Simulating effects of temperature on acoustic microwave filters

Abstract

A method of designing an acoustic microwave filter comprises generating a proposed filter circuit design having an acoustic resonant element with a defined admittance value, introducing a lumped capacitive element in parallel and a lumped inductive element in series with the resonant element, selecting a first capacitance value for the capacitive element and a first inductance value for the inductive element, thereby creating a first temperature modeled filter circuit design, simulating the first temperature modeled filter circuit design at a first operating temperature, thereby generating a first frequency response, selecting a second capacitance value for the capacitive element and a second inductance value for the inductive element, thereby creating a second temperature modeled filter circuit design, simulating the second temperature modeled filter circuit design at a second operating temperature, thereby generating a second frequency response, and comparing the first and second frequency responses to the frequency response requirements.

Claims

1. A method of creating an acoustic microwave filter in accordance with frequency response requirements over a temperature range, comprising: generating a temperature modeled filter circuit design that serves as an input to an acoustic filter manufacturing process, wherein generating said filter circuit comprises: generating an initial filter circuit design, comprising a plurality of acoustic resonator elements, based on the frequency response requirements; introducing a lumped inductive element in series with and a lumped capacitance element in parallel with each acoustic resonator element of the initial filter circuit design, wherein each lumped inductive element shifts a resonant frequency of the acoustic resonator element to which it is introduced and each lumped capacitance element shifts an anti-resonant frequency of the acoustic resonator element to which it is introduced; varying a capacitance value of each lumped capacitance element and an inductance value of each lumped inductive element based on a plurality of operating temperatures until the frequency response of the initial filter circuit design matches a particular frequency response requirement at a particular operating temperature.

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

3. The method of claim 1, wherein each 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.

4. The method of claim 1, wherein the frequency response requirements comprise a pass band.

5. The method of claim 4, wherein the passband is in the 500-3500 MHz range.

6. The method of claim 4, wherein the passband is in the 300 MHz to 10.0 GHz range.

7. The method of claim 4, wherein the passband is in the 300 MHz to 300 GHz range.

8. The method of claim 1, wherein the frequency response requirements comprise a passband and a stopband.

9. The method of claim 1, further comprising modeling each acoustic resonant element as a Butterworth-Van Dyke (BVD) model.

10. The method of claim 1, further comprising modeling each acoustic resonant element with a Coupling of Modes (COM) model.

11. The method of claim 1, further comprising modeling each acoustic resonant element with a Finite Element Model (FEM).

12. The method of claim 1, wherein the initial filter circuit design has an Nth order ladder topology.

13. The method of claim 1, wherein for purposes of varying the capacitance and inductance value based on a plurality of operating temperatures, the capacitance value and the inductance value are selected as a function of the product of respectively at least one scaling factor and the difference between the operating temperature and a baseline temperature.

14. The method of claim 13, further comprising: generating a reference filter circuit design having a plurality of circuit elements comprising a reference acoustic resonant element; constructing a reference acoustic microwave filter from the reference filter circuit design, the reference resonant element being composed of a first material, and the acoustic resonant element of the initial filter circuit design being composed of a second material the same as the first material; measuring a reference frequency response of the reference acoustic microwave filter at a reference operating temperature; and computing the at least one scaling factor based on the reference frequency response.

15. The method of claim 14, further comprising: introducing at least one lumped reference circuit element in parallel or in series with the reference resonant element; selecting at least one reference value respectively for the at least one lumped reference circuit element, thereby generating a temperature modeled reference filter circuit design; and iteratively simulating the temperature modeled reference filter circuit design at the reference operating temperature while changing the at least one reference value until a frequency response of the simulated reference filter circuit design matches the measured frequency response of the temperature modeled reference acoustic microwave filter at the reference operating temperature, thereby arriving at at least one final reference value.

16. The method of claim 15, wherein the at least one scaling factor is a function of the at least one final reference value divided by the difference between the reference operating temperature and a baseline operating temperature.

