Patent Publication Number: US-9847769-B2

Title: Tunable compensation circuit for filter circuitry using acoustic resonators

Description:
RELATED APPLICATIONS 
     This application claims the benefit of provisional patent application Ser. No. 62/317,675, filed Apr. 4, 2016, the disclosure of which is incorporated herein by reference in its entirety. 
     This application is a Continuation-in-Part of U.S. utility patent application Ser. No. 15/275,957, filed Sep. 26, 2016, which claims the benefit of provisional patent application Ser. No. 62/232,746, filed Sep. 25, 2015; the disclosures of which are incorporated herein by reference in their entireties. 
    
    
     FIELD OF THE INVENTION 
     The present disclosure relates to acoustic resonators and in particular to a tunable compensation circuit for filter circuitry using acoustic resonators. 
     BACKGROUND 
     Acoustic resonators, such as Surface Acoustic Wave (SAW) resonators and Bulk Acoustic Wave (BAW) resonators, are used in many high-frequency communication applications. In particular, SAW resonators are often employed in filter networks that operate frequencies up to 1.8 GHz, and BAW resonators are often employed in filter networks that operate at frequencies above 1.5 GHz. Such filters need to have flat passbands, have steep filter skirts and squared shoulders at the upper and lower ends of the passband, and provide excellent rejection outside of the passband. SAW- and BAW-based filters also have relatively low insertion loss, tend to decrease in size as the frequency of operation increases, and are relatively stable over wide temperature ranges. As such, SAW- and BAW-based filters are the filter of choice for many 3rd Generation (3G) and 4th Generation (4G) wireless devices and are destined to dominate filter applications for 5th Generation (5G) wireless devices. Most of these wireless devices support cellular, wireless fidelity (Wi-Fi), Bluetooth, and/or near field communications on the same wireless device and, as such, pose extremely challenging filtering demands. While these demands keep raising the complexity of wireless devices, there is a constant need to improve the performance of acoustic resonators and filters that are based thereon. 
     To better understand acoustic resonators and various terminology associated therewith, the following provides an overview of a BAW resonator. However, the concepts described herein may employ any type of acoustic resonator and are not limited to SAW- and BAW-based resonators. An exemplary BAW resonator  10  is illustrated in  FIG. 1 . The BAW resonator  10  generally includes a substrate  12 , a reflector  14  mounted over the substrate  12 , and a transducer  16  mounted over the reflector  14 . The transducer  16  rests on the reflector  14  and includes a piezoelectric layer  18 , which is sandwiched between a top electrode  20  and a bottom electrode  22 . The top and bottom electrodes  20  and  22  may be formed of Tungsten (W), Molybdenum (Mo), Platinum (Pt), or like material, and the piezoelectric layer  18  may be formed of Aluminum Nitride (AlN), Zinc Oxide (ZnO), or other appropriate piezoelectric material. Although shown in  FIG. 1  as each including a single layer, the piezoelectric layer  18 , the top electrode  20 , and/or the bottom electrode  22  may include multiple layers of the same material, multiple layers in which at least two layers are different materials, or multiple layers in which each layer is a different material. 
     The BAW resonator  10  is divided into an active region  24  and an outside region  26 . The active region  24  generally corresponds to the section of the BAW resonator  10  where the top and bottom electrodes  20  and  22  overlap and also includes the layers below the overlapping top and bottom electrodes  20  and  22 . The outside region  26  corresponds to the section of the BAW resonator  10  that surrounds the active region  24 . 
     For the BAW resonator  10 , applying electrical signals across the top electrode  20  and the bottom electrode  22  excites acoustic waves in the piezoelectric layer  18 . These acoustic waves primarily propagate vertically. A primary goal in BAW resonator design is to confine these vertically propagating acoustic waves in the transducer  16 . Acoustic waves traveling upward are reflected back into the transducer  16  by the air-metal boundary at the top surface of the top electrode  20 . Acoustic waves traveling downward are reflected back into the transducer  16  by the reflector  14  or by an air cavity, which is provided just below the transducer in a Film BAW Resonator (FBAR). 
     The reflector  14  is typically formed by a stack of reflector layers (RL)  28 , which alternate in material composition to produce a significant reflection coefficient at the junction of adjacent reflector layers  28 . Typically, the reflector layers  28  alternate between materials having high and low acoustic impedances, such as tungsten (W) and silicon dioxide (SiO 2 ). While only five reflector layers  28  are illustrated in  FIG. 1 , the number of reflector layers  28  and the structure of the reflector  14  varies from one design to another. 
