US2440886A - Method and means for processing piezoelectric crystals - Google Patents

Description

H. M. BACH May 4, 1948.

METHOD AND MEANS FOR PROCESSING PIEZO-ELECTRIC CRYSTALS Filed Aug. 29, 194:4v s Sheets-Sheet 1 Q m W o Wm M WY w n. w mm m CT P Km 5 NE a R N Spun/00.: M0055 Zlwuvwtom HENRY M. BA CH F1535. WWXM Arron Y May 4, 1948. EACH 7 2,440,886

METHOD AND MEANS FOR PROCESSING PIEZO-ELECTRIC CRYSTALS Filed Aug. 29, 1944 Sheets-Sheet 2 FREQUENCY 72 VAR/Ar/o/v IN T :2

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METHOD AND MEANS FOR PROCESSING PIEZO-ELEGTRIG CRYSTALS Filed Aug. 29, 1944 3 Sheets-Sheet 3 finrma DE was w, #M 1m flTroR/ Y awe/whoa HNRY M. BACH Patented May 4, 1948 METHOD AND MEANS FOR PROCESSING PIEZOELECTRIG CRYSTALS Henry M. Bach; flaws-once, N. Y., assignor to Premier Crystal Laboratories, Incorporated,

New York, N. Y.

Application August 29, 1944, Serial No. 551,737

This invention relates to Diezo-electric apparatus and more particularly to a method and means for-predeterminlng the performance characteristics of piezo-electric plates.

An object of this invention is to produce piezoelectric plates in which couplings between oscillations of desired frequencies and of extraneous, or undesired, frequencies are eliminated.

A further object of this invention is to produce piezo-electric plates in which activity dips or activity discontinuities over the working range of temperatures are eliminated.

A still further object of this invention is to eliminate the necessity of making a. large number of temperature runs in testing piezo-electric plates for satisfactory performance over the range of temperatures likely to be encountered in service.

A still further object of this invention is to predict the performance of piezo-clectric plates under a wide range of temperature conditions without actually submitting the plates to the said range of temperature conditions. v

A still further object oi. this invention is to select proper dimensions for a piezo-electric plate, the dimensions being so-related that spurious frequencies over the range of operating temperatures for the plate will be avoided and activity discontinuities over this range will not be present.

A still further object of this invention is to simulate artificially conditions which reveal the presence of spurious frequencies in a piezo-electric plate without subjecting the plate to a temperature run. I

Other objects will appear from the following description and claims when considered together with the accompanying drawings, wherein:

Figure 1 is a view in perspective of a typical piezo-electric plate showing the nomenclatures of the directions along which the lengths of the various dimensions are measured with respect to the direction of an applied electric field Ex normal to the lane or the plate.

Figure 2 is a view in perspective showing the relationship of the crystallographic directions in a typical piezo-electric plate with respect to an applied electric field Ex and the resolution of the electric field into component vectors associated with possible modes of motion along the crystallographic axes and also showing the resolution of a possible shear mode Yz.

Figure 3 is a schematic view of a circuit equivalent to a piezo-electric plate having no spurious modes of vibration for a given range of tempera- 11 Claims. (Cl. 171-327) 2 tures T1 to T2, said equivalent circuit being connected in a typical oscillator circuit in the same manner as the piano-electric plate would be connected.

Figure 3a is a schematic view of a circuit equivalent to a piezo-electric plate having spurious coupled modes of vibration capable of being excited within the given range of temperatures T1 to T2, to affect the performance of the plate, said equivalent circuit being connected in a typical oscillator circuit in the same manner as the piezoelectric plate would be connected.

Figure 4 is a set of curves illustrating the behavior of performance characteristics of the plate whose equivalent circuit is represented in Figure 7 3 over the range of temperatures T1 to T2.

Figure 4a is a set of curves illustrating the behavior of performance characteristics of the plate whose equivalent circuit is represented in Figure 3a over the range of temperatures T1 to T2, showing the effect of spurious modes.

Figure 5 is a schematic circuit showing one arrangement for artificially simulating a tempera ture cycle to detect the presence of spurious modes in a piezo-electric plate.