17. The method of claim 1, further comprising optimizing the initial filter circuit design, wherein the lumped capacitive element and the lumped inductive element are introduced into the proposed optimized filter circuit design.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The drawings illustrate the design and utility of preferred embodiments of the present invention, in which similar elements are referred to by common reference numerals. In order to better appreciate how the above-recited and other advantages and objects of the present inventions are obtained, a more particular description of the present inventions briefly described above will be rendered by reference to specific embodiments thereof, which are illustrated in the accompanying drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:

(2) FIG. 1 is a frequency response plot comparing the pass band of an acoustic filter circuit design simulated at different operating temperatures;

(3) FIG. 2 is a frequency response plot comparing the pass band of an acoustic filter circuit design simulated at different operating temperatures to the pass band of an actual acoustic filter measured at the same operating temperatures;

(4) FIG. 3 is a block diagram of a wireless telecommunications system;

(5) FIG. 4 is a flow diagram of a technique used to design a microwave acoustic filter for use in the wireless telecommunications system of FIG. 3;

(6) FIG. 5 is a schematic diagram of a conventional microwave acoustic filter arranged in an Nth order ladder topology;

(7) FIG. 6 is a schematic diagram illustrating the transformation of an acoustic resonator of the acoustic filter of FIG. 5 into an equivalent modified Butterworth-Van Dyke (MBVD) model;

(8) FIG. 7 is a schematic diagram illustrating the MBVD equivalent circuit of the conventional acoustic filter of FIG. 5;

(9) FIG. 8 is a schematic diagram illustrating an acoustic resonator having temperature compensating lumped circuit elements;

(10) FIG. 9 is a schematic diagram illustrating the transformation of the temperature modeled acoustic resonator of FIG. 8 into an equivalent modified Butterworth-Van Dyke (MBVD) model;

(11) FIG. 10 is a schematic diagram illustrating a temperature modeled acoustic filter circuit design using the acoustic resonator of FIG. 8;

(12) FIG. 11 is a flow diagram illustrating a technique for computing scaling factors for the temperature modeled lumped circuit elements;

(13) FIG. 12 is a frequency response plot comparing the pass band of an acoustic filter circuit design designed in accordance with the technique illustrated in FIG. 4 to the pass band of an actual acoustic filter constructed from the acoustic filter circuit design; and

(14) FIG. 13 is a block diagram of a computerized filter design system that can implement the computerized steps of the filter design technique of FIG. 4.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(15) The present disclosure describes a technique for designing acoustic wave (AW) microwave filters (such as surface acoustic wave (SAW), bulk acoustic wave (BAW), film bulk acoustic resonator (FBAR), microelectromechanical system (MEMS) filters)). This technique can be applied to AW microwave filters in the 300 MHz to 300 GHz frequency range, particularly in the 300 MHz to 10.0 GHz frequency range, and even more particularly in the 500 MHz to 3.5 GHz frequency range. Such AW microwave filters may be either fixed frequency and/or tunable filters (tunable in frequency and/or bandwidth and/or input impedance and/or output impedance), and may be used for single band or multiple band bandpass filtering and/or bandstop. Such AW microwave filters are advantageous in applications that have demanding electrical and/or environmental performance requirements and/or severe cost/size constraints, such as those found in the radio frequency (RF) frontends of mobile communications devices, including cellphones, smartphones, laptop computers, tablet computers, etc. or the RF front ends of fixed communications devices, including M2M devices, wireless base stations, satellite communications systems, etc.

(16) Example AW microwave filters described herein exhibit a frequency response with a single passband, which is particularly useful in telecommunication system duplexers. For example, with reference to FIG. 3, a telecommunications system 10 for use in a mobile communications device may include a transceiver 12 capable of transmitting and receiving wireless signals, and a controller/processor 14 capable of controlling the functions of the transceiver 12. The transceiver 12 generally comprises a broadband antenna 16, a duplexer 18 having a transmit filter 24 and a receive filter 26, a transmitter 20 coupled to the antenna 16 via the transmit filter 24 of the duplexer 18, and a receiver 22 coupled to the antenna 16 via the receive filter 26 of the duplexer 18.

(17) The transmitter 20 includes an upconverter 28 configured for converting a baseband signal provided by the controller/processor 14 to a radio frequency (RF) signal, a variable gain amplifier (VGA) 30 configured for amplifying the RF signal, a bandpass filter 32 configured for outputting the RF signal at an operating frequency selected by the controller/processor 14, and a power amplifier 34 configured for amplifying the filtered RF signal, which is then provided to the antenna 16 via the transmit filter 24 of the duplexer 18.