     The magnitude (Z) and phase (φ) of the electrical impedance as a function of the frequency for a relatively ideal BAW resonator  10  is provided in  FIG. 2 . The magnitude (Z) of the electrical impedance is illustrated by the solid line, whereas the phase (φ) of the electrical impedance is illustrated by the dashed line. A unique feature of the BAW resonator  10  is that it has both a resonance frequency and an anti-resonance frequency. The resonance frequency is typically referred to as the series resonance frequency (f s ), the anti-resonance frequency is typically referred to as the parallel resonance frequency (f p ). The series resonance frequency (f s ) occurs when the magnitude of the impedance, or reactance, of the BAW resonator  10  approaches zero. The parallel resonance frequency (f p ) occurs when the magnitude of the impedance, or reactance, of the BAW resonator  10  peaks at a significantly high level. In general, the series resonance frequency (f s ) is a function of the thickness of the piezoelectric layer  18  and the mass of the bottom and top electrodes  20  and  22 . 
     For the phase, the BAW resonator  10  acts like an inductance that provides a 90° phase shift between the series resonance frequency (f s ) and the parallel resonance frequency (f p ). In contrast, the BAW resonator  10  acts like a capacitance that provides a −90° phase shift below the series resonance frequency (f s ) and above the parallel resonance frequency (f p ). The BAW resonator  10  presents a very low, near zero, resistance at the series resonance frequency (f s ) and a very high resistance at the parallel resonance frequency (f p ). The electrical nature of the BAW resonator  10  lends itself to the realization of a very high Q (quality factor) inductance over a relatively short range of frequencies, which has proved to be very beneficial in high-frequency filter networks, especially those operating at frequencies around 1.8 GHz and above. 
     Unfortunately, the phase (φ) curve of  FIG. 2  is representative of an ideal phase curve. In reality, approaching this ideal is challenging. A typical phase curve for the BAW resonator  10  of  FIG. 1  is illustrated in  FIG. 3A . Instead of being a smooth curve, the phase curve of  FIG. 3A  includes ripple below the series resonance frequency (f s ), between the series resonance frequency (f s ) and the parallel resonance frequency (f p ), and above the parallel resonance frequency (f p ). The ripple is the result of spurious modes, which are caused by spurious resonances that occur in corresponding frequencies. While the vast majority of the acoustic waves in the BAW resonator  10  propagate vertically, various boundary conditions about the transducer  16  result in the propagation of lateral (horizontal) acoustic waves, which are referred to as lateral standing waves. The presence of these lateral standing waves reduces the potential Q associated with the BAW resonator  10 . 
     As illustrated in  FIG. 4 , a border (BO) ring  30  is formed on or within the top electrode  20  to suppress certain of the spurious modes. The spurious modes that are suppressed by the BO ring  30  are those above the series resonance frequency (f s ), as highlighted by circles A and B in the phase curve of  FIG. 3B . Circle A shows a suppression of the ripple, and thus of the spurious mode, in the passband of the phase curve, which resides between the series resonance frequency (f s ) and the parallel resonance frequency (f p ). Circle B shows suppression of the ripple, and thus of the spurious modes, above the parallel resonance frequency (f p ). Notably, the spurious mode in the upper shoulder of the passband, which is just below the parallel resonance frequency f p , and the spurious modes above the passband are suppressed, as evidenced by the smooth or substantially ripple free phase curve between the series resonance frequency (f s ) and the parallel resonance frequency (f p ) and above the parallel resonance frequency (f p ). 
     The BO ring  30  corresponds to a mass loading of the portion of the top electrode  20  that extends about the periphery of the active region  24 . The BO ring  30  may correspond to a thickened portion of the top electrode  20  or the application of additional layers of an appropriate material over the top electrode  20 . The portion of the BAW resonator  10  that includes and resides below the BO ring  30  is referred to as a BO region  32 . Accordingly, the BO region  32  corresponds to an outer, perimeter portion of the active region  24  and resides inside of the active region  24 . 
     While the BO ring  30  is effective at suppressing spurious modes above the series resonance frequency (f s ), the BO ring  30  has little or no impact on those spurious modes below the series resonance frequency (f s ), as shown by the ripples in the phase curve below the series resonance frequency (f s ) in  FIG. 3B . A technique referred to as apodization is often used to suppress the spurious modes that fall below the series resonance frequency (f s ). 
