COUPLED RESONATOR STRUCTURE

Abstract

Various arrangements for electrically coupling the electrodes of coupled resonator structures (CRSes) to form unique two- and three-terminal devices as well as the use of such CRSes in filter networks are disclosed.

Claims

1. A device comprising: a network input and a network output; a filter network coupled between the network input and the network output and comprising a plurality of coupled resonator structures that are electrically coupled together, wherein each coupled resonator structure (CRS) comprises: a substrate; a bottom transducer comprising a first bottom electrode over the substrate, a first piezoelectric layer over the first bottom electrode, and a first top electrode over the first piezoelectric layer; a first acoustic coupling structure over the bottom transducer; and a top transducer over the first acoustic coupling structure and comprising a second bottom electrode, a second piezoelectric layer over the second bottom electrode, and a second top electrode over the second piezoelectric layer, wherein the bottom transducer is vertically acoustically coupled to the top transducer via the first acoustic coupling structure, wherein an arrangement of a first CRS of the plurality of CRSes is one of a first arrangement, a second arrangement, a third arrangement, and a fourth arrangement, and an arrangement of a second CRS of the plurality of CRSes is a different one of the first arrangement, the second arrangement, the third arrangement, and the fourth arrangement, wherein: in the first arrangement, the second top electrode is a first terminal, the first bottom electrode is a second terminal, and the first top electrode is directly electrically coupled to the second bottom electrode to provide a third terminal of a first three terminal device; in the second arrangement, the second top electrode is a fourth terminal, the first top electrode is a fifth terminal, and the first bottom electrode is directly electrically coupled to the second bottom electrode to provide a sixth terminal of a second three terminal device; in a third arrangement, the first bottom electrode is directly electrically coupled to the second top electrode to provide a seventh terminal and the first top electrode is directly electrically coupled to the second bottom electrode to provide an eighth terminal of a first two terminal device; and in a fourth arrangement, the first bottom electrode is directly electrically coupled to the second bottom electrode to provide a ninth terminal and the first top electrode is directly electrically coupled to the second top electrode to provide a tenth terminal of a second two terminal device.

2. The device of claim 1 wherein the first CRS has the first arrangement, and the second CRS has the second arrangement.

3. The device of claim 1 wherein the first CRS has the first arrangement, and the second CRS has the third arrangement.

4. The device of claim 1 wherein the first CRS has the first arrangement, and the second CRS has the fourth arrangement.

5. The device of claim 1 wherein the first CRS has the second arrangement, and the second CRS has the third arrangement.

6. The device of claim 1 wherein the first CRS has the second arrangement, and the second CRS has the fourth arrangement.

7. The device of claim 1 wherein the first CRS has the third arrangement, and the second CRS has the fourth arrangement.

8. The device of claim 1 wherein the top transducer of the first CRS is structurally identical to the top transducer of the second CRS, and the bottom transducer of the first CRS is structurally identical to the bottom transducer of the second CRS.

9. The device of claim 8 wherein the first CRS has a first series resonance frequency, and the second CRS has a second series resonance frequency that is different than the first series resonance frequency.

10. The device of claim 1 wherein the first CRS has a first series resonance frequency, and the second CRS has a second series resonance frequency that is different than the first series resonance frequency.

11. The device of claim 1 wherein the plurality of CRSes form a ladder network.

12. The device of claim 11 wherein the first CRS is a shunt element of the ladder network, and the second CRS is a series element of the ladder network.

13. The device of claim 1 wherein an arrangement of a third CRS of the plurality of CRSes is a different one of the first arrangement, the second arrangement, the third arrangement, and the fourth arrangement than the arrangement of the first CRS and the arrangement of the second CRS.

14. The device of claim 1 wherein the arrangement of the first CRS of the plurality of CRSes is the first arrangement, the arrangement of the second CRS of the plurality of CRSes is the second arrangement, an arrangement of a third CRS of the plurality of CRSes is the third arrangement, and an arrangement of a fourth CRS of the plurality of CRSes is the fourth arrangement.

15. The device of claim 1 wherein the filter network further comprises at least one BAW resonator that is electrically coupled to the plurality of CRSes.

