Patent Publication Number: US-6211473-B1

Title: Electronic weighing apparatus utilizing surface acoustic waves

Description:
This application is a continuation-in-part of co-owned application Ser. No. 08/729,752 filed Oct. 7, 1996, now U.S. Pat. No. 5,910,647, which was a continuation 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 OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to electronic weighing devices. More particularly, the invention relates to an electronic weighing device which 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 12,000 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 compresses a column 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. 
     Co-owned application Ser. No. 08/489,365, previously incorporated by reference herein, discloses 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 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. In addition, in order to minimize the possibility that the oscillator will oscillate in two modes at the same time, the frequency response of the delay line is arranged so that no more than two modes coexist in the main lobe of the frequency response curve. This is achieved by the topology of the electrodes as well as the distance between the transmitting electrode and the receiving electrode. The gain of the amplifier is also chosen to be at least the absolute value of the greatest loss expected to be encountered at an oscillating frequency within the main lobe but not great enough to allow oscillation in two modes simultaneously. 
     According to a disclosed preferred embodiment, the surface acoustic wave has a wavelength of approximately 200 microns at 20 MHz. The gap between the substrates of the first and second transducers is as small as possible and preferably is less than 0.1 wavelength, i.e. 10-20 microns. The amplifier preferably has a gain of at least approximately 17 dB in order to guarantee natural oscillation, and preferably not more than approximately 30 dB so that the oscillator oscillates in only one mode at a time. The preferred manner of determining the cycle of the periodic output of the amplifier is to provide a second pair of transducers adjacent to the first pair and coupled to each other in the same type of delay line feedback loop. The second pair of transducers utilize a SAW with a different wavelength than the first pair of transducers, e.g. approximately 220 microns at 18 MHz. The output of the second amplifier is, therefore, a periodic function with a different frequency than the periodic function which is the output of the first amplifier. By combining the outputs of both amplifiers, a unique value is provided for each position of the elastic member. 
     Typically, the elastic member is chosen so that it will bend up to 150 microns under maximum load. Given the wavelength of the SAW, this results in about two to three modes of oscillation in the output of the first amplifier. 
     The provided apparatus can theoretically achieve an accuracy on the order of one part in one hundred thousand, e.g. one gram per hundred kilograms. In practice, however, a resolution on the order of one part in fifty thousand is readily achieved. It has been observed by the inventors herein that several factors have varying influence on the accuracy of the SAW system. These factors include reflected waves, temperature changes, and the frequency of the oscillator. Generally, reflected waves result in non-linearity of measurements, and temperature has an effect of about 70 ppm per degree C. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the invention to provide an electronic weighing apparatus which is accurate. 
     It is also an object of the invention to provide an electronic weighing apparatus which uses surface acoustic waves and is accurate over a broad range of weights. 
     It is another object of the invention to provide an electronic weighing apparatus which is compact and easy to construct. 
     It is a further object of the invention to provide an electronic weighing apparatus which is inexpensive to manufacture. 
     It is another object of the invention to provide an electronic weighing apparatus which utilizes surface acoustic waves and which is provided with means for reducing reflected waves. 
     It is still another object of the invention to provide an electronic weighing apparatus which maintains accuracy despite temperature gradients within the system. 
     It is yet another object of the invention to provide an electronic weighing apparatus which utilizes surface acoustic waves at a relatively high frequency. 
     In accord with these objects which will be discussed in detail below, the improved weighing apparatus of the present invention includes a base which supports a cantilevered elastic member upon which a load platform is mounted. The interior of the elastic member is hollowed and is provided with first and second piezoelectric transducers which are mounted on respective opposed posts. 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. 
     According to the invention, when a load is applied to the load platform, the cantilevered elastic member bends 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 bending 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. 
     According to one aspect of the invention, one or both substrates are provided with anti-reflection structure which may be an angled cut, a rounded end, or a surface damper. 
     According to a second aspect of the invention, the transducers are arranged on overlapping substrates which allows more room for a damping material to further reduce reflection and allows more room for additional transducers. 
     According to a third aspect of the invention, the transducers are coupled to a thermal sink to reduce the effects of thermal gradients across the transducers. 
     According to a fourth aspect of the invention, two pairs of transducers are provided and arranged to move in opposite directions which doubles the readability of measurements and also compensates for the effects of temperature gradients. 
     According to a fifth aspect of the invention, a thermal transducer channel is provided on the same substrate to measure the effects of temperature and thereby compensate for temperature effects. 
     According to a sixth aspect of the invention, a pair of differential transducers is arranged to measure the effects of temperature changes in the same acoustic channel in which displacement measurements are made. 
     According to a seventh aspect of the invention, a phase shift (preferably 180°) is introduced in the oscillator of the delay line, when required, in order for the oscillator to oscillate in the most optimal section of the frequency response curve (near the center) where temperature effects are minimized. 
