U.S. patent number 3,599,124 [Application Number 04/723,677] was granted by the patent office on 1971-08-10 for crystal filters.
This patent grant is currently assigned to Bell Telephone Laboratories Incorporated. Invention is credited to Warren L. Smith, Roger A. Sykes.
United States Patent |
3,599,124 |
Smith , et al. |
August 10, 1971 |
CRYSTAL FILTERS
Abstract
Three or more resonator-forming electrode pairs and a crystal
wafer on which they are mounted, form a multiresonator crystal
filter with respective inductors connected to two of the pairs. The
electrode pairs have masses such as to tune the frequency exhibited
by the unconnected resonator to a frequency f.sub.p. The inductors
tune the interelectrode capacitances of the connected resonators to
the frequency f.sub.p. The masses of electrodes in the connected
resonators tune the mechanical resonance of the crystal between the
electrodes to the frequency f.sub.p. The electrode spacings in view
of their masses are such as to achieve predetermined couplings
between resonators.
Inventors: |
Smith; Warren L. (Allentown,
PA), Sykes; Roger A. (Bethlehem, PA) |
Assignee: |
Bell Telephone Laboratories
Incorporated (Murray Hill, NJ)
|
Family
ID: |
24907224 |
Appl.
No.: |
04/723,677 |
Filed: |
April 24, 1968 |
Current U.S.
Class: |
333/32; 310/312;
333/189; 310/321; 333/191 |
Current CPC
Class: |
H03H
9/566 (20130101) |
Current International
Class: |
H03H
9/00 (20060101); H03H 9/56 (20060101); H03h
009/20 (); H03h 007/38 () |
Field of
Search: |
;333/72,30 ;310/9.5
;330/5.5 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Electronic Comm. Eng. of Japan...M. Onoe "Piezo-Elec. Resonators
Vibrating In Trapped Modes" Sept. 1965 p.84--93.
|
Primary Examiner: Saalbach; Herman Karl
Assistant Examiner: Baraff; C.
Claims
We claim:
1. An electromechanical filter comprising, in combination,
a body of piezoelectric material,
input electrode means sandwiching a first region of said body
therebetween,
output electrode means sandwiching a second region of said body
therebetween,
means for applying electrical energy to said input electrode
means,
means for extracting electrical energy from said output means,
intermediate electrode means sandwiching said body therebetween
located between said input and output electrode means,
each of said electrode means having sufficient mass to decrease
exponentially the amplitude of acoustic energy in said body as the
distance from said electrode means increases,
thereby to confine said acoustic energy substantially to a limited
acoustic field in said body close to said electrode means and away
from the edges of said body,
each of said electrode means being spaced at a preselected distance
within the acoustic field of each adjacent one of said electrode
means,
the portions of said body between each adjacent pair of said
electrode means being coupled acoustically as a result of the
combined effect of said mass and said distance whereby energy
transfer between said pairs is limited substantially to acoustic
energy,
inductor means connected to said input and output electrode means,
thereby to facilitate accurate shaping of the passband
characteristics of said filter,
said intermediate electrode means comprising a single pair of
short-circuited electrodes, said inductor means forming a
respective tuning circuit with each of said input and output
electrode means, and
each of said tuning circuits being tuned to the mechanical resonant
frequency of a respective one of the resonators formed by said
input and output means.
2. An electromechanical filter comprising, in combination,
a body of piezoelectric material,
input electrode means sandwiching a first region of said body
therebetween,
output electrode means sandwiching a second region of said body
therebetween,
means for applying electrical energy to said input electrode
means,
means for extracting electrical energy from said output means,
intermediate electrode means sandwiching said body therebetween
located between said input and output electrode means,
each of said electrode means having sufficient mass to decrease
exponentially the amplitude of acoustic energy in said body as the
distance from said electrode means increases,
thereby to confine said acoustic energy substantially to a limited
acoustic field in said body close to said electrode means and away
from the edges of said body,
each of said electrode means being spaced at a preselected distance
within the acoustic field of each adjacent one of said electrode
means,
the portions of said body between each adjacent pair of said
electrode means being coupled acoustically as a result of the
combined effect of said mass and said distance whereby energy
transfer between said pairs is limited substantially to acoustic
energy,
inductor means connected to said input and output electrode means,
thereby to facilitate accurate shaping of the passband
characteristics of said filter,
said intermediate electrode means comprising a plurality of pairs
of electrodes,
said inductor means forming a respective tuning circuit with each
of said input and output electrode means, and
each of said tuning circuits being tuned to the mechanical resonant
frequency of a respective one of the resonators formed by said
input and output means.
