Technique for designing acoustic microwave filters using LCR-based resonator models

1. A non-transitory computer-readable medium for designing a narrowband acoustic wave microwave filter to satisfy predetermined frequency response requirements having stored thereon instructions that, when executed by a processing device, cause the processing device to:

receive a set of predetermined frequency response requirements,

generate a modeled filter circuit design having a plurality of circuit elements comprising an acoustic resonant element defined by an electrical circuit model that comprises a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss by:

(a) defining a first resonator characteristic of the acoustic resonant element,

(b) selecting a physical model of the acoustic resonant element comprising one or more physical parameters,

(b) simulating the physical model of the acoustic resonant element to generate a second resonator characteristic and a first frequency response,

(c) comparing the first resonator characteristic to the second resonator characteristic,

(d) iteratively repeating (a) through (d) for each of one or more modified physical parameters until the comparison of the first resonator characteristic and the second resonator characteristic indicates a match,

(e) selecting an electrical circuit model of the acoustic resonant element comprising one or more electrical parameters,

(f) simulating the electrical circuit model to generate a second frequency response,

(g) comparing the first frequency response and the second frequency response, and

(h) iteratively repeating (e) through (h) for each of one or more modified electrical parameters in the electrical circuit model until the comparison of the first frequency response and the second frequency response indicates a match; and

generate a final circuit design for construction into an actual acoustic microwave filter, wherein generating said final circuit design comprises:

generating an optimized filter circuit design comprising a combination of circuit element values according to a gradient optimization;

comparing a frequency response of the optimized filter circuit design to the frequency response requirements;

selecting the optimized filter circuit design for construction into the actual acoustic microwave filter responsive to the comparison of the frequency response of the optimized filter circuit design to the predetermined frequency response requirements; and

generating a design description file comprising instructions to construct the optimized filter circuit design.

2. The medium of claim 1 , wherein the parallel static branch comprises a static capacitance, and the parallel motional branch comprises a motional inductance and a motional capacitance.

3. The medium of claim 1 , wherein the electrical circuit model comprises at least one resistor that models an electrical loss of the acoustic resonant element.

4. The medium of claim 1 , wherein the electrical circuit model comprises the Bragg Band branch.

5. The medium of claim 4 , wherein the Bragg Band branch comprises a series LRC circuit.

6. The medium of claim 1 , wherein the electrical circuit model comprises the parallel bulk mode function.

7. The medium of claim 6 , wherein the bulk mode function is a hyperbolic tangent function.

8. The medium of claim 7 , wherein the hyperbolic tangent function is

Y

=

h

*

(

1

-

1

10

(

freq

w

⁡

(

10

6

-

F

b

)

+

1

)

)

,

where Y is the bulk mode loss in dB; h is a scaling factor used to match the loss of the bulk mode; F b is a frequency in Hz used to match the onset frequency of the bulk mode, w is a scaling factor used to match the steepness of the onset of the bulk mode, and freq is the frequency of the input signal.

9. The medium of claim 1 , wherein the frequency response requirements comprise one or more of a frequency dependent return loss, insertion loss, rejection, and linearity.

10. The medium of claim 1 , wherein the acoustic resonant element is one of a surface acoustic wave (SAW) resonator, a bulk acoustic wave (BAW) resonator, a film bulk acoustic resonator (FBAR), and a microelectromechanical system (MEMS) resonator.

11. The medium of claim 1 , wherein the frequency response requirements comprise a pass band.

12. The medium of claim 11 , wherein the passband is in the 500-3500 MHz range.

13. The medium of claim 11 , wherein the passband is in the 300 MHz to 10.0 GHz range.

14. The medium of claim 11 , wherein the passband is in the 300 MHz to 300 GHz range.

15. The medium of claim 1 , wherein the modeled filter circuit design has an Nth order ladder topology.

16. The medium of claim 1 , wherein the physical model of the acoustic resonant element is selected using a Finite Element Model (FEM).

17. The medium of claim 1 , wherein selecting the physical model of the acoustic resonant element comprises selecting a physical parameter consisting of at least one of a material, one or more of a number of finger pairs, aperture size, mark-to-pitch ratio, and transducer metal thickness.

18. The medium of claim 1 , wherein each of the first and second resonator characteristics comprises one or both of a resonant frequency and a static capacitance.

