Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/30—Circuit design
  • G06F30/36—Circuit design at the analogue level
  • G06F30/373—Design optimisation
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
  • H03H9/46—Filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
  • H03H9/46—Filters
  • H03H9/462—Microelectro-mechanical filters
  • H03H9/465—Microelectro-mechanical filters in combination with other electronic elements
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/30—Circuit design
  • G06F30/32—Circuit design at the digital level
  • G06F30/327—Logic synthesis; Behaviour synthesis, e.g. mapping logic, HDL to netlist, high-level language to RTL or netlist
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/30—Circuit design
  • G06F30/36—Circuit design at the analogue level
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/30—Circuit design
  • G06F30/36—Circuit design at the analogue level
  • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
  • H03H7/01—Frequency selective two-port networks
  • H03H7/0115—Frequency selective two-port networks comprising only inductors and capacitors
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
  • H03H9/46—Filters
  • H03H9/54—Filters comprising resonators of piezoelectric or electrostrictive material
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
  • H03H9/46—Filters
  • H03H9/54—Filters comprising resonators of piezoelectric or electrostrictive material
  • H03H9/542—Filters comprising resonators of piezoelectric or electrostrictive material including passive elements
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
  • H03H9/46—Filters
  • H03H9/64—Filters using surface acoustic waves
  • H03H9/6423—Means for obtaining a particular transfer characteristic
  • H03H9/6433—Coupled resonator filters
  • H03H9/6483—Ladder SAW filters

Definitions

• the present inventions generally relate to microwave filters, and more particularly, to acoustic wave microwave filters.
• filter circuits utilized circuit elements, including inductors, capacitors, and transformers.
• AW Acoustic Wave
• BAW quartz bulk acoustic wave
• the equivalent circuit of an AW resonator has two resonances closely spaced in frequency called the "resonance” frequency and the "anti-resonance” frequency (see K.S. Van Dyke, "Piezo-Electric Resonator and its Equivalent Network” Proc. IRE, Vol. 16, 1928, pp.742-764).
• the image filter design methods were applied to filter circuits utilizing these quartz resonators, and two AW filter circuit types resulted: “ladder” and “lattice” AW filter designs (see L.
• the desired loss-less filter response is translated into a ratio of complex polynomials in the form of complex frequency dependent circuit response parameters such as scattering parameters, e.g. S21 and S1 1 .
• the S21 scattering parameter may be represented as follows: ( , . . . . . , , ,
• D(s) is the denominator polynomial
• m is the number of transmission zeroes
• n is the number of reflection zeroes
• K is a scale factor.
• the filter circuit element values may then be "synthesized” (calculated) exactly in the loss-less case from the ratio of complex polynomials. Neglecting losses, which are kept small in practice, the response of the "synthesized" circuit matches the desired response function.
• thin film surface acoustic wave (SAW) resonators and thin film BAW resonators were developed and began to be used at microwave frequencies (>500MHz).
• AW impedance element filter (IEF) designs were utilized which is an example of an Espen Kunststoff-type ladder acoustic wave filter design (see O. Ikata, et al., "Development of Low-Loss Bandpass Filters Using Saw Resonators for Portable Telephones", 1992 Ultrasonics Symposium, pp. 1 1 1 -1 15; and Ken-ya Hashimoto, Surface Acoustic Wave Devices in Telecommunications: Modeling and Simulation, Springer (2000), pp. 149-161 ).
• Image designed AW IEF bandpass filters in SAW and BAW implementations are often used for microwave filtering
• the duplexer a specialized kind of filter, is a key component in the front end of mobile devices.
• Modern mobile communications devices transmit and receive at the same time (using Code Division Multiple Access (CDMA), Wide-Band Code Division Multiple Access (WCDMA), or Long Term Evolution (LTE)) and use the same antenna.
• CDMA Code Division Multiple Access
• WCDMA Wide-Band Code Division Multiple Access
• LTE Long Term Evolution
• the duplexer separates the transmit signal, which can be up to 0.5Watt power, from the receive signal, which can be as low as a pico-Watt.
• the transmit and receive signals are modulated on carriers at different frequencies allowing the duplexer to select them; even so the duplexer must provide low insertion loss, high selectively, small circuit area, high power handling, high linearity, and low cost.
• a method of designing an acoustic microwave filter in accordance with frequency response requirements e.g., one or more of a frequency dependent return loss, insertion loss, rejection, and linearity or a passband (e.g., in 500-3500 MHz range) and a stop band
• the method comprises selecting an initial filter circuit structure including a plurality of circuit elements comprising at least one resonant element (e.g., a parallel L-C resonator combination of a capacitor and an inductor) and at least one other reactive circuit element (e.g., a capacitor).
• the initial filter circuit structure can be, e.g., an inline non-resonant-node circuit structure.
• An optional method further comprises selecting the structural type of each of the resonant element(s) from 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.
