Abstract:
A frequency adjustable surface acoustic wave oscillator uses circuitry in which the phase relationship between the corresponding input and output signals and the voltage applied to or received by transducer fingers is controlled in such a manner that the frequency of the surface acoustic wave oscillator is arbitrarily controlled over a wide range by digital means. This provides an oscillator that exhibits a wide tunable frequency range while providing low phase noise.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of the provisional application entitled “Digitally Tunable Surface Acoustic Wave Device” by Robert Hay, application Ser. No. 61/050113 filed May 2, 2008, and is hereby incorporated by reference in its entirety. 
    
    
     FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     JOINT RESEARCH AGREEMENT 
     Not applicable 
     SEQUENCE LISTING 
     Not applicable 
     FIELD OF THE INVENTION 
     The present invention relates to the field of surface acoustic wave (SAW) devices and in particular to digitally tunable oscillators using SAW devices. 
     BACKGROUND OF THE INVENTION 
     Surface Acoustic Wave (SAW) devices are frequently used as filters, signal processing components, and as the resonating components of oscillators for generating sinusoid signals. Use of these devices is typically limited to applications where a fixed or slightly tunable frequency response is suitable. 
     In contrast to a Bulk Acoustic Wave (BAW) device where the resonant frequency is generally determined almost exclusively by the physical properties and geometry of the piezoelectric material, the bandpass frequency and propagation delay properties of a particular SAW device are largely influenced by the mechanism by which signals are applied to and extracted from the piezoelectric substrate as well as the material properties. This mechanism is traditionally determined by a fixed metallization pattern known as the interdigitated transducer (IDT) which contains a single pair of connection terminals for the input signal and a similar pair of terminals for the output signal. A typical SAW device contains a sending and a receiving IDT. 
     Because of their elongated parallel structure, the interdigitated transducers (IDT) are also referred to as transducer fingers or just “fingers”. 
     SUMMARY OF THE INVENTION 
     The frequency adjustable SAW oscillator uses circuitry in which the phase relationship between the corresponding input and output signals and the voltage applied to or received by subsets of the transducer fingers is controlled in such a manner that the bandpass frequency of the SAW device is arbitrarily controlled over a wide range by digital means. This provides an oscillator that exhibits a wide tunable frequency range while providing low phase noise. 
     In one embodiment transmitting fingers interface with a portion of piezoelectric material and initiate a surface acoustic wave on the piezoelectric material. Receiving fingers, configured to receive the surface acoustic wave, interface with a second portion of the piezoelectric material and generate an electrical signal. Phase adjustable drivers connect to and drive each of the transmitting fingers. Phase adjustable receivers connect to each of the receiving fingers. A receiver summing network sums the receiver output from each of the phase adjustable receivers and produces a receiver summed output. A gain element amplifies the summed output and excites each of the phase adjustable drivers. 
     In another embodiment the frequency adjustable surface acoustic wave oscillator has a piezoelectric layer deposited onto a semiconductor. Transmitting fingers interface with a first portion of the piezoelectric layer, and initiate a surface acoustic wave on the piezoelectric layer. Receiving fingers interface with a second portion of the piezoelectric layer and receive the surface acoustic wave. Phase adjustable drivers sum phase-shifted versions of an input signal via transmission gates or switches and drive each of the transmitting fingers. Phase adjustable receivers connect multiple receiver transmission gates or switches to each receiver finger via a buffer. The output of each of the receiver transmission gates or switches connects to one of a multitude of receiver busses. A receiver summing system receives a phase-shifted version of each of the receiver busses and forms a summed output. A gain element receives the summed output and excites the input signal. 
