Patent Publication Number: US-10788358-B2

Title: Surface acoustic wave scale that automatically updates calibration information

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. Ser. No. 15/259,709, filed Sep. 8, 2016, which is a divisional of U.S. Ser. No. 13/742,713, filed Jan. 16, 2013, now U.S. Pat. No. 9,477,638, which claims benefit from U.S. Ser. No. 61/587,309, filed Jan. 17, 2012, the complete disclosures of which are hereby incorporated by reference herein. 
     The application is also related to co-owned U.S. patent application Ser. No. 09/775,748, filed Feb. 2, 2001, now U.S. Pat. No. 6,448,513, U.S. patent application Ser. No. 09/327,707 filed Jun. 9, 1999, now U.S. Pat. No. 6,211,473, U.S. patent application Ser. No. 08/729,752 filed Oct. 7, 1996, now U.S. Pat. No. 5,910,647, and U.S. patent application Ser. No. 08/489,365 filed Jun. 12, 1995, now U.S. Pat. No. 5,663,531, the complete disclosures of which are hereby incorporated by reference herein. 
    
    
     BACKGROUND 
     1. Field 
     This relates to electronic weighing devices, and more particularly to an electronic weighing device that employs surface acoustic waves to measure weight. 
     2. State of the Art 
     Precision electronic weighing devices are widely known in the art and there are many different technologies utilized in these electronic weighing devices. Laboratory scales or “balances” typically have a capacity of about 1,200 grams and a resolution of about 0.1 gram, although scales with the same resolution and a range of 30,000 grams are available. The accuracy of these scales is achieved through the use of a technology known as magnetic force restoration. Generally, magnetic force restoration involves the use of an electromagnet to oppose the weight on the scale platform. The greater the weight on the platform, the greater the electrical current needed to maintain the weight. While these scales are very accurate (up to one part in 120,000), they are expensive and very sensitive to ambient temperature. In addition, their range is relatively limited. 
     Most all other electronic weighing devices use load cell technology. In load cell scales, the applied weight bends an elastic member which has strain gauges bonded to its surface. The strain gauge is a fine wire which undergoes a change in electrical resistance when it is either stretched or compressed. A measurement of this change in resistance yields a measure of the applied weight. Load cell scales are used in non-critical weighing operations and usually have a resolution of about one part in 3,000. The maximum resolution available in a load cell scale is about one part in 10,000 which is insufficient for many critical weighing operations. However, load cell scales can have a capacity of several thousand pounds. 
     While there have been many improvements in electronic weighing apparatus, there remains a current need for electronic weighing apparatus which have enhanced accuracy, expanded range, and low cost. 
     The previously incorporated applications disclose an electronic weighing apparatus having a base which supports a cantilevered elastic member upon which a load platform is mounted. The free end of the elastic member is provided with a first piezoelectric transducer and a second piezoelectric transducer is supported by the base. Each transducer includes a substantially rectangular piezoelectric substrate and a pair of electrodes imprinted on the substrate at one end thereof, with one pair of electrodes acting as a transmitter and the other pair of electrodes acting as a receiver. The transducers are arranged with their substrates substantially parallel to each other with a small gap between them and with their respective electrodes in relatively opposite positions. The receiver electrodes of the second transducer are coupled to the input of an amplifier and the output of the amplifier is coupled to the transmitter electrodes of the first transducer. The transducers form a “delay line” and the resulting circuit of the delay line and the amplifier is a positive feedback loop, i.e. a natural oscillator. More particularly, the output of the amplifier causes the first transducer to emit a surface acoustic wave (“SAW”) which propagates along the surface of the first transducer substrate away from its electrodes. The propagating waves in the first transducer induce an oscillating electric field in the substrate which in turn induces similar SAW waves on the surface of the second transducer substrate which propagate in the same direction along the surface of the second transducer substrate toward the electrodes of the second transducer. The induced waves in the second transducer cause it to produce an alternating voltage which is supplied by the electrodes of the second transducer to the amplifier input. The circuit acts as a natural oscillator, with the output of the amplifier having a particular frequency which depends on the physical characteristics of the transducers and their distance from each other, as well as the distance between the respective electrodes of the transducers. 
     When a load is applied to the load platform, the free end of the cantilevered elastic member moves and causes the first transducer to move relative to the second transducer. The movement of the first transducer relative to the second transducer causes a change in the frequency at the output of the amplifier. The movement of the elastic member is proportional to the weight of the applied load and the frequency and/or change in frequency at the output of the amplifier can be calibrated to the displacement of the elastic member. The frequency response of the delay line is represented by a series of lobes. Each mode of oscillation is defined as a frequency where the sum of the phases in the oscillator is an integer multiple of 2π. Thus, as the frequency of the oscillator changes, the modes of oscillation move through the frequency response curve and are separated from each other by a phase shift of 2π. The mode at which the oscillator will most naturally oscillate is the one having the least loss. The transducers are arranged such that their displacement over the weight range of the weighing apparatus causes the oscillator to oscillate in more than one mode. Therefore, the change in frequency of the oscillator as plotted against displacement of the transducers is a periodic function. There are several different ways of determining the cycle of the periodic function so that the exact displacement of the elastic member may be determined. 
     It is generally known in the art of SAW technology that the frequency range in which the losses are the lowest is not necessarily the frequency range in which the oscillator exhibits the best phase linearity. From the teachings of the previously incorporated applications, those skilled in the art will appreciate that in a SAW displacement transducer such as disclosed in the previously incorporated applications, better phase linearity provides a more linear relationship between frequency and displacement. In the case of a weighing apparatus using a SAW displacement transducer as described in the previously incorporated applications, better phase linearity will result in a more linear relationship between weight and frequency. 
     It is known in the art of SAW oscillators that changing the topology of the oscillator transmitter and receiver can cause a broader bandwidth of the delay line and that a broader bandwidth results in better phase linearity. It is also known that using a smaller frequency range provides better linearity and that a smaller frequency range can be obtained with a longer delay line. Although these known methods can increase phase linearity in a SAW oscillator, the frequency range in which the best linearity is achieved for a particular oscillator is still not necessarily the range with the lowest losses. 
