material's first widespread application in electronics was in the form
of quartz crystals that were cut along certain axes in order to provide
resonance at specific frequencies. They are still used in modern circuits
as frequency-determining devices in oscillators and as frequency-selective
devices in filters. Many high Q and tailored frequency response applications
are now using polycrystalline ceramics for surface acoustic wave (SAW)
where crystals used to claim an exclusive domain. This article provides
a bit of theory of operation as well as application in radio circuits
using both fundamental and overtone frequencies.
May 1934 Radio News and Short-Wave
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Phenomena Underlying Radio: Piezo-Electric Effects
By E. B. Kirk
The strains in a crystal are approximately proportional to the applied
potential difference and if the potential is reversed the direction
of the strains is reversed also. It follows, therefore, that if the
potential is alternated in direction the plate will be set in vibration
at the same frequency. The dimensions of the plate cause it to have
various natural periods of vibration and if the frequency of the applied
voltage is made to approach one of these natural frequencies (different
along the different axes) the response of the crystal increases until,
if the two coincide, resonance occurs and the amplitude of vibration
may increase several hundredfold. If the applied voltage is too great,
the crystal can be broken by the violence of its own motion. When a
crystal is made to vibrate in this way, thereby calling into play the
converse effect, the direct effect is also involved, for the motion
of the plate with the charges on the faces gives rise to electrical
reactions on the circuit which is being used to supply the alternating
potential difference. The frequency at which the reaction takes place
is in most part dependent on the dimensions and the elastic constants
of the material. By accurate grinding the natural periods of vibration
along the various axes can be made any desired value and thus gives
a simple means for obtaining frequency standards. A device of this sort
is called a piezo-electric resonator.
Response frequencies of 32 x 47 x 2.760 mm parallel cut quartz
plate in region of major high frequency.
One crystal can furnish
a number of frequencies anyone of which can be called into action by
the proper adjustment of the driving circuit, for in addition to the
natural periods along the three axes the overtones of harmonics can
be used. These are 2, 3, 4 (and so on) times the fundamental frequencies.
We have considered a crystal plate working in a circuit which was driven
by an alternating electric potential. A most important advance was made
when it was discovered that a crystal could be used, in a vacuum-tube
circuit, for maintaining oscillations of constant frequency. A number
of circuits were worked with before the present ones were evolved, and
although it is still not ordinarily possible to obtain much more than
a watt or so of power directly from a crystal circuit, it is always
possible to amplify to any desired power level.
Response-frequency spectra of a parallel cut crystal plate at
different temperatures illustrating the interchange of activity
between the two frequencies as the frequencies f the two modes
of vibration pass through a coincident value.
of plate along optic axis = 47 mm.
Width along electric
axis = 19.35 mm.
Thickness along third axis = 2.75 mm.
(After lack: - mode of vibration and temperature coefficients
of quartz crystal plates. Bell telephone laboratories, reprint.
The uses to
which the direct and the converse piezo-electric effects can be turned
are rather impressive. We have mentioned before the use by the Curies
for the measurement of movements of 1/10,000,000 of a centimeter. It
is interesting to note that interferometry allows measurements to slightly
less than 1/10,000,000 cm., and although it has at present many more
chances for application, the crystal methods are superior for some purposes.
Crystals can also be used for the measurements of high pressures, as
in the explosion chambers of large guns. High-voltage measurements have
been previously mentioned; it has been used for the detection of currents
as small as 1/1,000,000,000,000 of an ampere. (The vacuum tube is still
ahead, being able to detect as little as 1/10,000,000,000,000,000 ampere.)
Piezo-electric oscillographs have been constructed by Wood; the supersonic
waves (in water) of Langevin are used for deep-sea sounding. submarine
signaling, and for the detection of underwater obstacles. Pierce has
used a quartz oscillator for the determination of the velocities of
waves of high frequencies in gases.
Crystals have also been
applied the study of vibrations in heavy machinery and we may expect
a rapid extension of its use to other laboratory and engineering measurements.
Hund has suggested the use of an unsymmetrical quartz plate for the
production of audio-frequency power. He has also suggested that a vibrating
plate could be used as an optical shutter, making it possible to measure
the velocity of light in a manner similar to Fizeau's mechanical shutter
arrangement; a very important suggestion, since the velocity of light
enters in such a fundamental way into the calculations of radio theory.
The optical properties and the behavior of quartz are most interesting.
There are many likely applications ahead in the fields of phototelegraphy,
facsimile transmission and television.
Multi-Resonance in Crystals
A crystal plate cut without reference to the orientation of
the three axes will in general respond to a large number of frequencies.
Plotting the response amplitude against the frequency gives results
similar to those shown in the above figure, which has been called the
frequency spectrum of the crystal plate. Usually there are one or more
frequencies in the spectrum of a plate giving responses sufficient to
drive a vacuum tube in the usual crystal oscillator circuit. Relations
between major response frequencies and the dimensions of a plate cut
by the Curie or perpendicular method are as follows: For this type of
plate there are two major response frequencies, one high and one low.
The high frequency which is a function of c, the thickness of the plate,
can be determined approximately from the relation f = K/c, where c is
the thickness of the plate in millimeters and K = 2.860 x 106
(giving a constant of approximately 105 meters per mm. of thickness).
The low frequency is a function of b, the dimension along the electric
axis, and is obtained by substituting the value of b in millimeters
for c in the above relation. With the parallel or 30° cut there is a
major high and low frequency, but in some cases the high frequency occurs
as two response frequencies a kilocycle or so apart (termed a doublet).
For thin plates of relatively large area the high frequency
is given approximately by the relation f = K/d where d is the thickness
in millimeters and K = 1.96 x 106. The low frequency, a function
of the width, e, of the plate, is obtained by substituting the value
of e in millimeters in the place of d
Posted February 14, 2014