     A method of implementing the frequency adjustable surface acoustic wave oscillator employs transmitting and receiving fingers adapted to transmit and receive respectively surface acoustic waves on a piezoelectric surface. A surface acoustic wave is transmitted onto the piezoelectric surface by controlling the phase of an input signal to each of the transmitting fingers. The receiving fingers receive the surface acoustic wave and produce a multitude of received signals. The phase of each of the received signals is adjusted. The phase-adjusted received signals are then summed. The resulting sum is amplified to generate the input signal. The input signal is then phase adjusted and applied to the transmitting fingers as described above. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The summary above, and the following detailed description will be better understood in view of the enclosed drawings which depict details of various embodiments. Like reference numbers designate like elements. It should however be noted that the invention is not limited to the precise arrangement shown in the drawings. The features, functions and advantages can be achieved independently in various embodiments of the claimed invention or may be combined in yet other embodiments. 
         FIG. 1  shows one embodiment of the frequency adjustable surface acoustic wave oscillator. 
         FIG. 2  shows one embodiment of a phase adjustable driver. 
         FIG. 3  shows one embodiment of a phase adjustable receiver. 
         FIG. 4  shows another embodiment of a phase adjustable driver. 
         FIG. 5  shows another embodiment of the frequency adjustable surface acoustic wave oscillator. 
         FIG. 6A  shows a profile view of one embodiment of the frequency adjustable surface acoustic wave oscillator. 
         FIG. 6B  shows a profile view of another embodiment of the frequency adjustable surface acoustic wave oscillator. 
         FIG. 7  shows an example of phase addition. 
         FIG. 8A  depicts a mid frequency waveform superimposed on a set of interdigitated fingers. 
         FIG. 8B  depicts a high frequency waveform superimposed on a set of interdigitated fingers. 
         FIG. 8C  depicts a low frequency waveform superimposed on a set of interdigitated fingers. 
         FIG. 8D  depicts a received waveform superimposed on a set of interdigitated fingers. 
         FIG. 9  is a flow chart of a method implementing the frequency adjustable surface acoustic wave oscillator. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, reference is made to the accompanying drawings that form a part thereof, and in which is shown by way of illustration specific exemplary embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that modification to the various disclosed embodiments may be made and other embodiments may be utilized, without departing from the spirit and scope of the present invention. The following detailed description is therefore, not to be taken in a limiting sense. 
       FIG. 1  shows one embodiment of the frequency adjustable surface acoustic wave oscillator  100 . A piezoelectric material  110  has a number of transmitting fingers  120  interfacing with a first portion of the piezoelectric material  125 . The transmitting fingers  120  are configured to initiate a surface acoustic wave  140  on the piezoelectric material  110 . A number of receiving fingers  130  interface with a second portion of the piezoelectric material  135 . 
     The receiving fingers  130  are configured to receive the surface acoustic wave  140  and generate an electrical signal  138 . Phase adjustable drivers  150 , each have a driver input  151  and a driver output  152 . The driver output  152  of each of the phase adjustable drivers  150  connects to one of the transmitting fingers  120 . 
     Each of the phase adjustable receivers  160  has a receiver input  161  and a receiver output  162 . Each of the receiver inputs  161  connects to one of the receiving fingers  130 . The inputs of a receiver summing network  170  connect to the receiver outputs  162  from each of the phase adjustable receivers  160 . The output of the receiver summing network  170  produces a receiver summed output  175 . A gain element  180  receives the summed output  175 . The output  185  of the gain element  180  connects to each of the driver inputs  151 . 
     In operation, the output  185  of the gain element  180  excites the driver inputs  151  of the phase adjustable drivers  150 . Each of the driver outputs  152 , provides a phase adjusted signal to one of the transmitting fingers  120 . The transmitting fingers  120  interface with a first portion  125  of the piezoelectric material  110  and initiate a surface acoustic wave  140  on the piezoelectric material  110 . The receiving fingers  130  interface with a second portion of the piezoelectric material  135 . The receiving fingers  130  receive the surface acoustic wave  140  and generate electrical signals  138 . The phase adjustable receivers  160  each receive an electrical signal  138  from a receiving finger  130  at receiver input  161 . The receiver summing network  170  sums the receiver outputs  162  from each of the phase adjustable receivers  160  and produces a receiver summed output  175 . The gain element  180  amplifies the summed output  175  and excites each of the driver inputs  151 . 