Figure 6 is a schematic circuit similar to Figure 5 but somewhat modified.

Figure '7 is a, schematic view diagrammatically illustrating another arrangement for artificially simulating a temperature cycle to detect the presence of spurious modes in a piezo-electric plate.

In the design and manufacture of piezo-electric plates, such as quartz oscillator plates, the proper performance of the vibrating plates over substantial variations in ambient temperature is an ever present problem.

The problem of the variation in frequency of the vibration as a function of temperature is rather academic. It is well known that the rate of change of vibration frequency F with temperature T and the temperature coefficient, the summation of dF/dT over any specified temperature interval T1 to T2, in the absence of coupled vibrations, is a function of the orientation of the quartz plate. By X-ray diffraction technique the orientation may be accurately measured and the temperature coeflicient held within preassigned limits.

However the variation in vibrating activity or amplitude (as measured conveniently by the direct current component of grid current in an 05- cillator, or by the output amplitude of the oscillator, etc.) is no such prosaic problem. It is appreciated that the cause of changes in activity iimction of temperature (solely within the vibrations are coupling to the desired vibrations at certain temperatures or over certain temperature intervals, and, as is well known in coupled circuit phenomena, causing variations in the desired vibration.

The usual types of vibration utilized in quartz plates include shears (both thickness" and face types), longitudinal, torsional and fiexural modes of vibration. These vibrations are excited by suitable electrical alternating current fields having an X or Y axis component. From the mathematical theory of elasticity and crystal structure the types of vibration that may be excited electrically by any certain electrical field are known. Known also are the types of vibration (and the approximate frequency relationship these vibrations will have to the desired vibration) that will be excited mechanically due to the desired vibration. Thus, as shown in Figures 1 and 2, if we have an Ex field, that is, a field directed normally to the YZ crystallographic plane, of proper frequency we may excite Xx, Yr, Zz or Yz vibrations electrically in a plate where the Xx vibrations are extensional vibrations in the X direction, Yr vibrations are extensional vibrations in the Y direction, Zz vibrations are extensional vibrations in the Z direction, and the Yz vibrations are face shear vibrations in the YZ plane. Mechanically, a YY vibration may couple (mechanically) to an Xx, a Zz or a Yz shear). The Yz shear may couple toflexural vibrations.

In the design of a particular vibrating quartz plate of frequency f, the engineer skilled in the art chooses a type of vibration most suited to comply with the performance requirements con..

sistent with manufacturing difficulty, material costs, etc. He then assigns the required orientation angles for the particular cut and calculates the linear dimensions.

In the final analysis the calculation of the linear dimensions is substantially an empirical computation. Consider, for example, the design of a high frequency thickness shear plate of the AT type. It may be shown that the frequency of a shear may be represented by the following equation:

where Ks is a constant depending on the shear elastic constant for a particular orientation and the density. 122 and n are integers, 1, 2, 3, etc., and A and B are the linear dimensions determining the shear. Let us consider an AT plate where m=l, n: 1, and wherein A, the dimension in the X direction, is very much greater than B, the dimension in the rotated Y (or Y) direction.

Frequency K,

It is known that the AT11 (XY' thickness shear) wherein the X, or length, dimension is greater than, say, twenty times the thickness, or Y, dimension of the plate, the frequency value is substantially approximated by:

where Y is expressed in millimeters and frequency in kilocycles per second.

The frequency as a second order effect is a function of the X dimension, increasing slightly as the X dimension is reduced:

where C'ec and p are constants for a given cut of The ATn frequency however does not vary inversely linearly with a variation in Y as indicated by (1) or (2). It is found that if the length and width dimensions are invariant but the thickness dimension Y is reduced in small intervals, the frequency increases continuously except for a substantial number of discontinuous regions.

These are due to couplings between the ATn shear and other modes of vibration mechanically excited by the ATn vibration at certain ratios of length, width and thickness.

