Abstract:
Methods and systems for forming accelerometers include forming a load beam supported at one end having an input interdigital transducer (IDT) and an output IDT. The load-beam has a cross section varying in the longitudinal direction effective to cause the load beam to deflect radially in response to an applied load. The cross section varies in width, height, or both.

Description:
BACKGROUND OF THE INVENTION 
   Surface acoustic wave (SAW) devices are a well known sensing means with many applications including use as accelerometers. A typical SAW device operates by measuring changes in the speed of acoustic waves propagating through the surface of a structure. Speed is measured by exciting a wave at one point on a structure and sensing its arrival at another point. Speed is also measured by measuring a resonating frequency at which a standing wave arises in a structure. 
   In one common SAW device, one or more interdigital transducers (IDT) are attached to a structure formed of a piezoelectric material, such as quartz, spaced apart from one another. An electrical signal is input into the transducers, which causes a surface acoustic wave due to the piezoelectric properties of the structure. A standing wave is created within the structure, the frequency of which varies with the strain in the structure. The resonating frequency is measured by an oscillator connected to the transducer and is used to calculate the force exerted on the structure. 
   An IDT is typically formed by two conductive patterns each having a series of fingers extending perpendicular to the direction of travel of the measured wave. The fingers of the two conductive patterns are interlaced, such that any locally excited voltage will result in a voltage difference between the two patterns. 
   SAW accelerometers detect strains in a load beam that result from inertial forces exerted on a load beam by a proof mass, or the mass of the load beam itself. In some materials, such as quartz, the speed of waves within the material increases with increasing strain on the material. Accordingly, increases in the speed of surface waves or increases in a resonating frequency of surface waves can be mapped to increases in acceleration. 
   Constant cross section beams as used in prior systems typically deflect parabolically such that the amount of strain in the load beam varies with position along the load beam. This results in unequal changes in the distance between the fingers of the IDT. The unequal spread of the fingers results in the detection of a wide band of frequencies, rather a single frequency, or narrower band of frequencies. 
   Unequal strain also causes unequal changes in propagating speed along the load beam. This in turn widens the band of frequencies at which standing waves will develop in the load beam. The resonating frequency in the load beam is measured by an oscillator that will tend to jump among the frequencies present in the IDT resulting in noise. Where a wide band of frequencies is present, the magnitude of the noise is greater. 
   The output of SAW accelerometers is often integrated to calculate the velocity and position of a vehicle. Any noise or inaccuracies in the output of an accelerometer will therefore be compounded by the integration calculation resulting in erroneous navigational data. It would therefore be an advancement in the art to provide a means for improving the accuracy of SAW accelerometers. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention provides methods and systems for improving accuracy of a SAW accelerometer. One method includes forming a load beam having a cross section varying in the longitudinal axis such that the load beam deflects radially in response to an applied load. IDTs secure to one or more surfaces of the load beam. The cross section is chosen to provide radial deflection in response to a point load positioned at the free end of the load beam or a distributed load extending along the length of the load beam. Radial deflection promotes equal strain along the length of the load beam, ensuring that any increase in the distance between elements, such as fingers forming the IDT, caused by the strain is proportional to the force exerted on the load beam  12 . In this manner, bias errors caused by the increase in distance are reduced. 
   In one embodiment, a cross section providing radial deflection is formed by contouring one or both of the lateral sides of the load beam to vary the width of the load beam. Such contouring may be performed by photolithography, deep ion etching, or the like. In other embodiments, the cross section is varied by contouring one or both of the top and bottom sides using magnetorheological finishing (MRF) or a diamond saw. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     The preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings. 
       FIG. 1  is a perspective view of a SAW accelerometer, in accordance with an embodiment of the present invention; 
       FIG. 2  is a plot of deflection of prior art load beams and deflection of load beams formed in accordance with an embodiment of the present invention; 
       FIG. 3  is a process flow diagram of a method for forming a load beam, in accordance with an embodiment of the present invention; 
       FIG. 4  is a top plan view of a plurality of load beams formed in a silicon wafer, in accordance with an embodiment of the present invention; 
       FIG. 5  is a side view of a load beam undergoing magnetorheological finishing, in accordance with an embodiment of the present invention; and 
       FIG. 6  is a perspective view of a SAW accelerometer formed in accordance with an embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to  FIG. 1 , a surface acoustic wave (SAW) accelerometer  10  includes a load beam  12  having a transducer  14  on a top surface thereof. In some embodiments, a second transducer  16  secures to the lower surface of the load beam  12 . Lead lines  18  connect the transducers  14 ,  16  to a signal processing circuit (not shown). A proof mass  20  secures to the free end of the load beam  12 . Alternatively, the proof mass  20  is omitted and inertial forces exerted on the load beam  12  itself cause stress within the load beam  12 . The load beam  12  secures to a support structure  22 , such as a block of quartz with which the load beam  12  is monolithically formed. 
   Referring to  FIG. 2 , while still referring to  FIG. 1 , the cross section of the load beam  12  varies with distance  24  from the support structure  22  such that the beam deflects radially, approximating a circular arc, as illustrated by curve  26 . The cross section may vary in height  28 , width  30 , or both. Variations in the height and width may be accomplished by contouring one or more sides of the load beam  12 . Constant cross section beams as used in prior systems typically deflect parabolically as shown by curve  32 . It is readily apparent that the amount of strain in curve  32  varies with position along the load beam  12 , whereas curve  26  has substantially constant strain along its length. 
   The present invention provides radial deflection of the load beam, resulting in substantially uniform strain along the load beam  12 . Substantially uniform strain along the load beam  12  ensures that any increase in separation between a plurality of fingers  34  forming the IDTs  14 ,  16  is proportional to the force exerted on the load beam. This promotes accuracy inasmuch as variation introduced by the increase in separation is proportional to the measured variable. The substantially equal strain along the length of the beam also reduces noise by narrowing the band of resonating frequencies in the load beam  12  such that an oscillator detecting the resonating frequency will jump within a smaller band of frequencies. 
     FIG. 3  illustrates a method  36  for forming a load beam  12  having radial deflection. At block  38 , the characteristic acceleration for the accelerometer  10  is determined. The characteristic acceleration may be the maximum, average, or most likely acceleration to which the accelerometer is subject. In some embodiments, multiple accelerometers are used each having a different characteristic acceleration such that each will have radial deflection at a different point along the range of accelerations to which the accelerometers  10  will be subject. 
   At block  40 , an inertial force exerted on the load beam  12  at the determined characteristic acceleration is determined. At block  42 , a load beam profile achieving radial deflection under the characteristic inertial force is calculated. At block  44 , the profile of the load beam  12  is formed according to the profile calculated at block  42 . 
   Referring to  FIG. 4 , in some embodiments, the width  30  of the load beam  12  is varied with distance to achieve the desired deflection. Width variations may be accomplished by contouring one or both lateral sides of the load beam  12 . In such embodiments, the load beam profile is typically formed in a quartz wafer  46  by photolithography, plasma oxide etching, or like semiconductor forming method. Where a proof mass  20  is used such that inertial forces are exerted primarily at the free end of the load beam, Equation 1 dictates the approximate width of the load beam  12  with distance  24  from the support  22 . In Equation 1, and other equations below, B(X) is the width of the load beam with respect to a distance X from the base, F is the characteristic force applied proximate a free end of the load beam  12  by the proof mass  20 , L is a total length of the load beam  12  (i.e. the distance from the support  22  to the proof mass  20 ), E is a modulus of elasticity of the load beam, and H is a height of the load beam. 
   