     Apodization tries to avoid, or at least significantly reduce, any lateral symmetry in the BAW resonator  10 , or at least in the transducer  16  thereof. The lateral symmetry corresponds to the footprint of the transducer  16 , and avoiding the lateral symmetry corresponds to avoiding symmetry associated with the sides of the footprint. For example, one may choose a footprint that corresponds to a pentagon instead of a square or rectangle. Avoiding symmetry helps reduce the presence of lateral standing waves in the transducer  16 . Circle C of  FIG. 3C  illustrates the effect of apodization in which the spurious modes below the series resonance frequency (f s ) are suppressed, as evidence by the smooth or substantially ripple free phase curve below the series resonance frequency (f s ). Assuming no BO ring  30  is provided, one can readily see in  FIG. 3C  that apodization fails to suppress those spurious modes above the series resonance frequency (f s ). As such, the typical BAW resonator  10  employs both apodization and the BO ring  30 . 
     As noted previously, BAW resonators  10  are often used in filter networks that operate at high frequencies and require high Q values. A basic ladder network  40  is illustrated in  FIG. 5A . The ladder network  40  includes two series resonators B SER  and two shunt resonators B SH , which are arranged in a traditional ladder configuration. Typically, the series resonators B SER  have the same or similar first frequency response, and the shunt resonators B SH  have the same or similar second frequency response, which is different from the first frequency response, as shown in  FIG. 5B . In many applications, the shunt resonators B SH  are detuned versions of the series resonators B SER . As a result, the frequency responses for the series resonators B SER  and the shunt resonators B SH  are generally very similar, yet shifted relative to one another such that the parallel resonance frequency (f p,SH ) of the shunt resonators approximates the series resonance frequency (f s,SER ) of the series resonators B SER . Note that the series resonance frequency (f s,SH ) of the shunt resonators B SH  is less than the series resonance frequency (f s,SER ) of the series resonators B SER . The parallel resonance frequency (f p,SH ) of the shunt resonators B SH  is less than the parallel resonance frequency (f p,SER ) of the series resonators B SER . 
       FIG. 5C  is associated with  FIG. 5B  and illustrates the response of the ladder network  40 . The series resonance frequency (f s,SH ) of the shunt resonators B SH  corresponds to the low side of the passband&#39;s skirt (phase 2), and the parallel resonance frequency (f p,SER ) of the series resonators B SER  corresponds to the high side of the passband&#39;s skirt (phase 4). The substantially aligned series resonance frequency (f s,SER ) of the series resonators B SER  and the parallel resonance frequency (f p,SH ) of the shunt resonators B SH  fall within the passband.  FIGS. 6A through 6E  provide circuit equivalents for the five phases of the response of the ladder network  40 . During the first phase (phase 1,  FIGS. 5C, 6A ), the ladder network  40  functions to attenuate the input signal. As the series resonance frequency (f s,SH ) of the shunt resonators B SH  is approached, the impedance of the shunt resonators B SH  drops precipitously such that the shunt resonators B SH  essentially provide a short to ground at the series resonance frequency (f s,SH ) of the shunt resonators (phase 2,  FIGS. 5C, 6B ). At the series resonance frequency (f s,SH ) of the shunt resonators B SH  (phase 2), the input signal is essentially blocked from the output of the ladder network  40 . 
     Between the series resonance frequency (f s,SH ) of the shunt resonators B SH  and the parallel resonance frequency (f p,SER ) of the series resonators B SER , which corresponds to the passband, the input signal is passed to the output with relatively little or no attenuation (phase 3,  FIGS. 5C, 6C ). Within the passband, the series resonators B SER  present relatively low impedance, whereas the shunt resonators B SH  present a relatively high impedance, wherein the combination of the two leads to a flat passband with steep low- and high-side skirts. As the parallel resonance frequency (f p,SER ) of the series resonators B SER  is approached, the impedance of the series resonators B SER  becomes very high, such that the series resonators B SER  essentially present themselves as open at the parallel resonance frequency (f p,SER ) of the series resonators (phase 4,  FIGS. 5C, 6D ). At the parallel resonance frequency (f p,SER ) of the series resonators B SER  (phase 4), the input signal is again essentially blocked from the output of the ladder network  40 . During the final phase (phase 5,  FIGS. 5C, 6E ), the ladder network  40  functions to attenuate the input signal, in a similar fashion to that provided in phase 1. As the parallel resonance frequency (f p,SER ) of the series resonators B SER  is passed, the impedance of the series resonators B SER  decreases and the impedance of the shunt resonators B SH  normalizes. Thus, the ladder network  40  functions to provide a high Q passband between the series resonance frequency (f s,SH ) of the shunt resonators B SH  and the parallel resonance frequency (f p,SER ) of the series resonators B SER . The ladder network  40  provides extremely high attenuation at both the series resonance frequency (f s,SH ) of the shunt resonators B SH  and the parallel resonance frequency (f p,SER ) of the series resonators. The ladder network  40  provides good attenuation below the series resonance frequency (f s,SH ) of the shunt resonators B SH  and above the parallel resonance frequency (f p,SER ) of the series resonators B SER . As noted previously, there is a constant need to improve the performance of acoustic resonators and filters that are based thereon. 
