Note: Descriptions are shown in the official language in which they were submitted.
CA 02237497 1998-0~-13
SELECTED OVERTONE RESONATOR WITH TWO OR MORE COUPLED
RESONANT THICKNESSES
BACKGROUND OF THE INVENTION
1. Field of the Invention.
This invention relates in general to resonators, and more particularly to a
piezoelectric resonator tuned to respond at a specific overtone o'f its parallel plate
resonant frequency.
2. Description of Related Art.
Crystals are widely used in frequency control applications because of their
unequaled combination of high Q, stability and small size. The Q values of crystal
units are much higher than those ~tt~in~ble with other circuit elements. In general-
purpose crystal units, typical Q's are in the range of 104 to 1 o6.
Some crystals, in particular qwartz crystals, are highly anisotropic, that is,
their properties vary greatly with crystallographic direction. For example, when a
quartz sphere is etched in hydrofluoric acid, the etching rate is more than 100 times
faster along the fastest etching rate direction, the Z-direction, than along the slowest
direction, the slow-X-direction. The constants of quartz, such as the thermal
expansion coefficient and the temperature coefficients of the elastic con~t~nt~, also
vary with direction. That crystal units can have zero temperature coefficients of
frequency is a consequence of the temperature coefficients of the elastic constants
ranging from negative to positive values.
The locus of zero-temperature-coefficient cuts in quartz 100 is shown in Fig.
1 a. The X 102, Y 104, and Z 106 directions have been chosen to make the
description of properties as simple as possible. The Z-axis 106 in Fig. la is an axis
of threefold symmetry in quartz; in other words, the physical properties repeat every
120~ as the crystal is rotated about the Z-axis 106. The cut may comprise a singly
rotated cuts 120 and double rotated cuts 130 having angles ~ 140 and ~ 142.
Fig. 1 b illustrates the relationship 150 of several different quartz cuts. The
cuts usually have two-letter names, where the "T" in the name indicates a
temperature-compensated cut. For instance, the AT-cut 160 was the first
temperature-compensated cut discovered. The FC 162, IT 164, BT 166, and RT 168
cuts are other cuts along the zero temperature coefficient locus. These cuts were
studied before the discovery of the SC cut 170 for some special properties, but are
rarely used today. Today, the highest-stability crystal oscillators employ SC cut 170
or AT cut 160 crystal units.
CA 02237497 1998-0~-13
A crystal typically includes suitably mounted and electroded plates of
crystalline quartz using bulk acoustic wave (BAW) vibrations. The plates, also
called wafers or blanks, are fabricated at a precise orientation with respect to the
crystallographic axes of the quartz material. Originally quartz plates were madeS from natural quartz, but today cultured quartz is used almost exclusively.
The cut and geometry of the quartz plate determine the resonator frequency
for a chosen mode of vibration of the plate. In general the plate resonant frequency
is inversely related to a plate dimension. Extension, face shear, flexure and
thickness are typical types of vibration. The cut and type of vibration are intim~tely
10 related and can be classified as low frequency or high frequency depending on the
range of resonant frequencies over which they are commonly used.
When designing an oscillator with stringent stability requirement.c, the
stability and accuracy of quartz frequency control is required. Quartz plates show a
mechanical movement or strain when subjected to an electrical charge. Conversely,
15 they show a potential difference between the two faces when subjected to a
mechanical stress. This relationship is known as the piezoelectric effect. Because of
its electro-mechanical properties, a crystal placed in an oscillator circuit can be made
to oscillate both mechanically and electrically, with its resonant frequency
determined primarily by its mechanical dimensions.
Normally quartz crystals have a uniform thickness between the electrodes.
However, a quartz plate will resonate vigorously when the driving frequency results
in an odd number [1,3,5,7, etc.] of acoustic half-wavelengths between the plates.
The number of half wavelengths in a uniformly thick area is known as the "overtone
number". At resonance "standing waves" occur that include, at fixed positions,
25 nodes (planes of zero amplitude), and antinodes (plains of maximum amplitude).