     From the foregoing, those skilled in the art will appreciate that in order to enhance the accuracy of a SAW displacement transducer such as that used in a weighing device, it would be desirable to cause the SAW oscillator to oscillate in the range having the best phase linearity. 
     As disclosed in the previously incorporated applications, weighing accuracy is affected by temperature. The previously incorporated applications disclose a SAW temperature oscillator having a transmitter and receiver on the same substrate. The temperature sensitivity of the load cell disclosed in the previously incorporated applications is approximately 500 ppm of the weight reading per 1° C. temperature change. Accuracy of 100 ppm of the weight reading can be achieved if temperature is measured to within 0.2° C. which represents a shift of about 1 kHz of the SAW temperature sensor. This shift is easy to measure in the short term. The resolution of the SAW temperature sensor is on the order of 0.001° C. However, the long term stability of the SAW temperature sensor can drift more than 1 kHz due to many factors including humidity. 
     In order to overcome some of these issues, co-owned U.S. patent application Ser. No. 09/775,748 (U.S. Pat. No. 6,448,513) discloses as one aspect the use of a “push oscillator” coupled to the delay line for injecting a strong RF signal at a frequency in the middle of the oscillation mode which exhibits the best phase linearity. The frequency of the “push oscillator” is determined experimentally when the scale is calibrated. The RF signal is injected periodically in short bursts. According to a second aspect of the same patent, the “push oscillator” frequency is generated by mixing the temperature oscillator with an adjustable fixed frequency oscillator. This immunizes the “push oscillator” from the affects of temperature. According to a third aspect of the same patent, a thermistor is provided for long term temperature stability. The SAW temperature sensor is periodically calibrated to the thermistor. According to a fourth aspect of the same patent, the SAW oscillators are not hermetically sealed and the SAW temperature sensor is used to correct the displacement sensor for changes in environmental conditions such as humidity. 
     Even with these improvements, SAW scales still do not meet certain criteria that are desirable for high accuracy scales. For example, while the zero stability of such SAW scales is in the desirable range of 1:50,000 to 1:100,000 (for a temperature range of 10° C.-40° C.), the stability of the span parameter (the weight reading after having zeroed the scale) is typically as low as around 1:10,000. It is desirable that the span parameter be in the same range (i.e., 1:50,000 to 1:100,000) as the zero stability. 
     The main cause of this problem is the fact that the process of determining the load for the scale consists of measuring the frequency of the SAW transducer under two conditions—first without load (the zero value) and the other under load from the platform (the weight value). A quality of the SAW scale is that zero stability and the span parameter stability for these two frequencies depends on their values within the pass band of the transducer. The zero stability for every point inside the pass band is very similar, but does have slight variations. As an example, without any load on the platform, the frequency of the delay line oscillator could be 92.9 MHz. Under load it could be 93.1 MHz. In this example the span parameter for a single mode is 200,000 Hz (0.2 Mhz). If the scale utilizes multiple modes, the span parameter is effectively 200,000 Hz times the number of modes of the scale. For five modes, the span parameter of the scale is effectively 1.0 MHz. 
     The span parameter is also dependent upon temperature. For example, for the exemplary spam parameter described above, the frequency of the delay line oscillator without load for two different temperatures can change (i.e., drift) by 1000 Hz, and the frequency of the delay line oscillator under load for the same two temperatures can change (i.e., drift) by 1050 Hz. This is a difference of 50 Hz and is referred to as absolute span drift. In this example, the relative span drift (absolute span drift/span parameter) is is 50 Hz/200,000 Hz (1:4000) (for a single mode), which is considered to be a poor result for a high accuracy scale. If the scale utilizes five modes, the absolute span drift (50 Hz) will be the same, but the full range will be five times larger and as a result the relative span drift will drop to 1:20,000, which is still higher than desired. In addition, this error will appear as a discontinuity and as a linearity distortion at the points of the border between modes. 
     In addition, given the wide range of temperatures under which industrial scales operate, −20° C. to +60° C., there is the potential for measurement error due to the mismatching of coefficients of thermal expansion (CTE) between the SAW transducer substrate and the material of the load cell. The transducer substrate is bonded to the load cell using a holder which is made from the same material as the remainder of the load cell; typically, a suitable alloy of aluminum. The transducer substrate and the holder material have significantly different CTEs which will subject the bonding line of the materials to a thermal stress. If the temperature changes significantly, the thermal stress between the materials, including the bonding line, causes some change on the zero reading of the scale which is determined by the exact position of the transducer substrate. Because the bonding material has some level of hysteresis and non-repeatability under stress, the shift of the zero reading can be very unpredictable. Various methods are known for bonding materials with mismatched CTEs, including high temperature or pressure bonding, including brazing or diffusion, or machining operations, including drilling holes or riveting. However, the transducer substrate material is not suitable for these kinds of operations because of fragility and high temperature concerns. 
     SUMMARY 
     According to one aspect, a method and apparatus are provided for automatically recalibrating a SAW scale for changing environmental factors. In this aspect, during a period of time when there is no change to weight applied to the scale (e.g., when there is no weight being applied to the scale), readings of SAW transducers which relate to weight indications and environmental factor indications are taken for each one of two adjacent operating modes of the scale, and two calibrated weight calculations are made utilizing those readings. The difference in calibrated weight calculations is then related to a variable utilized to transform the readings into weights, which is updated, thereby recalibrating the scale. Recalibration in this manner significantly reduces span drift and enhances linearity. 
     According to another aspect, an auxiliary sensor that is used to ascertain the operating mode of the SAW scale is adjusted (calibrated) by comparing the reading of the SAW sensor and the reading of the auxiliary sensor. 
     According to a further aspect, the SAW transducer is fabricated on a lithium niobate piezosubstrate and attached by glue to a metal holder. The thickness of the piezosubstrate is in a range between 0.1 and 0.3 mm and the thickness of the holder is at least ten times thicker than the piezosubstrate so that the piezosubstrate and holder can bend together without over-stressing the glue layer. In this manner stress on the glue is reduced during ambient temperature changes, thereby reducing or eliminating random hysteresis effects and resulting zero shifts. 