(18) The receiver 22 includes a notch or stopband filter 36 configured for rejecting transmit signal interference from the RF signal input from the antenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38 configured for amplifying the RF signal from the stop band filter 36 with a relatively low noise, a bandpass filter 40 configured for outputting the amplified RF signal at a frequency selected by the controller/processor 14, and a downconverter 42 configured for downconverting the RF signal to a baseband signal that is provided to the controller/processor 14. Alternatively, the function of rejecting transmit signal interference performed by the stop-band filter 36 can instead be performed by the duplexer 18. Or, the power amplifier 34 of the transmitter 20 can be designed to reduce the transmit signal interference.

(19) It should be appreciated that the block diagram illustrated in FIG. 3 is functional in nature, and that several functions can be performed by one electronic component or one function can be performed by several electronic components. For example, the functions performed by the up converter 28, VGA 30, bandpass filter 40, downconverter 42, and controller/processor 14 are oftentimes performed by a single transceiver chip. The function of the bandpass filter 32 can be performed by the power amplifier 34 and the transmit filter 24 of the duplexer 18.

(20) The exemplary technique described herein is used to design acoustic microwave filters for the front-end of the telecommunications system 10, and in particular the transmit filter 24 of the duplexer 18, although the same technique can be used to design acoustic microwave filters for the receive filter 26 of the duplexer 18 and for other RF filters.

(21) Referring now to FIG. 4, one exemplary technique 50 for designing an AW microwave filter will be described. First, the filter requirements, which comprise the frequency response requirements (including passband, return loss, insertion loss, rejection, linearity, noise figure, input and output impedances, etc.), as well as size and cost requirements, and environmental requirements, such as operating temperature range, vibration, failure rate, etc., are established by the application of the filter (step 52).

(22) Next, the structural types of circuit elements to be used in the AW filter are selected; for example, the structural type of resonator (SAW, BAW, FBAR, MEMS, etc.) and the types of inductor, capacitor, and switch, along with the materials to be used to fabricate these circuit elements, including the packaging and assembly techniques for fabricating the filter, are selected (step 54). In the particular example described herein, the selection of circuit element types are SAW resonators and capacitors constructed on a substrate composed of 42-degree XY-cut LiTaO3.

(23) Then, an initial filter circuit design is generated based on the frequency response requirements using a suitable design technique (step 56); for instance, using an image design or network synthesis design, such as those described in U.S. Pat. Nos. 8,701,065 and 9,038,005, which are expressly incorporated herein by reference. In the illustrated embodiment, the proposed filter circuit design has an Nth order ladder topology, such as those described in U.S. Pat. Nos. 8,751,993 and 8,701,065 and U.S. patent application Ser. No. 14/941,451, entitled Acoustic Wave Filter with Enhanced Rejection, which are all expressly incorporated herein by reference; although other filter topologies, such as in-line non-resonant-node, or in-line, or in-line with cross couplings, or in-line non-resonant node with cross couplings, etc., may be selected.

(24) Referring now to FIG. 5, one embodiment of a filter circuit design 100 will be described. The filter circuit design 100 is arranged in an Nth-order ladder topology (i.e., in this case, N=10 meaning the number of resonators equals 10). The filter circuit design 100 comprises a voltage source V, a source resistance S, a load resistance L, five series (or in-line) acoustic resonators Z.sub.S1-Z.sub.S5, and five parallel (or in-shunt) acoustic resonators Z.sub.P1-Z.sub.P5.

