Mechanical vibration for electronics: the quartz crystal

Celebrating a century since Alexander Nicholson at Bell Laboratories created the first crystal oscillator, quartz crystals remain the primary source of precise oscillations, extending up to UHF frequencies, utilizing quartz rather than Rochelle Salt (refer to the US patent). Quartz crystal oscillators operate based on the piezoelectric effect, which describes the voltage generated when piezoelectric materials are subjected to stress. In contrast, a quartz crystal oscillator applies voltage to create a small deformation within the crystal. The exact frequency produced by a quartz crystal is determined by the crystal's natural resonance, which can vary based on the vibrations' mode and the crystal's cut. A low-frequency crystal, such as one used in a watch (32.768 kHz), is cut differently than a crystal operating above 1 MHz.

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Envisioning a thin disc of quartz, it can either flex like a drum or compress and expand along its thinnest or longest dimensions. Each vibration mode possesses a unique natural frequency. At exceedingly high frequencies, the crystal may oscillate at its third, fifth, or even seventh or ninth harmonic (overtones), necessitating a specially designed oscillator to avoid oscillation at the fundamental frequency.

Buying Oscillators vs. Crystals

To simplify matters, purchasing an oscillator instead of just a crystal is advisable. The primary benefit of acquiring an oscillator is the assurance of specific characteristics such as tolerance and temperature stability. While quartz crystals also possess these traits, the ultimate performance of an oscillator is dependent on both the circuit design and the crystal used.

For instance, if you seek a highly stable oscillator regarding temperature, an internally temperature-compensated design known as a TCXO is advantageous. Oscillators offering stability better than +/-0.5 ppm across a 100°C temperature range are now widely available. In comparison, a crystal's stability might only reach +/-10 ppm, making a TCXO a more straightforward solution for achieving exceptional stability.

Programmable Solutions

There are programmable oscillators, like the Seiko Epson SG-series, which still incorporate a quartz crystal alongside a phase-locked loop (PLL) capable of generating frequencies other than the crystal's inherent frequency. The stability of such devices is directly tied to the quartz crystal, which may yield moderate performance with inherent phase noise due to the PLL. On a similar note, MEMS-based oscillators, such as the ASEMCC from Abracon, offer programmable features with performance that can match a +/-10 ppm standard.

Working with overtone crystals can be complex. Each crystal showcases resonance behavior, revealing a low impedance point at its series resonance and a slightly higher high impedance level at its parallel resonance.

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As we approach odd multiples of the fundamental frequency, we observe similar impedance shifts at reduced amplitudes. The term 'approximate' is used because the third harmonic (overtone) resonance does not always align perfectly with three times the fundamental frequency, nor do other harmonics. These subtle differences necessitate specifying whether you require a third or fifth overtone crystal when placing an order, rather than assuming that a fundamental crystal will perform correctly at three times the fundamental frequency.

The quality factor, or 'Q' of quartz crystals, can exceed 100, although higher harmonics generally display a lower Q.

Crystals Specification Challenges

The two distinct resonances of a crystal—series and parallel—can be illustrated through its equivalent circuit. Below lies a typical equivalent circuit for a 10 MHz crystal exhibiting a Q of approximately 1000.

When defining crystal specifications, one must consider load capacitance, as this influences the resonant frequency. Moreover, the drive level essential in designing crystal oscillators can affect frequency and aging. It becomes evident why purchasing a pre-manufactured oscillator is more practical, as the manufacturer handles comprehensive design details.

It's quite astonishing that after a century, the realm of electronics continues to rely heavily on mechanical vibrations.

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