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The Crystal as a Circuit Element

Quartz is a very interesting substance. It comes in the form of pretty crystals that can be cut or formed into many different shapes. As such, it is used as ornamentation or as jewelry. In electronics, however, we are interested in a different property: quartz crystals are piezoelectric.

What this means is simply that if a quartz crystal is mechanically stressed, it will develop a small voltage across itself. Conversely, if a voltage is applied across the crystal, it will twist or flex, thus producing a mechanical stress. In addition, depending on its size and shape, a quartz crystal has a natural mechanical resonance at a particular frequency. If we can send electrical pulses to the crystal at its resonant frequency, we can keep it vibrating for as long as we want. And if we use the electrical signal it generates while vibrating to trigger these pulses, we can have an oscillator operating at the specific resonant frequency of the crystal.

Although the resonance effect of the crystal is mechanically based, Equivalent circuit of a quartz crystal. the external circuit experiences approximately the electrical equivalent circuit shown to the right. The values of these components depend on how the crystal is cut, of course, but the possible range is very wide. While most crystals are designed and intended to operate somewhere in the range of 2 to 30 MHz, some crystals are made to operate at frequencies from the audio band to over 300 MHz.

In this equivalent circuit, RS represents both the electrical resistance of the leads and internal connections, and the mechanical losses of the crystal itself as it flexes. These losses are very small: RS is typically no more than 100Ω.

L represents the mechanical energy storage of the crystal itself. This is the primary factor in the entire crystal, and is measured in henries. CS is very small, on the order of a few hundredths of a picofarad. CP represents internal stray capacitances as well as part of the resonance of the crystal. This capacitor is on the order of a few picofarads.

A crystal is used as the main feedback element when the oscillator is intended to operate at a single frequency, and never deviate from that frequency. For example, the standard commercial AM radio broadcast band in the US covers the frequency band from 520 kHz to 1610 kHz. Each station is assigned a "channel" 10 kHz wide within that band. Its carrier frequency must be at the center of that channel, and must remain accurate to within 10 Hz. These requirements just beg for a crystal-controlled oscillator.

Looking again at the schematic diagram above, a typical crystal with a series resonant frequency of 1 MHz might have values of L = 1 henry and RS = 50Ω. The Q of the series-resonant circuit is 2πfL/R which is slightly greater than 125,600. This gives the crystal a bandwidth of about 8 Hz at 1 MHz.

As precise and accurate as a crystal oscillator is, it isn't good for all tasks. You wouldn't want it for a broadcast band radio receiver, for example, because you need to be able to tune the receiver to any radio station in range of the receiver. Therefore, radio receivers use LC oscillators which are accurate enough to be useful, and can be tuned to any channel within the broadcast band.

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