven’t found out how to hook it up. It appears to have only 4 connections, (+/- power? the antenna in is easy enough to figure out.)
    Would it supply power over its data link to the board?

      1. NMEA plus a 1 pulse per second reference (which gives you, to within a few ns, the start of each second) is standard fare. NMEA takes a little while to decode, plus the message comes AFTER the start of the new second, so you can use it in setup, but not for the absolute time.

  8. There is one area of ham radio where precision frequency standards are important – weak signal microwave and millimeter wave work. At frequencies above 10 GHz, and especially at 47 GHz and above, having a really accurate standard matters when you are trying to make long distance contacts using very narrow filters or digital modes that require long integration times. This is a pretty extreme use case for which a pretty small number of people are involved, but Rb or GPS disciplined oscillators are routinely used. Phase noise becomes an issue as well, and a GPS or Rb disciplined crystal ends up being a really excellent solution.

    1. Unfortunately, the FE-5660/5680s you get on eBay these days for reasonable cost are synthesizers, so their phase noise won’t really cut it for frequency multiplying applications.

        1. Well, but why wouldn’t you just discipline the OCXO from GPS?

          The only reason that I can think of is if you need it in a mobile context where a timing module wouldn’t be able to complete a proper survey or something like that. But even then, you’d need to calibrate the rubidium module first.

  9. Jenny, I am also a recovering addict :-) In the past 20 or so years, I’ve owned a cesium reference, two rubidiums, five GPSDO’s and assorted OCXO’s. Now I’m down to one GPSDO and a few small OCXO’s that are earmarked for projects.

    I also started to be seduced by the Dark Side of volt-nuttery, but after a few years of that, decided that 5.5 digit bench meters were more than sufficient for my hobby needs. I still get a bit antsy because both meters don’t agree to the last digit, but I console myself with the fact that they are both well within spec :-)

    Despite all of equipment and time that I invested, I was only a junior league time/volt nut. I will say that it was fun, and I learned a lot. But you are right – it is so easy to get sucked in.

    Gee, this looks interesting…

  10. Here in Australia we no longer have a broadcast frequency standard so were left with GPS in remote areas.

    What I find more interesting than simply the reference frequency is how it conveyed or distributes.

    I used to work in telecommunication before computers were a thing (commercial).

    We had to fit as many phone conversations as possible down a piece of coax and then perhaps to a microwave link. This was in the analogue days before digital.

    In telecommunications you need as much redundancy as economical so that a single point of failure didn’t effect much equipment. Things tended to made from repeated modules.

    There were 6 wires on each incoming circuit that went into a “channel”. 2 for voice (both ways) 2 for signaling forward and two for returned signalling. The signalling was MFC. The voice wires were split into transmit and receive with a hybrid circuit.

    The channel bandpass filter the audio so that the MFC wasn’t heard. Then the voice and signalling was bandpass filtered to a baseband.

    Three basebands went into a group circuit which downshifted on channel using lower side band modulation (LSB), left one channel as it was and up-shifted the third channel using upper side band (USB). Side bands don’t have a carrier frequency to be used as a reference at the other end.

    Three groups went into a group2 where the same thing happened. Then three group2 went to a group3 and so forth until you have a “master” which was about 9000 channels that went down the coax.

    Within every groups stage there is one incoming group or channel that was NOT modulated in that stage but may be modulated in another stage. From channel to master there was only one channel that wasn’t modulated by the local oscillator even though that channel would later be RF modulated for the link, perhaps microwave.

    Frequency references were sent on that one channel in each link so that we had a national frequency synchronization that wasn’t overly sensitive to drifts in the national master oscillator.

    The obvious problem is that a single reference frequency over that one channel is in fact modulated at the RF stage.

    To fix this problem the reference was sent as 1.4kHz and 2.4kHz mixed together. On the receiving end the 1.4kHz and 2.4kHz were separately bandpass filtered to separate them. The 1.4kHz was them modulated with the 2.4kHz and stripping off the lower side band gave a 1kHz reference that was completely independent of and frequency drift caused at the RF modulation stage.

    Later, with digital links, we just Quadrature Amplitude Modulated the digital data and sent it down the exact same channel circuitry for 9600bps.

  11. Hi, my name is James and I’m an addicted to T.M.I. too. I struggle with why does that have to be the significant digit? What if we’re missing something? I like assurance of not going out of tolerance and obviously specification. I know the noise comes from somewhere. I’m not trying to be a jerk or snappy. There is something in those derivations and coefficients that is part of the system variables. OK… not in some communities… especially at lunch/break.