16. The device of claim 15 wherein the first CRS has a first series resonance frequency, the second CRS has a second series resonance frequency that is different than the first series resonance frequency, and the at least one BAW resonator has a third series resonance frequency that is different than the first and second series resonance frequencies.

17. A coupled resonator structure (CRS) comprising: a substrate; a bottom transducer comprising a first bottom electrode over the substrate, a first piezoelectric layer over the first bottom electrode, and a first top electrode over the first piezoelectric layer; a first acoustic coupling structure over the bottom transducer; and a top transducer over the first acoustic coupling structure and comprising a second bottom electrode, a second piezoelectric layer over the second bottom electrode, and a second top electrode over the second piezoelectric layer, wherein the bottom transducer is acoustically coupled to the top transducer, the first top electrode is directly electrically coupled to the second top electrode, and the first bottom electrode is directly electrically coupled to the second bottom electrode.

18. The CRS of claim 17 wherein a series resonance frequency of the top transducer is about the same as a series resonance frequency of the bottom transducer.

19. The CRS of claim 17 wherein a series resonance frequency of the top transducer is different from a series resonance frequency of the bottom transducer.

20. The CRS of claim 17 wherein the top transducer is aligned directly over the bottom transducer.

21. A coupled resonator structure (CRS) comprising: a substrate; a bottom transducer comprising a first bottom electrode over the substrate, a first piezoelectric layer over the first bottom electrode, and a first top electrode over the first piezoelectric layer; a first acoustic coupling structure over the bottom transducer; and a top transducer over the first acoustic coupling structure and comprising a second bottom electrode, a second piezoelectric layer over the second bottom electrode, and a second top electrode over the second piezoelectric layer, wherein the bottom transducer is acoustically coupled to the top transducer, the first top electrode is directly electrically coupled to the second bottom electrode, and the first bottom electrode is directly electrically coupled to the second top electrode.

22. The CRS of claim 21 wherein a series resonance frequency of the top transducer is about the same as a series resonance frequency of the bottom transducer.

23. The CRS of claim 21 wherein a series resonance frequency of the top transducer is different from a series resonance frequency of the bottom transducer.

24. The CRS of claim 21 wherein the top transducer is aligned directly over the bottom transducer.

Description

BRIEF DESCRIPTION OF THE DRAWING FIGURES

[0035] The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure, and together with the description serve to explain the principles of the disclosure.

[0036] The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.

[0037] FIG. 1 illustrates a conventional Bulk Acoustic Wave (BAW) resonator.

[0038] FIG. 2 is a graph of the magnitude and phase of impedance over frequency responses as a function of frequency for an ideal BAW resonator.

[0039] FIGS. 3A-3C are graphs of phase responses for various BAW resonator configurations.

[0040] FIG. 4 illustrates a conventional BAW resonator with a border ring.

[0041] FIG. 5A is a schematic of a conventional ladder network.

[0042] FIGS. 5B and 5C are graphs of a frequency response for BAW resonators in the conventional ladder network of FIG. 5A and a frequency response for the conventional ladder network of FIG. 5A.

[0043] FIGS. 6A-6E are circuit equivalents for the ladder network of FIG. 5A at the frequency points 1, 2, 3, 4, and 5, which are identified in FIG. 5C.

[0044] FIG. 7 is a cross-section of a coupled resonator structure (CRS), according to one embodiment.

[0045] FIG. 8 is a simplified symbolic representation of the CRS of FIG. 7.

[0046] FIG. 9 is a first CRS arrangement.

[0047] FIG. 10 is an electrical equivalent of the CRS of FIG. 9.

[0048] FIG. 11 is a model of an impedance inverter.

[0049] FIG. 12 is a T-model of an impedance inverter.

[0050] FIG. 13 is an electrical equivalent with the T-model for the impedance inverter of the CRS of FIG. 9.

[0051] FIG. 14 is a pi-equivalent of the electrical equivalent of FIG. 13.

[0052] FIG. 15 is a symbol for the CRS arrangement of FIG. 9.

[0053] FIG. 16 is a second CRS arrangement.

[0054] FIG. 17 is a symbol for the second CRS arrangement.

