Understanding The Quartz Crystal Resonator

Accurate timing is one of the most basic requirements for so much of the technology we take for granted, yet how many of us pause to consider the component that enables us to have it? The quartz crystal is our go-to standard when we need an affordable, known, and stable clock frequency for our microprocessors and other digital circuits. Perhaps it&#;s time we took a closer look at it.

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The first electronic oscillators at radio frequencies relied on the electrical properties of tuned circuits featuring inductors and capacitors to keep them on-frequency. Tuned circuits are cheap and easy to produce, however their frequency stability is extremely affected by external factors such as temperature and vibration. Thus an RF oscillator using a tuned circuit can drift by many kHz over the period of its operation, and its timing can not be relied upon. Long before accurate timing was needed for computers, the radio transmitters of the s and s needed to stay on frequency, and considerable effort had to be maintained to keep a tuned-circuit transmitter on-target. The quartz crystal was waiting to swoop in and save us this effort.

Good Vibrations

The solution to the problem of tuned circuit frequency stability was to use a quartz crystal, a resonant element whose physical properties are significantly less susceptible than inductors or capacitors to external factors such as temperature. Quartz crystals are piezoelectric, which is to say that when you deform them they develop an electrical charge, and when an electrical charge is applied to them they in turn deform. You can thus electrically set up a physical vibration in a carefully cut quartz crystal. Just as tuning forks, gongs, and other elastic solids can show physical resonance, the crystal can be used as an electrical resonator.

A quartz crystal&#;s electrical equivalent model is that of a series tuned circuit in parallel with a capacitor, giving it some of the properties of both a parallel and a series tuned circuit. It differs though from the tuned circuit made from conventional components in having an extremely high Q factor, or narrow bandwidth. It can be incorporated in the feedback circuit of an oscillator in the same way as the tuned circuit, and the oscillator will then run happily at its resonant frequency.

Solid As A Rock

Practical crystals take the form of precisely-ground discs or wafers of synthetic quartz, with chemically deposited metal electrodes on either side. They are mounted in hermetically sealed packages to ensure their stability.

There are many crystal oscillator configurations, but the circuit you are most likely to encounter if you work with digital circuitry is the Pierce oscillator. You&#;ll find it implemented using discrete logic gates, as well as in a multitude of microprocessors and other ICs. The crystal is arranged with a couple of capacitors and a high-value bias resistor as a phase-shift network from output to input of an inverter. One of the capacitors may sometimes have a small variable capacitor in parallel, allowing very small frequency adjustments to be made to correct for the tolerance of individual crystals. At the resonant frequency of the crystal there is the required 180 degree phase shift across the crystal to sustain oscillation.

What you have just read is a very basic primer in what a crystal is, how it works, and how you might see it being used. That however will only give you part of the story, for there is more to the quartz resonator than first meets the eye.

It&#;s All In The Overtones

The resonant frequency of a quartz crystal is proportional to its dimensions . As the crystal becomes thinner, the frequency increases. Eventually as the frequency increases there comes a point at which the thickness of the material can not be reduced any further without the crystal breaking, so there is an upper frequency beyond which a crystal can not be made. It varies depending on the techniques employed, but it is usually somewhere above 20 MHz.

Of course, you will be pointing out that crystals are available at many times this frequency, so what&#;s up? The answer is that crystal frequencies above that figure are achieved through means of harmonic overtones. The sub-20 MHz frequency is merely the fundamental resonance, other resonances can be achieved in the same crystal at multiples of the fundamental. This effect can be readily demonstrated through standing waves in a tethered rope, or in the acoustic properties of a closed pipe as shown in the diagram.

In practice a crystal designed for overtone use will have resonances at odd multiples of its fundamental frequency. Thus for example an overtone crystal with a 10MHz fundamental frequency would also have overtone resonances at 30MHz and 50MHz.

Putting an overtone crystal in the Pierce circuit shown above will not cause it to oscillate at the overtone frequency though, instead it will run at its fundamental. An overtone oscillator must incorporate an extra tuned circuit designed to reject the fundamental frequency, leaving the most prominent of the overtone resonances to dictate the oscillation frequency. In our example from a CMOS logic app note, the inductor in the output network of the inverter performs this task.

There is another function besides the oscillator in which you may encounter crystals. In radio circuits their extremely narrow bandwidth means they can be daisy-chained to make an extremely selective filter. One method of generating a single-sideband transmission makes use of a crystal filter narrow enough to extract one sideband from a double-sideband suppressed carrier AM signal.

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The chances are that when you need a crystal-controlled clock these days you will reach for an off-the-shelf crystal oscillator module and never need to create your own. And when you need a higher frequency clock you&#;ll use a clock generator chip featuring a phase locked loop, so you&#;ll never need to make an overtone oscillator. But it does no harm to have a grounding in the basics when it comes to any commonly used component, and crystals are no exception.

[Featured and Thumbnail Arduino crystal image: DustyDingo [Public domain], via Wikimedia Commons.]

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Both ceramic resonators and quartz crystals work on the same principle: the vibrate mechanically when an AC signal is applied to them. Quartz crystals are more accurate and temperature stable than ceramic resonators. The resonator or crystal itself has two connections. On the left the crystal, right the ceramic resonator.

Like you say the oscillator needs extra components, the two capacitors. The active part which makes the oscillator work is an amplifier which supplies the energy to keep the oscillation going.

Some microcontrollers have a low-frequency oscillator for a 32.768 kHz crystal, which often has the capacitors built-in, so that you only need two connections for the crystal (left). Most oscillators, however, need the capacitors externally, and then you have thee connections: input from the amplifier, output to the amplifier, and ground for the capacitors. A resonator with three pins has the capacitors integrated.

The function of the capacitors: in order to oscillate the closed loop amplifier-crystal must have a total phase shift of 360°. The amplifier is inverting, so that's 180°. Together with the capacitors the crystal takes care of the other 180°.

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When you switch a crystal oscillator on it's just an amplifier, you don't get the desired frequency yet. The only thing that's there is a low-level noise over a wide bandwidth. The oscillator will amplify that noise and pass it through the crystal, upon which it enters the oscillator again which amplifies it again and so on. Shouldn't that get you just very much noise? No, the crystal's properties are such that it will pass only a very small amount of the noise, around its resonance frequency. All the rest will be attenuated. So in the end it's only that resonance frequency which is left, and then we're oscillating.

You can compare it with a trampoline. Imagine a bunch of kids jumping on it randomly. The trampoline doesn't move much and the kids have to make a lot of effort to jump just 20cm up. But after some time they will start to synchronize and the trampoline will follow the jumping. The kids will jump higher and higher with less effort. The trampoline will oscillate at its resonance frequency (about 1Hz) and it will be hard to jump faster or slower. That's the frequencies that will be filtered out.
The kid jumping on the trampoline is the amplifier, she supplies the energy to keep the oscillation going.

Further reading
MSP430 32 kHz crystal oscillators

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