     Those skilled in the art will appreciate the scope of the present disclosure and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures. 
     SUMMARY 
     The present disclosure relates to tunable filter circuitry including a series acoustic resonator between first and second nodes and a compensation circuit in parallel with the series acoustic resonator. The compensation circuit includes first and second inductors coupled in series between the first node and the second node, wherein the first inductor and the second inductor are negatively coupled with one another and a common node is provided between the first and second inductors. The compensation circuit also includes first and second shunt acoustic resonators, which are coupled in parallel with one another between the common node and a fixed voltage node. A first variable capacitor is also coupled between the common node and the fixed voltage node, wherein changing a capacitance of the first variable capacitor changes a bandwidth of a passband of the filter circuitry. A first switch may be coupled in series with the second shunt acoustic resonator, wherein the first switch and the second shunt acoustic resonator are coupled between the common node and the fixed voltage node. 
     The compensation circuit may also include a second variable capacitor, which is coupled in parallel with the at least one series acoustic resonator, wherein changing a capacitance of the second variable capacitor further changes the bandwidth of a passband of the filter circuitry. Bias circuitry may be included to provide a DC bias to one or more of the first and second shunt acoustic resonators, the series acoustic resonators, the first variable capacitor, and the second variable capacitor. 
     In one embodiment, a main series resonance is provided between the first node and the second node at a main resonance frequency through the series acoustic resonator. First and second series resonances at first and second resonance frequencies are provided between the first node and the second node through the compensation circuit, wherein the first and second resonance frequencies are different. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING FIGURES 
       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. 
         FIG. 1  illustrates a conventional Bulk Acoustic Wave (BAW) resonator. 
         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. 
         FIGS. 3A-3C  are graphs of phase responses for various BAW resonator configurations. 
         FIG. 4  illustrates a conventional BAW resonator with a border ring. 
         FIG. 5A  is a schematic of a conventional ladder network. 
         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 . 
         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 . 
         FIG. 7  illustrates an acoustic resonator in parallel with a compensation circuit, which includes a single shunt acoustic resonator. 
         FIG. 8  is a graph that illustrates exemplary frequency responses for the acoustic resonator, compensation circuit, and overall filter circuit of  FIG. 7 . 
         FIG. 9  illustrates an acoustic resonator in parallel with a compensation circuit, which includes at least two shunt acoustic resonators, according to a first embodiment. 
         FIG. 10  is a graph that illustrates exemplary frequency responses for the acoustic resonator, compensation circuit, and overall filter circuit of  FIG. 9 . 
         FIG. 11  is a graph that compares actual frequency responses of the filter circuits of  FIGS. 7 and 9 . 
         FIG. 12  illustrates a plurality of parallel acoustic resonators in parallel with a compensation circuit, which includes at least two shunt acoustic resonators, according to a second embodiment. 
         FIG. 13  is a graph that illustrates first exemplary frequency responses for the acoustic resonator, compensation circuit, and overall filter circuit of  FIG. 12 . 
         FIG. 14  is a graph that illustrates second exemplary frequency responses for the acoustic resonator, compensation circuit, and overall filter circuit of  FIG. 12 . 
         FIGS. 15A through 15D  illustrate transformation of the T-circuit impedance architecture of the compensation circuit of  FIG. 9  to a π (pi) impedance model. 
         FIG. 16  illustrates the filter circuit of  FIG. 9  using the π (pi) impedance model of  FIG. 15D . 
         FIG. 17  is a graph illustrating the overall shunt impedance, Zres, according to one embodiment. 
         FIG. 18  is a graph illustrating the series equivalent impedance, ZA, according to one embodiment. 
         FIGS. 19A and 19B  are graphs over different frequency ranges illustrating the absolute or magnitude of series impedance ZS, the series equivalent impedance ZA, and overall series impedance ZAs, according to one embodiment. 
         FIG. 20  illustrates an acoustic resonator in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a third embodiment. 
         FIG. 21  illustrates a series resonant inductor-capacitor (L-C) circuit in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a fourth embodiment. 
         FIG. 22  illustrates an acoustic resonator in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a fifth embodiment. 
         FIG. 23  illustrates an acoustic resonator in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a sixth embodiment. 
         FIG. 24  illustrates an acoustic resonator in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a seventh embodiment. 