[0055] FIG. 18 is an electrical equivalent of the second CRS arrangement.

[0056] FIG. 19 is a third CRS arrangement.

[0057] FIG. 20 is a symbol for the third CRS arrangement.

[0058] FIG. 21 is an electrical equivalent of the third CRS arrangement.

[0059] FIG. 22 is a fourth CRS arrangement.

[0060] FIG. 23 is a symbol for the fourth CRS arrangement.

[0061] FIG. 24 is an electrical equivalent of the fourth CRS arrangement.

[0062] FIG. 25 is a first filter network embodiment.

[0063] FIG. 26 is an electrical equivalent of the first filter network embodiment of FIG. 25.

[0064] FIG. 27 is a second filter network embodiment.

[0065] FIG. 28 is a third filter network embodiment.

[0066] FIG. 29 is a fourth filter network embodiment.

[0067] FIG. 30 is a switchable CRS arrangement.

[0068] FIG. 31 is a first tunable CRS arrangement.

[0069] FIG. 32 is a second tunable CRS arrangement.

[0070] FIG. 33 is a fifth filter network embodiment.

[0071] FIG. 34 is an electrical equivalent of the third filter network embodiment of FIG. 33.

[0072] FIG. 35 is a sixth filter network embodiment.

[0073] FIG. 36 is an electrical equivalent of the third filter network embodiment of FIG. 35.

[0074] FIG. 37 is a seventh filter network embodiment.

[0075] FIG. 38 is an electrical equivalent of the third filter network embodiment of FIG. 37.

[0076] FIG. 39 is an eighth filter network embodiment.

[0077] FIG. 40 is an electrical equivalent of the third filter network embodiment of FIG. 39.

[0078] FIG. 41 is a twelfth filter network embodiment.

[0079] FIGS. 42A and 42B are electrical equivalents of the twelfth filter network embodiment of FIG. 41.

DETAILED DESCRIPTION

[0080] The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the embodiments and illustrate the best mode of practicing the embodiments. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims.

[0081] It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and similarly, a second element could be termed a first element, without departing from the scope of the present disclosure. As used herein, the term and/or includes any and all combinations of one or more of the associated listed items.

[0082] It will be understood that when an element such as a layer, region, or substrate is referred to as being on or extending onto another element, it can be directly on or extend directly onto the other element or intervening elements may also be present. In contrast, when an element is referred to as being directly on or extending directly onto another element, there are no intervening elements present. Likewise, it will be understood that when an element such as a layer, region, or substrate is referred to as being over or extending over another element, it can be directly over or extend directly over the other element or intervening elements may also be present. In contrast, when an element is referred to as being directly over or extending directly over another element, there are no intervening elements present. It will also be understood that when an element is referred to as being connected or coupled to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being directly connected or directly coupled to another element, there are no intervening elements present.

[0083] Relative terms such as below or above or upper or lower or horizontal or vertical may be used herein to describe a relationship of one element, layer, or region to another element, layer, or region as illustrated in the figures. It will be understood that these terms and those discussed previously are intended to encompass different orientations of the device in addition to the orientation depicted in the figures.

[0084] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms a, an, and the are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms comprises, comprising, includes, and/or including when used herein specify the presence of stated features, integers, steps, operations, elements, and/or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

[0085] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0086] As defined herein, the term coupled without being preceded with the adjective acoustically refers to an electrical coupling as opposed to an acoustic coupling. The term acoustically coupled refers to an acoustic coupling as opposed to an electrical coupling. Further, the phrase about the same as when referring to the series resonance frequency of two or more devices means that the series resonance frequencies of the devices are within 0.1% of each other.

[0087] While the concepts provided herein are applicable to various technologies, these concepts are particularly useful in mobile terminals, such as mobile telephones, tablets, computers, and like smart devices. The following provides an overview of such devices. Today's mobile terminals must communicate using different communication technologies in different bands, which vary significantly in both bandwidth and frequency. To further complicate matters, data rates are ever increasing and the there is a need to transmit and receive over these different bands at the same time. As a result, mobile terminals have very complicated front-end configurations and are starting to employ multiple input multiple output (MIMO) transmission and reception technology, which requires the use of multiple antennas.