     According to an eighth aspect of the invention, two surface dampers are provided for each transducer. This is accomplished in one of two ways. According to one way, a surface mount damper is formed from a thin mylar film. According to the other way, a multistrip coupler is formed by an aluminized pattern of lines behind the transducer and a surface damper is provided behind the multistrip coupler. 
     According to a ninth aspect of the invention, long term stability is enhanced by sealing the transducer, preferably hermetically, and/or by providing a second hermetically sealed temperature transducer and by using the output of the sealed transducer to correct for the effects of temperature and humidity. 
     Additional objects and advantages of the invention will become apparent to those skilled in the art upon reference to the detailed description taken in conjunction with the provided figures. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic side elevation view of an exemplary embodiment of the invention; 
     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 plan view of a transducer having a first anti-reflection structure according to the invention; 
     FIG. 3 is an enlarged schematic side elevation view of a transducer having a second anti-reflection structure according to the invention; 
     FIG. 4 is an enlarged schematic side elevation view of a transducer having a third anti-reflection structure according to the invention; 
     FIG. 5 is an enlarged schematic side elevation view of an overlapping transducer system having anti-reflection structure according to the invention; 
     FIG. 6 is an enlarged schematic side elevation view of an overlapping differential transducer system according to the invention, incorporating anti-reflection structure and thermal sinks; 
     FIG. 7 is an enlarged schematic plan view of one pair of transducers of the system of FIG. 6; 
     FIG. 8 is an enlarged schematic plan view of the other pair of transducers of the system of FIG. 6; 
     FIG. 9 is an enlarged schematic side elevation view of a differential transducer system according to the invention, incorporating a split second channel; 
     FIG. 10 is an enlarged schematic plan view of one pair of transducers of the system of FIG. 9; 
     FIG. 11 is an enlarged schematic plan view of the other pair of transducers of the system of FIG. 9; 
     FIG. 12 is an enlarged schematic plan view of the first part of a differential transducer system having two pair of separate thermal transducer channels; 
     FIG. 13 is an enlarged schematic plan view of the second part of a differential transducer system having two pair of separate thermal transducer channels; 
     FIG. 14 is a schematic transparent view of the transducers of FIGS. 12 and 13 in an operative alignment; 
     FIG. 15 is an enlarged schematic side elevation view of a transducer system having a thermal transducer located in the same acoustic channel as the displacement transducers and an example of a circuit for the same; 
     FIG. 16 is an enlarged schematic plan view of the first part of the transducer system of FIG. 15; 
     FIG. 17 is an enlarged schematic plan view of the second part of the transducer system of FIG. 15; 
     FIG. 18 is an enlarged schematic side elevation view of a differential transducer system having two transducers sharing the same acoustic channel; 
     FIG. 19 is an enlarged schematic plan view of the first part of the transducer system of FIG. 18; 
     FIG. 20 is an enlarged schematic plan view of the second part of the transducer system of FIG. 18; 
     FIGS. 21-26 are a graphs of a portion of a frequency response curve for a delay line according to the invention showing modes of oscillation and phase shifting according to the invention; 
     FIG. 27 is a schematic diagram of a positive feedback loop with phase shifting according to the inventions 
     FIG. 28 is an enlarged schematic plan view of a transducer according to the invention illustrating the propagation of SAW waves; 
     FIG. 29 is a schematic transparent view of two transducers of the type shown in FIG. 28 in operative alignment; 
     FIG. 30 is an enlarged schematic side elevation view of the transducer system of FIG. 29; 
     FIG. 31 is a view similar to FIG. 28 showing one embodiment of a transducer with two surface dampers; 
     FIG. 32 is a view similar to FIG. 28 showing another embodiment of a transducer with two surface dampers; 
     FIG. 33 is a view similar to FIG. 29 showing two of the transducers of FIG. 32 in operative alignment; 
     FIG. 34 is a view similar to FIG. 1 illustrating one way of sealing the transducers; and 
     FIG. 35 is a view similar to FIG. 1 illustrating another way of sealing the transducers. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to FIGS. 1,  1   a , and  1   b , an electronic weighing apparatus  10  according to the invention 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 . 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 . 
     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. The substrates are preferably 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 parent 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 to propagate from the electrodes  20   b  to the electrodes  22   b.    
     According to presently preferred embodiments of the invention, 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 as small as possible and preferably no more than 0.1 wavelength. In one preferred embodiment described below, the gap is 5-10 microns. With such a gap, an oscillating system can typically be generated if the amplifier  24  has a gain of at least approximately 17 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 an 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 of the parent application. Depending on the application (e.g. maximum load to be weighed), the elastic member is made of aluminum or steel. The presently preferred elastic member exhibits a maximum displacement of 0.1 to 0.2 mm at maximum load. 
     It has been recognized by the inventors that reflected waves may occur on the substrate of the transmitting transducer which interfere with SAW wave generation and result in non-linearity of measurements. More particularly, when the wave  26  propagates along the substrate  20   a , it reaches the end  20   c  of the substrate and a portion of the wave is reflected back 180° toward the electrodes  20   b . The reflected wave interferes with the propagated wave  26 . In fact, a portion of the reflected wave is again reflected off the other end  20   d  of the substrate  20   a  causing additional interference. Reflected waves can also be a problem in the receiving transducer. FIGS. 2-4 show several anti-reflection structures according to the invention. 