     According to one assembly of the transducer the metal holder, the SAW transducer is fabricated on a lithium niobate piezosubstrate and attached by glue to a metal holder where the metal holder is chosen to be between one and 3.5 times the thickness of the piezosubstrate. In this manner, the aluminum holder and piezosubstrate will bend and stretch together without over-stressing the glue layer. 
     According to yet another assembly, in order to further minimize thermal stress, the SAW transducer is fabricated on a lithium niobate piezosubstrate, the metal holder is machined with a cantilevered beam that is permitted relative free rotation around the point at which it is connects to the main body of the holder. The lithium niobate piezosubstrate is bonded with a bonding agent at one end to the holder and at its other end the free end of the beam. In this manner, as the piezosubstrate stretches or shrinks due to temperature changes, the beam will bend with the piezosubstrate without over-stressing the bonding locations. 
     According to even another assembly, in order to still further minimize thermal stress, the SAW transducer is fabricated on a lithium niobate piezosubstrate, the piezosubstrate is bonded with a bonding agent to an intermediate bonding plate having a coefficient of thermal expansion (CTE) that closely matches that of the piezosubstrate. The intermediate bonding plate, which has a relatively different CTE from the metal holder, is bonded to the metal holder without a bonding agent. One embodiment of a bond between the intermediate plate and the metal holder comprises two pins offset out of the bonding line of the piezosubstrate and spaced relatively close together to reduce thermal stress between the pins as the SAW transducer is subject to thermal changes. In this manner, as the piezosubstrate stretches or shrinks due to temperature changes, the intermediate plate will similarly stretch or shrink without resulting in overstressing the bond between the piezosubstrate and the intermediate plate. 
     In accord with yet another assembly, in order to minimize thermal stress, the SAW transducer is fabricated on a lithium niobate piezosubstrate, the piezosubstrate is bonded with a bonding agent to an intermediate bonding plate having a closely matched CTE with the piezosubstrate, and the metal holder is machined with a cantilevered beam that is permitted relative free rotation around the point at which it is connects to the main body of the holder. The intermediate bonding plate is bonded to the metal holder with two pins, one extending into the cantilevered beam on one side of the piezosubstrate and one extending in the body of the holder on the other size of the piezosubstrate. By bonding to the cantilevered beam, stress is reduced even under harsh thermal cycling conditions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic side elevation view of an exemplary embodiment. 
         FIG. 1 a    is an enlarged schematic plan view of a first transducer. 
         FIG. 1 b    is an enlarged schematic plan view of a second transducer. 
         FIG. 2  is an enlarged schematic side elevation view of a transducer having anti-reflection structure. 
         FIG. 3  is an enlarged schematic side elevation view of a pair of transducers according to one embodiment. 
         FIGS. 4 and 5  are graphs of a portion of a frequency response curve for an exemplary delay line according to the invention showing modes of oscillation and phase shifting. 
         FIG. 6  is a simplified schematic diagram of circuits used in a weighing device. 
         FIG. 7  is a graph plotting load against a frequency function and showing “modes” of operation for an exemplary embodiment. 
         FIG. 8  is a graph showing exemplary changes in the load-frequency function plot due to environmental affects. 
         FIG. 9  is a flow chart implemented by the microprocessor of  FIG. 6  for automatic recalibration. 
         FIG. 10  is an enlarged schematic side elevation view of a pair of transducers according to another embodiment. 
         FIG. 11  is a schematic side elevation view of a piezosubstrate on a holder therefor. 
         FIG. 12  is a front perspective view of an assembly of the piezosubstrate of the transducer to the holder of  FIG. 11  in a manner which reduces thermal stress on the assembly. 
         FIG. 13  is a longitudinal section view across line  13 - 13  in  FIG. 12 . 
         FIG. 14  is a front perspective view of the holder shown in  FIG. 12 . 
         FIG. 15  is a longitudinal section view of another embodiment of an assembly of the piezosubstrate to the holder in a manner which reduces thermal stress on the assembly. 
         FIG. 16  is a longitudinal section view of yet another embodiment of an assembly of the piezosubstrate to the holder in a manner which reduces thermal stress on the assembly. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Referring now to  FIGS. 1, 1   a , and  1   b , an electronic weighing apparatus  10  includes a base  12  which supports a cantilevered elastic member  14  having a cut-out  15 , and upon which a load platform  16  is mounted. The cut-out  15  is provided with two opposed posts  17 ,  19  upon which are respectively mounted a first piezoelectric transducer  20  and a second piezoelectric transducer  22 . As is standard in the art, post  17  is rigidly coupled to base  12 , and post  19  is coupled to the elastic member  14 . The posts  17 ,  19  serve to locate the transducers  20 ,  22  at the center of the elastic member  14  and to mechanically couple the transducers to opposite ends of the elastic member  14 . According to one aspect, an auxiliary displacement sensor  18  is also provided. In one embodiment auxiliary displacement sensor  18  is a capacitive sensor with one plate  18   a  coupled to post  17  and the elastic member  14  serving as the other plate. If desired, a second plate could be attached to the elastic member. Alternatively, plates may be located such that one plate is stationary and the other can move as a function of the weight on platform  16 . Other embodiments of an auxiliary displacement sensor include one or more strain gauges coupled to the elastic member  14 , or one or more inductive members. As will be discussed in detail hereinafter, according to one aspect, the auxiliary displacement sensor is calibrated initially by the manufacturer, and the weighing apparatus is provided with a mechanism to automatically recalibrate the auxiliary displacement sensor over the life of the apparatus  10 . 