     
       
         
           
             
               
                 
                   B 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     
                       
                         Fx 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             3 
                             ⁢ 
                             L 
                           
                           - 
                           x 
                         
                         ) 
                       
                     
                   
                   
                     
                       EH 
                       3 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               
                                 L 
                                 2 
                               
                               - 
                               
                                 x 
                                 2 
                               
                             
                             ) 
                           
                           
                             1 
                             2 
                           
                         
                         - 
                         L 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
           
         
       
     
   
   In embodiments where the inertial forces exerted on the mass of the load beam  12  itself or a distributed load are used to detect acceleration, the width is calculated according to Equation 2, where P is equal to the amount of inertial force per unit length along the load beam  2 . 
   
     
       
         
           
             
               
                 
                   B 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     
                       Px 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           6 
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                         - 
                         
                           4 
                           ⁢ 
                           xL 
                         
                         + 
                         
                           x 
                           2 
                         
                       
                       ) 
                     
                   
                   
                     
                       ( 
                       
                         2 
                         ⁢ 
                         
                           EH 
                           3 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               
                                 L 
                                 2 
                               
                               - 
                               
                                 x 
                                 2 
                               
                             
                             ) 
                           
                           
                             1 
                             2 
                           
                         
                         - 
                         L 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
             
           
         
       
     
   
   Referring to  FIG. 5 , in some embodiments, the height  28  of the load beam  12  is varied to achieve radial deflection. The height  28  may be varied by contouring one of the top and bottom sides or both. Variations in height may be accomplished by means of a magnetorheological finishing (MRF) apparatus  48  programmed to dwell over portions of the load beam  12  to remove material such that the desired height profile is formed. Alternatively, a diamond saw, or like cutting tool may also be used. In such embodiments, the height  28  varies with distance  24  from the support  22  according to Equation 3, wherein H(X) is the height  28  of the load beam with respect to a distance X from the support  22 , B is the width  30 , and F is the inertial force exerted by the proof mass  20 . 
   