     Turning now to FIG. 2, a transducer  120  according to the invention includes a piezoelectric substrate  120   a  and a pair of electrodes  120   b  for generating a SAW wave  126 . According to the invention, the end  120   c  of the substrate  120   a  is cut at an angle relative to the propagation path of the SAW wave  126 . Thus, when the wave  126  reaches the end  120   c  of the substrate, any reflection of the wave is at an angle relative to the line of propagation so that the reflected wave does not interfere with the propagated wave. 
     Turning now to FIG. 3, a transducer  220  according to the invention includes a piezoelectric substrate  220   a  and a pair of electrodes  220   b  for generating a SAW wave  226 . According to the invention, the end  220   c  of the substrate  220   a  is rounded (e.g., by sandblasting) relative to the propagation path of the SAW wave  226 . Thus, when the wave  226  reaches the end  220   c  of the substrate it is scattered rather than reflected back. 
     Turning now to FIG. 4, a transducer  320  according to the invention includes a piezoelectric substrate  320   a  and a pair of electrodes  320   b  for generating a SAW wave  326 . According to the invention, a damper such as a soft elastomeric  320   d  is placed on the surface of the substrate adjacent the end  320   c . Thus, when the wave  326  reaches the damper  320   d , it is absorbed by the damper rather than reflected back. 
     Of the different anti-reflection structure described above, the damper material shown in FIG. 4 appears to be the presently preferred structure. Accordingly, as shown in FIG. 5, a pair of transducers  320 ,  322  are provided with damper material  320   d ,  322   d  adjacent ends  320   c ,  322   c  opposite electrodes  320   b ,  322   b  on the respective substrates  320   a ,  322   a . The transducers  320 ,  322  are advantageously arranged in an overlapping manner as shown in FIG.  5 . 
     As mentioned above, in addition to problems associated with reflected waves, changes in temperature adversely affect the accuracy the weighing apparatus. It is known from the parent application that overall changes in ambient temperature may be compensated for by including a temperature sensor in the weighing apparatus and using a look-up table for appropriate temperature corrections. However, in addition to overall changes in ambient temperature, it has been discovered that temperature gradients can occur across the substrates of the transducers. More particularly, it has been discovered that the lithium niobate substrates have a temperature effect of about 70 ppm per degree C. In a 20 Mhz system, this results in a change of 1.4 Khz per degree. In order to obtain the desired accuracy, the temperature difference between the transducers should be less than 0.01 degrees C. At 20 Mhz, the full scale output for one mode is about 200 Khz. Since the substrate shows a temperature effect of 1.4 Khz per degree C., this results in a 0.7% variation of the full scale per degree C. In order to maintain an accuracy of within 0.007% of the full scale, therefore, the temperature difference should be less than 0.01 degree C. 
     Several aspects of the present invention combine to help overcome the effects of temperature on the accuracy of the weighing apparatus. Some of these aspects also enhance the overall accuracy of the apparatus regardless of temperature effects. 
     FIGS. 6-8 show a pair of transducers  420 ,  422  according to the invention which embody several aspects of the invention. Referring now to FIGS. 6-8, the transducer system includes a transmitting transducer  420  and a receiving transducer  422 . The transmitting transducer  420  includes two piezoelectric substrates  420   a ,  420   a ′ which are mounted on one side a thermal sink  421 , and a thermal insulator  423  is mounted on the other side of the thermal sink  421 . The thermal sink  421  helps to maintain a constant temperature across both substrates  420   a ,  420   a ′ and the thermal insulator  423  helps to prevent ambient temperature changes from affecting the temperature of the thermal sink  421  and thus the substrates  420   a ,  420   a ′. Each substrate  420   a ,  420   a ′ has a pair of electrodes  420   b ,  420   b ′ at one end thereof and a surface damper  420   d ,  420   d ′ at the other end thereof. The substrates are arranged on the thermal sink so that their respective electrode pairs are close to each other and adjacent to the center of the transducer as seen best in FIGS. 6 and 7. The transmitting transducer  420 , therefore generates two SAW waves  426 ,  426 ′ which propagate in opposite directions from the approximate center of the transducer  420 . The dampers  420   d ,  420   d ′ serve to inhibit reflections of the SAW waves  426 ,  426 ′. 