     The first transducer  20  includes a substantially rectangular piezoelectric substrate  20   a  and a pair of electrodes  20   b  imprinted on the substrate at the upper end thereof. The second transducer  22  includes a substantially rectangular piezoelectric substrate  22   a  and a pair of electrodes  22   b  imprinted on the substrate at the lower end thereof. In one embodiment the substrates are made of lithium niobate. The transducers are arranged with their substrates substantially parallel to each other with a small gap “g” between them. The electrodes  22   b  of the second transducer  22  are coupled to the input of an amplifier (not shown) powered by a power source (not shown) and the output of the amplifier is coupled to the electrodes  20   b  of the first transducer  20 . The circuit arrangement is the same as shown in the previously incorporated U.S. patent application Ser. No. 08/489,365, previously incorporated herein by reference. The resulting circuit is a positive feedback loop natural oscillator, a “delay line”. The output of the amplifier generates an alternating voltage in the electrodes  20   b  of the first transducer  20  which generates a surface acoustic wave (“SAW”)  26  which propagates along the surface of the first transducer substrate  20   a  away from its electrodes  20   b . Since the substrate  20   a  of the first transducer  20  is relatively close to the substrate  22   a  of the second transducer  22 , an oscillating electric field which is induced as a result of the SAW waves  26  in the piezoelectric substrate  20   a  is able to in turn induce similar SAW waves  28  on the surface of the second transducer substrate  22   a  which propagate in the same direction along the surface of the second transducer substrate toward the electrodes  22   b  of the second transducer  22 . The induced waves  28  in the second transducer  22  cause the electrode  22   b  of the second transducer  22  to produce an alternating voltage which is provided to the input of the amplifier. As long as the gain of the amplifier  24  is larger than the loss of the system, the circuit acts as a natural oscillator with the output of the amplifier having a particular frequency which depends on the physical characteristics of the transducers and their distance from each other, as well as the distance between the respective electrodes of the transducers. In particular, the frequency of the oscillator is directly related to the time it takes for the SAW  26  to propagate from the electrodes  20   b  to the electrodes  22   b.    
     According to certain embodiments described in more detail below, the SAW  26  has a wavelength of approximately 100-200 microns at 20-50 MHz. In order to limit loss in the system, the gap “g” between the substrates of the first and second transducers is kept small. In one embodiment described below, the gap is 10-20 microns. With such a gap, an oscillating system can typically be generated if the amplifier  24  has a gain of at least approximately 25 dB. It will be appreciated that when a load (not shown) is applied to the load platform  16 , the free end of the cantilevered elastic member  14  moves down and causes the second transducer  22  to move relative to the first transducer  20 . In particular, it causes the electrodes  22   b  of the second transducer  22  to move away from the electrodes  20   b  of the first transducer  20 . This results in a lengthening of the “delay line”. The lengthening of the delay line causes a decrease in the frequency at the output of the amplifier. The displacement of the elastic member is proportional to the weight of the applied load and the frequency or decrease in frequency at the output of the amplifier can be calibrated to the distance moved by the elastic member. 
     It will be appreciated that locating the transducers at the center of the elastic member compensates for any torque on the member which would exhibit itself at the free end of the member. This results in an improved accuracy as compared to the weighing instrument disclosed in U.S. Pat. No. 5,663,531. Depending on the application (e.g. maximum load to be weighed), the elastic member is made of aluminum or steel. In one embodiment, the elastic member exhibits a maximum displacement of 0.1 to 0.2 mm at maximum load. 
     Reflected waves may occur on both piezosubstrates. Reflected waves interfere with the received signal. The interference causes an increase in non-linearity.  FIGS. 2 and 3  show an embodiment of anti-reflection structures. 
     Turning now to  FIGS. 2 and 3 , one embodiment of transducers  20 ,  22  (numbered  120 ,  122 ) is shown.  FIG. 2  illustrates the features of transducer  120  which is substantially identical to transducer  122 .  FIG. 3  illustrates the transducers mounted on holders  117 ,  119  to the posts  17 ,  19  of the elastic member  14  of  FIG. 1 . As shown in  FIG. 2 , the transducer  120  includes a lithium niobate substrate  120   a  with electrodes  120   b  attached thereto by glue  123 . The ends  120   c ,  120   d  of the substrate are tapered and polyurethane dampers  121   a ,  121   b  are placed at the ends to minimize reflection of the SAW waves. 
     According to one aspect, the lithium niobate substrate  120   a  and/or the holder  117  is/are adapted to reduce the stress on the glue when the ambient temperature changes significantly, thereby significantly reducing or eliminating random hysteresis effects and resulting zero shifts. In one embodiment the lithium niobate substrate  120   a  is adapted by providing a substrate of thickness between 0.25 mm and 0.1 mm. This may be done by grinding down or otherwise reducing the thickness of a thicker (e.g., 0.5 mm) lithium niobate piezosubstrate. The holder  117  is selected to be at least ten times the thickness of the piezosubstrate. In another embodiment, the holder selected to be between 1 and 3.5 times the thickness of the piezosubstrate such that the piezosubstrate and holder bend together like a bimetallic strip when the ambient temperature changes significantly. Thus, by way of example only, if the piezosubstrate is 0.5 mm thick, the holder is selected to be between approximately 0.5 mm and 1.75 mm thick, and if the piezosubstrate is 0.2 mm thick, the holder is selected to be between 0.2 mm and 0.7 mm thick. 
     Turning now to  FIGS. 10 and 11 , according to another embodiment of the transducer, the lithium niobate substrate is adapted to have reduced stress on the glue bond when the ambient temperature changes significantly, and consequently significantly reduced or eliminated random hysteresis effects and resulting zero shifts. A holder  317  for mounting the piezosubstrate  320  to arm  17  is provided. The holder  317  includes a support  330  and a substrate mounting face  338 . The support  330  includes two holes  332 ,  330 , and extends into a slot  17   a  in the arm  17  at which it is connected with mounting screws  336  to the arm  17 . The substrate mounting face  338  is oriented substantially orthogonal to and vertically offset relative to the end of the support  330 . In one embodiment, the holder  317  is machined from a unitary piece of material, e.g., metal, and more particularly, for example, the same aluminum alloy  2024  of which the remainder of the load cell is constructed. Aluminum alloy  2024  has a coefficient of thermal expansion (CTE) of approximately 25 ppm/° C., whereas the CTE of 128° YX lithium niobate substrate (in the direction of SAW propagation) is approximately 15 ppm/° C. Ordinarily, when materials of such different CTEs are bonded to each other and they undergo temperature changes, they are subject to thermal stress. If the temperature changes significantly, the thermal stress could cause some change on the zero reading of the scale. The amount of change is determined by the stress displacement of the substrate which is affected by the internal stress applied to the substrate by the bonding material between the substrate and the holder. Because the bonding material has some level of hysteresis and non-repeatability, the shift of the zero reading can be unpredictable. In order to significantly reduce or eliminate the potentially significant thermal stress that can result along a bonding interface, the substrate can be coupled to the holder as follows. 