Description
REFERENCE TO RELATED APPLICATIONS
This application relates to the copending applications Ser. No.
541,549, filed Apr. 11, 1966 and Ser. No. 558,338, filed June 17,
1966, both of W. D. Beaver and R. A. Sykes and assigned to the
assignee of the present application. This application also relates
to the copending application of R. L. Reynolds and R. A. Sykes Case
1--20, filed on or about Mar. 30, 1968 and also assigned to the
assignee of this application. The subject matter of these
applications are herewith made a part of this application as if
included herein.
BACKGROUND OF THE INVENTION
This invention relates to energy transfer devices using the
acoustical resonant properties of crystals, and particularly to
electric wave filters using an acoustically resonant crystal body
having mounted thereon separate electrode pairs to form respective
mutually coupled resonators and wherein electrical energy applied
to one of the electrode pairs is coupled through the body and
removed from another so that the filter transmits a predetermined
passband having predetermined characteristics.
While some kind of energy transmission can be expected whenever
electrical energy is applied to a pair of electrodes
piezoelectrically coupled to a crystal body and energy removed from
another pair of electrodes on the body, it has not always been
possible to obtain a controlled preselected characteristic or a
controlled smooth passband.
It has been proposed that the passbands be controlled with
additional components. Also the before-mentioned copending
applications disclose that controlling the masses and spacing of
electrode pairs allow the character of the transmission
characteristic or passband to be controlled without additional
components as long as the passband was limited to a frequency range
less than the frequency difference between the so-called resonant
and antiresonant frequencies of one electrode pair. It was also
discovered that within this frequency range the passband could be
controlled by mounting a number of extra electrode pairs on the
body between the further-separated input electrode pair and output
electrode pair. These intermediate electrode pairs served with the
body to form resonators that coupled the input resonator, formed by
the input electrodes and the crystal body, to the output resonator,
formed by the output electrodes and the crystal body. However, such
additional resonators were not suitable outside of that
resonant-to-antiresonant frequency range. In structures where an
intermediate electrode pair served to couple the input and output
pairs, the interelectrode capacitances of each electrode pair
imposed restrictions on the passband, which if they could be
overcome at all, appeared to require such cumbersome changes as to
forbid practical application. Thus such energy translating devices
or crystal filters possess practical limitations.
THE INVENTION
According to a feature of the invention three or more
resonator-forming electrode means covering respective portions of
the crystal body so that one of the electrode means is acoustically
coupled through the crystal body to the other two. Furthermore, the
other electrode means are given masses and dimensions such that
each portion of the body covered by the other two or more electrode
means exhibits a predetermined uncoupled mechanical resonant
frequency. Also respective inductances tune the capacitances formed
by the electrodes of the other electrode means to the predetermined
resonant frequency. At the same time the first electrode means are
made sufficiently massive to form with the portion of the body
which it covers a resonator having a tuning frequency in a given
relation with the mechanical resonant frequency.
According to another feature of the invention this given relation
is such that the tuning frequency is equal to the predetermined
mechanical resonant frequency. According to still another feature
of the invention the mechanical resonant frequency of each of the
other electrode means is the same.
According to yet another feature of the invention the electrode
means which couples the other two electrode means comprises a pair
of short-circuited electrodes. According to still another feature
of the invention the one electrode means which couples the other
two electrode means comprises a pair of open-circuited electrodes.
In the case of the short-circuited electrodes the uncoupled
mechanical resonant frequency of the body covered by one electrode
pair preferably is equal to the predetermined mechanical resonant
frequency of the other electrode means.