     The receiving transducer  422  includes a piezoelectric substrate  422   a  which is mounted on one side of a thermal sink  425 , and a thermal insulator  427  is mounted on the other side of the thermal sink  425 . The thermal sink  425  helps to maintain a constant temperature across the substrate  422   a  and the thermal insulator  427  helps to prevent ambient temperature changes from affecting the temperature of the thermal sink  425  and thus the substrate  422   a . The substrate  422   a  has two pairs of electrodes  422   b ,  422   b ′, each pair being located approximately at opposite rounded ends  422   c ,  422   c ′ of the substrate  422   a , and a surface damper  422   d  is located approximately at the center of the substrate  422   a . The receiving transducer  422 , therefore receives two SAW waves  428 ,  428 ′ which are induced respectively by the transmitted SAW waves  426 ,  426 ′, and which propagate in opposite directions. 
     The electrode pairs  420   b  and  422   b  are coupled to one amplifier to form one delay line oscillator and the electrode pairs  420   b ′ and  422   b ′ are coupled to a second amplifier to form a second delay line oscillator. From the foregoing, it will be appreciated that when the transducers  420 ,  422  move relative to each other as described above with reference to FIG. 1, one of the delay line oscillators will increase in frequency and the other delay line oscillator will decrease in frequency by an equal amount. This “differential” transducer system provides several benefits. The effects of ambient temperature are automatically accounted for and the resolution of the displacement measurement is doubled. 
     For example, if the frequency of a delay line oscillator is f 0  at a predefined temperature, the frequency after a change in ambient temperature can be expressed as f=f 0 (1+kΔt), where k is a constant and Δt is the change in ambient temperature. Similarly, if the frequency of a delay line oscillator is f 0  when no load is placed on the weighing apparatus, the frequency after the transmitter and receiver have been displaced by a load can be expressed as f=f 0 (1±gΔx), where g is a constant and Δx is the displacement (positive or negative) due to a particular load. The combined change in frequency Δf due to temperature and displacement, therefore equals f 0 (kΔt±gΔx). 
     Given the foregoing, it will be appreciated that the combined effects of temperature and displacement on the frequency of the delay line oscillators of FIGS. 6-8 can be expressed by the equations indicated below at (1) and (2) where f1 is the frequency of the oscillator which includes electrodes  420   b ,  422   b  and f2 is the frequency of the oscillator which includes electrodes  420   b ′,  422   b′.   
      Δf1=f1 0 kΔt+f1 0 gΔx  (1) 
     
       
         Δf2=f2 0 kΔt−f2 0 gΔx  (2) 
       
     
     The quantities Δf1, Δf2, f1 0 , and f2 0 , will therefore be known during any weight measurement and may be subjected to the cross product expressed below at (3). 
     
       
         (Δf1×f2 0 )−(Δf2×f1 0 )  (3) 
       
     
     By substituting equations (1) and (2) in expression (3), the expression listed below at (4) is obtained. 
     
       
         f2 0 f1 0 kΔt+f2 0 f1 0 gΔx−f1 0 f2 0 kΔt+f1 0 f2 0 gΔx  (4) 
       
     
     By combining terms, it will be appreciated that the effects of temperature will be canceled out of expression (4) and that expressions (3) and (4) can be expressed as the simplified equation listed below at (5). 
     
       
         (Δf1×f2 0 )−(Δf2×f1 0 )=2f1 0 f2 0 gΔx  (5) 
       
     
     It will therefore be appreciated that the differential transducer system described above, not only eliminates the affects of ambient temperature change from the weighing measurement, but also provides double the resolution scale of a single transducer system. Nevertheless, the system described with reference to FIGS. 6-8 will not automatically compensate for temperature gradients across the substrates of the transducer and that is why the transducer system is provided with the thermal sinks described above. It will also be appreciated that the overall length (height) of the transducer system is substantially doubled as compared with the non-differential system. In order to reduce the overall size of the transducer system and to increase the sensitivity and resolution of the system, the present invention preferably uses a frequency of approximately 50 mhz as compared to the 20 mhz frequency of the parent application. At this frequency, in order to achieve the desired accuracy (0.5 grams per 10 kg), the temperature difference between the substrates must be kept below 0.01 degrees C°. 
     FIGS. 9-11 show a schematic illustration of a differential transducer system similar to the one described above, but with both transducer channels operating on the same substrate and with one of the transducer channels being split. Referring now to FIGS. 9-11, the transducer system includes a transmitting transducer  520  and a receiving transducer  522 . The transmitting transducer  520  includes a piezoelectric substrate  520   a  which is mounted on one side a thermal sink  521 , and a thermal insulator  523  is mounted on the other side of the thermal sink  521 . The thermal sink  521  helps to maintain a constant temperature across the substrate  520   a  and the thermal insulator  523  helps to prevent ambient temperature changes from affecting the temperature of the thermal sink  521  and thus the substrate  520   a . A first transmitting electrode  520   b  is located at one end of the substrate  520   a  on a central axis thereof. A second transmitting electrode pair  520   c ,  520   d  is located at the other end of the substrate on opposite sides of the central axis. Each of the electrodes  520   c ,  520   d  is approximately half the wavelength of the electrode  520   b  and the electrodes  520   c ,  520   d  are coupled in parallel to form the electrode pair. The transmitting transducer  520 , therefore generates three SAW waves  526 ,  526 ′, and  526 ″. The first SAW wave  526  propagates along a central channel on the substrate and in a first direction. The second and third SAW waves  526 ′ and  526 ″ propagate along two side channels on the substrate an in a direction opposite to the first SAW wave. 