The main interfering modes are flexures, defined by X and Y, and shears, determined by X and Z. These may be calculated and linear dimensions may be assigned to X and Z for a given ATn frequency wherein these main interfering modes are suitably far removed so as not to be excited mechanically. However, activity dips (amplitude discontinuities) over a temperature range are still experienced due to additional secondary resonances which are extremely complex in form and whose calculation is extremely complicated.

In Fig. 3 the plate is represented by its equivalent electrical network for a given range of temperatures T1 to T2 and is connected in a conventional oscillator circuit containing an ammeter A for indicating the rectified grid current of the oscillator tube as a measure of the activity of the oscillator plate. M represents a network which is electrically equal to a, plate which, as defined above, is dimensioned to have no modes capable of being excited over the working temperature range of the plate other than the desired mode of oscillation. The circuit is characterized by th relatively high Q of network M with respect to that of the tank circuit. This enables oscillations to continue as long as they can be sustained in network M, assuming that the tank circuit is initially tuned substantially to the oscillation frequency of network M. The oscillation frequency of a circuit such as shown in Figure 3 is generally subject to variation due to the variation in the frequency-determining parameters thereof, in this case the equivalent electrical parameters of network M. This variation may be caused by any external means, including changes in temperature.

Fig. 4 illustrates how a continuous change in the parameters of network M, caused by changes in temperature over a range of temperatures T1 to T2 can affect the frequency and the activity of the circuit.

Figs. 3a and 4a show two ways of illustrating the presence of undesired couplings in an oscillator plate. In Fig. 3a, the plate is represented by its equivalent electrical network and is connected in a conventional oscillator circuit containing an ammeter A for indicating the rectified grid current of the oscillator tube as a measure of the activity of the oscillator plate. Mo represents the network for the desired mode of oscillation. M1, M: and Ma represent networks coupled to the desired mode network M0 in such a manner as to effectively reduce the rectified grid current indication at ammeter A at certain frequencies between the limits over which Mo will oscillate. The coupling characteristics are of course determined by the properties of the plate expressed in terms of electrical parameters for the networks M1, M: and Ma, etc., in relation to the parameters of Mo.

Due to a continuous change in circuit conditions, as described in connection with Figs. 3 and 4, the frequency associated with Mo will normally vary from frequency I to f" over a ran e of temperatures Tl to T2, as shown by broken line ii in Fig. 4a. Corresponding frequency drift characteristics exist for the spurious frequencies associated with M1, M2 and M3,- and are shown at l, 2 and 3, respectively, in Fig. 4a. At points A, B and C interference occurs between the desired mode and the spurious modes, resulting in activity dips, as shown at A, B and C in Fig. 4a.

In the conventional design and manufacture of quartz oscillator plates for example, AT plates, either the length and width dimensions are altered by a trial and error method so that at room temperature the ATu shear operates with maximum amplitude, or, in a second conventional method of procedure, predetermined values of X and Z are used. In both cases proper operation over the temperature range will only occur if no coupled modes exist over the temperature range. Now, the predetermined values of the above mentioned second method are also obtained by trial and error so that in obtaining the values it is required that each set'of trial dimensions for each desired frequency be tested continuously over the temperature range until a set of values is obtained that is free from couplings with reasonable man ufacturing tolerance on length and width.

In the above-mentioned first conventional method of design the only known measure of the goodness of the plate, that is, the correctness of the geometry, over the temperature range is a temperature test; if the plate has dips it must be re-edged in a cut-and-try manner and resubjected to the temperature run. In the second conventional method of design small deviations in orientation or dimensions are actually measured by the temperature run; if all the crystal units had no deviation in elastic constants and no deviation in dimensions all would be good, and would require no temperature run. As heretofore pointed out, however, in either method of manufacture a relatively great number of temperature runs are necessary as the plate is varied in its geometry until a satisfactory plate is finally obtained.

Thus, it is appreciated that according to the prior art procedures the time-consuming temperature run is a necessary test, and an instantaneous good or no-good measure at room temperature is not available.

By the teachings of this invention methods of instantaneous test are available to eliminate the need for the temperature run since the methods of this invention show up most quartz plates that would exhibit dips in the temperature test. It is readily apparent that such methods would be of great assistance to the "trial-and-error finisher whose percentage of rejects in the heat run on high activity crystals may run 50% or more, and furthermore would be of great assistance in the trial of predimensioned crystals and in the inspection and test of crystal blanks which may have been erroneously dimensioned.