By virtue of these features the passband limits previously imposed
by the interelectrode capacitances are eliminated with only two
inductors and without the need of additional reactive components
connected to the intermediate electrodes.
These and other features of the invention are pointed out in the
claims. Other objects and advantages of the invention will become
obvious from the following detailed description when read in light
of the accompanying drawing.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a partly schematic, partly plan drawing of a circuit
including a filter with a crystal body and embodying features of
the invention;
FIG. 2 is a partly schematic, partly sectional drawing of the
circuit in FIG. 1;
FIG. 3 is a schematic drawing of an all-electrical equivalent of
the circuit in FIGS. 1 and 2;
FIG. 4 is a graph illustrating the transmission characteristic of
the filter in FIGS. 1 and 2;
FIG. 5 is a partly schematic, partly sectional drawing of a test
arrangement for testing couplings between resonators in the circuit
of FIGS. 1 and 2;
FIG. 6 is a partly schematic, partly sectional drawing of another
circuit embodying features of the invention; and
FIGS. 7, 8 and 9 are drawings illustrating characteristics useful
for manufacturing the filters in the circuits of FIGS. 1, 2 and
6.
DESCRIPTION OF PREFERRED EMBODIMENTS
In FIG. 1 a source S applies a high frequency potential across a
tuning inductor L.sub.1 and across the first of eight pairs of
electrodes 12, 14; 16, 18; 20, 22; 24, 26; 28, 30; 32, 34; 36, 38;
and 40, 42, that are vapor-deposited or plated in alignment along a
chosen axis, such as the Z' crystallographic axis on a rectangular
AT-cut quartz crystal wafer or body 44. For clarity, the
thicknesses of the electrodes and wafer in FIG. 1 are exaggerated.
The individual electrodes of each of the pairs oppose each other
across the wafer. The source S by applying the high frequency
potential across the input electrodes 12 and 14 piezoelectrically
generates thickness shear vibrations in the crystal wafer 44. The
vibrations excite vibrations of equal frequency in the crystal
wafer portions between successive pairs of electrodes 12 to 42 and
generate electrical energy in the electrodes 40 and 42 across which
a tuning inductor L.sub.2 appears. Each electrode pair with the
wafer forms a resonator coupled to the adjacent resonators. A load
resistor R.sub.o receives electrical energy appearing across the
output electrodes 40 and 42 over a predetermined bandwidth B.sub.w.
The intermediate pairs of electrodes 16 through 38 are all short
circuited to each other and grounded.
The masses of the electrodes 12 through 42 affect the resonant
frequency of each of the resonators when considered alone by
lowering their respective frequencies from the fundamental
thickness shear mode frequency of the crystal wafer 44. Each of the
masses is such as to tune the individual resonator in the absence
of the others to the same frequency f.sub.O when measured in the
short circuit condition. The inductor L.sub.i tunes the total
effective electrical interelectrode capacitance C.sub.01 of the
first electrode pair 12 and 14, including the stray capacitances,
to the resonant frequency f.sub.O so that f.sub.0 equals 1/(2.pi.
L.sub.i C.sub.01). The inductor L.sub.o tunes the interelectrode
capacitance of the last pair of electrodes 40, 42 to the same
frequency f.sub.0 so that f.sub.0 equals 1/(2.pi. L.sub.o
C.sub.02). In FIG. 1 the electrodes 12 through 42 are substantially
equal so that C.sub.01 = C.sub.08 = C.sub.0, and L.sub.i =
L.sub.o.