     The receiving transducer  522  includes a piezoelectric substrate  522   a  which is mounted on one side of a thermal sink  525 , and a thermal insulator  527  is mounted on the other side of the thermal sink  525 . The thermal sink  525  helps to maintain a constant temperature across the substrate  522   a  and the thermal insulator  527  helps to prevent ambient temperature changes from affecting the temperature of the thermal sink  525  and thus the substrate  522   a . The substrate  522   a  has a first receiving electrode  522   b  and a second receiving electrode pair  522   c ,  522   d . The receiving electrode  522   b  is at one end of the substrate on a central axis thereof and the receiving electrodes  522   c ,  522   d  are located at the other end of the substrate on opposite sides of the central axis. The receiving electrodes  522   c ,  522   d  are half the wavelength of the electrode  522   b  and are coupled in parallel to each other. The receiving transducer  522 , therefore receives three SAW waves  528 ,  528 ′, and  528 ″ which are induced respectively by the transmitted SAW waves  526 ,  526 ′,  526 ″. 
     The arrangement shown in FIGS. 9-11 has several advantages. The SAW wave propagation channels are closer together on the same substrate and therefore the temperature gradient between them will be smaller. The overall size of the transducer system is smaller. In addition, the transducers are axially symmetrical which enhances mechanical performance. 
     FIGS. 12-14 show a schematic illustration of a differential transducer system similar to the one described above, but with additional electronic means for measuring the temperature of the substrates. Referring now to FIGS. 12-14, a transmitting transducer  620  includes a first piezoelectric substrate  620   a  and a second piezoelectric substrate  620   a ′, both of which are mounted on a base  623  which is preferably constructed as a sandwich of insulating and conductive materials as described above with reference to FIG.  6 . The first piezoelectric substrate  620   a  is provided with a first pair of transmitting electrodes  620   b  at a lower central portion thereof and the second piezoelectric substrate  620   a ′ is provided with a second pair of transmitting electrodes  620   b ′ at an upper central portion thereof. In addition, first piezoelectric substrate  620   a  is provided with two pair of electrodes  630   a ,  630   b  which are spaced apart from each other and arranged off center from the first pair of transmitting electrodes  620   b . The electrodes  630   a ,  630   b  are respectively a transmitter and receiver which are used to measure the temperature of the substrate  620   a  as described below. Accordingly the substrate  620   a ′ is also provided with two pair of temperature measuring electrodes  630   a ′,  630   b′.    
     A receiving transducer  622  includes a first piezoelectric substrate  622   a  and a second piezoelectric substrate  622   a ′, both of which are mounted on a base  627  which is preferably constructed as a sandwich of insulating and conductive materials as described above with reference to FIG.  6 . The first piezoelectric substrate  622   a  is provided with a first pair of receiving electrodes  622   b  at an upper central portion thereof and the second piezoelectric substrate  622   a ′ is provided with a second pair of transmitting electrodes  622   b ′ at a lower central portion thereof. In addition, the first piezoelectric substrate  622   a  is provided with two pair of temperature measuring electrodes  632   a ,  632   b  which are spaced apart from each other and arranged off center from the first pair of transmitting electrodes  522   b . The substrate  522   a ′ is also provided with two pair of temperature measuring electrodes  632   a ′,  632   b′.    
     The transducer arrangement shown in FIGS. 12-14 incorporates several of the features of the transducer arrangement described above with reference to FIGS. 6-8. The electrode pairs  620   b ,  620   b ′,  622   b ,  622   b ′ are arranged to provide a differential displacement measurement system as described above. In this regard, and with reference to FIG. 14, it will be appreciated that the differential system utilizes two acoustic channels which are centrally located, one on the upper pair of substrates and the other on the lower pair of substrates. In addition, it will be appreciated that the transmitting substrates are slightly larger than the receiving substrates and therefore overlap the receiving substrates with the same advantages as described above. According to a presently preferred embodiment, the transmitting transducer  620  is approximately 45 mm long and the space between the first and second substrates is approximately 5 μm. The receiving transducer  622  is approximately 10 mm shorter than the transmitting transducer and the space between the first and second receiving substrates is approximately 5 μm. 
     As mentioned above, each of the four piezoelectric substrates is provided with a two pair of temperature measuring electrodes which are arranged as a fixed position delay line on each substrate. Each of the four sets of temperature measuring electrodes is coupled to a respective amplifier and thereby forms a natural oscillator which preferably oscillates at a frequency which is different from the frequency at which the displacement measuring oscillators oscillate. Since the temperature measuring electrode sets are stationary on their respective substrates, the frequency of their respective oscillators will vary only due to changes in temperature. With this provided arrangement, the temperature of each of the four substrates can be determined and accounted for when making displacement and weight measurements. 