The lowest resonant frequency of a crystal, known as the "fundamental
frequency", is inversely proportional to the thickness of the crystal. There arepractical limits to how thin a crystal can be made. Thus, for high frequencies, a high
"overtone," which is very nearly an integer multiple of the fundamental frequency, is
30 desired. This integer multiple of the fundamental frequency is referred to as the
overtone number. The term " 15' overtone" will be used herein to mean the
fundamental frequency since one times this frequency is the same frequency.
Quartz crystal accuracy and stability far surpass the performance obtained by
circuits utili7.ing conventional capacitors, inductors, and resistors. A typical two-
35 point mount package 200 for a crystal is shown in Fig. 2. The crystal consists of a
quartz blank 202 with a metal electrode 204 on each of the two major surfaces. The
electrodes 204 are connected to mounting clips 206 at a bonding area 208. The
CA 02237497 1998-0~-13
mounting clips 206 couple the crystal to a leaded header or base 210. At a laterstage, the crystal is encapsulated by welding a cover 220 over the assembly.
This crystal behaves electrically as the circuit in Fig. 3. This circuit is called
the equivalent circuit for the crystal. The mechanical losses of the crystal appear as
5 an equivalent series resistance~ R1 302, while the mechanical elasticity of the crystal
is equivalent to a series capacitor, C, 304. C0 306 is the parallel capacitance
associated with the holder and the electrode capacitance. The frequency of a crystal
operating at series resonance is given by:
f~ 2rI~
At series resonance the reactance of C, 304 and L, 310 are equal and opposite.
Thus, the net reactance of the series circuit is zero. At this point the crystal appears
as a resistance R, 302.
It is known to tune resonators so that they respond to a specific overtone of
its parallel plate resonant frequencies. One approach is reduce the blank diameter to
15 degrade its response at the fundamental and higher modes below the desired
overtone frequency and to increase its response at the frequency of the desired
overtone. Another approach is to apply mass loading in the form of a metal ring.Fig. 4 illustrates this mass loading structure 400. In Fig. 4, a metal ring 402
substantially circumscribes a top electrode 404 over a quartz blank 406. A similar
20 pattern is also applied to the bottom of the quartz blank 406.
Nevertheless each of the above methods has its disadvantages. The first
method leads to the blank diameter becoming inconveniently small thereby causingproblems in manufacturing. In the second method, the metal ring 402 introduces
unwanted parasitic capacity in the resonator circuit which can reduce the output25 power and degrade the oscillator quality factor (Q).
It can be seen that there is a need for a resonator that allows easier
establishment of a resonant frequency.
It can also be seen that there is a need for a resonator tuned to respond at a
specific overtone frequency.
SUMMARY OF THE INVENTION
To overcome the limitations in the prior art described above, and to
overcome other limitations that will become ~palelll upon reading and
understanding the present specification, the present invention discloses a dual
35 overtone crystal.
CA 02237497 1998-0~-13
The present invention solves the above-described problems by providing a
resonator that allows easier establi~hment of a resonant frequency. While the
present invention is primarily described with reference to quartz crystals, those
skilled in the art will readily recognize that the invention is equally applicable to any
piezoelectric material. Moreover, those skilled in the art will recognize that the
present invention is equally applicable to a dielectric resonator.
A system in accordance with the principles of the present invention includes a
first section having a first thickness and a second section having a second thickness.
The first thickness and the second thickness are selected to cause the nodes and the
10 antinodes of the crystal to align when the cr,vstal is stimulated.
Other embodiments of a system in accordance with the principles of the
invention may include alternative or optional additional aspects. One such aspect of
the present invention is that the first section has a thickness an even number of half
wave lengths thicker than the second section.
Another aspect of the present invention is that the first and second sections
have a thickness equal to a prime number of half wave lengths.
Another aspect of the present invention is that the alignment of the nodes and
antinodes allows the first section and the second section to resonate at the same
frequency.