[0088] The concepts described below relate to different arrangements for electrically coupling the top and bottom transducers 58, 46 of a CRS, wherein the different arrangements correspond to different impedance behaviors over frequency. These arrangements afford designers tremendous flexibility in filter design. A first arrangement is illustrated in FIG. 9. An input is coupled to the top electrode 60 of the top transducer 46, and an output is coupled to a bottom electrode 50 of the bottom transducer 58. The bottom electrode 62 of the top transducer 46 and the top electrode 48 of the bottom transducer 58 are coupled to ground, or other fixed voltage node.

[0089] An electrical model of this arrangement is illustrated in FIG. 10. Two capacitors C0 are coupled between the input and ground, and the output and ground, respectively. The coupling structure 54 is represented by an impedance inverter 66 with an acoustic coupling coefficient Ka. A first series LC circuit is coupled between the input and the impedance inverter 66, and a second LC circuit is coupled between the impedance inverter 66 and the output. The impedance inverter 66 is also coupled to ground. Each LC circuit includes a series coupled inductor Ln, which has a value of Ln, and a capacitor Cn, which has a value of Cn. For FIGS. 10, C10 and C13 have a capacitance of C0, capacitors C11 and C12 have a capacitance of Cm, and inductors L10 and L11 have an inductance of Lm.

[0090] As illustrated in FIG. 11, a model of the impedance inverter 66 will have input and output voltages Va, Vb, respectively, and input and output currents Ia and Ib, respectively. If an impedance Z is connected to port B, the impedance Zinv seen on port A is equal to Ka.sup.2/Z (Zinv=Ka.sup.2/Z).

[0091] FIG. 12 illustrates an exemplary electrical network that acts as an impedance inverter. The network is effectively a T network with three inductors, wherein the series connected inductors are coupled between port A and port B and have a value of L. An inductor that has a value of +L is coupled and shown between the node where the series connected inductors are coupled in ground. With this configuration, the following holds true:

[00001]$\left[\begin{array}{c}\mathrm{Va}\\ \mathrm{Ia}\end{array}\right]=\left[\begin{array}{cc}0& -\mathrm{jwL}\\ -j.Math.\text{/}.Math.\mathrm{wL}& 0\end{array}\right]\left[\begin{array}{c}\mathrm{Vb}\\ -\mathrm{Ib}\end{array}\right]$
Va=+rw*L*Ib;

Vb=+rw*L*Ia;

Vb=Z*Ib where Z is the load impedance tied to node B; and

Va/Ia=Zinv=+(L*w).sup.2/Z.

For FIG. 12, L12 and L13 have inductance values of L, while inductor L14 has an inductance of +L.

[0092] Since Zinv.sup.2=Ka.sup.2/Z, Ka=L*w, where w is 2**f, where f is frequency. FIG. 13 shows the electrical equivalent of the CRS using the electrical equivalent of the impedance inverter 66. Notably, FIG. 13 is effectively a T-type electrical equivalent. FIG. 14 represents a pi-type electrical equivalent of the electrical equivalent of FIG. 13. For FIGS. 14, L15 and L16 have inductances of Lm+L, capacitors C14 and C15 have capacitances of C0, and capacitors C16 and C17 have capacitances of Cm.

[0093] The pi-type electrical equivalent includes a series impedance ZA that extends between the input that output, an input shunt element coupled between the input and ground, and an output shunt element coupled between the output and ground. Each of the input and output shunt elements are made of an impedance Zs wherein Zm+j*Lw is in parallel with a capacitance C0. Each shunt impedance Zs is equivalent to that of a shunt resonator that has a series resonance frequency, fs, occurring at 1/(2**((Lm+L)*Cm)). Notably, the series resonance frequency, fs, for the shunt impedance Zs is based on the Lm+L inductance, where L is the coupling equivalent inductance based on Ka=Lw. The series impedance ZA between the input and output is such that ZA=(Zm+j*L*w)*(Zmj*L*w)/(j*L*w)=(Zm.sup.2+(L*w).sup.2)/(j*L*w), where Zm=1/(j*Cm*w)+j*Lm*w. A symbol for the CRS arrangement A1 of FIG. 9 is provided in FIG. 15. CRS arrangement A1 is a non-inverted coupling arrangement. The next arrangement, CRS arrangement A2, which is illustrated in FIG. 16, is an inverted coupling arrangement.