     As seen in FIG. 14, each of the two measuring electrode sets operates in a separate acoustic channel. It is possible, however, to provide two measuring electrode sets which operate in almost the same channel. This minimizes the thermal gradient between the two channels. FIGS. 15-17 illustrate one embodiment of such an arrangement. 
     Turning now to FIGS. 15-17, a transmitting transducer  720  includes a piezoelectric substrate  720   a  with a pair of transmitting electrodes  720   b  located at a lower end thereof and a pair of receiving electrodes  730  located at an upper end thereof. A receiving transducer  722  includes a piezoelectric substrate  722   a  with a pair of receiving electrodes  722   b  at an upper end thereof. It will be appreciated that the transmitting and receiving electrodes  720   b ,  722   b  are arranged with amplifier  750  to form a delay line for measuring displacement and weight as described above. In addition, the receiving electrodes  730  on the transmitting substrate form a stationary delay line with amplifier  760  and the transmitting electrodes  720   b  for measuring the temperature of the transmitting substrate  720   a . The amplifiers  750  and  760  may be operated simultaneously if the delay lines have significantly different frequencies. Alternatively, the amplifiers  750 ,  760  may be switched on and off alternatingly. It will be appreciated that all of the electrodes operate in the same acoustic channel. The transducer system shown in FIGS. 15-17 is a non-differential system wherein the temperature of the transmitting substrate is assumed to be close to that of the receiving substrate. However, it is possible to apply the technology of this system to a differential system wherein separate measurements are made for the two channels. Such a system is shown in FIGS. 18-20. 
     Turning now to FIGS. 18-20, a transmitting transducer  820  includes a piezoelectric substrate  820   a  with a pair of transmitting electrodes  820   b  located at a lower end thereof and a pair of transceiving electrodes  830  located at an upper end thereof. A receiving transducer  822  includes a piezoelectric substrate  822   a  with a pair of receiving electrodes  822   b  at an upper end thereof and a pair of transceiving electrodes  832  at a lower end thereof. It will be appreciated that the transmitting and receiving electrodes  820   b ,  822   b  are arranged to form a delay line for measuring displacement and weight as described above. In addition, the transceiving electrodes  830  and  832  can be used to form a stationary delay line with respective electrodes  820   b ,  822   b  or may be used with each other to form a displacement measuring delay line which is differential to the delay line formed by electrodes  820   b ,  822   b . In operation, the four electrode pairs may be multiplexed such that at one moment, two differential displacement measuring delay lines are activated and at another moment two stationary temperature measuring delay lines are activated. In this manner, the temperature of each substrate can be ascertained prior to or even during temperature measurement. It will be appreciated that all of the electrodes operate in the same acoustic channel. 
     As mentioned above and in the parent application, the delay lines according to the invention may oscillate in more than one mode and within each mode, the gain will vary as the frequency changes. According to the invention, the phase of the oscillator may be shifted ±180° in order to increase gain (decrease loss). FIGS. 21-26 illustrate how the modes of oscillation change during weighing and how phase shifting can be used to increase gain. 
     Referring now to FIG. 21, in the idle state, with no weight applied to the scale, the delay line will oscillate at a frequency “f 0 ” which is shown in FIG. 21 as the point having the most gain (least loss). The optimal gain area of the graph of FIG. 21 is shown in the shaded area surrounding f 0  and represents a range of ±100 Khz, for example. This area is considered optimal not only because it is the area of least loss, but because it is the area wherein the curve exhibits the least “non-linearity” and is least influenced by temperature. As described in detail in the parent application, the delay line may oscillate in any of several modes and the modes are separated from each other by a phase difference of 2π. In the example shown in FIG. 21, the frequency f 0  has a lower mode f 0 −2πω and a higher mode f 0 +2πω, where ω is the interger one, the phase difference between the modes representing approximately 340 Khz in this example. As weight is added to the scale, the delay line will oscillate at a higher frequency “f 0 +n”. For example, after adding a relatively small weight, the frequency of oscillation will rise to f 0 +70 Khz which is shown in FIG. 22 as f 1 . 
     Referring now to FIG. 22, it will be seen that the new frequency of oscillation f 1  is still within the optimal gain area and the higher and lower modes of oscillation have greater loss than the mode at f 1 . It will be appreciated, however, that with the addition of additional weight, the frequency f will soon pass out of the optimal gain area. For example, an additional weight could shift the frequency an additional 50 Khz to the position shown in FIG.  23 . 
     Referring now to FIG. 23, an oscillation frequency f 2  which is approximately 120 Khz higher than f 0 , would move the frequency out of the optimal gain area. Nevertheless, as shown in FIG. 23, the higher and lower modes of oscillation would still show greater loss than the central mode at f 2 . Those skilled in the art will therefore appreciate that from this point onward, additional weight will raise the frequency of oscillation though an increasingly high loss area until the lower mode achieves greater gain than the central mode which is shown in FIG.  24 . 
