Quartz crystal filter

- summary, overview or tutorial about the basics of the quartz crystal filter describing its operation, use, design and specification.

Quartz crystal filters provide an effective means of realising filter solutions for many high performance radio frequency filter applications. The high Q values that quartz crystals possess can be utilised in bandpass filters for use in areas such as radio receivers. These quartz crystal filters are far superior to those that could be manufactured using LC components. Although they are more costly than LC filters, the performance of a quartz crystal filter is still superior and in terms of cost they actually provide excellent value for money.

Today, quartz crystal filters can be designed with pass bands ranging from frequencies in the kilohertz region up to many Megahertz - with the latest technology this can rise to 100 MHz and more. However for the best performance and lowest costs the passband of the filter is generally kept to below about 30 MHz or so.


Quartz crystal overview

Quartz crystals use the piezo electric effect to convert the incoming electrical impulses into mechanical vibrations. These vibrations are affected by the mechanical resonances of the crystal, and as the piezo electric effect operates in both directions, the mechanical resonances affect the electrical stimuli, being reflected back into the electrical circuit.

The levels of Q that can be achieved using quartz crystals range into figures well over 10 000. Values of 100 000 are widely used in filters and values can sometimes reach 500 000. By utilising this level of performance, quartz crystal filters can achieve very high levels of performance. This can be reflected in the crystal filters very narrow filter bandwidths and sharp cut-off curves.


Quartz crystal cuts

When manufacturing the quartz crystal blanks used to make the electronic components used in filters, the angle at which these blanks are cut from the unprepared crystal, have a major bearing on the properties. A form of cut known as the AT cut is used for most radio applications. This provides the optimum set of parameters for most radio applications. The size of the crystal blank using this cut is such that it is sufficiently robust to withstand the manufacturing process without a high level of failures and rejects, and to withstand the vibration that is likely to be expected in use. Additionally the level of spurious responses is low. A further advantage is that the temperature stability is high. The final angle of the cut can be adjusted to ensure that the temperature characteristic is optimum for the particular application for which it is intended. Even a difference of 2 minutes of arc can be detected, although the normal manufacturing spread is around 3 minutes of arc.

In addition to this the cut of the quartz crystal governs the way in which it vibrates. As there are several modes in which a crystal can vibrate it is necessary to choose a cut in which unwanted modes are not easy to excite. If they are present then they will be seen as spurious responses in the crystal filter.


Quartz crystal filter parameters

There are two main areas of interest for a filter, the pass band where it accepts signals and allows them through, and the stop band where it rejects them. In an ideal world a filter would have a response something like that shown below. Here it can be seen that there is an immediate transition between the pass band and the stop band. Also in the pass band the filter does not introduce any loss and in the stop band no signal is allowed through.

Ideal filter response showing passband and stopband

The response of an ideal filter

In reality it is not possible to realise a filter with these characteristics and a typical response more like that shown in Figure 3. It is fairly obvious from the diagram that there are a number of differences. The first is that there is some loss in the pass band. Secondly the response does not fall away infinitely fast. Thirdly the stop band attenuation is not infinite, even though it is very large. Finally it will be noticed that there is some in band ripple.

Quartz crystal filter response

Typical response of a real filter

In most filters the attenuation in the pass band is normally relatively small. For a typical crystal filter figures of 2 - 3 dB are fairly typical. However it is found that very narrow band filters like those used for Morse reception may be higher than this. Fortunately it is quite easy to counteract this loss simply by adding a little extra amplification in the intermediate frequency stages and this factor is not quoted as part of the receiver specification.

It can be seen that the filter response does not fall away infinitely fast, and it is necessary to define the points between which the pass band lies. For receivers the pass band is taken to be the bandwidth between the points where the response has fallen by 6 dB, i.e. where it is 6 dB down or -6 dB.

A stop band is also defined. For most receiver filters this is taken to start at the point where the response has fallen by 60 dB, although the specification for the filter should be checked this as some filters may not be as good. Sometimes a filter may have the stop band defined for a 50 dB attenuation rather than 60 dB.


Shape factor

It can be seen that it is very important for the filter to achieve its final level of rejection as quickly as possible once outside the pass band. In other words the response should fall as quickly as possible. To put a measure on this, a figure known as the shape factor is used. This is simply a ratio of the bandwidths of the pass band and the stop band. Thus a filter with a pass band of 3 kHz at -6dB and a figure of 6 kHz at -60 dB for the stop band would have a shape factor of 2:1. For this figure to have real meaning the two attenuation figures should also be quoted. As a result the full shape factor specification should be 2:1 at 6/60 dB.


Quartz crystal filter design parameters

When a quartz crystal filter is designed factors such as the input and output impedance as well as bandwidth, crystal Q and many other factors need to be taken into account.

Some of the chief factors are obviously the bandwidth, shape fact, and ultimate cutoff. Although it is very much a simplification, these factors are dependent upon the number of poles (equivalent to the number of crystals), their Q value, and their individual frequencies.

Further factors such as the maximum bandwidth that can be achieved is controlled by the filter impedance and also the spurious responses that are present in the individual quartz crystal elements. The location of the important responses for quartz crystal filters can be controlled by the size of the plates deposited onto the crystals. By making them smaller the responses also become less critical. The down side of this is that the impedance of the overall quartz crystal filter rises. This means that the quartz crystal filter will need impedance transformers at the input and the output. This obviously needs to be avoided if at all possible, but for wide band filters it is often the only option.


Summary

Quartz crystal filters are widely used in many applications, and particularly for radio applications. Here these quartz crystal filter provide an exceptional level of performance, and bearing this in mind their cost is very reasonable.

By Ian Poole

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