The operation of the filter in FIG. 1 may best be understood by
considering it in connection with the equivalent circuit shown in
FIG. 3 wherein the portions representing the structure composed of
the crystal body 44 and the electrodes 12 through 42 are designated
F. Here, the source S applies high frequency potentials across a
capacitor C.sub.01 representing the electrical interelectrode
capacitance of the electrodes 12 and 14. The source S has an
internal resistance R.sub.s. A capacitance transformer composed of
a capacitance Tee having two capacitor C.sub.1 in the series arm
and a capacitor -C.sub.1 in the shunt leg represent the
piezoelectric coupling between the electrodes 12 and 14 and the
wafer 44 and serve to apply the input energy from the source S to a
shunt resonant circuit composed of an inductor L.sub.1 and
capacitor C.sub.1 representing the resonant structure of the wafer
40 between the electrodes 12 and 14. The resonant circuit composed
of inductor L.sub.1 and C.sub.1 is tuned to the frequency f.sub.0
on the basis of the thickness of wafer 44, the dimensions and
masses of electrodes 12 and 14. Thus, 1/(2.pi. C.sub.1 L.sub.1)=
f.sub.0. The inductor L.sub.i connected across the capacitor
C.sub.01 and the electrodes 12 and 14 tunes the capacitor C.sub.01
to the frequency f.sub.0 so that the latter equals 1/(2.pi. L.sub.i
C.sub.01 ). The energy appearing in the resonator L.sub.1 C.sub.1
excites a plurality of resonators L.sub.2, C.sub.2 ; L.sub.3,
C.sub.3 ; L.sub.4, C.sub.4 ; L.sub.5, C.sub.5 ; L.sub.6, C.sub.6 ;
L.sub.7, C.sub.7 ; and L.sub.8, C.sub.8. Here C.sub.1 = C.sub.2 =
C.sub.3 = C.sub.4 = C.sub.5, = C.sub.6 = C.sub.7 = C.sub.8, and
L.sub.1 = L.sub.2 = L.sub.3 = L.sub.4 = L.sub.5 = L.sub.6 = L.sub.7
= L.sub.8. This is done by means of inductive .pi. coupling
sections S.sub.12, S.sub.23, S.sub.34, S.sub.45, S.sub.56, S.sub.67
and S.sub.78, each of which is composed of a series inductor
L.sub.n(n+1) and two shunt arms -L.sub.n(n+1), where n = 1, 2...7.
Thus the section S.sub.34 is composed of a series inductor L.sub.34
and two shunt inductors -L.sub.34. The excitation of the other
resonators corresponds to the effect of the vibration of wafer 44
between electrodes 12 and 14 exciting through the intermediate
material similar vibrations of the same frequency in the wafer
portions between the respective pairs of electrodes 16 to 42. The
respective resonators L.sub.1, C.sub.1, etc., each represent the
vibration frequency of the individual resonating portion of the
wafer when the other resonating portions are detuned from the
passband region. The inductive sections S.sub.12, S.sub.23, etc.,
represent the coupling between successive resonators and result in
frequency shifts of the vibrating portions between the wafers.
The energy appearing across the resonator L.sub.8, C.sub.8,
representing the energy between the electrodes 40 and 42, is
piezoelectrically coupled to the capacitance C.sub.08 representing
the total interelectrode capacitance across the electrodes 40 and
42, by means of an output capacitance transformer corresponding to
the piezoelectric coupling between the electrodes and wafer 44. A
capacitance Tee circuit formed of two series capacitor arms C.sub.1
and C.sub.1 and a shunt leg -C.sub.1, similar to the input
capacitance transformer, forms the output capacitance transformer.
The electrical energy appearing there passes to a load resistor
R.sub.o. The inductor L.sub.o tunes the capacitance C.sub.08 to the
frequency f.sub.0.
In the equivalent circuit of FIG. 3, the portion W.sub.e represents
the equivalent circuit of the wafer material. The portion T.sub.e
represents the piezoelectric coupling between the wafer material
and the electrodes and the portion E.sub.e represents the total
electrical capacitances of the electrodes.