• SAW surface acoustic wave
• BAW bulk acoustic wave
• FBAR film bulk acoustic resonator
• MEMS microelectromechanical system
• the method further comprises selecting lossless circuit response variables based on the frequency response requirements (e.g., in the form of a ratio between numerator polynomials defining transmission zeroes and denominator polynomials defining reflection zeroes multiplied by a scale factor), and selecting a value for each of the circuit elements based on the selected circuit response variables to create an initial filter circuit design.
• the frequency response requirements e.g., in the form of a ratio between numerator polynomials defining transmission zeroes and denominator polynomials defining reflection zeroes multiplied by a scale factor
• the method further comprises transforming the resonant element(s) and the other reactive circuit element(s) of the initial filter circuit design into at least one acoustic resonator model to create an acoustic filter circuit design.
• the acoustic resonator model is a Butterworth-Van Dyke (BVD) model.
• the other reactive circuit element(s) may comprise an in-shunt admittance inverter in series with the in-shunt parallel L-C -resonator combination, and an in-shunt non-resonant susceptance in parallel with the in-shunt parallel L-C resonator combination, and the in-shunt parallel L-C resonator combination, in-shunt admittance inverter, and in-shunt non-resonant susceptance may be transformed into one of the BVD model(s).
• the in-shunt parallel L-C resonator combination and the in-shunt admittance inverter may be transformed into an in- shunt series L-C resonator combination, and the in-shunt series L-C resonator combination and in-shunt non-resonant susceptance may be transformed into the one BVD model.
• the one BVD model may be an in-shunt BVD model.
• the reactive circuit element may further comprise two in-line admittance inverters coupled to a node between the in-shunt parallel L-C resonator combination and the in-shunt non-resonant susceptance, and the in-shunt BVD model and the two in-line admittance inverters may be transformed into an in-line BVD model and a reactance in series with the in-line BVD model.
• a plurality of resonant elements, a plurality of reactive circuit elements, and a plurality of resonator models are provided.
• the method may further comprise dividing the initial filter circuit design into a plurality of sub-set circuit designs, each of which includes one of the resonant elements and one or more of the plurality of reactive circuit elements, wherein, for each sub-set circuit design, the resonant element and the reactive circuit element(s) are transformed into a respective one of the acoustic resonator models.
• the method further comprises adding parasitic effects to the acoustic filter circuit design to create a pre-optimized filter circuit design, optimizing the pre- optimized filter circuit design to create a final filter circuit design (e.g., by inputting the pre-optimized filter circuit design into a filter optimizer to create the final filter circuit design), and constructing the acoustic microwave filter based on the final filter circuit design.
• An optional method further comprises performing an element removal optimization of the pre-optimized filter circuit design to create the final filter circuit design.
• the method may optionally comprise changing the order in which the plurality of resonant elements in the pre- optimized filter circuit design are disposed along a signal transmission path to create a plurality of filter solutions, computing a performance parameter for each of the filter solutions, comparing the performance parameters to each other, and selecting one of the filter solutions as the pre-optimized circuit design based on the comparison of the computed performance parameters.
• the final circuit design comprises a plurality of acoustic resonators, and the difference between the lowest resonant frequency and the highest resonant frequency of the plurality of acoustic resonators in the final filter circuit design is at least one time, preferably at least two times, and more preferably at least three times, the maximum frequency separation of a single resonator in the plurality of acoustic resonators.
• FIG. 1 is a block diagram of a wireless telecommunications system
• FIG. 2 is a flow diagram illustrating a network synthesis technique used to design an acoustic filter in accordance with one method of the present inventions
• Fig. 3 is a schematic diagram of an in-line non-resonant node filter used as the initial filter circuit structure for the network synthesis technique of Fig. 2;
• Fig. 5 is an equivalent circuit schematic diagram for a Butterworth-Van Dyke (BVD) acoustic wave resonator model
• Fig. 6 is a sub-set circuit design taken from the initial filter circuit structure (design) of Fig. 3 in accordance with the network synthesis technique of Fig. 2, whereby an in-line acoustic resonator is incorporated into the initial filter circuit design of Fig. 3
• Figs. 7-9 are circuit transformations sequentially made to the sub-set circuit design of Fig. 6 in accordance with the network synthesis technique of Fig. 2;
• Fig. 10 is another sub-set circuit design taken from the initial filter circuit structure of Fig. 3 in accordance with the network synthesis technique of Fig. 2;
• Figs. 11 -13 are circuit transformations sequentially made to the sub-set circuit design of Fig. 10 in accordance with the network synthesis technique of Fig. 2, whereby an in-shunt acoustic resonator is incorporated into the initial filter circuit structure of Fig. 3;
• Fig. 14 is a schematic diagram of an acoustic filter circuit design generated from the sub-set acoustic circuit designs of Figs. 9 and 13 in accordance with the network synthesis technique of Fig. 2;