         FIG. 25  illustrates two series acoustic resonators in parallel with a compensation circuit including at least two shunt acoustic resonators, according to an eighth embodiment. 
         FIG. 26  illustrates two series acoustic resonators in parallel with a compensation circuit including at least two shunt acoustic resonators, according to a ninth embodiment. 
         FIG. 27  illustrates a communication circuit that is configured to provide a tunable passband for the filter circuit, according to a tenth embodiment. 
         FIG. 28  is a graph illustrating a variable frequency response and the associated return loss for the embodiment of  FIG. 27 . 
         FIG. 29  illustrates a communication circuit that is configured to provide a tunable passband for the filter circuit, according to an eleventh embodiment. 
         FIG. 30  illustrates a communication circuit that is configured to provide a tunable passband for the filter circuit, according to a twelfth embodiment. 
         FIGS. 31 and 32  are graphs illustrating a variable frequency response and the associated return loss for a first example of the embodiment of  FIG. 30 . 
         FIGS. 33 and 34  are graphs illustrating a variable frequency response and the associated return loss for a second example of the embodiment of  FIG. 30 . 
         FIG. 35  illustrates a communication circuit that is configured to provide a tunable passband for the filter circuit, according to a thirteenth embodiment. 
         FIG. 36  illustrates a communication circuit that is configured to provide a tunable passband for the filter circuit, according to a fourteenth embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     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. 
     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. 
     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. 
     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. 
     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. 
     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. 
     The present disclosure relates to tunable filter circuitry including a series acoustic resonator between first and second nodes and a compensation circuit in parallel with the series acoustic resonator. The compensation circuit includes first and second inductors coupled in series between the first node and the second node, wherein the first inductor and the second inductor are negatively coupled with one another and a common node is provided between the first and second inductors. The compensation circuit also includes first and second shunt acoustic resonators, which are coupled in parallel with one another between the common node and a fixed voltage node. A first variable capacitor is also coupled between the common node and the fixed voltage node, wherein changing a capacitance of the first variable capacitor changes a bandwidth of a passband of the filter circuitry. A first switch may be coupled in series with the second shunt acoustic resonator, wherein the first switch and the second shunt acoustic resonator are coupled between the common node and the fixed voltage node. 
     The compensation circuit may also include a second variable capacitor, which is coupled in parallel with the at least one series acoustic resonator wherein changing a capacitance of the second variable capacitor further changes the bandwidth of a passband of the filter circuitry. Bias circuitry may be provided to provide a DC bias to one or more of the first and second shunt acoustic resonators, the series acoustic resonators, the first variable capacitor, and the second variable capacitor. 
     In various embodiments, the compensation circuit provides three primary functions. The first is to provide a negative capacitive behavior, such that a negative capacitance is presented in parallel with the at least one series acoustic resonator. As such, the effective capacitance of the at least one series acoustic resonator is reduced, which functions to shift the parallel resonance frequency f p  higher. The second function is to add one or more additional series resonances between the first and second nodes. The combination of shifting the parallel resonance frequency f p  higher and adding additional series resonances through the compensation circuit allows for passbands of greater bandwidth while maintaining excellent out-of-band rejection. The third function is to dynamically control the bandwidth of the passbands. Details are provided below. 
     Turning now to  FIG. 7 , a series resonator B 1  is shown coupled between an input node I/P and an output node O/P. The series resonator B 1  has a series resonance frequency f s  and inherent capacitance, which generally limits the bandwidth of filters that employ the series resonator B 1 . In the case of a Bulk Acoustic Wave (BAW) resonator, the capacitance of the series resonator B 1  is primarily caused by its inherent structure, which looks and acts like a capacitor, in part because the series resonator includes the top and bottom electrodes  20 ,  22  ( FIG. 1 ) that are separated by a dielectric piezoelectric layer  18 . While BAW resonators are the focus of the example, other types of acoustic resonators, such as Surface Acoustic Wave (SAW) resonators, are equally applicable. 
     A compensation circuit  42  is coupled in parallel with the series resonator B 1  and functions to compensate for some of the capacitance presented by the series resonator B 1 . The compensation circuit  42  includes two negatively coupled inductors L 1 , L 2  and a shunt resonator B 2 . The inductors L 1 , L 2  are coupled in series between the input node VP and the output node O/P, wherein a common node CN is provided between the inductors L 1 , L 2 . The inductors L 1 , L 2  are magnetically coupled by a coupling factor K, wherein the dots illustrated in association with the inductors L 1 , L 2  indicate that the magnetic coupling is negative. As such, the inductors L 1 , L 2  are connected in electrical series and negatively coupled from a magnetic coupling perspective. As defined herein, two (or more) series-connected inductors that are negatively coupled from a magnetic perspective are inductors that are:
         connected in electrical series; and   the mutual inductance between the two inductors functions to decrease the total inductance of the two (or more) inductors.