     The piezoelectric material  110  of  FIG. 1  can be any number of commonly known piezoelectric materials. Examples include, but are not limited to, zinc oxide, quartz, lithium tantalate, lithium niobate, gallium arsenide, cadmium sulphide, lithium tetraborate, langasite, bismuth germanium oxide, and aluminum nitride. The various piezoelectric materials have different properties including propagation speed of the acoustic wave, loss characteristics, and temperature coefficient. Those skilled in the art of surface acoustic wave devices choose the piezoelectric material based on the specific application. 
     In some embodiments all the electronic components of  FIG. 1  including the phase adjustable drivers  150 , phase adjustable receivers  160 , summing network  170 , gain element  180  and their associated buffers and interconnections are built on a common semiconductor substrate  600  ( FIG. 6 ). In yet other embodiments the piezoelectric material  110  is deposited onto the surface of the semiconductor substrate  600  ( FIG. 6 ). There may be an underlying dielectric layer  610  between the semiconductor substrate  600  and the piezoelectric material  110 . This may be chosen based on several criteria including hardness, passivation properties, semiconductor process and propagation velocity. A range of materials are suitable for the dielectric material  610  ranging from silicon dioxide, silicon nitride, or a diamond-like carbon. Additional details are presented in conjunction with  FIG. 6 . 
       FIG. 2  shows one embodiment of the phase adjustable drivers  150  of  FIG. 1 . A driver summing block  210  has inputs  215   a ,  215   b  and an output  212 . A first adjustable gain amplifier  230  has an input  235  and an output  232 . The input  235  connects to the driver input  151 . The output  232  connects to an input  215   a  of the driver summing block  210 . A second adjustable gain amplifier  240  has an input  245  and an output  242 . The input  245  connects to the driver input  151  via a phase-shifter  250 . The output  242  connects to an input  215   b  of the driver summing block  210 . The output  212  of the driver summing block  210  connects to the output  152  of the phase adjustable driver  150 . 
     In operation the phase adjustable driver  150  receives the driver input  151  at the input  235  of the first adjustable gain amplifier  230  and a phase shifted version of input  151  via the phase-shifter  250  at the input  245  of the second adjustable gain amplifier  240 . In some embodiments the phase-shifter  250  is chosen to provide a 90 degree phase shift of the signal at input  151 . The phase shift of phase-shifter  250  can be accomplished in a number of ways. In some embodiments, the phase shifter  250  is implemented as a delay element. In other embodiments the phase-shifter is a power splitter/combiner or hybrid coupler known to those skilled in the art. The driver summing block  210  adds the amplifier outputs  232  and  242  received at the summer inputs  215   a  and  215   b . Each of the adjustable gain amplifiers  230  and  240  have a gain that varies from negative through zero to positive. In this example the phase-shifter  250  provides a phase shift of 90 degrees. For example assume the signal on input  151  has an amplitude of 1 and a reference phase of 0 degrees. Amplifier  230  can produce a signal on output  232  ranging from 1 to −1 where −1 represents an amplitude of 1 with a phase shift of 180 degrees. In a similar manner amplifier  240  can produce a signal on output  242  ranging from amplitude of 1 at 90 degrees to 1 at 270 degrees. When the signals at outputs  232  and  242  are added by the summer block  210 , the phase of the signal at output  212  can range from 0 degrees to 360 degrees. This variable phase signal connects to the phase adjustable driver output  152  and drives the transmitting fingers  120  of  FIG. 1   
       FIG. 3  shows one embodiment of the phase adjustable receivers  160  of  FIG. 1 . A common in-phase summing block  360  has input  365   a  and an output  362 . A common phase-shifted summing block  370  has input  375   a  and an output  372 . A receiver summing block  310  has inputs  315   a  and  315   b  and an output  312 . The output  362  connects to the input  315   a  and the output  372  connects to the input  315   b  via a delay phase-shifter  380 . Two adjustable gain amplifiers  330  and  340  have inputs  335  and  345  respectively and connect to one of the plurality of receiving fingers  130  of  FIG. 1  via node  390 . The output  332  of adjustable gain amplifier  330  connects to an input  365   a  of the common in-phase summing block  360 ; and the output  342  of the adjustable gain amplifier  340  connects to input  375   a  of the common phase-shifted summing block  370 . 
