Quartz crystals and the quartz crystal resonator

- overview, information or tutorial about the basics of quartz crystals, and they may be used as a quartz crystal resonator in a radio frequency oscillator or filter.

This overview or tutorial about quartz crystals and their applications in electronics is split into several pages, each addressing a particalar aspect of quartz crystal technology or the applications in fliters and crystal oscillators:

Quartz crystals are widely used in today's electronics circuits as high quality tuned circuits or resonators. Despite their high performance quartz crystals are cheap to produce and they find many uses in applications from oscillator clock circuits in microprocessor boards, the timing element in digital watches as well as their more traditional applications in radio frequency applications where they may be used as the resonators in highly stable quartz crysal oscillators of high performance crystal filters.

As the name implies quartz crystal resonators are made from quartz, a naturally occurring form of silicon, although most of that used for electronics applications is manufactured synthetically these days. The components rely on the remarkable properties of quartz for their operation. When placed into an electronic circuit a crystal acts as a tuned circuit. However it has an exceptionally high Q. Ordinary LC tuned circuits may exhibit values of a few hundred if carefully designed and constructed, but quartz crystals exhibit values of up to 100 000. Apart from their Q, crystals also have a number of other advantages. Their stability is remarkably good with respect to temperature and time. In fact most crystals will have these figures specified and they might typically be ±5 ppm (parts per million) per year for the ageing and ±30 ppm over a temperature range of 0 to 60 degrees Celsius.

How quartz crystal resonators work

A quartz crystal resonator depends on the piezo-electric effect to work. This effect converts a mechanical stress in a crystal to a voltage and vice versa. In this way the piezo-electric effect converts the electrical impulses to mechanical stress which is subject to the very high Q mechanical resonances of the crystal, and this is in turn linked back into the electrical circuit.

The quartz crystal can vibrate in several different ways, and this means that it has several resonances, all on different frequencies. Fortunately the way in which the quartz crystal blank is cut from the original crystal itself can very significantly reduce this. In fact the angle of the faces relative to the original crystal axes determines many of its properties from the way it vibrates to its activity, Q, and its temperature co-efficient. There are three main ways in which a crystal can vibrate: longitudinal mode, low frequency face shear mode, and high frequency shear. A cut known as the AT cut used for most crystals used in traditional radio and electronics circuits uses the high frequency shear mode.

 

Equivalent circuit of a quartz crystal resonator

To analyse the electrical response of a quartz crystal resonator, it is very often useful to depict it as the equivalent electrical components that would be needed to replace it. This equivalent circuit is can then be used to analyse its response and predict its performance. The basic equivalent circuit of a crystal is shown below. In this circuit C1 represents the capacitance between the electrodes. L, C, and R represent the vibrational characteristics of the crystal. The inductance results from the mass of the material, C from the compliance, and R arises from the losses of which the greatest contributor is frictional losses.

Looking at this circuit it can be seen that there are two ways in which the circuit can resonate. One is from the resonance of L and C which provides a series resonance, giving a very low value of impedance at resonance. This is determined by the value of the resistance R. In this mode the external circuit has very little effect on the crystal resonance.

The other is a parallel resonance providing a very high impedance. This occurs when the combination of L, and C has an inductive reactance that equals C1 together with any value of capacitance provided by the external circuit. It is for this reason that crystals designed to operate in this mode have a value of load capacitance specified. This value of capacitance must be provided by the external circuit if the crystal is to operate at its specified frequency.

Quartz crystal resonators can operate in either mode, and in fact the difference between the parallel and series resonant frequencies is quite small. Typically they are only about 1% apart. Of the two modes, the parallel mode is more commonly used, but either may be found. Oscillator circuits for using the different modes are naturally different, as one oscillates when the crystal reaches its maximum impedance whilst the other operates when the crystal reaches its minimum impedance.

Apart from their use in oscillators, quartz crystals find uses in filters. Here they offer levels of performance that cannot be achieved by other forms of filter. Often several crystals may be used in one filter to provide the correct shape.

How quartz crystal resonators are made

The individual quartz crystal resonators are manufactured from large man-made crystals that are generally several inches long. They are around two inches in diameter and have a hexagonal cross section. The individual quartz crystals are cut from the large crystal using diamond wheels. These are required in view of the hardness of the material. The angle of the cut to the axes of the original crystal is determined very accurately to ensure the final crystal has the right properties. The blanks that are created from the cutting process are in the form of discs, often about the size of a small coin, although this varies according to their final frequency of operation. Once the blanks have been cut they are lapped using a very fine paste to bring them to nearly the right size. The lapping paste normally consists of very fine silicon carbide or aluminium oxide. The final stage of preparation usually involves chemical etching, because this process enables the required very fine finish to be obtained.

The next stage in manufacture involves mounting the quartz crystal. Silver or gold contacts are chemically deposited onto both sides of the blank. The amount of metal that is used in this process can be used to trim the operating frequency of the crystal to its final value. Finally the crystal is mounted into its can or glass envelope. This is either evacuated or filled with an inert gas to minimise ageing.

Specifying quartz crystal resonators

When choosing a quartz crystal resonator there are many parameters that need to be selected. Many are fairly simple like the tolerance figures. However a few of the others need a little extra explanation. One is the type of resonance. Like any tuned circuit a crystal can have a parallel or series form of resonance as shown. This will have to be specified. If the crystal is to have a parallel resonance then a load capacitance will have to be chosen. This is required because any capacitance across the crystal will alter its resonance slightly. Typically this might be 30 pF, but it will be dependent upon the circuit to be used. Also the tolerance required must be specified. The closer the tolerance, the more expensive the crystal will be, so it is wise not to over-specify the item.

Quartz crystal resonator overview

Quartz crystal resonators are widely used within the electronics industry. They can be sued in quartz crystal oscillators and crystal filters where they provide exceptionally high levels of performance. In addition to this, low cost elements with lower tolerance specifications are widely used in crystal oscillators for microprocessor board clocks where they are used as cheap resonator elements. Whatever its use a quartz crystal resonator provides an exceptionally high level of performance for the cost of its production.

Further pages from this tutorial
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