(25) Each of the acoustic resonators Z may be described by a modified Butterworth-Van Dyke (MBVD) model 110 illustrated in FIG. 6, thereby resulting in the equivalent filter circuit design illustrated in FIG. 7. MBVD models 110 may also describe SAW resonators, which may be fabricated by disposing interdigital transducers (IDTs) on a piezoelectric substrate, such as crystalline Quartz, Lithium Niobate (LiNbO.sub.3), Lithium Tantalate (LiTaO.sub.3) crystals or BAW (including FBAR) resonators or MEMS resonators. Each MBVD model 110 includes a motional capacitance C.sub.m, a static capacitance C.sub.0, a motional inductance L.sub.m, and a resistance R. The motional capacitance C.sub.m and motional inductance L.sub.m may result from the interactions of electrical and acoustical behavior, and thus, may be referred to as the motional arm of the MBVD model. The static capacitance C.sub.0 may result from the capacitance of the structure, and thus, may be referred to as the static (non-motional) capacitance of the MBVD model. The resistance R may result from the electrical resistance of the acoustic resonator. Alternatively, rather than using an MBVD model, the acoustic resonator may be an arbitrary one-port impedance produced by other types of suitable models, such as a Coupling-of-Modes (COM) model or Finite Element Model (FEM).

(26) The parameters of the MBVD model 110 are related by the following equations:

(27) $\begin{array}{cc}{?}_R=\frac{1}{\sqrt{L_m{C}_m}};& \left[1\right]\\ \frac{{?}_A}{{?}_R}=\sqrt{1+\frac{1}{?}},& \left[2\right]\end{array}$
where ?.sub.R and ?.sub.A may be the respective resonance and anti-resonance frequencies for any given acoustic resonator, and gamma ? may depend on a material's property, which may be further defined by:

(28) $\begin{array}{cc}\frac{C_0}{C_m}=?.& \left[3\right]\end{array}$
Typical ? values may range from about 12 to about 18 for 42-degree X Y cut LiTaO.sub.3. The frequency separation of an acoustic resonator means the difference between its resonant frequency and its anti-resonant frequency. The percentage separation of an acoustic wave resonator is the percentage frequency separation between its resonant frequency and anti-resonant frequency, and can be computed, as follows:

(29) $\begin{array}{cc}\mathrm{percentage}\mathrm{separation}=\sqrt{1+\left(1/?\right)}-1& \left[4\right]\end{array}$
where ? is the ratio of the static to the motional capacitance of the resonator (equation [3]), as determined by the material properties of the piezoelectric material and modified by the geometry of the device.

(30) It can be appreciated from equation [1] that the resonant frequency of each of the acoustic resonators will depend on the motional arm of the BVD model 110, whereas the filter characteristics (e.g., bandwidth) will be strongly influenced by ? in equation [2]. The Quality factor (Q) for an acoustic resonator 110 may be an important figure of merit in acoustic filter design, relating to the loss of the element within the filter. Q of a circuit element represents the ratio of the energy stored per cycle to the energy dissipated per cycle. The Q factor models the real loss in each acoustic resonator, and generally more than one Q factor may be required to describe the loss in an acoustic resonator. Q factors may be defined as follows for the filter examples. The motional capacitance C.sub.m may have an associated Q defined as Q.sub.cm=10.sup.8; the static capacitance C.sub.0 may have an associated Q defined as Q.sub.c0=200; and motional inductance L.sub.m may have an associated Q defined as Q.sub.Lm=1000. (Here for simplicity the loss in the motional resonance is lumped into the motional inductance and the motional capacitance is considered to be essentially loss-less.) Circuit designers may typically characterize SAW resonators by resonant frequency ?.sub.R, static capacitance C.sub.0, gamma ?, and Quality factor QL.sub.m. For commercial applications, QL.sub.m may be about 1000 for SAW resonators, and about 3000 for BAW resonators.

(31) Referring back to FIG. 4, the filter circuit design 100 is next optimized via a suitable computer optimization technique to search for the combination of circuit element values that best matches the desired filter response, thereby creating a proposed filter circuit design having defined values for all of the circuit elements, including admittance values for the acoustic resonators Z (step 58). Design tools, including Agilent Advanced Design System (ADS), among others, may use numerical optimization methods, such as Monte Carlo, gradient, etc., to improve the proposed filter circuit design. In one embodiment, one or more circuit elements in the proposed filter circuit design can be removed during the optimization process, such as disclosed in U.S. Pat. No. 8,751,993, which has been expressly incorporated herein by reference.