     In operation the two adjustable gain amplifiers  330  and  340  receive the signal from one of the receiving fingers  130  of  FIG. 1  at node  390  via inputs  335  and  345 . The adjustable gain amplifiers  330  and  340  have a gain that ranges from negative through zero to positive. The output  332  of adjustable gain amplifier  330  is added to the output of other adjustable gain amplifiers (not shown) by common in-phase summing block  360 . Similarly the output  342  of adjustable gain amplifier  340  is added to the output of other adjustable gain amplifiers (not shown) by common phase-shifted summing block  370 . Receiver summing block  310  adds the output  362  of common in-phase summing block  360  to the output  372  of phase-shifted summing block  370  via its inputs  315   a  and  315   b  after it is shifted in phase by the phase-shifter  380 . In some embodiments the delay phase-shifter  380  is chosen to provide a 90 degree phase shift of the signal at output  372 . The phase shift of phase-shifter  380  can be accomplished in a number of ways. In some embodiments, the phase shifter  380  is implemented as a delay element. In other embodiments the phase-shifter  380  is a power splitter/combiner or hybrid coupler known to those skilled in the art. When the phase shifter  380  provides a 90 degree phase shift, the received signal at node  390  can be adjusted in phase from 0 to 360 degrees by adjusting the gain of the amplifiers  330  and  340 . The phase adjusted output appears at the summed output  312 . 
     The common in-phase summing block  360  and common phase-shifted summing block  370  of  FIG. 3  are shared by a number of adjustable gain amplifiers. In practice each of the summing blocks  360  and  370  have multiple inputs. These other inputs, not shown, receive the outputs of the adjustable gain amplifiers associated with other receiving fingers  130  of  FIG. 1 . In some embodiments the phase shifter  380  is implemented with a delay that approximates a 90 degree or quadrature phase shift. When phase-shifter  380  is implemented with a delay, the degree of phase shift will vary as a function of the input signal frequency at node  390 . Some implementations have a tapped delay or adjustable delay to more accurately control the phase shift. The adjustable gain of the amplifiers  330  and  340  can compensate for variations of the phase shifter from 90 degrees. 
       FIG. 4  shows another embodiment of the phase adjustable drivers  150  of  FIG. 1 . A tapped delay  400  has an input  405  that connects to the phase adjustable driver input  151  of  FIG. 1 . A number of taps  402   a - d  present delayed versions of the input  405  to the inputs of switches  420   a - d . Each of the switches  420   a - d  is interposed between one of the taps  402   a - d  of the tapped delay line  400 , and one of the inputs  415   a - d  of the summing block  410 . In this embodiment the switches  420   a - d  are represented as transmission gates. The output of the summing block  412  connects to the output of the phase adjustable driver  152  of  FIG. 1 . 
     In operation the taps  402   a - d  of the delay line  400 , output delayed versions of the input  405 . In some embodiments, the delays represent phase shifts of 0, 90, 180 and 270 degrees of the input  405  which is connected to the driver input  151  of  FIG. 1 . The switches  420   a - d , control whether the signals on the taps  402   a - d  are inputted to the inputs  415   a - d  of the summing block  410 . Each of the switches  420   a - d  has a control input, not shown, that allows the switch to either pass or not pass the signal from its respective tap  402   a - d  to its respective summing block input  415   a - d . The summing block  410  adds the signals present at the inputs  415   a - d  and outputs the sum on the output  412  of the summing block  410 . The output  412  connects to the output of the phase adjustable driver  152  of  FIG. 1  ultimately driving a transmitting finger  120  of  FIG. 1 . 
     In embodiments where the four taps  402   a - d  represent phase shifts of 0, 90, 180 and 270 degrees, eight unique combinations are available at output 412. The table below shows how phase shifted versions of the input  405  are possible at the output  412  by turning on one or two switches  420   a - d  at a time. 
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 420a 
                 420b 
                 420c 
                 420d 
                 Output 412 
               