Corresponding to the conditions of FIG. 1, the electrodes 16
through 38 are short circuited. Therefore, the capacitances
C.sub.02 to C.sub.07 are also short circuited. The effect of these
short circuits is actually to place an infinite impedance or open
circuit across each one of the resonators C.sub.2, L.sub.2 to
C.sub.2, L.sub.7. This can be seen from computing the values of the
total capacitances C.sub.t across one of the capacitances such as
C.sub.2. Here the capacitor C.sub.1 in the leg of the capacitance
transformer circuit to C.sub.02 is shunted across the capacitor
-C.sub.1. The capacitor -C.sub.1 on the other hand is then in
series with the capacitor C.sub.1 in the other arm of the
capacitance Tee. The total value of capacitance C.sub.t across the
resonator L.sub.2, C.sub.2 equals C.sub.1 (C.sub.1 -
C.sub.1)/(C.sub.1 + C.sub.1 - C.sub.1)= 0. The capacitance thus
equals zero and the corresponding reactance X.sub.CT =
1/2.pi.fC.sub.t is infinite. Therefore the effect of the short
circuits across each of resonators L.sub.21, C.sub.02 to L.sub.7,
C.sub.07 is effectively to place infinite reactances across the
particular resonators and have substantially no effect upon their
tuning.
At the same time the inductors L.sub.i and L.sub.o and the
impedances R.sub.s and R.sub.o which form shunt resonant circuits
with the capacitors C.sub.01 and C.sub.08 represent respective
impedances composed of infinite reactances and respective
resistances R.sub.s and R.sub.o at the frequency f.sub.0. Thus at
frequency f.sub.o the capacitance Tees reflect these low
resistances and parallel-resonant circuits L.sub.i, C.sub.01 and
L.sub.o, C.sub.08 across resonators C.sub.1, L.sub.1 and C.sub.8,
L.sub.8 as high resistances and zero reactances if the values of
R.sub.s and R.sub.o are low. This is so because the reflected
impedance such as Z.sub.01 across the resonator L.sub.1, C.sub.1 at
f.sub.o equals [(R.sub.s + X.sub.C1)(- X.sub.C1)/(R.sub.s +
X.sub.C1 - X.sub.C1)] -X.sub.C1 = X.sub.C1 .sup.2 /R.sub.s, where
X.sub.C1 = 1/j2.pi.f.sub.o C.sub.1 is the reactance of C.sub.1 at
the frequency f.sub.o. Thus at frequency f.sub.o the reflected
impedance Z.sub.01 = 1/4.pi..sup.2 f.sub.o .sup.2 C.sub.1 .sup.2
R.sub.s, a real value. If R.sub.s is small compared to the
reactance of C.sub.1 Z.sub.01 is a large resistance. Similarly if
R.sub.o is small compared to the reactance of C.sub.1 Z.sub.08 is
large.
As a result, each of the resonators C.sub.1, L.sub.1 to C.sub.8,
L.sub.8, representing the resonators formed by the electrodes 12 to
42 and the wafer 44 is tuned to substantially the same frequency
f.sub.o.
The passband formed by such tuning depends upon the coupling
between each successive pair of resonators. FIG. 4 illustrates a
passband available from a circuit such as shown in FIGS. 1 and 2.
The desired degree of coupling necessary to produce particular
passbands is available from ordinary circuit theory. The actual
coupling between adjacent resonators can be measured by determining
the frequency shifts imparted by one of a pair of resonators upon
the other.
The circuit of FIG. 5 illustrates the method for determining the
coupling between successive pairs of electrodes. Here, a variable
frequency source 60 applies a high frequency signal across one of
the two pairs of electrodes between which the coupling is to be
measured. A meter 62 measures the input voltage. The resonator to
which the coupling is to be measured such as that formed by the
electrodes 24 to 26 is short circuited. The remaining electrodes
are maintained open circuited to detune the resonators formed by
them. The applied frequency from the source 60 is noted at the two
lowest voltages measured by the meter 62 as the frequency output of
the source 60 varies. These two noted frequencies f.sub.A and
f.sub.B are formed by the effect of inductive section S.sub.34 upon
the resonators L.sub.3, C.sub.3 and L.sub.4, C.sub.4 which
represent the resonators formed by the electrodes 20, 22 and 24,
26. The coupling k is equal to (f.sub.b - f.sub.A)/ f.sub.B
f.sub.A. If open circuiting the electrodes, such as 12 to 18 and 28
to 42 in FIG. 5, whose couplings are not being considered in any
measurement does not adequately detune them so that they are
outside of the measurement scope, additional inductance or
capacitance may be added to detune them further.
