Mechanical vibration for electronics: the quartz crystal

It is now 100 years since Alexander Nicholson at Bell Laboratories built and patented the first crystal oscillator, and crystals are still the main source of accurate oscillations up to UHF frequencies using quartz instead of Rochelle Salt (see US patent ). Quartz crystal oscillators use the piezoelectric effect. The piezoelectric effect refers to the voltage produced when a piezoelectric material is stressed. A quartz crystal oscillator uses the effect the opposite way round &#; a voltage applied to the crystal produces a tiny deformation of the crystal. The precise frequency of a quartz crystal relies on the natural resonance of the crystal. This resonance can be in different planes or vibration modes depending on the frequency of the crystal and the way the crystal is cut. A low-frequency crystal for a watch (32.768kHz) will be cut differently to a crystal for above 1MHz.
It may seem surprising that crystals can cover such a wide range of frequencies without being the size of a brick for low frequencies or impossibly tiny for high frequencies, but that comes down to the cut and vibration mode. The image below is from the Total Frequency Control (TFC) document
which is worth reading if you want more detail on quartz crystals, particularly temperature effects.

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If you imagine a thin disc of quartz then it could flex like a drum or compress and expand across its thinnest dimension, or its longest dimension. The natural frequency of each vibration mode will be quite different. For very high frequencies the crystal will be forced to oscillate at is third, fifth or even seventh or ninth harmonic (overtone). This requires a specially tuned oscillator design to make sure you don&#;t oscillate at the fundamental frequency.

To avoid having to get involved in oscillator design you can buy an oscillator rather than just a crystal. The advantage of buying an oscillator is that you will have guaranteed characteristics such as tolerance and temperature stability. While these are characteristics of a quartz crystal as well, the final performance you get from your own oscillator will depend on the circuit as well as the crystal.

For example, an oscillator with very high-temperature stability would be internally temperature-compensated (a TCXO). Oscillators with stability of better than +/-0.5ppm over 100C temperature range or more are readily available. A crystal would typically be fifty times worse, and even a high stability crystal would be +/-10ppm over temperature. So, if you want very high stability, a TCXO is the easy option rather than trying to temperature compensate your own crystal oscillator.

There are oscillators available which can be programmed to the desired frequency such as the Seiko Epson SG- series. They still contain a quartz crystal but also a phase locked loop (PLL) to generate frequencies other than the crystal frequency. Stability will only be as good as the quartz crystal and they are usually only moderate performance devices. There will also be phase noise due to the PLL. Similarly, there are MEMS-based oscillators which are programmable such as the ASEMCC from Abracon. Performance varies but can be as good as +/-10ppm.

Overtone crystals can be tricky things to work with. Any crystal will have a resonance as shown below. There is a low impedance point where the crystal has its series resonance and a high impedance slightly higher in frequency where the crystal has its parallel resonance.

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At approximate odd multiples of the fundamental frequency, you will find the same impedance changes but at lower amplitude. I say &#;approximate&#; because the third harmonic (overtone) resonance is usually slightly different from three times the fundamental and the same for other harmonics. The difference is slight but means that you need to specify that you want a third overtone or fifth overtone crystal when ordering and don&#;t just use a fundamental crystal and expect it to work at exactly three times the fundamental frequency when operated at its third harmonic. An overtone crystal is no different to a normal crystal &#; it is just tuned for the frequency of operation in the overtone mode and with the characteristics specified for overtone operation.

The quality factor or &#;Q&#; of quartz crystals can be very high e.g. or more, although the Q at higher harmonics is less.

The two resonances of a crystal (series and parallel) can be understood by reference to its equivalent circuit. Below is a typical equivalent circuit for a 10MHz crystal with a Q of around .

When specifying crystals, the load capacitance is important because it becomes part of the resonant circuit and so affects the resonant frequency. When designing crystal oscillators you also need to take into account the drive level as this can affect the frequency as well as aging. You can see why it is easier to buy a ready-made oscillator where the manufacturer has done all the design work for you.

It is surprising to me that after 100 years, electronics is still very dependant on a mechanical vibration.

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