[0094] CRS arrangement A2 is the same as that of FIG. 9, with the exception that the top electrode 48 of the bottom transducer 58 is coupled to the output (instead of ground), and the bottom electrode 50 of the bottom transducer 58 is coupled to ground (instead of the output). A symbol for the CRS arrangement A2 is illustrated in FIG. 17, and a pi-type electrical equivalent of the CRS arrangement is illustrated in FIG. 18. Notably, the impedance structure is substantially the same as that illustrated in FIG. 14, with the exception that the shunt inductors have a value of Lm-L and the series impedance ZA is negative due to the inversion of the electrical coupling of the top and bottom electrodes 48, 50 of the bottom transducer 58. In essence, swapping the electrical connections for the top and bottom electrodes 48, 50 of the bottom transducer 58 inverts the impedance ZA, which is mathematically represented as making the impedance ZA negative. A similar effect is provided for the coupling equivalent inductance L. As a result, the inductance values for the shunt elements are LmL (instead of Lm+L, as provided in CRS arrangement A1 of FIG. 14). For FIGS. 18, L15 and L16 have inductances of LmL, capacitors C14 and C15 have capacitances of C0, and capacitors C16 and C17 have capacitances of Cm.

[0095] As a result, the shunt impedance at both the input and output for CRS arrangement A2 is Zmj*Lw in parallel with C0m, which again is an equivalent impedance of a shunt acoustic resonator that has a series resonance frequency at 1/(2**((LmL)*Cm)). Notably, the series resonance frequency is now based on LmL (instead of Lm+L, as provided in the CRS arrangement A1), where L is the coupling equivalent inductance based on Ka=Lw (i.e. negative coupling with corresponds to an electrical inversion of phase). Accordingly, swapping the connections for the top and bottom electrodes 48, 50 of the bottom transducer 58 for a CRS, without changing any physical characteristics, such as size, shape, material compositions, layer thicknesses, and the like, changes the series resonance frequency between 1/(2**((LmL)*Cm)) and 1/(2**((Lm+L)*Cm)). Being able to choose different series resonance frequencies for the same CRS configuration provides designers greater flexibility in circuit and layout design, especially when designing ladder or like filter networks with CRS and other BAW resonators 10.

[0096] The above CRS arrangements A1 and A2 are effectively three terminal devices, which include an input, and output, and ground terminals. The following embodiments employ the concepts described above in a two terminal configuration, which has an input terminal and an output terminal, wherein there is a virtual ground provided in the coupling structure 54.

[0097] FIG. 19 illustrates a third CRS arrangement A3, wherein the top electrode 60 of the top transducer 46 and the bottom electrode 50 of the bottom transducer 58 are coupled to the input. The bottom electrode 62 of the top transducer 46 and the top electrode 48 of the bottom transducer 58 are coupled to the output. The equivalent impedance is illustrated in FIG. 20. For FIG. 20, capacitor C18 has a capacitance of 2C0.sub.3 capacitor C19 has a capacitance of 2Cn, and inductor L17 has an inductance of (Lm+L)/2.

[0098] This equivalent impedance of CRS arrangement A3 has a series resonance frequency at 1/(2**((Lm+L)*Cm)), which is made of an equivalent inductance of (Lm+L)/2. This is considered a non-inverted coupling configuration with an acoustic coupling coefficient of +Ka. A standard BAW resonator 10 that corresponds in shape, size, and materials to the one of the top or bottom transducers 46, 58 would have a series resonance frequency at 1/(2**((Lm)*Cm)). The equivalent impedance of the CRS arrangement A3 is effectively that of a capacitance of 2C0 in parallel with a series coupled inductance of (Lm+L)/2 and a capacitance of 2*Cm. A symbol for the CRS arrangement A3 of FIG. 19 is provided in FIG. 21.