Suitable dimensions for the structure of FIGS. 1 and 2 follow.
These dimensions are only examples and should not be taken as
limiting. According to this example the crystal body is composed of
an AT-cut quartz crystal 1 inch long, 0.400 inches wide and
approximately 0.0061 inches thick. The dimensions of the electrode
pairs 12 through 42 are 0.0734 inches along the long direction of
the crystal body, that is along the Z' axis, by 0.0916 inches along
the X-axis. The electrode separations d.sub.1 through d.sub.7
between the edges having the long dimensions are:
d.sub.1 = 0.01171 inches
d.sub.2 = 0.01478 inches
d.sub.3 = 0.01531 inches
d.sub.4 = 0.01542 inches
d.sub.5 = 0.01531 inches
d.sub.6 = 0.01478 inches
d.sub.7 = 0.01171 inches
These spacing dimensions have tolerances of .+-.0.0001 inches,
respectively. The masses of the electrodes are such as to achieve
respective platebacks of 2 percent. The term "plateback" is defined
in the before-mentioned copending applications and represents a
measure of the masses or the effects of the masses of the
electrodes. Specifically, plateback constitutes the fractional drop
(f- f.sub.0)/f in the resonant frequency f.sub.0 of a crystal body
electroded with a single pair of electrodes, from the fundamental
thickness shear frequency f of the unelectroded crystal body due to
increasing masses of the electrodes. This takes into account the
fact that as the masses of the electrodes are increased, the
resonant frequency of the individual resonator as measured with
other resonators detuned is lowered.
The resulting coupling coefficients k between successive pairs from
left to right in FIGS. 1 and 2 are 1.54.times. 10.sup..sup.-3,
1.245.times. 10.sup..sup.-3, 1.200.times. 10.sup..sup.-3,
1.192.times. 10.sup..sup.-3, 1.200.times. 10.sup..sup.-3,
1.245.times. 10.sup..sup.-3 and 1.54.times. 10.sup..sup.-3. The
structure of FIGS. 1 and 2 passes the midband frequency of 10.7
megahertz. The width of the passband is 25 kilohertz. The resonator
inductance L.sub.1 through L.sub.8 is 34 millihenries. The filter
is intended to operate between a source having an impedance of 3000
ohms and a load of 3000 ohms. The inductors L.sub.i and L.sub.o are
0.154 millihenries, respectively. R.sub.s = 3000 ohms.
The frequency bandwidth over which a filter such as shown in FIGS.
1 and 2 operates to furnish a continuous passband as shown in FIG.
4 is wider than hitherto available with such crystal structures. In
the past it had been assumed that such smooth bandwidths, rather
than being limited by other considerations such as the mechanical
coupling between resonators, were limited by the effect on the
passband of the piezoelectric coupling of the body to the
capacitance of each of the electrodes 12 to 42. However, the
equivalent circuit of FIG. 3, reveals that the piezoelectric
coupling operates to impose the interelectrode capacitance
differently upon the intermediate resonators than on the input and
output resonators. Specifically when the source and load are
applied across the input and output resonators the capacitors
C.sub.1 in the arms of the capacitor Tee lie in the main energy
path. This has a different effect from the capacitor Tee on the
intermediate resonators C.sub.2, L.sub.2 to C.sub.7, L.sub.7. There
the capacitor Tee representing the piezoelectric coupling is
substantially shunted across the energy path. This effect is true
even when the electrodes 16 to 38 are open circuited.
While short circuiting of intermediate electrodes 16 through 38 is
often desirable for the purpose of limiting the effects upon the
capacitance C.sub.o, that is any of the capacitances C.sub.01 to
C.sub.08 of leads and reflected capacitances, the open-circuited
condition is often desirable. Under these circumstances, the
equivalent circuit of FIG. 3 changes only by having the short
circuits of C.sub.02 to C.sub.07 removed. The uncoupled resonant
frequencies of each of the interior resonators C.sub.2, L.sub.2 to
C.sub.7, L.sub.7 representing the resonators formed by the wafer 44
and electrodes 16 through 38 are now each detuned by the effect of
the detuning capacitance C.sub.T representing the piezoelectric
coupling and the interelectrode capacitances C.sub.02 to C.sub.07
which are now unshorted.