(32) The effects of temperature variations on the proposed filter circuit design can be simulated by adding two discrete components to each acoustic resonator Z in the filter: a series inductor to shift the resonant frequency of the respective acoustic resonator Z, and a parallel capacitor to shift the anti-resonant frequency of the respective acoustic resonator Z. In particular, a lumped capacitive element C.sub.T is introduced in parallel and a lumped inductive element L.sub.T is introduced in series with each acoustic resonator Z of the proposed filter circuit design (FIG. 8) to create a temperature modeled filter circuit design 200, as illustrated in FIG. 10 (step 60). As illustrated in FIG. 9, each of the acoustic resonators Z of the temperature modeled filter design 200 can be replaced with the MBVD model 110 illustrated in FIG. 6.

(33) Next, a selected number of temperature modeled circuit designs corresponding to different operating temperatures (e.g., three operating temperatures of 0? C., 20? C., and 100? C.) are created and simulated by varying the capacitance values for the capacitive elements C.sub.T and inductance values for the inductive elements L.sub.T for each respective operating temperature to be simulated. The capacitance values and inductances values for each operating temperature can be computed as a function of that operating temperature. In one embodiment, the capacitance value for each capacitive element C.sub.T and the inductance value for each inductive element L.sub.T are computed in accordance with the following equations:
C.sub.Tn=kc.Math.An.Math.(T.sub.op?T.sub.base),[6]
where C.sub.Tn is the capacitance value of the nth acoustic resonator in the temperature modeled filter circuit design, k.sub.C is a scaling constant for the capacitive elements, A.sub.n is the area of the nth acoustic resonator, T.sub.op is the operating temperature, and T.sub.base is a baseline temperature at which it is assumed that C.sub.Tn equals zero (e.g., room temperature); and
L.sub.Tn=K.sub.L(T.sub.op?T.sub.base),[7]
where L.sub.Tn is the inductance value of the nth acoustic resonator in the temperature modeled filter circuit design, k.sub.L is a scaling constant for the inductive elements, T.sub.op is the operating temperature, and T.sub.base is a baseline temperature at which it is assumed that L.sub.Tn equals zero (e.g., room temperature).

(34) To this end, capacitance values for the capacitive elements C.sub.T and inductance values for the respective inductive elements L.sub.T are selected, thereby creating a temperature modeled filter circuit design that shifts the defined admittance values of the respective acoustic resonators Z to different admittance values (step 62). As a general rule, the inductance values for all of the inductive elements L.sub.T will be the same, whereas the capacitance values for all of the capacitive elements C.sub.T will be the same only if the areas of the acoustic resonators Z are the same. The temperature modeled filter circuit design is then simulated at a defined operating temperature, thereby generating a frequency response (step 64). The first and second capacitance values may be, e.g., in the range of ?40 pF-40 pF, and more specifically in the range of ?4 pF-4 pF, and the first and second inductance values may be, e.g., in the range of ?10 nH-10 nH, and more specifically in the range of ?1 nH-1 nH.

(35) Additional temperature modeled filter circuit designs corresponding to different operating temperatures can be created by selecting different capacitance values and inductance values. In particular, if not all the selected number of operating temperatures have been simulated (i.e., if not all of the temperature modeled filter circuit designs have been simulated) (step 66), different capacitance values for the capacitive elements C.sub.T and inductance values for the respective inductive elements L.sub.T are selected, thereby creating another temperature modeled filter circuit design that shifts the defined admittance values of the respective acoustic resonators Z to different admittance values (step 62), and then the other temperature modeled filter circuit design is simulated at another defined operating temperature, thereby generating a frequency response (step 64). This process is repeated until all of the temperature modeled filter circuit designs have been simulated. If the simulated frequency responses of the temperature modeled filter circuit designs do not satisfy the frequency response requirements at the defined operating temperatures (step 68), a different initial filter circuit design may be generated and optimized to create another proposed filter circuit design (steps 56 and 58) and then, temperature modeled filter circuit designs can be generated from the other proposed filter circuit design and simulated (steps 60-66). Once the simulated frequency responses of the temperature modeled filter circuit designs satisfy the frequency response requirements at the defined operating temperatures (step 68), an actual acoustic filter is constructed based on the most recent proposed filter circuit design (step 70). Preferably, the circuit element values of the actual acoustic filter will match the corresponding circuit element values in the most recent proposed filter circuit design.

