# 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

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.

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.

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.

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?