These and various other advantages and features of novelty which characterize
the invention are pointed out with particularity in the claims annexed hereto and form a
part hereof. However, for a better understanding of the invention, its advantages, and
the objects obtained by its use, reference should be made to the drawings which forrn a
further part hereof, and to accompanying descriptive matter, in which there are
25 illustrated and described specific examples of an apparatus in accordance with the
invention.
BRIEF DESCRIPTION OF THE DRAWINGS
Referring now to the drawings in which like reference numbers represent
30 corresponding parts throughout:
Fig. 1 a illustrates the locus of zero-temperature-coefficient cuts in quartz;
Fig. lb illustrates the relationship of several different quartz cuts,
Fig. 2 illustrates a typical two-point mount package;
Fig. 3 illustrates an equivalent circuit for a crystal;
Fig. 4 illustrates a mass loading method for increasing the response of the
blank at the frequency of the desired overtone;
Fig. 5 illustrates a face view of a dual overtone resonator according to the
present invention; and
CA 02237497 1998-0~-13
Figs. 6a-i illustrate different embodiments of a dual overtone resonator
according to the present invention.
DETAILED DESCRIPTION OF THE INVENTION
In the following description of the exemplary embodiment, reference is made
to the accompanying drawings which form a part hereof, and in which is shown by
way of illustration the specific embodiment in which the invention may be practiced.
It is to be understood that other embodiments may be utilized as structural changes
may be made without departing from the scope of the present invention.
The present invention provides a plate having a thinner and a thicker portion
that causes the nodes and the antinodes in the two portions to align.
The present invention solves the above-described problems by providing a
resonator that allows easier establi~hment of a resonant frequency. While the
present invention is primarily described with reference to quartz crystals, those
15 skilled in the art will readily recognize that the invention is equally applicable to any
piezoelectric material. Moreover, those skilled in the art will recognize that the
present invention is equally applicable to a dielectric resonator.
Fig. 5 illustrates a face view 500 of a dual overtone resonator according to
the present invention. A first charge electrode area 502 has a thickness associated
20 with a first overtone. A second charge electrode area 504 has a thickness associated
with a higher overtone. In Fig. 5, the thickness of the first charge electrode area 502
is seven half wave lengths. The thickness of the second electrode charge area 504
has a thickness of five half wave lengths.
Thus according to the invention, a crystal oscillator structure may be formed
25 having a thin area 504 and a thicker area 502 under the electrode plates. Thethickness of the thicker portion 502 must be an even number of half wave lengthsgreater than that of the thinner section 504. The thinner section 504 must be aligned
with the thicker section 502 such that the nodes and the antinodes in the two sections
502, 504 will be perfectly aligned. If the half wave length numbers in each section
30 are prime, then the frequency spectrum of the resonator will be restricted to the
lowest frequency that resonates simultaneously in both section and the odd
numbered overtones of that frequency. In this case, both areas 502, 504 of the
crystal will resonate. If the entire area between electrodes can resonate at a given
frequency, establishment of resonance at this frequency is much easier than if only
35 part of this area can resonate. Thus, for the case of three or more half wavelengths
in the thinner area 504, the lowest resonance that is easily established is an overtone
of the fundamental frequency of the thinner section 504.
CA 02237497 1998-0~-13
Figs. 6a-i illustrate different embodiments 600 of a dual overtone resonator
according to the present invention. In Figs. 6a-i, the thicker portion 602 always has
a thickness of seven half wave lengths. However, those skilled in the art will
recognize that the invention is not limited to a dual overtone resonator having a thick
portion of seven half wave lengths. Other embodiments may be developed which
are consistent with the teaçhing of the invention, i.e., forming a crystal having two
different thicknesses which result in the nodes and the antinodes in the two sections
becoming perfectly aligned. Furthermore, those skilled in the art will recognize that
the placement of thicker and thinner portions described herein below could be
10 reversed.
