Surface acoustic wave filters with substrate thickness selected from plural non-contiguous thickness ranges
Surface acoustic wave (SAW) filters and methods of fabricating SAW filters are disclosed. A filter includes a piezoelectric wafer having a thickness within one of a plurality of noncontiguous thickness ranges that define piezoelectric wafers upon which filter circuits meeting predetermined requirements can be fabricated according to a predetermined design using a predetermined fabrication process, and a filter circuit fabricated on the piezoelectric substrate according to the predetermined design using the predetermined fabrication process.
1. A method of producing a filter device that satisfies a set of performance requirements, comprising:
fabricating one or more filter circuits on a piezoelectric wafer, each filter circuit comprising two or more surface acoustic wave (SAW) resonators;
determining a thickness of the piezoelectric wafer for at least some of the one or more filter circuits;
selecting a filter circuit with the thickness of the piezoelectric wafer within one of a plurality of noncontiguous acceptable thickness ranges, the acceptable thickness ranges separated by unacceptable thickness ranges where the filter circuit cannot satisfy one or more requirements from the set of performance requirements, and
completing the filter using the selected filter circuit.
2. The method of claim 1 , wherein thicknesses not within any of the plurality of noncontiguous acceptable thickness ranges define piezoelectric wafers upon which filter circuits satisfying all of the set of performance requirements can be fabricated.
3. The method of claim 1 , further comprising bonding a backing substrate to the piezoelectric wafer prior to fabricating the one or more filter circuits.
4. The method of claim 1 , further comprising:
prior to selecting the filter circuit, determining the plurality of noncontiguous acceptable thickness ranges by:
creating a model of the filter circuit including admittances of relevant plate modes in parallel with the admittances of the two or more SAW resonators,
analyzing the performance of the model as a function of the piezoelectric wafer thickness, and
identifying piezoelectric wafer thickness ranges where the performance of the model satisfies all of the one or more requirements as the plurality of acceptable thickness ranges.
5. The method of claim 4 , wherein the real and imaginary components, Y re and Y im respectively, of the admittance of each plate mode are given by the equations:
Y re =g 0 *sin 2 z/z 2 , and
Y im =g 0 *(sin 2 z− 2 z )/ z 2 ,
where z=g 1 (f−f n )/f n , f is frequency, f n is the resonant frequency of the plate mode, and g 0 and g 1 are parameters determined by fitting the equations for Y re and Y im to measured admittance data for one or more exploratory SAW resonators.
6. The method of claim 5 , wherein
the resonant frequencies of plate modes associated with a particular SAW resonator of the two or more SAW resonators are given by the equation:
f n =nc/ 2 t,
where f n is the resonant frequency of a plate mode with a mode index n, where n is a positive integer; t is a thickness of the piezoelectric wafer; and c is an effective speed of sound for plate modes associated with the particular SAW resonator.
7. The method of claim 6 , wherein the effective speed of sound for plate modes associated with the particular SAW resonator is given by the equation:
c=af res +b,
where f res is a resonant frequency of the particular SAW resonator and a and b are constants determined by fitting the equation for f n to measured plate mode resonant frequencies for two or more exploratory SAW resonators having different resonant frequencies.
8. The method of claim 1 , wherein the filter is a band-pass filter and the set of performance requirements includes a bandwidth.
9. The method of claim 1 , wherein the set of performance requirements include one or more of a lower frequency, an upper frequency, and a maximum insertion loss for a pass band; a lower frequency, an upper frequency, and a minimum insertion loss for each of one or more stop bands; and a maximum reflection coefficient and/or a maximum voltage standing wave ratio (VSWR) at the input of the filter when driven by a source with a predetermined source impedance.
10. A filter device that satisfies a set of performance requirements, comprising:
a filter circuit comprising two or more surface acoustic wave (SAW) resonators, the filter circuit selected from a plurality of filter circuits fabricated on a piezoelectric wafer, the filter circuit selected to have a piezoelectric wafer thickness within one of a plurality of noncontiguous acceptable thickness ranges, the acceptable thickness ranges separated by unacceptable thickness ranges where the performance of the filter circuit cannot satisfy at least one requirement from the set of performance requirements.
11. The filter of claim 10 , wherein the plurality of noncontiguous acceptable thickness ranges define piezoelectric wafers upon which filter circuits satisfying the set of performance requirements can be fabricated.
12. The filter of claim 10 , further comprising a backing substrate bonded to the piezoelectric wafer prior to fabrication of the one or more filter circuits.
13. The filter of claim 10 , wherein, prior to selection of the filter circuit, the plurality of noncontiguous acceptable thickness ranges are determined by:
creating a model of the filter circuit including admittances of relevant plate modes in parallel with the admittances of the two or more SAW resonators,
analyzing the performance of the model as a function of the piezoelectric wafer thickness, and
identifying piezoelectric wafer thickness ranges where the performance of the model satisfies all of the one or more requirements as the plurality of acceptable thickness ranges.
14. The filter circuit of claim 13 , wherein the real and imaginary components, Y re and Y im respectively, of the admittance of each plate mode are given by the equations:
Y re =g 0 *sin 2 z/z 2 , and
Y im =g 0 *(sin 2 z− 2 z )/ z 2 ,
where z=g 1 (f−f n )/f n , f is frequency, f n is the resonant frequency of the plate mode, and g 0 and g 1 are parameters determined by fitting the equations for Y re and Y im to measured admittance data for one or more exploratory SAW resonators.
15. The filter circuit of claim 14 , wherein
the resonant frequencies of plate modes associated with a particular SAW resonator of the two or more SAW resonators are given by the equation:
f n =nc/ 2 t,
where f n is the resonant frequency of a plate mode with a mode index n, where n is a positive integer; t is a thickness of the piezoelectric wafer; and c is an effective speed of sound for plate modes associated with the particular SAW resonator.
16. The method of claim 15 , wherein the effective speed of sound for plate modes associated with the particular SAW resonator is given by the equation:
c=af res +b,
where f res is a resonant frequency of the particular SAW resonator and a and b are constants determined by fitting the equation for f n to measured plate mode resonant frequencies for two or more exploratory SAW resonators having different resonant frequencies.
17. The filter of claim 10 , wherein the filter is a band-pass filter and the one or more requirements includes a bandwidth.
18. The filter of claim 10 , wherein the one or more requirements include one or more of a lower frequency, an upper frequency, and a maximum insertion loss for a pass band; a lower frequency, an upper frequency, and a minimum insertion loss for each of one or more stop bands; and a maximum reflection coefficient and/or a maximum voltage standing wave ratio (VSWR) at the input of the filter when driven by a source with a predetermined source impedance.