[0099] A fourth CRS arrangement A4 is illustrated in FIG. 22. CRS arrangement A4 is an inverting variant of the CRS arrangement A3 of FIG. 19. In particular, the top electrode 60 of the top transducer 46 and the top electrode 48 of the bottom transducer 58 are coupled to the input. The bottom electrode 62 of the top transducer 46 and the bottom electrode 50 of the bottom transducer 58 are coupled to the output to provide a two terminal device that has an equivalent impedance illustrated in FIG. 23. For FIG. 23, capacitor C18 has a capacitance of 2C0.sub.3 capacitor C19 has a capacitance of 2*Cm, and inductor L17 has an inductance of (LmL)/2.

[0100] The equivalent impedance of CRS arrangement A4 has a series resonance frequency at 1/(2**((LmL)*Cm)), which is made of an equivalent inductance of (LmL)/2. As noted, this is considered an inverted coupling arrangement with an acoustic coupling coefficient of Ka. A standard BAW resonator 10 that corresponds in shape, size, and materials to the one of the top or bottom transducers 46, 58 would have a series resonance frequency at 1/(2**((Lm)*Cm)). The equivalent impedance of the CRS arrangement A4 is effectively that of a capacitance of 2C0 in parallel with a series coupled inductance of (LmL)/2 and a capacitance of 2*Cm. A symbol for the CRS arrangement A4 of FIG. 22 is provided in FIG. 24.

[0101] With reference to FIG. 25, filter networks, such as filter network N1, may be constructed using multiple ones of the CRS arrangements A1, A2, A3, and A4. For the filter network N1, a CRS arrangement A1 is coupled to an input, a CRS arrangement A2 is coupled to an output, and a CRS arrangement A4 is coupled between the CRS arrangements A1, A2, as illustrated. This configuration is provided merely as an example, as any number of CRS arrangements AX may be employed in a variety of ways to provide a desired transfer function. The equivalent impedance of the filter network N1 is illustrated in FIG. 26. The equivalent inductance values for CRS arrangement A2 is Lm1+L, the equivalent inductance for CRS arrangement A4 is (Lm2L)/2, and the equivalent inductance for the CRS arrangement A2 is Lm3L. Again, the exact same CRS structure may be employed in each of the CRS arrangements A1, A4, and A2, yet the different configurations allow each of these CRS arrangements A1, A4, and A2 to have different series resonance frequencies based on the equivalent inductance values (i.e. Lm+L, LmL).

[0102] Notably, the configurations for each of the CRS arrangements A1, A4, A2, may be the same or different with respect to size, shape, layer thicknesses, series resonance frequencies, and the like. These differences are represented by the variations in component and coupling values. For CRS arrangement A1, there is a positive coupling coefficient equal to Ka1=L1w, for CRS arrangement A4, there is a negative coupling coefficient represented by Ka2=L2w, and for CRS arrangement A2, there is a negative coupling coefficient represented by Ka3=L3w.

[0103] Accordingly, for the CRS arrangement A1, impedance Za1=[1/(jCm1*w)+j*(Lm1L)w]*[1/(jCm1*w)+j*(Lm1+L)w]/(j*L*w), for impedance Za3 of CRS arrangement A2, Za3=[1/(jCm3*w)+j*(Lm3L)w]*[1/(jCm3*w)+j*(Lm3+L)w]/(j*L*w). For CRS arrangement A4, the impedance is represented by a capacitance of 2C0 in parallel with a capacitance of 2*Cn2 in series with an inductance (Ln2L)/2. For FIG. 26, capacitors C20, C21, C22, and C23 have a capacitance of C0, capacitors C24 and C25 have a capacitance of Cn1, capacitors C26 and C27 have a capacitance of Cn3, capacitor C28 has a capacitance of 2C0, and capacitor C29 has a capacitance of 2*Cn2. Inductors L26 and L27 have inductances of Lm1+L, inductors L28 and L30 have inductances of Lm3L, and inductor L32 has an inductance of (Lm2L)/2.