     Turning now to FIG. 24, an oscillation frequency f 3 , which is approximately 170 Khz higher than f 0  would cause a shift to the lower mode of oscillation f 3 −2πω. It will be appreciated, however, that even after the mode shift, the frequency of oscillation must shift through approximately 70 Khz more before oscillation of the lower mode will occur in the optimal gain area. According to the invention, therefore, it is possible to apply a phase shift of πω to the oscillator in order to force early oscillation in the optimal gain area. For example, as shown in FIGS. 23 and 24 as soon as the oscillation frequency f 2  exhibits loss which indicates it is no longer in the optimal gain area, a phase shift of −πω is applied. This causes the oscillator (delay line) to oscillate at f 2 −πω which, as can be seen in FIG. 23, is within the optimal gain area of the frequency response curve. This phase shift will maintain the frequency of oscillation f 3 −πω within the optimal area even when the frequency rises to f 3  as shown in FIG.  24 . Eventually, however, additional weight on the scale will raise the frequency of oscillation to a point where the phase shifted frequency is outside the optimal gain area. 
     For example, as shown in FIG. 25, when the frequency of oscillation f 4  is increased to approximately f 0 +255 Khz, the phase shifted central mode of oscillation f 4 −πω will exit the optimal gain area. At this point, according to the invention, the −πω phase shift is discontinued and the oscillator will oscillate in its lower mode f 4 −2πω which is within the optimal gain area. If additional weight is added to the scale, the frequency of oscillation will continue to rise until the lower mode of oscillation passes beyond the optimal gain area as shown in FIG.  26 . 
     Referring now to FIG. 26, if the frequency f 5  is raised to approximately f 0 +400 Hhz, the lower mode oscillation f 5 −2πω will pass beyond the optimal gain area. According to the invention, at this point, a −πω phase shift will be applied to the oscillator. This will cause the lower mode of oscillation to reside at f 5 −3πω which is within the optimal gain area. 
     FIG. 27 shows a simplified schematic diagram of a positive feedback loop with phase shifting according to the invention. Referring now to FIG. 27, a simplified delay loop according to the invention includes a first transducer  920 , a second transducer  922 , a first differential amplifier  950 , a second differential amplifier  952 , a pair of matching transformers  954 ,  956 , a frequency counter and amplifier controller  958 , and an output processor and weight display  960 . The first transducer  920  includes a piezoelectric substrate  920   a  and electrodes  920   b . The second transducer  922  includes a piezoelectric substrate  922   a  and electrodes  922   b . The electrodes  920   b  are coupled via the matching transformer  954  to the inputs of the differential amplifiers  950 ,  952  in a parallel manner. The electrodes  922   b  are coupled to the outputs of the amplifiers  950 ,  952  via the matching transformer  956 . As shown in FIG. 27, the polarity of the outputs of the amplifier  950  is opposite to the polarity of the outputs of the amplifier  952 . In addition, the enable input of each amplifier is coupled to the frequency counter and amplifier controller  958  which is also coupled to the outputs of the amplifiers. According to the invention, the amplifiers  950 ,  952  are turned on at one time by the frequency counter and amplifier controller  958 . It will be appreciated that the phase of the outputs of the amplifiers differs by 180° or π. Thus, in order to apply or remove a phase shift, one of the amplifiers is turned off and the other is turned on. Those skilled in the art will appreciate that other circuits can be utilized to produce substantially the same type of phase shifting and that the circuit of FIG. 27 is merely one example. According to the example shown in FIG. 27, the frequency counter and amplifier controller  958  monitors the output of the amplifier  950  and detects when the frequency passes beyond the optimal gain area as described above, e.g., increases by 100 Khz. When the frequency increases by a preselected amount, the frequency counter and amplifier controller  958  turns off amplifier  950  and turns on amplifier  952 . The frequency counter and amplifier controller  958  then monitors the output of amplifier  952 . After the frequency increases by an additional preselected amount, e.g. 100 Khz, the frequency counter and amplifier controller  958  turns off amplifier  952  and turns on amplifier  950 . While the frequency counter and amplifier controller  958  is monitoring frequencies, the frequencies are passed to the output processor and weight display  960  which analyzes the frequency of oscillation, correlates the frequency with a particular weight according to the methods described in the parent application, and displays the weight. 
     Turning now to FIGS. 28-30, those skilled in the art will appreciate that the transducers, e,g, transducer  1020  in FIG. 28 propagate SAW waves in several directions. In a transducer having a so-called “uni-directional topology”, a primary SAW wave  1026  is propagated by the electrodes  1020   b  toward the edge  1020   c  and is damped by the anti-reflection damper  1020   e  as described above. Another, albeit lower amplitude SAW wave  1026   a  is propagated in the opposite direction toward edge  1020   d . It is desirable that additional anti-reflection damping be provided for this wave also. However, as can be seen from FIGS. 29 and 30, there is no room between the transducers  1020  and  1022  to provide dampers like  1020   e  and  1022   e  while still maintaining the close spacing between the transducers. FIG. 31 shows one solution to the problem. 