     In the embodiment of  FIGS. 12 through 14 , the holder  317  is machined with a cantilevered beam  340  having a free end  342  and a rotation point  344  at which the beam is connected to the mounting face  338  of the holder and about which the beam is permitted relatively free rotation. The mounting face  338  has a first recess  346  for receiving damping adhesive  348  between and in contact with the piezosubstrate  320  and the holder, such as RTV silicone adhesive, to suppress parasitic bulk waves. In one embodiment the adhesive is a relatively soft material so that it will not introduce thermal stress. Suppression of bulk waves prevents distortion of SAW line linearity and therefore maintains linearity of the scale. Linearly spaced from the first recess  346  is a smaller second recess  350  acting a reservoir for bonding agent overflow, as explained further below. If desired or necessary, additional front face recesses can be formed for receiving damping agent or bonding agent overflow. 
     The substrate  320 , provided with electrodes  320   b , is bonded with a bonding agent to the face  338  at only two points: the first point  352  at or adjacent at the free end of the cantilevered beam and the second point  354  just to the far side of the second cavity  350 . Because the points of bonding are small, the bonding will not introduce thermal stress. Any overflow of bonding agent at one end will flow to the sides of the beam  340 , whereas any additional agent at the second end of the substrate will enter the second cavity  350  to ensure that the substrate  320  seats close to and with planarity to the holder face  338 . Then, when the piezosubstrate  320  stretches or shrinks due to temperature changes, the beam  340  will bend about the rotation point with the piezosubstrate. Because the expansion or contraction of the piezosubstrate is in a range of at most several microns, and the length of the beam  340  is several thousand microns, it can be assumed that the free end  342  of the beam is moving in the direction of SAW propagation. 
     Temperature changes that cause the piezosubstrate  320  to expand or shrink a different amount than the face  338  of the holder will not cause significant stress to be applied to the bonding points  352 ,  354  because the free end  342  of the beam allows thermal expansion of the piezosubstrate without resistance. This can be confirmed, as follows. 
     First, for comparison purposes, assume a piezosubstrate which is 10 mm in length, 2 mm wide, and 0.5 mm thick bonded to an aluminum substrate holder with a thin layer of bonding agent between the two. Also, assume a holder substrate of 3.3 mm. Because the substrate of the holder is significantly thicker than the piezosubstrate, a change in temperature of approximately 10° C. can cause the piezosubstrate to be stretched by approximately 1 micron. The force applied to the piezosubstrate through the bonding adhesive is calculated as F=SeE, where S is cross-sectional area of the piezosubstrate, which is 1 mm 2 , e is strain, which is 0.0001, and E is Young&#39;s modulus of the piezosubstrate, which is 21000 kg/mm 2 . This corresponds to approximately 2000 grams force. 
     Now consider the force under the modified assembly. The beam  340  is 1 mm thick in the plane of bending at the rotation point  344 , 3.3 mm wide (the thickness of the face  338 ) and 7.6 mm in length (between the rotation point  344  and the free end  342 ). When the temperature changes by 10° C., the free end  342  of the beam which is bonded to the piezosubstrate  320  will yield by the same 1 micron and the force required for this amount of bending can be estimated as F=3 dEl/L 3 , where d is the displacement of the free end, which is 1 micron, E is the Young&#39;s modulus of the aluminum alloy, which is 7000 kg/mm 2 , I is a moment of inertia of the beam, which is 0.275 mm 4 , and L is a length of the beam, which is 7.6 mm. This corresponds to approximately 14 grams of force, less than 1 percent of the force to which the piezosubstrate is subject when adhesive bonded along its entire surface to the holder. Thus, almost all of the stress applied to the bonding points  352 ,  354  is eliminated with the described assembly. Moreover, the beam  340  is not subject to hysteresis or non-repeatability, because it is manufactured as part of the holder  317  with no special bonding to the holder. 
     Turning now to  FIG. 15 , another embodiment of an assembly avoids any bonding agent directly between the piezosubstrate and the plate holder, which have very different CTEs from each other. It is known that the CTE for 128° YX lithium niobate is very different for its different axes. The length of the piezosubstrate, extending along the axis of SAW propagation, is much bigger than the width. Therefore, it is more important to achieve the best match of the respective CTEs of the piezosubstrate and the holder in the direction of SAW propagation, rather than in other directions. The CTE in this direction is CTE of 15 ppm/° C. In accord with this embodiment, an intermediate plate  460  having a CTE approximating that of the piezosubstrate  420  in the direction of SAW propagation is bonded to the face  438  of the holder  417 , and the piezosubstrate  420  is bonded to the intermediate plate  460  using a suitable bonding material  466 , e.g., epoxy adhesive. One exemplar material for the intermediate plate  460  is stainless steel A316, which has a CTE of 16 ppm/° C. Stainless steel A316 also can be machined and endure high temperature and pressure. In one embodiment the intermediate plate  460  is relatively thick, e.g., 0.06 inch, to maintain a high degree of flatness during machining operations. Importantly, the intermediate plate  460  is bonded to the face  438  of the aluminum alloy holder  417  without an adhesive bonding agent. Rather, to “bond” the intermediate plate  460  and the face  438  of the metal holder  417 , two pins  462 ,  464  are inserted through the plate and holder to stably connect them together. The pins  462 ,  464  are offset to be located to one side of the adhesive bonding line  466  between the piezosubstrate  420  and the intermediate plate  460 , and in one embodiment are spaced relatively close together. In this manner, as the piezosubstrate  420  stretches or shrinks due to temperature changes, the intermediate plate  460  will similarly stretch or shrink without resulting in overstressing the adhesive bond  466  between the piezosubstrate  420  and the intermediate plate  460 . Further, all thermal stress is limited to the small space  468  between the pins as the SAW transducer is subject to thermal changes. 