(36) The scaling factors k.sub.C and k.sub.L of equations [6] and [7] can be determined by measuring the frequency responses of an actual acoustic filter and fitting data of simulated temperature-compensated filter circuits to the frequency responses of the actual acoustic filter. In particular, with reference to FIG. 11, one technique 80 for determining the scaling factors k.sub.C and k.sub.L will now be described. First, a reference filter circuit design having a plurality circuit elements comprising at least one acoustic resonator is generated (step 82), and then, an actual reference acoustic microwave filter is constructed from the reference filter circuit design (step 84). The acoustic resonator(s) of this reference filter are composed of the same material as the acoustic resonators of the proposed filter circuit design 100, so that the scaling factors determined from the reference filter can be accurately used to generate the temperature modeled filter designs 200 from the proposed filter circuit design 100. Next, a reference frequency response of the actual reference filter is measured at a reference (e.g., room temperature) (step 86).

(37) Each of the first and second scaling factors k.sub.C and k.sub.L is then computed based on the first reference frequency response. In particular, a lumped reference capacitive element is added in parallel and a lumped reference inductive element is added in series with each of the reference acoustic resonator(s) in a similar manner as the capacitive element(s) and inductive elements(s) are added to the proposed filter circuit design 100 in FIG. 5, thereby generating a reference temperature modeled filter circuit design (step 88).

(38) Then, the capacitance value of the reference capacitive element(s) and the reference inductance value of the reference inductive elements(s) that match the simulated frequency response of the temperature modeled reference filter circuit design at the reference operating temperature to the measured frequency response of the actual reference acoustic filter is determined (step 90). For example, the temperature modeled reference filter circuit design can be iteratively simulated at the reference operating temperature while changing the capacitance value of the reference capacitive element(s) and the reference inductance value of the reference inductive element(s) until the frequency response of the simulated temperature modeled reference filter circuit design matches the measured frequency response of the reference acoustic microwave filter at the reference operating temperature, thereby arriving at a first reference capacitance value C.sub.REF1 and a first reference inductance value L.sub.REF1.

(39) The first scaling factor k.sub.C is then computed in accordance with the following equation (step 92):

(40) $\begin{array}{cc}{k}_C=\frac{C_{\mathrm{REF}}}{A.Math.\left(T_{\mathrm{REF}}-T_{\mathrm{base}}\right)},& \left[8\right]\end{array}$
where k.sub.C is the first scaling factor, C.sub.REF is the reference capacitance value, A is the area of the reference acoustic resonator, T.sub.REF is the reference operating temperature, and T.sub.base is the baseline operating temperature (e.g., room temperature); and the second scaling factor k.sub.L is then computed in accordance with the following equation (step 94):

(41) $\begin{array}{cc}{k}_L=\frac{L_{\mathrm{REF}}}{\left(T_{\mathrm{REF}}-T_{\mathrm{base}}\right)},& \left[9\right]\end{array}$
where k.sub.L is the second scaling factor, L.sub.REF is the reference inductance value, T.sub.REF is the reference operating temperature, and T.sub.base is the baseline operating temperature.

(42) It should be appreciated that additional scaling factors may be computed for different operating temperature ranges. For example, a first set of scaling factors k.sub.C1 and k.sub.L1 can be associated with the temperature range 0? C.-50? C., and a second set of scaling factors k.sub.C2 and k.sub.L2 can be associated with the temperature range 50? C.-100? C. The first set of scaling factors k.sub.C1 and k.sub.L1 can be determined by measuring the frequency response of the reference filter in accordance with equations [8] and [9] using, e.g., 25? C. as the reference operating temperature; and the second set of scaling factors k.sub.C2 and k.sub.L2 can be determined by measuring frequency responses of the reference filter at two reference operating temperatures (e.g., 50? C. and 100? C.), iteratively simulating the temperature modeled reference filter circuit design at the first reference temperature while changing the capacitance value of the reference capacitive element(s) and the reference inductance value of the reference inductive element(s) until the frequency response of the simulated temperature modeled reference filter circuit design matches the measured frequency response of the reference acoustic microwave filter at the first reference operating temperature, thereby arriving at a first reference capacitance value C.sub.REF1 and a first reference inductance value L.sub.REF1, and iteratively simulating the temperature modeled reference filter circuit design at the second reference temperature while changing the capacitance value of the reference capacitive element(s) and the reference inductance value of the reference inductive element(s) until the frequency response of the simulated temperature modeled reference filter circuit design matches the measured frequency response of the reference acoustic microwave filter at the second reference temperature, thereby arriving at a second reference capacitance value C.sub.REF2 and a second reference inductance value L.sub.REF1.