It will be further apparent that by the teachings of this invention a rapid method is provided for arriving at a satisfactory set of dimensions for a quartz plate, said dimensions being of such value as to allow their successful use in predimensioning technique.

Referring again to Fig. 4a, thedesired frequency of vibration of the quartz plate at any point between the limits T1 and T2 would be given from curve 0. The other frequencies mechanically excited would be given by curves I, 2, 3, etc. Now when the temperature is varied over a specifled range, say from T1 to T2, the respective frequencies will vary according to Fig. 4a. I! at any temperature within the range T1 to T2 the frequency of the main mode is equal to the frequency of amechanically excited interfering secondary mode, as at A, B, C, etc, of Fig. 4a, the amplitude of the desired frequency will undergo a change which will be a function of the magnitude of the coeillcient of coupling between the desired frequency and the interfering mode. Likewise over a range adjacent the temperatures at which the interfering modes are equal to the main mode in frequency the amplitude of the main mode will be changed, the magnitude of the change being a function of the coeilicient of coupling and the proximity to the temperature at which the interfering mode becomes equal in frequency to the main mode.

In the general case of a vibrating quartz plate which experiences a change in temperature from a first value To to a second value Ta, the frequency of the plate, F, at the second temperature Ta and the rate of change of frequency with temperature at Ta in the absence of discontinuities for any type of vibration F may be expressed as follows:

wherein the values for the K" constants depend on the temperature coefficient of the linear dimensions, the temperature coefficient of the elastic modulus for the particular vibration, and the density of quartz. The elastic modulus of course varies as a function of orientation. For a particular type of vibration at a particular orientation, then, the values of the K constants are fixed.

For all practical purposes, powers higher than the third in Equation 3 may be neglected, that is. values of K4 K: are negligible with respect to K1, K2 and IQ. As a matter of fact, in most cases where the main made is a longitudinal extensional vibration, K2 and Ka approach zero. These include Xx, Yr and Zz, wherein K1 is of much greater magnitude than either K2 or K3. For the low-drift shear modes (AT, BT, CT, DT, ET, ET, Q, etc.) Kl and K2 approach zero and K: is of importance. that is, the form of (3) is a parabola in the latter and a straight line in the former. The rate of change of frequency with temperature (4) in the latter is linear, varying from a positive to a negative value and passing through zero, and in the former is a constant (independent of temperature) of negative value. For the coupled longitudinal bars K2 is of importance and K1 and K1 approach zero, and for the GT cut K1 and K2 approach zero and K3 is of importance.

In almost all cases of mechanically coupled modes coupled to low coeilicient modes the frequency-temperature characteristic of the mechanically coupled mode will have K1 of such greater magnitude than K: or K1 that Krand K: may be ignored and the frequency-temperature 7 characteristic of said mechanically coupled considered linear.

Dlscontinuities in the amplitude of a desired vibration I over the. temperature range, then, are caused by the displacementof a single mechanically coupled mode or a number of mechanically coupled modes relative to f. The frequency of any mechanically coupled mode fM will be a function of the elastic modulus associated with the particular vibration, the density of quartz, and the linear dimensions determining the vibration. These parameters vary with temperature; when the parameters have a certain value (at a certain temperature TX) that places them in proximity to J, the vibration of I will mechanically excite the frequency in and as it: passes through 1 the vibration of I will be affected as a function of the magnitude of the coefficient of coupling. 1 changes slowly in comparison to most of the mechanically coupled modes as a function of temperature.

A further discussion of coupling between modes of motion in quartz crystals will be found in Quartz Crystals for Electrical Circuits by Raymond A. Heising, D. Van Nostrand Co., Inc., New York, 1946, pages 221 to 240.