     Using this assembly, a scale was tested for ranges of temperatures +6° C. to 20° C. and then to 50° C. and then back to between +6° C. to 20° C. several times. The thermal cycling showed very low hysteresis and non-repeatability regarding zero shift. The scale meets NTEP requirements for 1:15000. 
     It is noted that an intermediate plate  460  of large thickness such as in the assembly of  FIG. 15  can be subject to relatively high levels of thermal stress at the pins  462 ,  464 . Thus, referring to  FIG. 16 , another assembly embodiment is provided in which such thermal stress is essentially eliminated even under harsh cycling conditions. The SAW transducer is fabricated on a lithium niobate piezosubstrate  520 , the piezosubstrate  520  is bonded with a bonding agent  566  to an intermediate plate  560  having a CTE that closely matches the piezosubstrate (in the direction of SAW propagation), and the face  538  of the metal holder  517  is machined with a cantilevered beam  540  that is permitted relative free rotation around a rotation point at which the beam is connected to the main body of the holder. The intermediate plate  560  is bonded to the face  538  of the metal holder with two pins  562 ,  564 , one extending into the cantilevered beam  540  on one side of the piezosubstrate  520  and one extending in the face  538  on the other size of the piezosubstrate. As discussed in reference to the embodiment shown in  FIGS. 12 through 14 , it is appreciated that by coupling the intermediate plate  560  at one end to the cantilevered beam and at its other end of the face  538 , without bonding agent extending along the interference therebeneath, thermal stress is effectively eliminated from the assembly. 
     As mentioned above and in the previously incorporated application, the delay line may oscillate in more than one mode and within each mode, the gain will vary as the frequency changes. Referring now to  FIGS. 4 and 5 , in the idle state, with no weight applied to the scale, the delay line will oscillate at a frequency “f” which is shown in  FIG. 4  as the point having the most gain (least loss). The optimal gain area of the graph of  FIG. 4  is shown in the shaded area surrounding f and represents a range of ±100 Khz, for example. This area is considered optimal because it is the area of least loss. However, it is not necessarily the area of best phase linearity. After experimenting, it may be discovered that oscillation in a different mode, e.g. the shaded area of  FIG. 5 , will produce better phase linearity. According to one aspect, the oscillator is forced to oscillate in the mode of best phase linearity by injecting a strong RF signal having a frequency at the midpoint of the desired mode of oscillation. The RF signal is injected by a “push oscillator” coupled to the SAW wave receiver as described in more detail below with reference to  FIG. 6 . According to one embodiment, the RF signal has a strength of approximately 100 my as compared to the SAW oscillator&#39;s strength of approximately 10 my. The RF signal may be injected for a short time (as short as 0.01 seconds) before each weight measurement. 
     As mentioned above, and described in detail in the previously incorporated applications, the effects of temperature can be further corrected by providing a separate SAW temperature sensor on the same substrate as one of the displacement transducers. According to one embodiment, the SAW displacement oscillator operates at 55 MHz and the SAW temperature oscillator operates at 57 MHz. According to another aspect described in more detail below with reference to  FIG. 6 , the temperature oscillator is used in conjunction with an adjustable 2 MHz oscillator and a mixer to produce the “push oscillator” frequency and automatically adjust the “push oscillator” frequency for temperature changes. 
     As seen in  FIG. 6 , an exemplary circuit  200  includes the displacement SAW transducer formed by the transmitter  122   b  on the substrate  122  and the receiver  120   b  on the substrate  120  coupled to each other by the amplifier  202 . In addition, the circuit includes a temperature SAW transducer formed by the transmitter  124  and receiver  126  on the substrate  122  coupled to each other by the amplifier  204 . The output of amplifier  202  is a frequency Fw which varies according to displacement of the substrates relative to each other, which is an indication of weight when the transducers are arranged as shown in  FIG. 1 . According to one embodiment, the frequency Fw is nominally 54 MHz. Fw will also vary according to temperature. The output of amplifier  204  is a frequency Ft which varies only according to temperature and humidity and which is nominally 57 MHz. The frequencies Fw and Ft are mixed (subtracted) at the mixer  206  to produce a nominal frequency of 3 MHz which varies according to weight and which is temperature compensated. The output frequency of the mixer  206  is input to a microprocessor  208  which calculates weight as described in the previously incorporated applications and displays the weight on display  210 . According to this embodiment, the output Ft of amplifier  204  is also mixed via mixer  212  with a 54 MHz signal from oscillator  214  to produce a signal which is nominally 3 MHz and which varies only with temperature and humidity. The signal Fw-Ft provides a temperature adjusted weight signal which accounts for the affects of temperature on the SAW oscillators. It does not compensate for temperature effects on the Youngs modulus of the elastic member ( 14  in  FIG. 1 ). The signal output from mixer  212  is a pure temperature indicator and is used to adjust the weight calculation for the effects of temperature on the Youngs modulus of the elastic member. 
     According to one aspect, a “push oscillator” is formed from an adjustable oscillator  216 , a mixer  218 , and a modulator  220 . The oscillator  216  has a nominal frequency of 2 MHz which is mixed via the mixer  218  with the output of amplifier  204  to produce an output frequency Fi which is (Ft—approx. 2 MHz). This frequency Fi is used to index the modulator  220  which produces the “push oscillator” output to the input of amplifier  202 . As shown in  FIG. 6 , the modulator  220  and the oscillator  216  are both coupled to the microprocessor  208 . The microprocessor  208  is programmed to periodically activate the modulator  220  to inject the push frequency as described above. In addition, the microprocessor advantageously is utilized to adjust the oscillator  216  to determine the frequency of the “push oscillator”. The oscillator  216  may be initially adjusted via a simple variable resistor or variable capacitor. However, it is further adjusted by the microprocessor during operation of the scale. One of these advantages is that the microprocessor can adjust the oscillator  216  to produce the phase shifting described in the previously incorporated applications. In addition, it can be used to produce much larger frequency shifts than were possible in the previously incorporated applications. This results in more accurate determinations of which weight range the scale is in. As described in the previously incorporated applications, the oscillator operated as a periodic function where the same frequencies were repeated over different weight ranges. A phase shift of ±π was used to determine which weight range the scale was operating in. As the weight increased, the same phase shift produced a larger frequency shift (because of the increased length of the delay line) and the frequency shift could be used to determine the weight range. However, under some circumstances, the phase shift resulted in a frequency shift which was too small to accurately determine. In one embodiment the push oscillator can be used to produce ±4π phase shifts. 