[0104] Another filter example N2 is provided in FIG. 27, wherein five CRS arrangements A1, A2, A3, A4, and A4 are illustrated. CRS arrangement A1 is coupled between an input and port P1, CRS arrangement A4 is coupled between port P1 and port P2, and CRS arrangement A2 is coupled between port P2 and the output. Further, a first shunt CRS arrangement A4 is coupled between port P1 and ground, or other fixed voltage node. CRS arrangement A3 is coupled between port P2 and ground, or other fixed voltage node. CRS arrangement A1 is positively coupled with an acoustic coupling coefficient Ka1=L1w. CRS arrangement A4 is negatively coupled with a coupling coefficient of Kas1=L1sw. CRS arrangements A1 and A4 employ identical CRSes, but are electrically connected in different manners. CRS arrangement A4 is also negatively coupled and has an acoustic coupling coefficient of Ka2=L2w. CRS arrangement A3 is positively coupled with an acoustic coupling coefficient of Kas2=L2sw. CRS arrangements A4 and A3 have identical CRSes, but are electrically coupled differently. CRS arrangement A2 is negatively coupled and has an acoustic coupling coefficient of Ka3=L3w. The different coupling coefficients indicate that the structure of the CRSes in CRS arrangements A1 and A4 are the same, the structures of the CRSes of CRS arrangements A4 and A3 are the same, but are different than the structures of either of the CRSes for the CRS arrangement of A1, A4, and A2.

[0105] FIG. 28 illustrates a filter network N3, which is a variant of the filter network N2 of FIG. 24. The difference is that shunt inductors LS are coupled in series with the CRS arrangements A4 and A3 respectively, and ground. With the additional inductances provided in the CRS arrangements A4, A3, the inductance that is often provided in the shunt elements for a ladder network may be reduced, which in turn reduces cost and the space required for the filter network N3.

[0106] Yet another variant is illustrated in FIG. 29. In essence, filter network N4 is an extension of filter network N2, and combines both CRS arrangements A1, A2, A3, A4, and A4 with at least two additional BAW resonators 10 and 10. In particular, CRS arrangement A1 is coupled between the input and port P1, CRS arrangement A4 is coupled between port P1 and P2, CRS arrangement A2 is coupled between port P2 and port P3, and BAW resonator 10 is coupled between port P3 and the output. In a shunt arrangement, CRS arrangement A4 is coupled between port P1 and ground, CRS arrangement A3 is coupled between port P2 and ground, and BAW resonator 10 is coupled between port P3 and ground.

[0107] FIG. 30 illustrates a circuit configuration that allows for the CRS arrangement to be tunable, or configurable, by employing switches S1-S4. In particular, an input is coupled to the top electrode 60 of the top transducer 46 and to one side of both switches S1 and S2. The output is coupled to the bottom electrode 62 of the top transducer 46, as well as the first terminal of switches S3 and S4. The second terminals of switches S1 and S3 are coupled to the top electrode 48 of the bottom transducer 58. Similarly, the second terminals of switches S2 and S4 are coupled to the bottom electrode 50 of the bottom transducer 58. Closing switches S2 and S3 while leaving switches S1 and S4 open provides CRS arrangement A3. Closing switches S1 and S4 while leaving switches S2 and S3 open provides CRS arrangement A4. As such, the use of switches, such as switches S1-S4, allow a given CRS to be dynamically configured as either CRS arrangement A3 or A4, respectively.

[0108] FIGS. 31 and 32 illustrate a tunable CRS arrangements for CRS arrangements A3 and A4. The tuning may be dynamically applied after manufacture, or varied and then set during manufacturing. The tuning includes employing techniques to modify the acoustic coupling coefficient Ka that is provided by the coupling structure 54. Since tuning could be provided by changing material thicknesses, compositions, adding or subtracting metallic or non-metallic elements, blowing fuses, or the like that would effectively modify the acoustic coupling coefficient in a known manner. For the CRS arrangement A3 of FIG. 31, changing the acoustic coupling coefficient Ka effectively changes the effective inductance L in the equation (Lm+L)/2. Similarly, For the CRS arrangement A4 of FIG. 32, changing the acoustic coupling coefficient Ka effectively changes the effective inductance L in the equation (LmL)/2.