               
                   
               
             
             
               
                 1 
                 0 
                 0 
                 0 
                  0 degrees 
               
               
                 1 
                 1 
                 0 
                 0 
                  45 degrees 
               
               
                 0 
                 1 
                 0 
                 0 
                  90 degrees 
               
               
                 0 
                 1 
                 1 
                 0 
                 135 degrees 
               
               
                 0 
                 0 
                 1 
                 0 
                 180 degrees 
               
               
                 0 
                 0 
                 1 
                 1 
                 225 degrees 
               
               
                 0 
                 0 
                 0 
                 1 
                 270 degrees 
               
               
                 1 
                 0 
                 0 
                 1 
                 315 degrees 
               
               
                   
               
             
          
         
       
     
     In the table above, a 1 indicates that the control to the respective switch is on allowing the switch to pass a signal from its input to its output. A 0 indicates that the control to the respective switch is off preventing the signal from passing from the switch input to output. The eight phase angles above may be suitable in some applications instead of the more complex variable gain amplifiers  230  and  240  of  FIGS. 2 and 3 . Many variations of  FIG. 4  are possible. For example, while four delays are shown in  FIG. 4 , other numbers of delays are possible. Another embodiment may employ eight taps and eight switches feeding a summer with eight inputs. This alternative embodiment enables more phase resolution. Additionally, since the phase shift associated with a particular delay depends on the frequency of the input signal, a larger number of taps increases the range of frequencies covered. 
     The tapped delay  400  of  FIG. 4  is shown in conjunction with one phase adjustable driver. In many embodiments, a single tapped delay is employed by all the phase adjustable drivers. Suitable buffering between the taps and the switches prevents the effect of loading the taps by the switches. The embodiment depicted in  FIG. 4  uses transmission gates as switches. Other embodiments can use other types of switches including, but not limited to, diode switches or other types of semiconductor switches. 
     Each of the switches, represented by transmission gates  420   a - d  in  FIG. 4  has one of two states, either open, not passing a signal, or closed, passing a signal. This binary nature, either open or closed, on or off, lends itself to digital control. A single binary bit can control each switch. A series of binary bits can control each of the adjustable phase drivers. A designer can increase or decrease the number of taps and switches depending upon the application. The control bits can be shifted into the circuit by a serial bit stream into shift registers. The approach of programming the switches by means of a series of binary bits allows flexibility in the overall design. 
       FIG. 5  shows another embodiment of the frequency adjustable surface acoustic wave oscillator. A piezoelectric layer  110  is deposited onto a semiconductor  600  ( FIG. 6 ). Transmitting fingers  120  interface with a first portion  125  of the piezoelectric layer  110 . The transmitting fingers  120  are configured to initiate a surface acoustic wave  140  on the piezoelectric layer  110 . Receiving fingers  130  interface with a second portion  135  of the piezoelectric layer  110 . The receiving fingers  130  are configured to receive the surface acoustic wave  140 . Phase adjustable drivers  150 , each have a summer  530  with summer output  535  and summer inputs  531 - 534 . The summer outputs  535  connect to a corresponding one of the transmitting fingers  120 . Each of the summer inputs  531 - 534  receives a version of an input signal  151  via switches  541 - 544 , buffers  581 - 584  and phase-shifter  585 . Receiver busses QRneg, QRpos, IRneg, and IRpos feed a receiver summing system  560 . The receiver summing system  560  uses buffers  561 - 564 , phase-shifter  565  and summers  567 - 569  to form phase-shifted versions of the receiver busses QRneg, QRpos, IRneg, and IRpos. These phase-shifted versions of the busses QRneg, QRpos, IRneg, and IRpos represent various phases of the signal on the receiving finger  130 . The receiver summing system  560  generates a summed output  590 . Receiver switches  571 - 574  and buffer  570  make up each phase adjustable receiver. The inputs of the receiver switches  571 - 574  connect to one receiver finger via a buffer  570 , the output of each of the receiver switches connect to one of the receiver busses QRneg, QRpos, IRneg, and IRpos. A gain element  180  receives the summed output  590  and excites the input signal  151 . 