• Fig. 15 is a schematic diagram of a pre-optimized filter circuit design realized from the acoustic filter circuit design of Fig. 14 in accordance with the network synthesis technique of Fig. 2;
• Fig. 16 is a table illustrating the element values of the pre-optimized filter circuit design of Fig. 15;
• Fig. 17 is a S21 frequency response plot of the pre-optimized filter circuit design of Fig. 15;
• Fig. 18 is a schematic diagram of an optimized filter circuit design created by inputting the pre-optimized filter circuit design into a computerized filter optimizer and performing an element removal design technique in accordance with the network synthesis technique of Fig. 2;
• Fig. 19 is a table illustrating the element values of the optimized filter circuit design of Fig. 18;
• Fig. 20 is an S21 frequency response plot of the optimized filter circuit design of Fig. 18;
• Figs. 21 a and 21 b are S1 1 frequency response plots of the optimized filter circuit design of Fig. 18;
• Figs. 22-24 are circuit transformations sequentially made to the sub-set circuit design of Fig. 10 in accordance with the network synthesis technique of Fig. 2, whereby in-shunt acoustic resonators are incorporated into the resonant branches of the initial filter circuit design of Fig. 3;
• Fig. 25 is a schematic diagram of an acoustic filter circuit design generated from the sub-set acoustic circuit design of Fig. 24 in accordance with the network synthesis technique of Fig. 2;
• Fig. 26 is a schematic diagram of another pre-optimized filter circuit design realized from the acoustic filter circuit structure of Fig. 25 in accordance with the network synthesis technique of Fig. 2;
• Fig. 27 is a table illustrating the element values of the pre-optimized filter circuit design of Fig. 26;
• Fig. 28 is a S21 Band 5 frequency response plot of the filter circuit design of Fig. 25 after optimization
• Fig. 29 is a S21 Band 8 frequency response plot of the filter circuit design of Fig. 25 after optimization
• Fig. 30 is a schematic diagram of still another pre-optimized filter circuit design generated in accordance with the network synthesis technique of Fig. 2;
• Fig. 31 is a S21 Band 5 frequency response plot of the filter circuit design of Fig. 30 after optimization.
• Fig. 32 is a S21 Band 8 frequency response plot of the filter circuit design of Fig. 30 after optimization.
• the present disclosure describes a network synthesis technique for designing acoustic wave (AW) microwave filters (such as surface acoustic wave (SAW), bulk acoustic wave (BAW), film bulk acoustic resonator (FBAR),
• AW acoustic wave
• SAW surface acoustic wave
• BAW bulk acoustic wave
• FBAR film bulk acoustic resonator
• MEMS microelectromechanical system filters
• This network synthesis technique yields better performing and/or lower cost AW microwave filters (i.e., at frequencies greater than 500MHz) over previous AW microwave filter design methods.
• 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 frontends of fixed communications devices, including M2M devices, wireless base stations, satellite communications systems, etc.
• RF radio frequency
• Example AW microwave filters described herein exhibit a frequency response with a single passband and a single stopband, which is particularly useful in telecommunication system duplexers where a passband with a closely spaced stopband is required.
• 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.
• 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.
• RF radio frequency
• VGA variable gain amplifier
• 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.
• LNA low noise amplifier
• the function of rejecting transmit signal interference performed by the stop-band filter 36 can instead be performed by the duplexer 18.
• the power amplifier 34 of the transmitter 20 can be designed to reduce the transmit signal interference.
• Fig. 1 the block diagram illustrated in Fig. 1 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.
• 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.
• the exemplary network synthesis 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.
• 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).
• the design targets the following requirements: one passband from 1850 MHz to 1910 MHz with a maximum insertion loss requirement of 2 dB, and three stopbands, a first one from 1930 MHz to 1990 MHz with a minimum rejection of 44 dB, a second one from 2010 MHz to 2025 MHz and a minimum rejection of 20 dB, and a third one from 21 10 MHz to 2155 MHz with a minimum rejection of 45 dB.
• 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).
• the selection of circuit element types are SAW resonators and capacitors constructed on a substrate composed of 42-degree XY-cut LiTa03.
• structure shall refer to the element types and their interconnections without consideration the values of the elements.
• an in-line non-resonant-node initial filter circuit structure 100 generally comprises a signal transmission path 102 having an input 104 (represented by node S) and an output 106 (represented by node L), a plurality of nodes 108 (represented by nodes S, 1 , 2 . . . n) disposed along the signal transmission path 102, a plurality of resonant branches 1 10 respectively coupling the nodes 108 to ground, and a plurality of non-resonant branches 1 12 respectively coupling the nodes 108 to ground in respective parallel to the resonant branches 1 10.
• the initial filter circuit structure 100 further comprises a plurality of in-shunt resonant elements 1 14 (represented by susceptances B R1 , B R2 . . . B Rn ) respectively located in the resonant branches 1 10 and a plurality of in-shunt non-resonant elements 1 16 (represented by admittance inverters J-n , J22 ⁇ ⁇ ⁇ Jnn) in series with the resonant elements 1 14.