     As shown in FIG. 31, the transducer  1120  is provided with a thin anti-reflection damper  1120   f  between the electrodes  1120   b  and the edge  1120   d . The damper  1120   f  is made from a layer of MYLAR which is approximately three microns thick. The MYLAR is glued to the substrate  1120   a . One disadvantage of this solution is that the glue used to affix the MYLAR is approximately seven microns thick. The resulting thickness of approximately ten microns is too thick to maintain the optimal close spacing desired between two transducers. A different solution is shown in FIGS. 32 and 33. 
     The transducer  1220  shown in FIG. 32 is provided with a multistrip coupler  1220   g  and an anti-reflection damper  1220   h  which is similar in size to the damper  1220   e . The coupler  1220   g  is made from an aluminized pattern which is printed on the substrate  1220   a  and which is designed to redirect SAW waves from the electrodes  1220   b  toward the damper  1220   h . According to a presently preferred embodiment, the coupler includes one hundred parallel lines spaced with a period of approximately 0.7 times the wavelength of the SAW waves. Those skilled in the art will appreciate that types of couplers, using different patterns, can achieve similar results. 
     As shown in FIG. 33, the arrangement of FIG. 32 allows the close placement of two transducers  1220  and  1222  with relatively thick dampers  1220   e ,  1220   h ,  1222   e ,  122   h  while maintaining a close spacing between the substrates  1220   a ,  1222   a.    
     As mentioned above, in order to assure good long term stability, it is desirable that the transducers be sealed. Turning now to FIG. 34, a weighing apparatus  110  is similar to the apparatus  10  shown in FIG. 1 with similar reference numerals (increased by 100) referring to similar structure. As shown in FIG. 34, transducers  620 ,  622  (having on board temperature sensors) are sealed by providing a sealing box  102  which covers the entire elastic member  114 . A rolling diaphragm  104  permits movement of the elastic member  114  and the load platform  116  relative to the box  102 . 
     Another way to seal the transducers is shown in FIG. 35 which illustrates a weighing apparatus  210  is similar to the apparatus  10  shown in FIG. 1 with similar reference numerals (increased by 200) referring to similar structure. According to this embodiment, a flexible sleeve  202  is placed over the transducers  620 ,  622  and sealed to the posts  217 ,  219 . The sleeve may be made of a light weight LATEX or similar material. It will be appreciated that other methods of sealing the transducers can yield similar results. 
     As mentioned above, the effects of temperature and long term degradation can be further corrected by providing a seperate hermetically sealed SAW temperature sensor in addition to the temperature sensors on board the transducers in the elastic member. This is particularly useful if the temperature sensors on board the transducers in the elastic member are not hermetically sealed or if the seal ( 102 ,  202 ) is not perfectly hermetic. According to this aspect of the invention, two weight corrections can be made based on the temperature sensed by the hermetically sealed unit. As shown in equation 6, the effects of temperature on the elastic member ( 114 ,  214 ) can be compensated for to yield a corrected weight Wc from a non-corrected weight Wn based on the temperature To in ° C. of the hermetically sealed transducer at the time the weight is measured and the temperature Tc in ° C. of the hermetically sealed transducer at the time the unit was calibrated. The constant 55×10 −5  is based on a Youngs modulus as well as other parameters for a particular aluminum elastic member. Other elastic members will require a different constant. 
     
       
         Wc=Wn+(Wn*(Tc−To)*(55×10 −5 )  (6) 
       
     
     It will be appreciated that equation 6 may be implemented using any highly accurate temperature sensor. As shown in equation 7, long term effects (such as absorption of water vapor and other degredation effects due to incomplete sealing) on the weight measuring transducer can be compensated for to yield a corrected weight Wc based on the uncorrected weight Wn, the reading Th (in Mhz) sensed by the hermetically sealed transducer, and the reading Tn (in Mhz) sensed by the non-sealed temperature sensor, where fc is the center frequency (in Mhz) for both sensors.              Wc   =     Wn   -     (     Wn   *       Th   -   Tn     fc       )               (   7   )                         
     There have been described and illustrated herein several embodiments of an electronic weighing apparatus utilizing surface acoustic waves. While particular embodiments of the invention have been described, it is not intended that the invention be limited thereto, as 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 geometries of the base, elastic member, and load platform have been disclosed, it will be appreciated that other geometries could be utilized. Also, while particular wavelengths have been disclosed, it will be recognized that other wavelengths could be used with similar results obtained. Moreover, while particular configurations have been disclosed in reference to the location of transmitting and receiving electrodes, it will be appreciated that the respective locations of transmitters and receivers could be reversed. Furthermore, while several different aspects of the invention have been disclosed as solving various problems, it will be understood that the different aspects of the invention may be used in combination with each other in configurations other than those shown. It will therefore be appreciated by those skilled in the art that yet other modifications could be made to the provided invention without deviating from its spirit and scope as so claimed.