The detuning capacitance C.sub.T in each case equals C.sub.1
[C.sub.1 C.sub.0 /(C.sub.1 + C.sub.0)- C.sub.1 ]/[C.sub.1 + C.sub.1
C.sub.0 /(C.sub.1 + C.sub.0)- C.sub.1 ]. Thus C.sub.T is equal to
-C.sub.1 .sup.2 /C.sub.0. Therefore, the open-circuit f.sub.oc
frequency which can be tested as shown in FIG. 5 except by open
circuiting the electrodes 24 and 26 and short circuiting the
electrodes 12, 14, 16, 18, 28, 30, 32, 34, 36, 38, 40 and 42,
includes the effects of the interelectrode capacitances C.sub.0 and
the effect of the piezoelectric coupling. This constitutes a
raising of the frequency from f.sub.o because the resultant
capacitance is negative. The resonators formed by the electrodes 12
and 14 as well as the electrodes 40 and 42 as represented by
L.sub.1, C.sub.1 and L.sub.8, C.sub.8 are alone, without the effect
of C.sub.0, tuned to the frequency f.sub.oc. As before the effects
of piezoelectric coupling of capacitors C.sub.01 and C.sub.08 are
obviated by tuning the capacitances C.sub.01 and C.sub.08 with the
inductors L.sub.i and L.sub.o to the frequency of the resonators
L.sub.1, C.sub.1 and L.sub.8, C.sub.8. Here that frequency is
f.sub.oc. In FIG. 6 the tuning of the uncoupled resonators, as
considered alone, formed by electrodes 16 to 38, and represented by
L.sub.2, C.sub.2 to L.sub.7, C.sub.7, capacitors C.sub.1, -C.sub.1
and C.sub.o, to the frequency f.sub.oc is accomplished by making
the masses of the electrodes 16 to 38 to be greater than the
electrodes 12, 14 and 40, 42. This reduces the uncoupled resonant
frequency f.sub.o of each until the total resulting frequency of
each open-circuited resonator is f.sub.oc. The increased masses
achieve the previously mentioned plateback that reduces the
resonant frequency of each resonator. The relative masses of each
electrode pair, that is, the relative platebacks are determined not
only to achieve proper tuning but to achieve the desired coupling.
The greater the plateback on successive resonators, the smaller the
coupling between them.
An example of the dimensions suitable for the structure of FIG. 6
is as follows. These dimensions again are only examples and should
not be taken as limiting. According to this example the crystal
body is composed of an AT-cut quartz crystal, 1.4 inches long,
0.400 inches wide and approximately 0.0087 inches thick. The
dimensions of the electrode pairs 12 through 42 are 0.1050 inches
along the long direction of the body, that is along the Z' axis, by
0.1304 inches across the Z' axis. The electrode separation d.sub.1
to d.sub.7 between the edges having the long dimensions are:
d.sub.1 = 0.0167 inches
d.sub.2 = 0.0211 inches
d.sub.3 = 0.0218 inches
d.sub.4 = 0.0220 inches
d.sub.5 = 0.0218 inches
d.sub.6 = 0.0211 inches
d.sub.7 = 0.0167 inches
The spacing dimensions have tolerances of .+-.0.0001 inches,
respectively. The masses of the electrodes are such as to achieve
respective platebacks of 2 percent. The resulting respective
coupling coefficients k between successive pairs from left to right
in FIG. 6 are 1.54.times. 10.sup.-.sup.3, 1.245.times.
10.sup.-.sup.3, 1.200.times. 10.sup.-.sup.3, 1.192.times.
10.sup.-.sup.3, 1.200.times. 10.sup.-.sup.3, 1.245.times.