• in-shunt resonant elements 1 14 represented by susceptances B R1 , B R2 . . . B Rn
• in-shunt non-resonant elements 1 16 represented by admittance inverters J-n , J22 ⁇ ⁇ ⁇ Jnn
• the initial filter circuit structure 100 further comprises a plurality of in-shunt non-resonant elements 1 18, two of which couple the node S and node L to ground (represented by susceptances B NS and B NL respectively) and four of which are respectively located in the non-resonant branches 1 10 (represented by B N1 , B N2 . . . B Nn ).
• the initial filter circuit structure 100 further comprises a plurality of in-line non-resonant elements 120 (represented by admittance inverters Jsi , J12, J23 ⁇ ⁇ ⁇ Jn-i , n, JnL.) respectively coupling the nodes S, 1 , 2 . . . n, L together.
• the initial filter circuit structure 100 may further comprise a plurality of tuning elements (not shown) for adjusting the frequencies of the resonant elements 1 14 and/or values of the non-resonant elements 120, and an electrical controller (not shown) configured for tuning the initial filter circuit structure 100 to a selected narrow-band within a desired frequency range by varying selected ones of the non- resonant elements 1 16-120.
• the initial filter circuit structure 100 is useful for network synthesis of reconfigurable bandpass filters, provided that the high Q-factor resonant elements 1 14 used to realize the susceptance B R values are well-described by a parallel L-C resonator combination, i.e. tank circuit, as shown in Fig. 4.
• BVD models 122 may also describe SAW resonators, which may be fabricated by disposing interdigital transducers (IDTs) on a piezoelectric substrate, such as crystalline Quartz, Lithium Niobate (LiNb0 3 ), Lithium Tantalate (LiTa0 3 ) crystals or BAW (including FBAR) resonators fabricated in materials such as quartz or Aluminum Nitride, or MEMS resonators.
• IDTs interdigital transducers
• the BVD model 122 includes a motional capacitance C m 124, a static capacitance Co 126, and a motional inductance L m 128.
• the motional capacitance Cm 124 and motional inductance L m 128 may result from the interactions of electrical and acoustical behavior, and thus, may be referred to as the motional arm of the BVD model 122.
• the static capacitance Co 126 may result from electrical behavior of the structure alone (conductors, dielectrics and gaps), and thus, may be referred to as the static (non-motional) capacitance of the BVD model 122.
• COR and COA 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:
• Typical ⁇ values may range from about 12 to about 18 for 42-degree X Y cut LiTa0 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:
• ⁇ is the ratio of the static to the motional capacitance of the resonator (equation [4]), as determined by the material properties of the piezoelectric material and modified by the geometry of the device.
• the resonant frequency co R of an acoustic resonator means the frequency where the magnitude of the impedance reaches a local minimum and the phase of the impedance crosses zero.
• the anti-resonant frequency COA of an acoustic resonator means the frequency where the magnitude of the impedance reaches a local maximum and the phase of the impedance crosses zero.
• the resonant frequency of each of the acoustic resonators will depend on the motional arm of the BVD model 122, whereas the filter characteristics (e.g., bandwidth) will be strongly influenced by ⁇ in equation [2].
• the Quality factor (Q) for an acoustic resonator 122 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.
• Circuit designers may typically characterize SAW resonators by resonant frequency co R , static capacitance C 0 , gamma ⁇ , and Quality factor QL m .
• QL m may be about 1000 for SAW resonators, and about 3000 for BAW resonators.
• the frequency response requirements are then mapped to a normalized design space (step 58).
• the mapping may be performed using a suitable algorithm, such as a square-root/quadratic mapping technique (see George L. Matthaei, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, McGraw-Hill Book Company, pp. 95-97, 438-440 (1964), or a logarithmic/exponential mapping technique more suitable to acoustic wave resonators.
• a suitable algorithm such as a square-root/quadratic mapping technique (see George L. Matthaei, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, McGraw-Hill Book Company, pp. 95-97, 438-440 (1964), or a logarithmic/exponential mapping technique more suitable to acoustic wave resonators.
• a suitable algorithm such as a square-root/quadratic mapping technique (see George L. Matthae
• ⁇ ⁇ /2 ⁇ is the geometric center frequency of the passband or stopband
• ⁇ /2 ⁇ is the real frequency
• ⁇ is the mapped frequency
• ⁇ is the ratio of the static to the motional capacitance of the resonator
• Q R is the mapped resonant frequency of the resonator
• ⁇ ⁇ is the mapped anti-resonant frequency of the resonator.
• lossless circuit response variables are provided in the form of a ratio between numerator polynomials defining transmission zeroes and denominator polynomials defining reflection zeroes multiplied by a scale factor, as provided in equation [1 ] (step 60).
• the total number of transmission zeroes may be greater equal to or greater than the total number of reflection zeroes, and often one or more reflection zeroes will lie outside any passband of the filter.
• circuit design shall refer to the circuit structure with consideration to the values of the elements making up the circuit structure.
