Page 264 - Electrical Properties of Materials

246 Dielectric materials

we have maximum transmission. At twice the frequency, where d is a whole
wavelength, the contribution from neighbouring finger pairs will be opposite,
and the transducer will produce no net acoustic wave. This shows that the delay
line cannot be a very broad-band device, but it shows in addition that by having
a frequency-dependent output, we might be able to build a filter. The paramet-
ers at our disposal are the length of overlap between fingers (l on Fig. 10.20)
and the relative position of the fingers, the former controlling the strength of
coupling and the latter the relative phase. It turns out that excellent filters can
be produced which are sturdy, cheap, and better than anything else available
in the MHz region. In the stone-age days of radio, when we were younger,
such a band-pass filter was accomplished by a series of transformers tuned by
capacitors. These would appear ridiculously bulky compared to today’s micro-
electronic amplifiers, so a SAW band-pass filter on a small chip of piezoelectric
ceramic with photoengraved transducers is compatible in bulk and in techno-
logy with integrated circuits, and much cheaper than the old hardware. One of
the applications is in television sets.
What else can one do with SAW devices? One of the applications is quite
a fundamental one related to signal processing. The problem to be solved is
posed as follows. If a signal with a known waveform and a lot of noise arrives
at the input of a receiver, how can one improve the chances of detecting the
signal? The answer is that a device exists which will so transform the signal
as to make it optimally distinguishable from noise. The device is called, rather
inappropriately, a matched filter. It turns out that SAW devices are particularly
suitable for their realization. They are vital parts of certain radar systems.
We cannot resist mentioning one more application that will soon appear on
the market: a device that monitors the pressure of car tyres while on the road.
The heart of the device is a SAW resonator inserted into the tyre. The useful
information is contained in its resonant frequency which is pressure depend-
ent. The resonator is interrogated by a pulse from the transmitter attached to
the wheel arch. It re-radiates at its resonant frequency providing the pressure
information that is then displayed on the instrument panel.
I shall finish this section by mentioning electrostriction, a close relative of
piezoelectricity. It is also concerned with mechanical deformation caused by
an applied electric field, but it is not a linear phenomenon. The mechanical
deformation is proportional to the square of the electric field, and the relation-
ship applies to all crystals whether symmetric or not. It has no inverse effect.
The mechanical strain does not produce an electric field via electrostriction.
Biased electrostriction is, however, very similar to piezoelectricity. If we ap-
ply a large d.c. electric field E 0 , and a small a.c. electric field, E 1 , then the
relationship is

γ is a proportionality factor. 2 ~ 2
S = γ (E 0 + E 1 ) = γ E +2γ E 0 E 1 ,
0 (10.71)
and we find that the a.c. strain is linearly proportional to the amplitude of the
a.c. field.
We would like to conclude this section, following our sophisticated account
of signal processing, with a more down-to-earth application of piezoelectrics
that most of us use in our homes. This is the gas igniter. The piezoelectric most
often used is called PZT, a composite ceramic of lead titanate and zirconate.