(43) The scaling factor k.sub.C2 is then computed in accordance with the following equation:

(44) $\begin{array}{cc}{k}_C=\frac{C_{\mathrm{REF}2-}{C}_{\mathrm{REF}1}}{A.Math.\left(T_{\mathrm{REF}2}-T_{\mathrm{REF}1}\right)},& \left[10\right]\end{array}$
where k.sub.C is the scaling factor, C.sub.REF2 is the second reference capacitance value, C.sub.REF1 is the first reference capacitance value, A is the area of the reference acoustic resonator, T.sub.REF2 is the second reference operating temperature (e.g., 100? C.), and T.sub.REF1 is the first reference operating temperature (e.g., 50? C.).

(45) The scaling factor k.sub.L2 is then computed in accordance with the following equation:

(46) $\begin{array}{cc}{k}_L=\frac{L_{\mathrm{REF}2-}{L}_{\mathrm{REF}1}}{\left(T_{\mathrm{REF}2}-T_{\mathrm{REF}1}\right)},& \left[11\right]\end{array}$
where k.sub.L is the scaling factor, L.sub.REF2 is the second reference inductance value, L.sub.REF1 is the first reference inductance value, T.sub.REF2 is the second reference operating temperature (e.g., 100? C.), and T.sub.REF1 is the first reference operating temperature (e.g., 50? C.).

(47) The acoustic microwave filter design illustrated in FIG. 5 was optimized in accordance with the technique illustrated in FIG. 4, and then an actual acoustic microwave filter was constructed from the optimized acoustic microwave filter design. Referring to FIG. 12, the frequency responses of the acoustic microwave filter design simulated at ?20? C. and 100? C. (dashed lines) can be compared to the frequency responses of the corresponding actual acoustic microwave filter measured at ?20? C. and 100? C. (solid lines). It can be readily seen that the left and right sides of the passbands of the simulated frequency responses at ?20? C. and 100? C. respectively match the left and right sides of the passbands of the actual frequency responses at ?20? C. and 100? C.

(48) Referring first to FIG. 13, a computerized filter design system 300 may be used to design an acoustic filter using the design technique 50. The computerized filter design system 300 generally comprises a user interface 302 configured for receiving information and data from a user (e.g., parameter values and filter specifications at steps 52 and 54) and outputting an optimized filter circuit design to the user; a memory 304 configured for storing filter design software 308 (which may take the form of software instructions, which may include, but are not limited to, routines, programs, objects, components, data structures, procedures, modules, functions, and the like that perform particular functions or implement particular abstract data types), as well as the information and data input from the user via the user interface 302; and a processor 306 configured for executing the filter design software. The filter design software program 308 is divided into sub-programs, in particular, a conventional filter design synthesizer 310 (which can be used to generate the initial filter circuit design at step 56), a conventional filter optimizer 312 (which can be used to optimize and simulate the filter design at steps 58 and 64), and a filter design engine 314 that controls the design synthesizer 310 and filter optimizer 312 and adds and determines the values of the lumped capacitive and inductive elements at steps 60 and 62 in order to generate the optimized final circuit design.

(49) Although particular embodiments of the present invention have been shown and described, it should be understood that the above discussion is not intended to limit the present invention to these embodiments. It will be obvious to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the present invention. For example, the present invention has applications well beyond filters with a single input and output, and particular embodiments of the present invention may be used to form duplexers, multiplexers, channelizers, reactive switches, etc., where low-loss selective circuits may be used. Thus, the present invention is intended to cover alternatives, modifications, and equivalents that may fall within the spirit and scope of the present invention as defined by the claims.