[0109] FIG. 33 illustrates yet another embodiment, wherein a CRS arrangement A3 is coupled in parallel with a CRS arrangement A2. The equivalent impedance is illustrated in FIG. 34. For FIG. 34, capacitors C40 and C41 have capacitances of C0, capacitors C42 and C43 have capacitances of Cm, capacitor C44 has a capacitance of 2*Cms, and capacitor C45 has a capacitance of 2C0s. Inductors L40 and L41 have inductances of LmL, and inductor L42 has an inductance of (Lms+L)/2.

[0110] FIG. 35 illustrates yet another embodiment, wherein a CRS arrangement A4 is coupled in parallel with a CRS arrangement A2. The equivalent impedance is illustrated in FIG. 36. For FIG. 236, capacitors C40 and C41 have capacitances of C0, capacitors C42 and C43 have capacitances of Cm, capacitor C44 has a capacitance of 2*Cms, and capacitor C45 has a capacitance of 2C0s. Inductors L40 and L41 have inductances of LmL, and inductor L42 has an inductance of (LmsL)/2.

[0111] FIG. 37 illustrates yet another embodiment, wherein a CRS arrangement A3 is coupled in parallel with a CRS arrangement A1. The equivalent impedance is illustrated in FIG. 38. For FIG. 38, capacitors C40 and C41 have capacitances of C0, capacitors C42 and C43 have capacitances of Cm, capacitor C44 has a capacitance of 2*Cms, and capacitor C45 has a capacitance of 2C0s. Inductors L40 and L41 have inductances of Lm+L, and inductor L42 has an inductance of (Lms+L)/2.

[0112] FIG. 39 illustrates yet another embodiment, wherein a CRS arrangement A4 is coupled in parallel with a CRS arrangement A1. The equivalent impedance is illustrated in FIG. 40. For FIG. 40, capacitors C40 and C41 have capacitances of C0, capacitors C42 and C43 have capacitances of Cm, capacitor C44 has a capacitance of 2*Cms, and capacitor C45 has a capacitance of 2C0s. Inductors L40 and L41 have inductances of Lm+L, and inductor L42 has an inductance of (LmsL)/2. FIGS. 33-40 illustrate embodiments that may be referred to as an N-tail or transversal filter. For further details on such filters that are constructed of BAW resonators 10, reference is made to U.S. Pat. No. 9,698,756; and to U.S. patent application Ser. No. 15/275,957 filed Sep. 26, 2016; Ser. No. 15/347,428 filed Nov. 9, 2016; Ser. No. 15/586,374 filed May 4, 2017; Ser. No. 15/697,658 filed Sep. 7, 2017; and Ser. No. 15/701,759 filed Sep. 12, 2017, the disclosures of which are incorporated herein by reference in their entireties.

[0113] FIG. 41 illustrates a CRS arrangement A3 in parallel with a CRS arrangement A4, wherein the resulting structure is equivalent to a single BAW resonator 10. The equivalent impedance networks are illustrated in FIGS. 42A and 42B. FIG. 42A shows that the equivalent impedance looks like two parallel BAW resonators of the same configuration, which reduces to the equivalent shown in FIG. 42B, wherein the impedance equivalent is represented by a capacitance of 4C0s in parallel with an LC impedance Z, wherein Z=[1/(j*2*Cm*w)+j*(LmL)/2*w]*[1/(j*2*Cm*w)+j*(Lm+L)/2*w]/[1/(j*Cm*w)+j*Lm*w]. For FIG. 42A, capacitors C50 and C51 have capacitances of 2C0s, capacitors C52 and C53 have capacitances of 2*Cm, inductor L50 has an inductance of (Lm+L)/2, and inductor L51 has an inductance of (LmL)/2. For FIG. 42B, capacitor C60 has a capacitance of 4C0s, capacitors C61 and C62 have capacitances of 2*Cm, inductor L60 has an inductance of (LmL)/2, and inductor L61 has an inductance of (Lm+L)/2.

[0114] Notably, the same or similarly sized BAW resonators 10 and 10 as well as the CRS arrangements A1, A2, A3, A4, and A4, may include transducers of the same or similar size, yet the ability to change the electrical connections to change the series resonance frequencies fs provide tremendous flexibility in using similarly sized transducers while achieving the different series resonance frequencies, which are often needed to create various filters, including ladder filters.