19. The medium of claim 18 , wherein optimizing the modeled filter circuit design comprises optimizing the one or both of a resonant frequency and a static capacitance according to a gradient optimization.

20. A non-transitory computer-readable medium for designing a narrowband acoustic wave microwave filter to satisfy predetermined frequency response requirements having stored thereon instructions that, when executed by a processing device, cause the processing device to:

receive a set of predetermined frequency response requirements,

generate a modeled filter circuit design having a plurality of circuit elements comprising an acoustic resonant element defined by an electrical circuit model that comprises a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss by:

(a) defining a first resonator characteristic of the acoustic resonant element,

(b) selecting a physical model of the acoustic resonant element comprising one or more physical parameters,

(b) simulating the physical model of the acoustic resonant element to generate a second resonator characteristic and a first frequency response,

(c) comparing the first resonator characteristic to the second resonator characteristic,

(d) iteratively repeating (a) through (d) for each of one or more modified physical parameters until the comparison of the first resonator characteristic and the second resonator characteristic indicates a match,

(e) selecting an electrical circuit model of the acoustic resonant element comprising one or more electrical parameters,

(f) simulating the electrical circuit model to generate a second frequency response,

(g) comparing the first frequency response and the second frequency response, and

(h) iteratively repeating (e) through (h) for each of one or more modified electrical parameters in the electrical circuit model until the comparison of the first frequency response and the second frequency response indicates a match; and

generate a final circuit design for construction into an actual acoustic microwave filter, wherein generating said final circuit design comprises:

generating an optimized filter circuit design comprising a combination of circuit element values according to a gradient optimization;

comparing a frequency response of the optimized filter circuit design to the frequency response requirements by:

simulating the electrical circuit model of the acoustic resonant element of the optimized filter circuit design to generate a third set of resonator characteristics,

simulating the physical model of the acoustic resonant element to generate a fourth set of resonator characteristics,

comparing the third set of resonator characteristics to the fourth set of resonator characteristics,

modifying a physical parameter of the physical model of the acoustic resonator based on the comparison,

simulating the physical model of the acoustic resonant element with the modified physical parameter to generate another frequency response,

replacing the electrical circuit model of the acoustic resonant element in the optimized filter circuit design with the other frequency response to create a modified optimized filter circuit design,

simulating the modified optimized filter circuit design to create an optimized frequency response;

selecting the optimized filter circuit design for construction into the actual acoustic microwave filter responsive to a comparison of the optimized frequency response matching the predetermined frequency response requirement; and

generating a design description file comprising instructions to construct the optimized filter circuit design.

21. The medium of claim 20 , wherein each of the third and fourth sets of resonator characteristics comprises one or both of a resonant frequency and a static capacitance.

22. A non-transitory computer-readable medium for designing a narrowband acoustic wave microwave filter to satisfy predetermined frequency response requirements having stored thereon instructions that, when executed by a processing device, cause the processing device to:

receive a set of predetermined frequency response requirements,

generate a modeled filter circuit design having a plurality of circuit elements comprising an acoustic resonant element defined by an electrical circuit model that comprises a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss via an iterative comparison and modification of physical parameters of the acoustic resonant element; and

generate a final circuit design for construction into an actual acoustic microwave filter, wherein generating said final circuit design comprises:

generating an optimized filter circuit design comprising a combination of circuit element values according to a gradient optimization;

comparing a frequency response of the optimized filter circuit design to the frequency response requirements by:

simulating the electrical circuit model of the acoustic resonant element of the optimized filter circuit design to generate a third set of resonator characteristics,

simulating the physical model of the acoustic resonant element to generate a fourth set of resonator characteristics,

comparing the third set of resonator characteristics to the fourth set of resonator characteristics,

modifying a physical parameter of the physical model of the acoustic resonator based on the comparison,

simulating the physical model of the acoustic resonant element with the modified physical parameter to generate another frequency response,

replacing the electrical circuit model of the acoustic resonant element in the optimized filter circuit design with the other frequency response to create a modified optimized filter circuit design,

simulating the modified optimized filter circuit design to create an optimized frequency response;

selecting the optimized filter circuit design for construction into the actual acoustic microwave filter responsive to a comparison of the optimized frequency response matching the predetermined frequency response requirement; and

generating a design description file comprising instructions to construct the optimized filter circuit design.