     As mentioned above, in one embodiment the oscillator  216  is initially adjusted with a variable resistor or variable capacitor to ensure oscillation on the mode of best phase linearity. Initial calibration is performed as follows: Known weights are placed on the scale and the frequency of the oscillator output is determined for different weights and the modes of oscillation are noted. The push oscillator is tuned to operate in one mode and experiments are conducted to measure linearity. The experiments are repeated for each mode. The push oscillator is then tuned to push to the mode of best linearity. 
     Also, as mentioned above, the auxiliary displacement sensor  18  is initially calibrated by placing known weights on the scale and providing (capacitive) readings. These readings are correlated by the microprocessor  208  to the readings of SAW delay line so that the mode in which the scale is operating can be determined. In other words, and as will be discussed in more detailed below, different loads on the pan or platform  16  can produce the same frequency response in the SAW delay line such that a weight determination cannot be made unless the mode is known. Because the auxiliary displacement sensor  18  has a one-to-one correspondence between output readings and weight (i.e., it does not have multiple modes), it provides information to the microprocessor from which a determination is made as to what mode the system is in. However, it will be recognized by those skilled in the art that the auxiliary sensor will typically be much less accurate and stable than the overall SAW scale. However, for a SAW scale with, e.g., 6 modes and 0.2 mm displacement, the stability of, e.g., a capacitive sensor with 10% change of its capacitance under 100% load should be 0.5% for the temperature range −20° C. to 50° C. 
     In order to achieve this level of stability, according to one aspect, from time to time (e.g., regularly, such as every day or month, but possibly at random times), the reading of the SAW sensor and the reading of the auxiliary sensor are compared, and the reading of the auxiliary sensor is adjusted (recalibrated) to match the reading of the SAW scale. The reading of the SAW sensor and auxiliary sensor may be done whether or not there is weight on the scale. This comparison and adjustment technique is effective because the primary sensor of a SAW scale, the SAW delay line oscillator, has very good stability (relative drift on the order of 10 parts per million of its central frequency in one year), whereas the reading of the auxiliary sensor is not as stable, but drifts relatively slowly. This means that after proper calibration of the SAW scale auxiliary sensor, it will always show the correct mode number in spite of its inherent instability. This will maintain the high overall accuracy of the scale. 
     Turning now to  FIGS. 7-9 , a mechanism for automatic recalibration of the scale is provided that reduces span drift. In this aspect, during a period of time when there is no change to a weight applied to the scale (i.e., the weight is static), (e.g., when there is no weight being applied to the scale, or when the weight being applied is steady), readings of SAW transducers that relate to weight indications and environmental factor indications are taken for each one of two adjacent operating modes of the scale, and two calibrated weight calculations are made utilizing those readings. The difference in calibrated weight calculations is then related to a variable utilized to transform the readings into weights, which is updated, thereby recalibrating the scale. Recalibration in this manner significantly reduces span drift and enhances linearity. 
     More particularly, a load-frequency function graph seen in  FIG. 7 , where the x-axis indicates weight (P), and the y-axis is a frequency function X(f)=Ft/Fw, with Ft being the SAW reference sensor frequency indication output by amplifier  204  of the delay line oscillation loop  124 ,  126 ,  204 , and Fw being the SAW weight frequency indication output by amplifier  202  of the delay line oscillation loop  120   b ,  122   b ,  202 . As will be appreciated by those skilled in the art,  FIG. 7  presents a saw-tooth function, where the same frequency function X(f) can represent multiple weights P. This multiple to one mapping is indicative of multiple “modes”. In  FIG. 7 , three modes (−1, 0 and 1) are shown, although the SAW scale can include four, five, six or more modes. 
     It can be shown that the relationship between the frequency function X(f) and the weight P may be expressed according to the equation:
 
 P =[ W *( X−X 0)*{( N 0+ S )/ N 0}* AW* ( t−t 0)]+[ Dp*S*AP *( t−t 0)]  (1)
 
     where W is the inverse of the slope of the zero mode;
         X is the value of X(f) at weight P=P;   X0 is the value of X(f) at weight P=P0 (at initial calibration, typically when there is no weight on the scale);   S is the number of the mode (e.g., S= . . . , −2, −1, 0, 1, 2, . . . );   N0 is the number of wavelengths between the transducers of the SAW delay line at P=0;   Dp is a beat period for the scale (i.e., the distance along the x-axis between the saw teeth, which equates to the amount of weight required to cause the scale to change modes) and which is constant for the scale;   AW is the temperature coefficient of the inverse slope, which is determined during an initial calibration process by changing the temperature;   AP is the temperature coefficient of the “beat”, which is likewise determined during an initial calibration process;   t is the current temperature; and   t0 is the temperature at the time of initial calibration of the scale.       

     All of the values in equation (1) are may be determined by the microprocessor  208  or stored in memory associated with the microprocessor  208 . X and X0 may be determined indirectly from the outputs of mixers  206  and  212 , or, if desired, values of Ft and Fw may be supplied directly (as shown by dotted lines in  FIG. 6 ) to the microprocessor  208 . A few points are of note with respect to the variables of equation (1). First, temperature coefficient AW is generally a composite of a number of environmental effects, including the characteristics of the piezosubstrate (typically lithium niobate) of the SAW transducer and the characteristics of the load cell material (typically aluminum). Second, at any specific time, the inverse slope W for all modes will be the same. Third, the weight P0 does not necessarily occur at a transition from one mode (S=−1) to another mode (S=0), although it is shown that way in  FIG. 7  for convenience. Fourth, mode 0 does not necessarily start where there is no weight on the scale (pan). 