It is obviously impossible to vary the aforemenmode tioned intrinsic frequency determining param-' eters associated with the mechanically coupled modes in a given plate of fixed geometry without affecting the main mode frequency determining parameters substantially, except by varying the temperature. This invention deals with the variation of f by an external means other than temperature over a substantial range to see if, due to this artificially induced variation in f, the amplitude of f varies discontinuously. If the amplitude of f does vary discontinuously then we may be sure that f is mechanically exciting coupled modes and the plate when temperature-tested will exhibit a discontinuity over the temperature range due to the presence of the coupled modes. The invention further discloses methods for quickly ascertaining optimum dimensions for a particular frequency plate as required in predimensioning technique without resorting to countless time-consuming temperature runs. It further discloses a new method of finishing crystals by the trial and error" method.

It is usually found that the temperature coefficient of a coupled mode in is negative, that is, the value of K1 is positive in (3) and (4). However, room, or test, temperature Ta is usually toward the center of the temperature range over which the plate must operate. Hence, even if the suspected in is above or below I at room temperature Ta it can cause trouble at either a plus or minus temperature with respect to Ta. If the suspected -fM has a negative temperature coefficient and in is greater than 1 at Ta. then in will cause trouble at a temperature above Ta, as can readily be seen from Fig. 4a if Ta is assumed to be to the left of TxA and T2 represents an increase in. temperature over T1. If fur is less than f at TR, it will cause trouble at a temperature below Ta, as can be seen from Fig. 4a if Ta is assumed to be to the right of TxC.

Accordingly, in one embodiment of the invention. the quartz plate to be tested is placed in an oscillating circuit wherein the frequency of the crystal may be varied over a substantial range rapidly in a smooth and continuous manner, as for example by changing the input reactance into which the crystal looks. Two examples of such a circuit are shown in Figs. 5 and 6 respectively.

In Fig. 5 the variable capacitor Cp is shunted across the crystal for this purpose, whereas in Fig. 6 the variable capacitor C8 is in series with the crystal for the same purpose. Obviously other means of varying the crystal input reactance may be employed within the spirit of this invention. The osci'lator is designed to develop a substantial voltage across the quartz plate. As the parallel reactance Cp of Fig. 5 or the series reactance C8 of Fig. 6 is varied, the frequency i will vary. If f mechanically excites an jiu it will be observed by a discontinuous variation in the oscillator D. C. grid meter A as f is varied continuously. Whenever Ta is substantially in the center of the required performance temperature range, a discontinuity in the amplitude of .f as f is varied indicates a plate which will exhibit at least a single break in its activity over the temperature range. If the Ta is the lower, or upper, extremity of the required performance temperature range, it may be that in will move in a, direction away from f over the required performance temperature range and will not cause a discontinuity. This is easily demonstrated by the following example:

Suppose the plate is being tested-at the lower extremity of the required performance temperature range and f is being varied by a condenser such as Cp in Fig. 5 in parallel with the quartz plate. The discontinuity in the amplitude of f is found at a substantially higher capacity setting of said condenser than the crystal looks into in the ultimately specified oscillator circuit. The crystal is heated a convenient amount (say 1 to 5 C.) by allowing it to oscillate for a minute or so, or by any other means. If it is found that the discontinuity has moved to a lower ,f frequency, that is, condenser Cp capacity has to be increased to "tune in the discontinuity, then it is known that the dFM/dT is negative. (If the increment of in and the increment of T are known the temperature coefficient of In is known and the value of K1 thereof may be evaluated.) It may then be assumed that since we are testing at the low extremity of the tempera ture range and since In will at least have the same increment as over the range, there is no chance for this particular in to couple with 1 over the specified temperature range.

Other variations are obvious, such as In with positive coeflicient and higher than 1 at the low extremity of the temperature range, in with negative coefficient and above f at the high end of the temperature range, etc.

Whenever a more accurate instantaneous scanning is desired, the room temperature check may be expanded to checks at one or more points at convenient spots over the temperature range. It is most convenient for the finisher to have two roughly controlled ovens operating midway between Ta and the lower and upper 61(- tremities of the temperature range respectively. If his finished plate is satisfactory after the room temperature vari-f test it is tested at one of the other temperatures, usually the one below Ta. If still satisfactory it is checked at the third temperature. If satisfactory it is passed into the temperature run. Crystals so tested will show an extremely high passing percentage in the temperature run.