    I had this idea one day that I was going to make a radio telescope (I still get the idea occasionally) and try to use something in space as an oscillator standard like a Hydrogen line. Then I read about GPS… and bought kit though haven’t finished the work bench yet. I even have some of the components for the radio telescope and that was one of the reasons I was wondering if someone in Australia would buy and ship me the kelvar braid (great price from red2go) so I can leave an array of lower frequency cones out at a listening station.

    Well, for now… Great article Jenny.

    1. I can note that of course someone was kind enough to sell and ship me an old not way to overpriced Clansman Antenna wire element metal spool, NSN 5820 99 620 7373 that I’m not even sure is kevlar though is supposed to be. Lately, I’ve been pondering a dual loop magnetic loop array with high relative permeability core material and did find I still have powdered iron in my old chemistry kit when digging around. Was thinking about annealing in Hydrogen to study and apply the process and measure the effect.

  12. Oddly enough my first measuring standard was a DVM built by my father for one of those correspondence courses, and for a while the O’scope that was also part of it. Now I use a DVM made by Simpson, and sometimes a Tek 2213A O’scope. So I see where most of you are coming from. As for GPS devices, I looked at one of the ones that our friends at Adafruit make up for their wearable line of gadgets. It and the matching Arduino like device could be stuffed in a vest, not worn by a person however….. But all of that is besides the point.

  13. Is interesting that the typical atomic clock isn’t measuring isotopic decay. There is a magnetic resonance nuclear electron effect going on.

    Be interesting to have a lab bench DIY frequency standard project, hacked to make cost effective (I’ve seen the cesium standards on eBay before) project and like I still think there is a way to make a standard not with visible observations of say a pulsar with a telescope… using extraterrestrial RF with a radio telescope that is more longer term stable and not effected by the earths atmosphere and seasonal challenges.

    1. OK, so I had to read up on the latest and greatest NIST standards since USP/NF/EP methods don’t really apply here. Here is the latest on the The Primary Time and Frequency Standard for the United States, the NIST-F1 Cesium Fountain Atomic Clock:

      Man, that’s more intensely detailed of an operation than I last read maybe… ew… 20 yrs ago now. What happened to the U.S. owning pharma so we don’t premature age? HHhmmm… that’s another more than frequency of some other variables standard issue.

      Last task I had to do with time was the Telephone Time-of-Day Service for timers:

      Frequency accuracy was determine with the NIST SRM’s for the various spectrometers… and not really the oscillators on the circuits.

      Interesting learning the electronics and RF side of the systems now days. I wonder if they do a more insulated oven controlled oven controlled with pressure control (if not already) to stabilize more. Basically, when PV=nRT isn’t enough… I’ll digress.

  14. It’s a pain I know. Mine isn’t frequency though. It started with time to the fractional millisecond. How can a server farm survive with drift of a minute? Of a second? They need to be tenths of milliseconds, definitely!

    Now I’m more concerned about physical measures. What is “flat”? I want a flat driveway so I can work on my car. That probably doesn’t need to be within 0.001″. What about for a workbench? A CNC mill? I can want 0.001″, but survive with 0.1″. Until I start building nanobots, that is. [wrings hands]

  15. 1. ANY discussion of precise and accurate time-keeping hardware MUST include the power supply and interconnect signal integrity. A simple example is marrying a capable reference with a bad noisy power supply, which results in increased jitter/phase-noise. Don’t discount ground loops either.

    2. Has Google hacked NTPD in Android so it is a (yet another) “Spy On You” vector? There’s low-hanging fruit there when it comes to network time-keeping for the Google Goons to keep an eye on you.

    1. That’s an interesting idea, I have a couple of 26MHz xtal ovens doing nothing at the moment, if I seal one in a jar and set them both up to be in phase at 1000mbar, I’ll check the difference against the barometers in the hallway (yes I have a collection) at times of high and low pressure.

  16. Hi Jenny, thanks for an interesting article. The off air frequency standards you mentioned were not caesium. The R4 200kHz transmitter used a HP ( there were 3 in a shielded room) rubidium frequency standard. I believe that MSF at that time was a rubidium as well, but that theirs was locked to the caesium standard at NPL Teddington.
    In the photo at the following link of the Droitwich control room in 1981, in the right hand bay, is an Evershed paper chart recorder. Above this is a 2U 60kHz MSF receiver. The output of this and our local 200kHz drive were fed via a network to the chart recorder. We had to turn the chart recorder on for an hour a day to measure our drift against MSF. That and many valve meter readings had to be taken and recorded by hand in a log. Such was the life of a young engineer.

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