 
The shunt resonator B 2  is coupled between the common node CN and ground, or other fixed voltage node.
       

     To compensate for at least some of the capacitance of the series resonator B 1 , the compensation circuit  42  presents itself as a negative capacitance within certain frequency ranges, when coupled in parallel with the series resonator B 1 . Since capacitances in parallel are additive, providing a negative capacitance in parallel with the (positive) capacitance of the series resonator B 1  effectively reduces the capacitance of the series resonator B 1 . With the compensation circuit  42 , the series resonator B 1  can actually function as a filter (instead of just a resonator) and provide a passband, albeit a fairly narrow passband, instead of a more traditional resonator response (solid line of  FIG. 2 ).  FIG. 8  graphically illustrates the frequency responses of the series resonator B 1  (inside the block referenced B 1 ), the compensation circuit  42  (inside the block referenced  42 ), and the filter circuit in which the compensation circuit  42  is placed in parallel with the series resonator B 1 . As illustrated, the filter circuit provides a relatively narrow passband. Further detail on this particular circuit topology can be found in the co-assigned U.S. patent application Ser. No. 15/004,084, filed Jan. 22, 2016, and titled RF LADDER FILTER WITH SIMPLIFIED ACOUSTIC RF RESONATOR PARALLEL CAPACITANCE COMPENSATION, and U.S. patent application Ser. No. 14/757,651, filed Dec. 23, 2015, and titled SIMPLIFIED ACOUSTIC RF RESONATOR PARALLEL CAPACITANCE COMPENSATION, which are incorporated herein by reference. 
     While beneficial in many applications, the narrow passband of the circuit topology of  FIG. 7  has its limitations. With the challenges of modern day communication systems, wider passbands and the ability to provide multiple passbands within a given system are needed. Fortunately, Applicants have discovered that certain modifications to this topology provide significant and truly unexpected increases in passband bandwidths and, in certain instances, the ability to generate multiple passbands of the same or varying bandwidths in an efficient and effective manner. 
     With reference to  FIG. 9 , a modified circuit topology is illustrated wherein the circuit topology of  FIG. 7  is modified to include an additional shunt resonator B 3 , which is coupled between the common node CN and ground. As such, a new compensation circuit  44  is created that includes the negatively coupled inductors L 1  and L 2 , which have a coupling coefficient K, and at least two shunt resonators B 2 , B 3 . The compensation circuit  44  is coupled in parallel with the series resonator B 1 . When the series resonance frequencies f s  of the shunt resonators B 2 , B 3  are different from one another, unexpectedly wide bandwidths passbands are achievable while maintaining a very flat passbands, steep skirts, and excellent cancellation of signals outside of the passbands. 
       FIG. 10  graphically illustrates the frequency responses of the series resonator B 1  (inside the block referenced B 1 ), the compensation circuit  44  (inside the block referenced  44 ), and the filter circuit in which the compensation circuit  44  is placed in parallel with the series resonator B 1 . As illustrated, the filter circuit with compensation circuit  44  provides a much wider passband ( FIG. 10 ) than the filter circuit with compensation circuit  42  ( FIG. 8 ). 
     While  FIGS. 8 and 10  are graphical representations,  FIG. 11  is an actual comparison of the frequency response of the filter circuit using the different compensation circuits  42 ,  44 , wherein the filter circuit using compensation circuit  44  provides a significantly wider and better formed passband (solid line) than the filter circuit using compensation circuit  42  (dashed line). 
     As illustrated in  FIG. 12 , the concepts described herein not only contemplate the use of multiple shunt resonators B 2 , B 3 , which are coupled between the common node CN and ground, but also multiple series resonators, such as series resonators B 1  and B 4 , which are coupled in parallel with one another between the input node VP and the output node O/P. The series resonance frequencies f s  of the series resonators B 1 , B 4  are different from one another, and the series resonance frequencies f s  of the shunt resonators B 2 , B 3  are also different from one another and different from those of the series resonators. While only two series resonators B 1 , B 4  and two shunt resonators B 2 , B 3  are illustrated, any number of these resonators may be employed depending on the application and the desired characteristics of the overall frequency response of the circuit in which these resonators and associated compensation circuits  44  are employed. While the theory of operation is described further subsequently,  FIGS. 13 and 14  illustrate just two of the many possibilities. 