Figs. 6a-b illustrate 7,5 dual overtone resonator 610. In Fig. 6a, the thinner
portion 612 of the dual overtone resonator is formed by m~t~hining a flat circular
hole 614 of two half wave lengths in a first face 604 of the plate resulting in a
thinner portion 612 of five half wave lengths. The depth chosen in machining the15 circular hole 614 should be uniform over the area of the bottom. Fig. 6b illustrates a
7,5 dual overtone resonator wherein flat circular holes 616, 618 of one half wave
length each are machined on both sides 604, 606 of the resonator. Those skilled in
the art will recognize that the machining method is not meant to be limited to any
method in particular. For example, m~hininp is most often accomplished by
20 masked chemical etching, but a laser or ion-beam machining method could also be
used.
Figs. 6c-e illustrate 7,3 dual overtone resonator 630. In Fig. 6c, the thinner
portion 632 of the dual overtone resonator is formed by machining a flat circular
hole 634 of four half wave lengths in a first face 604 of the plate resulting in a
25 thinner portion 632 of three half wave lengths. Fig. 6d illustrates a dual overtone
resonator wherein a first hole 636 is m~çhined on a first side 604 of the resonator to
a depth of three half wave lengths. Then a second hole 638 is m~hined on the
second side 606 of the resonator to a depth of one half wave length. Thus, the
thinner portion 632 has a thickness of three half wave lengths.
Fig. 6e illustrates a dual overtone resonator wherein a first hole 640 is
machined on a first side 604 of the resonator to a depth of two half wave lengths.
Then a second hole 642 is machined on the second side 606 of the crystal to a depth
of two half wave lengths. Again, the thinner portion 636 has a thickness of three
half wave lengths.
Figs. 6f-i illustrate 7,1 dual overtone resonators 650. In Fig. 6f, the thinner
portion 652 of the dual overtone resonator is formed by machining a flat circular
hole 654 of six half wave lengths in a first face 604 of the quartz plate resulting in a
thinner portion 652 of one hali'wave length. Fig. 6g illustrates a dual overtone
CA 02237497 1998-0~-13
resonator wherein a first hole 656 is m~rhined on a first side 604 of the resonator to
a depth of five half wave lengths. Then a second hole 658 is m~ ined on the
second side 606 of the crystal to a depth of one half wave length. Thus, the thinner
portion 652 has a thickness of one half wave lengths.
Fig. 6h illustrates a dual overtone resonator wherein a first hole 660 is
m~r.l~ined on a first side 604 of the resonator to a depth of four half wave lengths.
Then a second hole 662 is machined on the second side 606 of the resonator to a
depth of two half wave lengths. Again, the thinner portion 652 has a thickness of
three half wave lengths.
Finally, Fig. 6i illustrates a dual overtone resonator wherein a first hole 664
is machined on a first side 604 of the resonator to a depth of three half wave lengths.
Then a second hole 666 is m~ ined on the second side 606 of the resonator to a
depth of three half wave lengths. Again, the thinner portion 652 has a thickness of
three half wave lengths.
In summary, a resonator may be formed which has two or more sections with
each having a different thickness and alignment with one another that results in the
nodes and the antinodes in the two sections becoming perfectly aligned. The
thickness of the thicker portion is an even number of half wave lengths greater than
the thinner section. Further, if the half wave length numbers are both prime, the
20 lowest possible frequency where perfect ~lignment occurs is a specific overtone of
the thinner section and a higher specific overtone of the thicker section. There will
also be a series of higher frequencies where perfect alignment occurs which are odd
overtones of the lowest frequency. However, those skilled in the art will recognize
that other embodiments having dimensions which have not been illustrated may be
25 developed which are consistent with the teaching of the invention. Moreover, those
skilled in the art will recognize that then invention is not meant to be limited to
circular-shaped crystals. Other crystal shapes in accordance with the invention
could be utili7t~-1, e.g., rectangular (AT strip).
The foregoing description of the exemplary embodiment of the invention has
30 been presented for the purposes of illustration and description. It is not intended to
be exhaustive or to limit the invention to the precise forrn disclosed. Many
modifications and variations are possible in light of the above teaching. It is
intended that the scope of the invention be limited not with this detailed description,
but rather by the claims appended hereto.