The value of the Vari-J test to the engineer in the task of pro-dimensioning plates is readily apparent. The test provides a means of following the mechanically coupled modes untilthey 9 are outside the working range; when a potentially interfering In is present in a plate, an edge dimension may be altered slightly until the vari-l test shows the plate to be satisfactory.

A variable air gap holder may be used for varying! separately or in combination with the varable reactance method above described. A variation in f of as much as 0.1% by the combination is entirely practical.

Another embodiment of the vari-f test is extremely useful in the design of predimensioned thickness shear crystals. A crystal of known linear dimensions X, Y and Z is given a very light coat of plating. The crystal is then oscillated in a vacuum (which increases the crystal frequency). Plating is gradually deposited on the quartz plate while it is oscillating, said plating being efiected by'an evaporation process. This is continued until the amplitude of the thickness shear vibration becomes so weak due to loading of the plating layer on the oscillating plate that oscillation can not be sustained. The frequency of the thickness shear will have been decreased from an original value I to a final value I. At certain frequencies, or over certain frequency ranges, say, at f1, f2, f3 In between I and I the amplitude of oscillation (as conveniently indicated by a D. C. grid current meter in the oscillator) will have changed discontinuously due to the presence of coupling between the thickness shear vibration and the mechanically excited parasitic modes. The proper, or optimum, value for the shear vibration for the given X and Z dimensions may be assigned by choosing the cleanest region, that is, a value of f substantially midway in the largest region free from coupling. For the given X and Z dimensions this then will provide a satisfactory I value. To translate to any other frequency desired the following transformation is employed:

-X =X %-Z' =Z and Y',.= 5

wherein the o subscripts represent the values obtained for optimum in the preceding pararaphs and the d subscripts represent values for the desired frequency id.

A diagrammatic sketch of the apparatus employed is shown in Fig. '7. The apparatus herein disclosed is extremely simplified. The specimen plate 5 which is to be investigated and which has been previously given a light coat of plating is placed under a bell Jar IS. A window frame" type of electrode 25, similar to that disclosed in applicants Patent No. 2,327,487 is placed over the quartz plate, the outer length and width dimensions of the frame being larger than the quartz plate in order to prevent plating from being deposited on the edges of the plate. Connections from frame electrode and 7 base electrode are made to an external oscil- Both recorder strip charts move at the same rate of speed. The specimen plate I is of convenient linear dimensions X0 and Z'c accurately known, and of frequency (determined by Y'o) in the same range as that for which the desired dimensionplaced in the aforementioned equipment, oscillated. and the air under the bell jar I! is removed. Plating is applied to the specimen in a smooth and continuous manner and the effect on frequency and activity of the plate as a function of plating is recorded permanently on the strip chart recorder. If the frequency of the specimen before the plating run was iand the ultimate frequency at the conclusion of the run was 1 a group of frequencies f1, is, is in will be observed on the frequency chart at which the activity chart shows dips. In fact, ranges fzviAou will be found wherein substantial activity depressions are present. These activity clips will be accompanied by discontinuities in the frequency curve. The frequency curve from I to j in fact would contain discontinuities in the same manner as aforementioned, if the thickness of the plate were to be reduced by grinding, holding X and Z dimensions constant.

Certain regionson the charts wherein for a substantial change in frequency no discontinuities are present will be observed. Choosing, say, the largest clean region, that is, wherein the band between discontinuities, in to fN-l, is a maximum, and calculating ft from an optimum frequency for the thickness shear for the particular X and Z dimensions used is provided. By the transformation Equations 5 the dimensions for the desired frequency in are computed. Plates then are made up with the proper Xu and 2's dimensions but of varying Y's dimensions so that the frequencies of the plates vary about in in small increments. By the use of the "vari-j" test and then by careful temperature runs it will be found that all plates within a frequency is plus or minus Aid are free from dips. From the equations the maximum tolerances on X and Z dimensions may be assigned.