• equivalent circuit transformations may then be performed to reduce the number of circuit elements, or change the type of circuit elements, the size of the circuit, or the realizability of the individual circuit elements to create an acoustic filter circuit design (step 64). These transformations do not substantially change the response of the initial lossless circuit design, and may utilize equivalent circuit transformations, such as equating a J-inverter to an equivalent capacitive or inductive PI- or T-network.
• a shunt-resonator/two J-inverter combination may be transformed into a single series resonator; a series- resonator/two J-inverter combination may be transformed into a single shunt resonator, multiple parallel capacitances may be combined into a single capacitor, or to otherwise eliminate capacitors negative capacitors may be removed by combining with positive parallel capacitors to yield a single positive capacitor, multiple series inductors may be combined into a single inductor, or to otherwise eliminate inductors negative inductors may be removed by combining with positive series inductors to yield a single positive inductor, or other equivalent circuit transformations may be performed to obtain a lossless circuit that may have the target circuit response, but be smaller, less costly, and/or more realizable than the initial lossless circuit design.
• one particular type of circuit transformation involves transforming the initial filter circuit design 100 into a suitable structure in which an acoustic resonator model, and in this case a BVD model 122, can be incorporated.
• This circuit transformation can best be performed by dividing the initial filter circuit design 100 into multiple subsets equal to the number of resonating elements 1 14.
• Each sub-set includes the circuit elements that are coupled to each node to which a resonant branch 1 10 and a non-resonant branch 1 12 are coupled. The nature of each sub-set will depend on whether a shunt acoustic resonator or an in-line acoustic resonator is desired.
• a particular subset circuit design includes a resonant element 1 14 (susceptance B R ) coupled from the respective node 108 to ground, a non-resonant element 1 16 (admittance inverter J) coupled in series with the resonant element 1 14, a non-resonant element 1 18 (susceptance B N ) coupled from the respective node 108 to ground in parallel to the resonant element 1 14 (susceptance B R ), and two non-resonant elements 120 (admittance inverters J) coupled in-line to the respective node 108.
• the sub-set 130a includes node 1 , and thus, resonant element B R1 is coupled from the respective node 108 to ground, admittance inverter element J- 11 is coupled in series with the resonant element B R1 , non-resonant element B N1 is coupled from the respective node 108 to ground in parallel with the resonant element B R1 , and two admittance inverters Jsi and J 12 coupled in-line with the respective node 108.
• the admittance inverter J-n is replaced with a capacitive Pl-network (capacitors -Cn, Cn, and -Cn), and the resonating element Bi R is replaced with a parallel L-C resonator combination of an inductance (inductor L R1 ) and a capacitance (capacitor C R1 ).
• the circuit sub-structure 132 represented by the Pl-network consisting of capacitors -Cn , Cn, and -Cn and the parallel L-C resonator combination of the inductor L R1 and the capacitor C R1 can be transformed into a series L-C resonator combination 134 of an inductance (inductor L R1 ) and capacitance (capacitor C R1 ).
• this series L-C combination 134 can be realized by the series resonance leg of a BVD model 122, so that it can be better incorporated into the circuit sub-structure 132.
• the static capacitance Co of the BVD model 122 must be accommodated.
• C 0 R1 represents the static capacitance of the BVD model 122 and B N1' is given by the relationship B N1 - aj(C 0 R1 ).
• the susceptance B N1 , two in-line admittance inverters Jsi and J 12 , and shunt acoustic resonator 122 can then be transformed into an in-line acoustic resonator 122a and a series reactance 136 (designated Xi), as illustrated in Fig. 9.
• a particular sub-set includes a resonant element 1 14 (susceptance B R ) coupled from the respective node 108 to ground, a non-resonant element 1 16 (admittance inverter J) coupled in series with the resonant element 1 14, and a non-resonant element 1 18 (susceptance B N ) coupled from the respective node 108 to ground in parallel to the resonant element 1 14 (susceptance B R ).
• a resonant element 1 14 susceptance B R
• a non-resonant element 1 16 admittance inverter J
• a non-resonant element 1 18 susceptance B N
• the sub-set 130b includes node 2, and thus, resonant element B R2 is coupled from the respective node 108 to ground, admittance inverter element J 2 is coupled in series with the resonant element B R2 , and non-resonant element B N2 is coupled from the respective node 108 to ground in parallel with the resonant element B R2 .
• the admittance inverter J22 is replaced with a capacitive Pl-network (capacitors -C-22, C22, and -C22), and the resonating element B R2 is replaced with a parallel L-C resonator combination of an inductance (inductor L R2 ) and a capacitance (capacitor C R2 ).
• the circuit sub-structure 132 represented by the Pl-network consisting of capacitors -C22, C22, and -C22 and the parallel L-C resonator combination of the inductor L R2 and the capacitor C R2 can be transformed into a series L-C combination 134 of an inductance (inductor L R2 ) and capacitance (capacitor C R2 ).