     For  FIG. 13 , there are two series resonators B 1 , B 4  and two shunt resonators B 2 , B 3 , with different and relatively dispersed series resonance frequencies f s .  FIG. 13  graphically illustrates the frequency responses of the combination of the two series resonators B 1 , B 4  (inside the block referenced BX), the compensation circuit  44  with two shunt resonators B 2 , B 3  (inside the block referenced  44 ), and the filter circuit in which the compensation circuit  44  is placed in parallel with the series resonators B 1 , B 4 . As illustrated, the filter circuit in this configuration has the potential to provide a passband that is even wider than that for the embodiment of  FIGS. 9 and 10 . For example, passbands of greater than 100 MHz, 150 MHz, 175 MHz, and 200 MHz are contemplated at frequencies at or above 1.5 GHz, 1.75 GHz, and 2 GHz, respectively. In other words, center-frequency-to-bandwidth ratios (fc/BW*100) of 3.5% to 9%, 12%, or greater are possible, wherein fc is the center frequency of the passband and BW is the bandwidth of the passband. If multiple passbands are provided, BW may encompass all of the provided passbands. Further, when multiple passbands are provided, the passbands may have the same or different bandwidths or center-frequency-to-bandwidth ratios. For example, one passband may have a relatively large center-frequency-to-bandwidth ratio, such as 12%, and a second passband may have a relatively small center-frequency-to-bandwidth ratio, such as 2%. Alternatively, multiple ones of the passbands may have a bandwidth of 100 MHz, or multiple ones of the passbands may have generally the same center-frequency-to-bandwidth ratios. In the latter case, the bandwidths of the passbands may inherently be different from one another, even though the center-frequency-to-bandwidth ratios are the same. 
     For  FIG. 14 , there are four series resonators, which are coupled in parallel with one another (not shown), and two shunt resonators (not shown) with different and more widely dispersed series resonance frequencies f s .  FIG. 14  graphically illustrates the frequency responses of the combination of the four series resonators (inside the block referenced BX), the compensation circuit  44  with two shunt resonators B 2 , B 3  (inside the block referenced  44 ), and the filter circuit in which the compensation circuit  44  is placed in parallel with four series resonators. As illustrated, the filter circuit in this configuration provides multiple passbands, which are separated by a stop band. In this embodiment, two passbands are provided; however, the number of passbands may exceed two. The number of passbands and the bandwidth of each of the passbands is a function of the number of shunt and series resonators B 1 -B 4  and the series resonance frequencies f s  thereof. 
     The theory of the compensation circuit  44  follows and is described in association with  FIGS. 15A through 15D and 16 . With reference to  FIG. 15A , assume the compensation circuit  44  includes the two negatively coupled inductors L 1 , L 2 , which have an inductance value L, and two or more shunt resonators BY, which have an overall shunt impedance Zres presented between the common node CN and ground. While the inductance values L of the negatively coupled inductors L 1 , L 2  are described as being the same, these values may differ depending on the application. Also assume that the one or more series resonators BX present an overall series impedance ZS. 
     As shown in  FIG. 15B , the two negatively coupled and series-connected inductors L 1 , L 2  (without Zres) can be modeled as a T-network of three inductors L 3 , L 4 , and L 5 , wherein series inductors L 3  and L 4  are connected in series and have a value of L(1+K), and shunt inductor L 5  has a value of −L*K, where K is a coupling factor between the negatively coupled inductors L 1 , L 2 . Notably, the coupling factor K is a positive number between 0 and 1. Based on this model, the overall impedance of the compensation circuit  44  is modeled as illustrated in  FIG. 15C , wherein the shunt impedance Zres is coupled between the shunt inductor L 5  and ground. The resulting T-network, as illustrated in  FIG. 15C , can be transformed into an equivalent π (pi) network, as illustrated in  FIG. 15D . 
     The π network of  FIG. 15D  can be broken into a series impedance ZA and two shunt equivalent impedances ZB. The series equivalent impedance ZA is represented by two series inductances of value L*(1+K), where K&gt;0, and a special “inversion” impedance Zinv. The inversion impedance Zinv is equal to [L(1+K)ω] 2 /[Zres−jLKω], where ω=2πf and f is the frequency. As such, the series equivalent impedance ZA equals j*2*L(1+K)ω+Zinv and is coupled between the input node I/O and the output node O/P. Each of the two shunt equivalent impedances ZB is represented by an inductor of value L(1−K) in series with two overall shunt impedances Zres. 