Another method of varying the frequency of the plate in a gradual and continuous manner to locate interfering modes of vibration could be by continuous exposure to high intensity X-ray radiation or to bombardment by radio-active emission. It is possible to change the physical constants, and hence the vibration frequency, of a piano-electric quartz plate by distorting the lattice structure of the quartz. This is taught by an article by Edward F. Holden appearing in The American Mineralogist, Journal of the Mineralogical Society of America, vol. 10, No. 9, Sept. 1925, entitled "The cause of color in smoky quartz and amythyst wherein the coloration of quartz is traced to exposure to such radiation or bom- ,bardment, and a paper in the Proceedings of the Physical Society, London, vol. XLV, part 4, read April 7, 1933, entitled Quartz as a standard for accurate lattice spacing measurements, by A. J. Bradley and A. H. Jay, wherein the discolored quartz is shown to have a distorted lattice structure (and hence changed frequency-determining physical constants) This invention is not limited to the above specifically described methods but contemplates any method of varying the desired vibration frequency with respect to the secondary spectrum ing information is required. The specimen is over a substantial range to locate the frequencies at which the desired vibrations are coincident with secondary mechanically coupled vibrations determined by the geometry of the plate. It further contemplates any method of varying the frequency and simultaneously observing the eflect of the secondary vibrations on the desired frequency. 7

Numerous modifications are possible, and I do not therefore wish to be limited to the precise embodiments shown and described herein, but desire to include and have protected by Letters Patent all forms and modifications of my invention which come within the scope of the appended claims.

What is claimed is:

1. A method of testing a piezoelectric plate without changing its geometry at substantially constant temperature to locate secondary modes in the vicinity of the main mode which mi ht interfere with the main mode over the workin temperature range of the plate, comprising the steps of varying the frequency of the main mode continuously over a range of frequencies by varying the input impedance of the plate and observing the effect of such variation on the amplitude of the main mode.

2. The method of claim 1, and wherein the frequency of the main mode is varied by varying the shunt capacitance across the plate.

3. The method of claim 1, and wherein the frequency of the main mode is varied by placing capacitance in series with the plate and varying said capacitance.

4. A method of testing a piezoelectric plate without changing its geometry to detect secondary modes in the vicinity of the main mode which might interfere with the main mode over the working temperature range of the plate, comprising the steps of varying the frequency of the 'main mode continuously over a range of frequencies with the plate held substantially at a constant temperature, observing the effect of such variation on the amplitude of the main mode, changing the temperature of the plate by an amount which is small compared to the working range of temperatures, again varying the frequency of the main mode, and again observing the effect of the variation in frequency of the main mode on the amplitude of said main mode.

5. The method of claim 4, and wherein the frequency of the main mode is varied by varying the input reactance of the plate.

6. The method of claim 4, and wherein the frequency of the main mode is varied by varying the shunt capacitance across the plate.

7. The method of claim 4, and wherein said constant temperature is approximately the lower extremity of the working temperature range of the plate.

8. The method of claim 4, and wherein said constant temperature is approximately the higher extremity of the working temperature range of the plate.

9. A method of testing a piezoelectric plate without changing its geometry to locate secondary modes inthe vicinity of the main mode which might interfere with the main mode over the working temperature range of the plate, comprising the steps of holding the temperature of the plate substantially constant at a first temperature value in its working temperature range, varying the frequency of the main mode continuously over a range of frequencies, observing the effect of such variation on the amplitude of the main mode, changing the temperature of the plate to a second substantially constant temperature value in its working temperature range, again varying the frequency of the main mode, and again observing the effect of the frequency variation on the amplitude of said main mode.

10. The method of claim 9, and wherein said second temperature value is approximately midway between said first temperature value and the lower extremity of the working temperature range.

11. The method of claim 9, and wherein said second temperature value is approximately midway between said first temperature value and the upper extremity of the working temperature range.

HENRY M. BACH.

REFERENCES cr'ran The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,886,815 Hund Nov. 8, 1932 1,985,620 Heising May 15, 1934 1,994,228 Osnos Mar. 12, 1935 2,111,382 Bokovoy Mar. 15, 1938

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