     In practice, the SAW scales do not exactly follow equation (1). This is primarily because the SAW IDT (transmitter and receiver of the SAW delay line, known as the Inter Digital Transducer) have different temperature (or environmental) zero shifts for different frequencies (i.e., different weights on the scale) in response to environmental changes and aging processes. In one aspect, this effect is substantially linear, because of the range of frequency that is being used is kept small. 
     It should be appreciated that the frequency shift due to environment effects at zero will be the same as the frequency shift due to environment at the beginning point of each mode. For example, if there is a shift of 1000 Hz at P0, there will also be a shift of exactly 1000 Hz at P0+Dp and also at P0+2*Dp, etc. But there will not be an exactly 1000 Hz shift at any other point along the graph of each mode. An example of this is seen in  FIG. 8 . 
     In the example of  FIG. 8 , the scale is arranged such that the frequency of the delay line changes by 10 Hz per gram, and the beat period Dp is 30,000 grams which corresponds to 300,000 Hz (300 khz). At temperature t=T1, with zero weight on the platform (i.e., at P=P0), for mode #0, the frequency of the delay line is 93.00 Mhz. The SAW oscillator can then be used to change the mode of measurement from mode #0 to to mode #−1 using a “mode selector”. This can be accomplished by the “push oscillator”  216  as previously described or by another means, such as a narrow band filter. For mode #−1, for the same zero weight on the platform, the frequency of the delay line is 93.30 Mhz. If 30,000 grams are placed on the platform of the scale while in mode #0, the frequency of the delay line will also be 93.30 Mhz. 
     At some later point in time, the calibration of the scale is checked at the same temperature T1. It is found that for P=P0 (no weight on the platform), for mode #0, the frequency of the delay line has stayed the same, i.e., 93.00 Mhz. But for mode #−1, the frequency of the delay line is 93.2998 Mhz—this is a zero shift of −200 Hz. For this example where the frequency of the delayline changes by 10 Hz per gram, a zero shift of −200 Hz corresponds to a shift of (−)20 grams. This same shift of (−)20 g will be seen for every instance where the frequency of the delay line is in the 93.30 Mhz frequency range (i.e., for each mode). As a result, the inverse slope W of the saw-tooth function shown in  FIG. 8 , is now changed to W′. This can be described by the equation:
 
 W′=W* [1−(∂ P/Dp )]  (2)
         where ∂P is the change in weight measurement (i.e., old weight minus new weight), here 20 grams.       

     In this example W′=W*[1−(20 g/30,000 g)]=W*[1-0.00066]=W*0.999333. It should be noted that in  FIG. 8 , the change in the inverse slope is highly exaggerated for purposes of illustration. 
     Now, if W is replaced with W′ in equation (1), the value of P will change for every weight for every mode. In this way, the initial calibration for the scale has been corrected without use of any external calibration mass. The result of this recalibration is a significant improvement of the overall accuracy of the scale. For example, the specification for linearity for a five mode SAW scale was enhanced from 1:20000 to 1:60000. Similarly, sensitivity drift was reduced to less than 1 ppm per 1° C. in a range 10° C.-40° C. 
       FIG. 9  is a flow chart implemented by the microprocessor  208  of  FIG. 6  with respect to the automatic recalibration aspect. 
     At step  1200 , a determination is made by microprocessor  208  that the weight on the scale is not changing (i.e., either there is nothing on the platform—a “null load”, or the weight on the platform is not changing) for a desired period of time (e.g., one minute, or five minutes, or any other desired amount of time) and that the scale is in a particular mode (denoted mode S for purposes of illustration). 
     At step  1210 , a measurement of temperature t is made as is a measurement of X(f), where X(f)=Ft/Fw. Ft is the SAW reference sensor frequency indication output by amplifier  204  of the delay line oscillation loop  124 ,  126 ,  204 . Fw is the SAW weight frequency indication output by amplifier  202  of the delay line oscillation loop  120   b ,  122   b ,  202 . 
     At step  1212 , a value for P is calculated with the scale in mode S according to equation (1) set forth above: P=[W*(X−X0)*{(N0+S)/N0}*AW*(t−t0)]+[Dp*S*AP*(t−t0)], where the variables are as previously defined. These variables are stored in memory by the microprocessor  208 . 
     At step  1214 , the delay line with amplifier  202  is caused to operate in an adjacent mode (i.e., mode S+1, or mode S−1), e.g., by causing the push oscillator  216  to provide a different frequency that is injected by modulator  220  and provided to amplifier  202 . 
     At step  1216 , a second value for P is calculated according to equation (1) for the scale in the adjacent mode. Then, at step  1218 , the second weight measurement is subtracted from first weight measurement to get a weight difference ∂P. With the calculated weight different, a modified inverse of the slope W′ is calculated at step  1220  according to equation (2) set forth above: W′=W*[1−(∂P/Dp)]. The calculated value of this variable W′ is stored in memory by the microprocessor  208 . 
     At step  1222 , the new inverse slope W′ is substituted (stored) as the new value for the variable W as a recalibration. In other words, the value for the inverse slope variable W is updated with a new calculated value of W′. Steps  1200 - 1222  may be repeated on a regular basis or whenever the processor determines at  1200  that the weight on the scale is static. 
     There have been described and illustrated herein several embodiments of SAW scale improvements and related methods. While particular embodiments have been described, it is not intended that the disclosure be limited thereto, and it is intended that the invention be as broad in scope as the art will allow and that the specification be read likewise. Thus, while particular equations have been disclosed with respect to converting frequency indications to weight determinations, it will be appreciated that other equivalent equations could be used as well. Similarly, while particular modes (e.g., mode 0 and mode −1) were described as being utilized in the recalibration process, it will be appreciated that any adjacent modes could be utilized (e.g., 1 and 2, 0 and 1, etc.) In addition, while particular values of frequencies, frequency shifts, beat periods, etc., were disclosed in particular examples, it will be understood that other values for these variables will be specific for the particular scale. Further, it will be understood that equivalent parts may be used for the described elements. For example, any suitable processor may be used as the “microprocessor”. It will therefore be appreciated by those skilled in the art that yet other modifications could be made without deviating from the spirit and scope of the invention.