     In operation the phase adjustable drivers  150 , each receive four versions of the input  151 . Input  531 , representing a 0 degree phase shift, receives a non-inverted, minimally delayed version of input  151  via buffer  581  and switch  541 . Input  532 , representing a 180 degree phase shift receives an inverted, version of input  151  via inverting buffer  582  and switch  542 . Input  533 , representing a 90 degree phase shift, receives a non-inverted, phase-shifted version of input  151  via phase-shifter  585 , buffer  583 , and switch  543 . Input  534 , representing a 270 degree phase shift, receives an inverted, phase-shifted version of input  151  via phase-shifter  585 , inverting buffer  584 , and switch  544 . A summer  530  adds the summer inputs  531 - 534 . The summer output  535  drives a corresponding one of the transmitting fingers  120 . The transmitting fingers  120  initiate an acoustic wave  140  onto the piezoelectric layer  110 . Receiving fingers  130  interface with a second portion  135  of the piezoelectric layer  110  and receive the surface acoustic wave  140 . The inputs of the receiver switches  571 - 574  receive the signal from receiver fingers  130  via a buffer  570 . The output of each of the receiver switches  571 - 574  drives one of the receiver busses QRneg, QRpos, IRneg, and IRpos. The receiver summing system  560  adds a phase-shifted or buffered version of each of the receiver busses QRneg, QRpos, IRneg, and IRpos and outputs a signal  590 . IRpos, is buffered by buffer  561  and is added to summed output  590  by summers  568  and  569 . IRpos represents a 0 degree phase shift of the signal at receiving finger  130 . IRneg, is inverted by inverting buffer  562  and is added to summed output  590  by summers  568  and  569 . IRneg represents a 180 degree phase shift of the signal at receiving finger  130 . QRpos, is buffered by buffer  563 , phase-shifted by phase-shifter  565  and is added to summed output  590  by summers  567  and  569 . QRpos represents a 90 degree phase shift of the signal at receiving finger  130 . QRneg, is inverted by inverting buffer  564 , phase-shifted by phase-shifter  565  and is added to summed output  590  by summers  567  and  569 . QRneg represents a 270 degree phase shift of the signal at receiving finger  130 . A gain element  180  amplifies the summed output  590  and excites the input signal  151 . 
     The phase of the transmitting fingers  120  of  FIG. 5  are controlled by enabling or disabling each of the switches  541 - 544 . Similar to the discussion of  FIG. 4 , the embodiment shown in  FIG. 5  has eight possible phase angles for each of the phase adjustable drivers  150 . Control bits, not shown, set each of the switches  541 - 544  to open or closed. The various combinations of the four switches enable phases of 0, 45, 90, 135, 180, 225, 270, and 315 degrees when the phase-shifter  585  corresponds to a 90 degree phase shift. Other embodiments are possible by increasing or decreasing the number of phase-shifters and switches. The phase-shifter  585  itself may also be programmable to expand the frequency range of the overall system. The phase shift of phase-shifters  565  and  585  can be accomplished in a number of ways. In some embodiments, the phase shifters  565  and  585  are implemented as delay elements. In other embodiments the phase-shifters are power splitters/combiners or hybrid couplers known to those skilled in the art. 
       FIG. 6A  shows a profile view of a semiconductor material  600 . A piezoelectric material  110  is deposited on top of the semiconductor material  600 . In some embodiments the buffers, amplifiers, delays, phase-shifters, summers, connections, and switches are fabricated in or on the semiconductor material  600 . The transmitting fingers  120  interface with a portion  125  of the piezoelectric material  110  while the receiving fingers  130  interface with a portion  135  of the piezoelectric material  110 . In some embodiments the fingers  120  and  130  are part of the metal layers associated with the semiconductor process. 