• this series L-C combination 134 can be realized by the series resonance leg of a BVD model 122, so that it can be better incorporated into the circuit sub-structure 132.
• the static capacitance Co of the BVD model 122 must be accommodated. This can be accomplished by replacing the parallel susceptance B 2N with a capacitance (C 0 R1 and susceptance B N1 ), as shown in Fig. 12.
• Co R2 represents the static capacitance of the BVD model 122 and B N2' is given by the relationship B N2 - aj(C 0 R2 ).
• an in-shunt acoustic resonator 122b can be realized, as illustrated in Fig. 13.
• the initial filter circuit design 100 can be divided into alternating sub-sets 130a and 130b, such that a filter circuit design having alternating in-line acoustic resonators 122a and in-shunt resonators 122b can be generated.
• an initial filter circuit design 100 with nine resonators B R can be transformed into an acoustic filter circuit structure 150a having five in-line acoustic resonators 122a and four in-shunt acoustic resonators 122b arranged in an alternating fashion, as illustrated in Fig. 14.
• circuit transformation step is described as being performed on the initial filter circuit design (i.e., after calculating the mapped and normalized circuit elements values), it should be appreciated that the circuit transformations step can be performed on the initial filter circuit structure (i.e., prior to calculating the mapping and normalized circuit element values) to create an acoustic filter circuit structure, in which case, the mapped and normalized circuit element values for the acoustic filter circuit structure can be computed to create an acoustic filter circuit design.
• the circuit elements of the acoustic filter circuit design 150a are unmapped to a real design space (i.e., lossless circuit elements (L's and C's) with real frequencies) in accordance with the inverse of the mapping technique initially used to map the frequency response requirements to the normalized design space (step 66).
• a real design space i.e., lossless circuit elements (L's and C's) with real frequencies
• the mapping technique initially used to map the frequency response requirements to the normalized design space.
• the logarithmic mapping technique of equation [5] was used to map the frequency response requirements to the normalized space
• the following logarithmic unmapping equation can be used to unmap the normalized circuit element values to the real design space:
• any B value can be realized by either an L or a C depending on the sign of B.
• Unmapping of the normalized circuit values yields the realized circuit shown in Fig. 15 along with the values of the resonant frequencies COR and static
• parasitic effects are added to the acoustic filter circuit design 150a using an electromagnetic simulator, such as Sonnet® Software, and adding busbar (interconnection) losses to arrive at a pre-optimized filter circuit design (step 68).
• the losses of the acoustic resonators may be included by associating a Q factor for the respective circuit elements.
• the pre-optimized filter circuit design is then input into a computerized filter optimizer to create a final filter circuit design (step 70).
• an element removal optimization (ERO) technique is implemented during the
• multi-band filters designed in accordance with the network synthesis technique illustrated in Fig. 2 will have resonances and resonators with resonant frequencies spanning ranges that are relatively large in contrast to microwave acoustic filters designed in accordance with prior art image design techniques and simple extensions thereof.
• one measure to which the span of resonance frequencies of a filter or its resonators can be compared is the frequency separation of the resonator in the filter with the highest resonant frequency.
• ⁇ is greater than about 12. Any parasitic capacitance from the realization of the acoustic resonator may increase the ⁇ and therefore decrease the percentage separation, while parasitic inductance may effectively decrease ⁇ .
• the percentage separation is 4.0833%, and therefore, the separation of the resonator with the highest resonant frequency is about 88.1 MHz (i.e., a resonant frequency of 2151 .57 MHz times the percent separation of 4.0833%).
• Another measure to which the span of resonance frequencies of a filter or its resonators can be compared is the average frequency separation of its resonators, in this case 77.32 MHz.
• Figs. 21 (a) and 21 (b) show the return loss (S1 1 ) of the filter defined in Figs. 18-19. Return loss minima correspond to resonances of the filter circuit and also correspond to reflection zeroes of the initial filter design.
• Fig. 21 (a) shows the resonances of the filter primarily responsible for forming the filter passband, N1 through N7. The frequency difference between the highest and lowest resonance shown in Fig. 21 (a) is 102 MHz or about 1 .32 times the average frequency separation of the resonators.
• the frequency difference between the highest and lowest resonance of the combined Figs. 21 (a) and 21 (b) is 349 MHz (2173-1824 MHz), or about 4.51 times the average frequency separation of the resonators, while the frequency difference between the highest and lowest frequency resonators in the filter is 459.37 MHz (2151 .57-1892.2 MHz), or about 5.94 times the average frequency separation of the resonators.
• the difference between the lowest resonance frequency and the highest resonance frequency of the passband resonances in the final filter circuit design will be at least 1 .25 times the average separation of the resonators.
• multi-band filters designed in accordance with the network synthesis technique illustrated in Fig. 2 will have resonators as well as resonances corresponding to reflection zeroes that are located relatively far from the passband in contrast to filters designed in accordance with prior art image design techniques, wherein the resonators and resonances corresponding to reflection zeroes are confined to the passband or very close to it.