     
       
         
           
             
               
                 
                   H 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 = 
                 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         
                           
                             Fx 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 3 
                                 ⁢ 
                                 L 
                               
                               - 
                               x 
                             
                             ) 
                           
                         
                       
                       
                         EB 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     L 
                                     2 
                                   
                                   - 
                                   
                                     x 
                                     2 
                                   
                                 
                                 ) 
                               
                               
                                 1 
                                 2 
                               
                             
                             - 
                             L 
                           
                           ) 
                         
                       
                     
                     ) 
                   
                   
                     1 
                     3 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
             
           
         
       
     
   
   In embodiments where the mass of the load beam  12  itself is used to detect inertial forces or a distributed load is used, the height  28  is calculated according to Equation 4. 
   
     
       
         
           
             
               
                 
                   H 
                   ⁡ 
                   
                     ( 
                     x 
                     ) 
                   
                 
                 = 
                 
                   
                     ( 
                     
                       
                         
                           Px 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               6 
                               ⁢ 
                               
                                 L 
                                 2 
                               
                             
                             - 
                             
                               4 
                               ⁢ 
                               xL 
                             
                             + 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           EB 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       L 
                                       2 
                                     
                                     - 
                                     
                                       x 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 
                                   1 
                                   2 
                                 
                               
                               - 
                               L 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   
                     1 
                     3 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
           
         
       
     
   
   The foregoing equations assume the following: 
   Radial deflection, Y(X) of the load beam  12  is determined by the equation 
   
     
       
         
           
             Y 
             ⁡ 
             
               ( 
               x 
               ) 
             
           
           = 
           
             
               
                 ( 
                 
                   
                     L 
                     2 
                   
                   - 
                   
                     x 
                     2 
                   
                 
                 ) 
               
               
                 1 
                 2 
               
             
             - 
             L 
           
         
       
     
   
   The moment of inertia, I, of the load beam  12  is calculated according to the equation 
   
     
       
         
           I 
           = 
           
             
               
                 BH 
                 3 
               
               12 
             
             . 
           
         
       
     
   
   Deflection, Y(X) in the load beam  12  is a function of the moment of inertia, I, for point loads F, such as those imposed by the proof mass  20  of  FIG. 1 , imposed a distance L from the support of a cantilever beam is described by the equation 
   
     
       
         
           
             Y 
             ⁡ 
             
               ( 
               x 
               ) 
             
           
           = 
           
             
               
                 
                   Fx 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       3 
                       ⁢ 
                       L 
                     
                     - 
                     x 
                   
                   ) 
                 
               
               
                 6 
                 ⁢ 
                 EI 
               
             
             . 
           
         
       
     
   
   Deflection, Y(X) in the load beam  12  as a function of the moment of inertia, I, for distributed load P, such as the inertial force exerted on a load beam  12  without a proof mass  20  shown in  FIG. 4 , is described by the equation 
   
     
       
         
           
             Y 
             ⁡ 
             
               ( 
               x 
               ) 
             
           
           = 
           
             
               
                 
                   Px 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       6 
                       ⁢ 
                       
                         L 
                         2 
                       
                     
                     - 
                     
                       4 
                       ⁢ 
                       xL 
                     
                     + 
                     
                       x 
                       2 
                     
                   
                   ) 
                 
               
               
                 24 
                 ⁢ 
                 EI 
               
             
             . 
           
         
       
     
   
   The foregoing equations are illustrative of one method of determining a profile for a load beam  12  having substantially radial deflection. Other methods including computer modeling and experimentation may be used to determine profiles providing radial deflection under a particular load. Radial deflection may also be made by varying both width and height. The basic shape of the cross section may be square, rectangular, or any other shape providing radial deflection. 
     FIG. 6  is a perspective view of a SAW accelerometer  100  formed in accordance with a method of the present invention. The accelerometer  100  includes load beam  120  as a varying cross-section (width 300, height 280) that varies along the longitudinal axis of the load beam  120 . 
   While the preferred embodiment of the invention has been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined entirely by reference to the Claims that follow.