       FIG. 6B  shows a profile view of a semiconductor material  600 . A dielectric layer  610  is deposited on top of the semiconductor material  600 . A piezoelectric material  110  is deposited on top of the dielectric layer  610 . In some embodiments the buffers, amplifiers, phase-shifters, summers, connections, and switches are fabricated in or on the semiconductor material  600 . The transmitting fingers  120  interface with a portion  125  of the piezoelectric material  110  while the receiving fingers  130  interface with a portion  135  of the piezoelectric material  110 . In some embodiments the fingers  120  and  130  are deposited as a separate metal layer. Connections between the fingers  120  and  130  and associated components on the semiconductor process are realized with feed throughs or other methods known to those skilled in the art of semiconductor processes. 
     In  FIG. 6B , the spacing between the transmitting and receiving fingers  120  and  130  is shown as lambda/2. In some embodiments, lambda is chosen as the geometric mean of the wavelengths of the highest and lowest frequencies of the frequency adjustable SAW oscillator. Consider for example a lowest frequency of 100 MHz, a highest frequency of 200 MHz and a propagation speed of an acoustic wave of 3000 meters/second. The geometric mean of the two frequencies is (100 MHz*200 MHz)^0.5=141.4 MHz. The wavelength of 141.4 MHz on a 3000 meter/second piezoelectric material is 3000/141.4 MHz=21.2 micrometers. The spacing between adjacent transmitting or receiving fingers  120  or  130  is half of this value or 10.6 micrometers. Other embodiments may employ other spacings. 
       FIG. 7  shows a graphical representation of the phases available from the embodiment presented in  FIG. 5 . The phases of 0, 90, 180 and 270 are available from the buffers  581 ,  582 ,  583 , and  584  respectively when the phase-shifter  585  provides a 90 phase shift of the input signal  151 . By vector addition, the phase 45 is obtained by the addition of phases 0 and 90; 135 is obtained by the addition of phases 90 and 180; 225 is obtained by the addition of phases 180 and 270; and 315 is obtained by the addition of phases 270 and 0. Additional phases are possible in other embodiments by changing the value of the phase-shifter  585  or adding additional phase-shifters and switches. 
       FIGS. 8A ,  8 B and  8 C show a graphical means to determine the phase for each finger given a desired frequency. The figures depict a set of 16 fingers  0 - 15  spaced equally apart. The dashed vertical lines represent the centerline of each finger. The spacing between fingers is scaled to represent the half wavelength discussed earlier. A sine wave superimposed on the fingers represents the desired frequency. The sine wave is scaled to the match the scale used to space the fingers. The left side of the graph is labeled 0, 45, 90, 135 and 180 and represents the phases for the ascending portion of the sine wave. The right side of the graph is labeled 180, 225, 270 and 315 and represents the phases for the descending portion of the sine wave. By finding the intersection of the sine wave with each of the vertical lines representing the fingers, one can determine the needed phase shift for each finger by reading the phases on the left for the ascending portion of the wave and reading the phases on the right for the descending portion of the wave. In  FIG. 8A  the phase shifts for fingers  0  through  15  are: 0, 180, 0, 180, 0, 180, 0, 180, 0, 180, 0, 180, 0, 180, 0, and 180.  FIG. 8A  represents a simple case because the finger spacing is one half the wavelength of the sine wave. 
       FIG. 8B  shows a sine wave of a higher frequency than that of  FIG. 8A . The phase for each finger can be obtained using the same technique as used for  FIG. 8A . In  FIG. 8B  the phase shifts for fingers  0  through  15  are: 0, 240, 160, 5, 270, 170, 25, 305, 180, 55, 335, 190, 90, 355, 200, and 120 degrees. The available phases shown in  FIG. 7  are 0,45, 90,135,180, 225, 270 and 315 degrees. By assigning the closest available phase shift from  FIG. 7  to the desired phase shifts in  FIG. 8B , one obtains 0, 225, 180, 0, 270, 180, 45, 315, 180, 45, 315,180, 90, 0, 215 and 135 degrees. The use of mathematical curve fitting techniques are also possible. In cases where more precision is needed, modifications to the circuit of  FIG. 5  can add additional phases or adjustable delays/phase-shifts to reduce the difference between the desired and available phases. 