• resonances corresponding to reflection zeroes occur at frequencies where the local return loss (and/or S1 1 ) minima and local insertion loss (and/or S21 ) maxima coincide to within less than about five percent of the maximum frequency separation— less than about 4.405 MHz for this example.
• resonances corresponding to reflection zeroes occur at local minima and at local maxima of the delay of S1 1 (not shown).
• some resonances corresponding to reflection zeroes are located outside and far from the passband (1850 MHz to 1910 MHz).
• the frequency difference between a resonance corresponding to a reflection zero and the nearest passband edge may be greater than once, perhaps greater than 1 .25 times, and perhaps greater than twice, the maximum frequency separation (about 88.1 MHz in this example).
• reflection zeroes are located up to 3.40 times the average resonator separation (77.32 MHz) from the edge of the passband.
• reflection zeroes N1 , N2 are 43.33% and 28.33% below the lower edge of the passband
• reflection zeroes N6, N7 are 13.33% and 26.67% above the upper edge of the passband. Reflection zeroes N1 , N2, N6, and N7 are contiguous with each other.
• Reflection zeroes N8, N9 which are not contiguous with the passband reflection zeroes N1 , N2, N6, N7, are 31 1 .67% and 438.33% above the upper edge of the passband.
• the insertion loss of the final filter circuit design is preferably less than 3dB, and more preferably less than 2dB.
• an actual microwave filter is constructed based on the final filter circuit design (step 72).
• the circuit element values of the actual microwave filter will match the corresponding circuit element values in the final filter circuit design.
• a survey of different frequency responses may be analyzed and compared at various points in the network synthesis technique 50.
• a survey of different frequency responses may be analyzed and compared based on different versions of the acoustic filter circuit design 150a generated at step 68 to arrive at a pre-optimized circuit design that is input into the computerized filter optimizer to create the final filter circuit design at step 70.
• different acoustic resonator frequency orderings between input and output may be performed.
• the order in which the acoustic resonators are disposed along the signal transmission path may be changed to create multiple filter solutions, one or more performance parameters may be computed for each of the filter solutions, the performance(s) parameters for the different filter solutions can be compared to each other, and the best filter solution (and thus, ordering of the resonators) may be selected based on this comparison.
• This survey process may address all possible permutations of the ordering of the acoustic resonator frequencies in the real filter circuit design.
• the performance parameters may be, e.g., one or more of an insertion loss, return loss, rejection, group delay, node voltages, branch currents, either at specific or multiple frequencies in order to evaluate each circuit response against desired performance characteristics in the filter requirement.
• the survey process may yield quantitative or qualitative performance metric values indicating how a specific circuit may perform versus the filter requirement.
• the survey process may also address all realizable values of the static capacitances Co of the resonators, all permutations of positive (inductive) and or negative (capacitive) values (parities) of J-inverters, and other parameters that may be varied in the lossless design that may not change its response function, but may change the response of a realizable low-loss circuit. Further details discussing a survey process that reorders resonant frequencies is disclosed in U.S. Patent No. 7,924,1 14.
• the filter requirements have been described in this embodiment as defining fixed passbands and stopbands, it should be appreciated that the filter requirements can define multiple reconfigurable passbands and/or stopband.
• the design may be reconfigurable between two states: a first state (called Band 5) that passes frequencies between 824 MHz and 849 MHz with less than 3.5 dB insertion loss and rejects frequencies between 869 MHz and 894 MHz by at least 40 dB; and a second state (called Band 8) that passes frequencies between 880 MHz and 915 MHz with less than 3.5 dB insertion loss and rejects frequencies between 925 MHz and 960 MHz by at least 40 dB (step 52).
• the circuit element type is selected as SAW resonators constructed on 15-degree Y-cut LiTa03 substrates and capacitors integrated onto the 15-degree Y-cut LiTa03 substrate (step 54).
• the initial filter circuit structure 100 illustrated in Fig. 3 is selected based on the passband(s) and/or stopband(s) obtained from the frequency response requirements (step 56). In this case, the number of resonators is six. Then, the frequency requirements are mapped into normalized space (step 58), a lossless circuit response is selected in the form of a polynomial ratio (step 60), and the mapped and normalized circuit element values in the initial filter circuit structure 100 are then calculated from these polynomials using a coupling matrix or parameter extraction methods or equivalent circuit synthesis techniques to create an initial filter circuit design (step 62).
• step 64 equivalent circuit transformations are performed on the initial filter circuit design 100 to accommodate acoustic resonators.
• the circuit transformation divides the initial filter circuit design 100 into multiple sub-set circuit designs equal to the number of resonating elements 1 14 (in this case, six), resulting in six shunt acoustic resonators.