10.sup.-.sup.3 and 1.54.times. 10.sup.-.sup.3. The structure of
FIG. 6 passes a midband frequency of 7.5 megahertz and a passband
width of about 17.5 kilohertz. The resonator inductance in each
resonator is 48.5 millihenries. The filter is intended to be driven
by a source impedance of 3000 ohms and when the output of the
electrodes 40 and 42 is applied across a load R.sub.o of 3000 ohms.
L.sub.i and L.sub.0 are 0.220 millihenries, respectively. R.sub.s =
3000.
The invention thus eliminates the limitations previously placed
upon such filters by the piezoelectric coupling of the
electrodes.
Because according to the invention the coupling is controlled
between adjacent resonators, a wider passband is available than
would be obtained otherwise with the particular crystal
material.
The crystal structure of FIGS. 1, 2 and 6 is manufactured by first
selecting the total bandwidth and calculating on the basis of
ordinary circuit theory the needed coupling coefficients between
each pair of electrodes. Electrode sizes and suitable platebacks
are chosen from curves such as in FIGS. 7, 8 and 9 which have been
developed for structures wherein two pairs of electrodes are
coupled to each other. Where t is the thickness of the wafer and r
is the width of the electrodes, r/t is generally made equal to 12
although in practice any value between 6 and 20 is usable. A value
of 15t is frequently chosen as the length of the electrodes normal
to the coupling axis for good suppression of other modes. The
fundamental thickness shear mode frequency f is chosen from the
formula f= f.sub.0 /(1- P.sub.B) where P.sub.B is the fractional
shift in frequency due to mass loading of the electrodes and equal
to (f- f.sub.0)/f.
The manufacture of filters such as shown in FIGS. 1, 2 and 6 starts
by first cutting a wafer from a quartz crystal having the desired
crystallographic orientation such as an AT cut. The wafer is then
lapped and etched to a thickness t corresponding to the fundamental
shear mode index frequency f. Masks with cutouts placed on each
face of the crystal wafer serve for depositing the electrodes. The
geometry of the electrodes is determined by considering the desired
bandwidths and convenient platebacks.
The proper separation d between the electrodes of adjacent pairs
may be determined from graphs such as those of FIGS. 7, 8 and 9
which show variation in coupling (f.sub.B - f.sub.A)/ f.sub.B
f.sub.A for various ratios of electrode separation d to wafer
thickness and for various platebacks as well as various values of
r/t at one center frequency.
To obtain chosen platebacks gold or nickel is deposited such as by
evaporation in layers through the masks so as to make connections
possible and achieve about half the total desired plateback. Energy
for measurement is applied separately to each pair of electrodes
and mass added to the electrodes until a shift corresponding to the
total plateback occurs. This is done until the pair resonates at
the desired overall center frequency f.sub.o . During this
depositing procedure the other electrode pairs are detuned by
keeping them either open circuited when making the circuit of FIG.
1 or short circuited when making the circuit of FIG. 6. However, it
may be necessary to obviate the effect of the other pairs by
terminating them inductively or capacitively. The coupling and
responses of each pair of coupled resonators are then measured as
described in FIG. 5 and the desired bandwidths should prevail.
Adjustments may be made by slight variation in the plateback of
each pair of electrodes.
The invention furnishes a reliable energy-translating system and
filter which can be constructed not only simply but to cover
wide-bandwidth passbands.
The FIGS. 7, 8 and 9 are examples of empirically derived graphs for
a filter having two coupled resonators operating unaffected by
other resonators within a frequency range and about a center
frequency. The graphs are useful for determining suitable
parameters. The values f.sub.B - F.sub.A can be considered measures
of the coupling k= (f.sub.B - f.sub.A)/ f.sub.B f.sub.A. The value
(f.sub.B - f.sub.A)/f.sub.A is an approximation where f.sub.B is
close to f.sub.A. In the graphs r is the electrode dimension in the
direction along which the electrodes are aligned.
While embodiments of the invention have been shown in detail, it
will be obvious to one skilled in the art that the invention may be
embodied otherwise without departing from its spirit and scope.
* * * * *