       FIG. 8C  shows a sine wave of a lower frequency than that of  FIG. 8A . The phase for each finger can be obtained using the same technique as used for  FIG. 8A . In  FIG. 8C  the phase shifts for fingers  0  through  15  are: 0, 120, 205, 355, 90, 190, 335, 55, 180, 305, 25, 170, 270, 5, 155, and 240 degrees. The available phases shown in  FIG. 7  are 0, 45, 90, 135, 180, 225, 270 and 315 degrees. By assigning the closest available phase shift from  FIG. 7  to the desired phase shifts in  FIG. 8C  one obtains 0, 135, 215, 0, 90, 180, 315, 45, 180, 315, 45, 180, 270, 0, 135 and 225 degrees. The use of mathematical curve fitting techniques are also possible. Waveforms representing other frequencies are treated in a manner similar to those shown in  FIGS. 8B and 8C . 
       FIG. 8D  shows a graphical means to determine the phase for each receiving finger given a desired frequency.  FIG. 8D  represents a signal with a delay between the transmitting and receiving fingers such that the signal arrives at the first receiving finger with a phase angle of 160 degrees delayed from the phase of the input signal. This delay/phase shift is determined from the distance between the transmitting and receiving fingers and the propagation velocity of the acoustic wave. In order to rotate the phase of this signal so that it is in phase with the input signal, it is necessary to insert a phase delay corresponding to (360°-160°) or 200°. Selecting from the available phases of  FIG. 7 , the closest matching phase is 180°, corresponding to (360°-180°). The same algorithm is applied to the received signal from all of the fingers. The use of mathematical curve fitting techniques are also possible. Various curve fitting techniques can be used to reduce the mean of the errors between the desired and available phase shifts. Waveforms representing other receive frequencies are treated in a manner similar to those shown in  FIG. 8D . 
       FIG. 9  is a flowchart depicting a method of implementing a frequency adjustable surface acoustic wave oscillator. It is to be understood that while the method depicted by the flowchart of  FIG. 9  describes particular steps and order of execution, other embodiments and order of execution can also be used. The method begins at  905 . Step  910  provides transmitting and receiving fingers adapted to transmit and receive respectively surface acoustic waves on a piezoelectric surface. Step  915  transmits a surface acoustic wave onto the piezoelectric surface by controlling the phase of an input signal to the transmitting fingers. Step  920  receives the surface acoustic wave with the receiving fingers to produce received signals. Step  925  adjusts the phase of each of the received signals. Step  930  sums the phase adjusted received signals. Step  935  amplifies the summed signals to generate the input signal. The continuous nature of this method is indicated by the loop  940 . 
     Steps  915  and  925  adjust the phase of the signals associated with the transmitting and receiving fingers respectively. Some of the several methods to accomplish this phase adjustment were described in the discussion associated with  FIGS. 1 ,  2 ,  3 ,  4 ,  5 , and  7 . For example, the embodiment of  FIG. 5  can be described as a method where the input signal or a received signal is multiplied by a gain factor which is a negative number (inverted), zero (turned off) or positive number (turned on); and a delayed or phase-shifted version of the input signal is multiplied by another negative number, zero or positive number. A simple gain factor is represented by two binary bits. A binary value of 00 turns off both of the switches  541  and  542  of  FIG. 5  resulting in a gain of zero. A binary value of 10 turns on switch  541  resulting in a gain of one by passing a non-inverted value of the input  151 . A binary value of 01 turns on switch  542  resulting in a gain of negative one passing an inverted value of the input  151 . The sum of the two resulting signals is a phase adjusted version of the original signal. Since in this embodiment there are 8 allowable states of switches  541 - 544 , these can be controlled by 3 binary bits and appropriate logic. 
     Although this invention has been described in terms of certain preferred embodiments, other embodiments that are apparent to those of ordinary skill in the art, including embodiments that do not provide all of the features and advantages set forth herein, are also within the scope of this invention. Rather, the scope of the present invention is defined only by reference to the appended claims and equivalents thereof.