• the sub-set 130 illustrated in Fig. 6 can be transformed by replacing the admittance inverter Jsi with a capacitive Pl- network (capacitors -Csi , Csi, and -Csi), the admittance inverter J 2 with a capacitive Pl-network (capacitors -Ci 2 , Ci 2 , and -Ci 2 ), the admittance inverter Jn with a capacitive Pl-network (capacitors -Cn , Cn , and -Cn), and the resonating element Bi R with a parallel L-C resonator combination of an inductance (inductor L R1 ) and a capacitance (capacitor C R1 ), as illustrated in Fig.
• the circuit sub-structure 132 represented by the Pl-network consisting of capacitors -Cn, Cn , and -Cn and the parallel L-C resonator combination of the inductor L R1 and the capacitor C R1 can be transformed into a series L-C combination 134 of an inductance (inductor L R1 ) and capacitance (capacitor C R1 ).
• the three adjacent parallel capacitances and susceptances (-Csi, -C 12 , and Bi N ) are replaced with a capacitance (C 0 R1 and susceptance B-i N ), as shown in Fig.
• Co R1 represents the static capacitance of the BVD model 122 and B N1 is given by the relationship B N1 - co(Csi + C 12 + Co R1 ).
• B N1 is given by the relationship B N1 - co(Csi + C 12 + Co R1 ).
• an in-shunt acoustic resonator 122 can be realized, as illustrated in Fig. 24.
• the other sub-sets 130 of the initial filter circuit design 100 can be transformed in the same manner to arrive at an acoustic filter circuit structure 150b having six in-shunt acoustic resonators 122, as illustrated in Fig. 25.
• the circuit elements of the acoustic filter circuit structure 150b are then unmapped into real space (step 66), and parasitic effects are added to the acoustic filter circuit structure 150b to arrive at a pre-optimized circuit design (step 68).
• the losses of the circuit elements may be included by associating a Q factor for the respective circuit elements.
• a busbar (interconnection) resistance of Rs 0.5 ohms is also added for each acoustic resonator.
• switch parasitics of 3pF/(mm gate width) and 1 .0 Ohm*(mm gate width) are also added.
• the pre-optimized filter circuit design is input into a computer filter optimizer with the optional ERO technique to create a final circuit design (step 70).
• switches are added to each branch where the impedance is different between the two bands, thus, creating a single circuit from the two separate designs to be optimized, as illustrated in Fig. 26.
• the gate width of each switch, value of an inductor or capacitor (if needed), and the circuit configuration of the branch is selected, so that the impedance of a given branch will be the required band 5 impedance in one switch state and the required band 8 impedance in the other switch state.
• the ERO technique is then repeated on the combined circuit.
• the optimization process yields the resonant frequencies co R and static capacitances C 0 for each resonator, and the capacitances and inductances of the capacitors and inductors, as shown in Fig. 27, which when simulated, resulted in the frequency response for band 5 illustrated in Fig. 28 and the frequency response for band 8 illustrated in Fig. 29.
• a survey of different frequency responses may be analyzed and compared at various points in the network synthesis technique 50.
• a survey of different frequency responses may be analyzed and compared based on different versions of the acoustic filter circuit design 150a generated at step 68 to arrive at a pre-optimized circuit design that is input into the computerized filter optimizer to create the final filter circuit design at step 70.
• pairs of circuits are produced with each possible ordering of resonator frequencies, each possible parity of the J inverters (inductor or capacitive), and a selection of static capacitance C 0 values for the resonators.
• a filter constructed in accordance with the network synthesis technique can have fixed passbands and/or stopbands that are reconfigurable prior to final completion of the filter, but be fixed after completion of the filter.
• a lossless circuit model can be realized to create a filter having either a passband centered at either 836.5 MHz (Band 5) or 897.5 MHz (Band 8). This lossless circuit has been created by transforming the initial filter circuit design 100 illustrated in Fig. 3 using three SAW resonators.
• the transformation technique illustrated in Figs. 10-13 can be utilized to transform circuit sub-sets (each including a resonant element 1 14 (susceptance B R ) coupled from the respective node 108 to ground, a non-resonant element 1 16 (admittance inverter J) coupled in series with the resonant element 1 14, and a non-resonant element 1 18 (susceptance B N ) coupled from the respective node 108 to ground in parallel to the resonant element 1 14 (susceptance B R )) into three in-shunt acoustic resonators.
• the circuit element type is selected as SAW resonators constructed on 42-degree Y-cut LiTa03 substrates and capacitors integrated onto the 42-degree Y-cut LiTa03 substrate.
• the filter can be reconfigured prior to completion by altering the values of the series elements between the resonators (in this case, Csi , Ci 2 , C 23 , C 3 L) and the non-resonant shunt elements (in this case, l_s, L-i , L 2 , L3, U).
• the filter can then be constructed using either the values of the non-resonant elements for Band 5 or the values of the non-resonant elements for Band 8.
• the optimization process yields the static capacitances Co for each resonator, and the capacitances and inductances of the capacitors and inductors, as shown in Fig. 30, which when simulated, resulted in the frequency response for band 5 illustrated in Fig. 31 and the frequency response for band 8 illustrated in Fig. 32.

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