     Notably, the series equivalent impedance ZA has a negative capacitor behavior at certain frequencies at which broadband cancellation is desired and has series resonance at multiple frequencies. In general, the series equivalent impedance ZA has a multiple bandpass-bandstop characteristic in that the series equivalent impedance ZA will pass some frequencies and stop others. When the series equivalent impedance ZA is placed in parallel with the series impedance ZS of the series resonators BX, which can also have a multiple bandpass-bandstop characteristic, a broadband filter or a filter with multiple passbands may be created. 
       FIG. 16  illustrates the series impedance ZS of the series resonators BX in parallel with the series equivalent impedance ZA of the compensation circuit  44 . The overall series impedance ZAs represents the series impedance ZS in parallel with the series equivalent impedance ZA. The two shunt impedances ZB are respectively coupled between the input port VP and ground and the output port O/P and ground. The primary focus for the following discussion relates to the series equivalent impedance ZA and its impact on the series impedance ZS when the series equivalent impedance ZA is placed in parallel with the series impedance ZS. 
     As noted previously, the series equivalent impedance ZA provides two primary functions. The first provides a negative capacitive behavior, and the second provides one or more additional series resonances between the input node VP and the output node O/P. These additional series resonances are provided through the series equivalent impedance ZA and are in addition to any series resonances that are provided through the series impedance ZS of the series resonators BX. To help explain the benefits and concept of the negative capacitive behavior provided by the series equivalent impedance ZA, normal capacitive behavior is illustrated in association with the overall shunt impedance Zres, which is provided by the shunt resonators BY.  FIG. 17  graphs the absolute (magnitude) and imaginary components of the overall shunt impedance Zres, which is formed by two shunt resonators BY, which are coupled in parallel with one another. 
     The series resonance frequency f s  for each of the two shunt resonators BY occurs when the absolute impedance (abs(Zres)) is at or near zero. Since there are two shunt resonators BY, the absolute impedance (abs(Zres)) is at or near zero at two frequencies, and as such, there are two series resonance frequencies f s . The parallel resonance frequencies f p  occur when the imaginary component (imag(Zres)) peaks. Again, since there are two shunt resonators BY, there are two parallel resonance frequencies f p  provided by the overall shunt impedance Zres. 
     Whenever the imaginary component (imag(Zres)) of the overall shunt impedance Zres is less than zero, the overall shunt impedance Zres has a capacitive behavior. The capacitive behavior is characterized in that the reactance of the overall shunt impedance Zres is negative and decreases as frequency increases, which is consistent with capacitive reactance, which is represented by 1/jωC. The graph of  FIG. 17  identifies three regions within the impedance response of the overall shunt impedance Zres that exhibit capacitive behavior. 
     Turning now to  FIG. 18 , the series equivalent impedance ZA is illustrated over the same frequency range as that of the overall shunt impedance Zres, which was illustrated in  FIG. 17 . The series equivalent impedance ZA has two series resonance frequencies f s , which occur when the absolute impedance (abs(ZA)) is at or near zero. The two series resonance frequencies f s  for the series equivalent impedance ZA are different from each other and slightly different from those for the overall shunt impedance Zres. Further, the number of series resonance frequencies f s  generally corresponds to the number of shunt resonators BY in the compensation circuit  44 , assuming the series resonance frequencies f s  are different from one another. 
     Interestingly, the imaginary component (imag(ZA)) of the series equivalent impedance ZA is somewhat inverted with respect to that of the overall shunt impedance Zres. Further, the imaginary component (imag(ZA)) of the series equivalent impedance ZA has a predominantly positive reactance. During the portions at which the imaginary component (imag(ZA)) is positive, the reactance of the series equivalent impedance ZA again decreases as frequency increases, which is indicative of capacitive behavior. However, the reactance is positive, whereas traditional capacitive behavior would present a negative reactance. This phenomenon is referred to as negative capacitive behavior. Those portions of the imaginary component (imag(ZA)) of the series equivalent impedance ZA that are positive and thus exhibit negative capacitive behavior are highlighted in the graph of  FIG. 18 . 
     The negative capacitive behavior of the series equivalent impedance ZA for the compensation circuit  44  is important, because when the series equivalent impedance ZA is placed in parallel with the series impedance ZS, the effective capacitance of the filter circuit is reduced. Reducing the effective capacitance of the filter circuit shifts the parallel resonance frequency f p  of the series impedance ZS higher in the frequency range, which is described subsequently, and significantly increases the available bandwidth for passbands while providing excellent out-of-band rejection. 
     An example of the benefit is illustrated in  FIGS. 19A and 19B . The solid line, which is labeled abs(VG), represents the frequency response of the filter circuit illustrated in  FIG. 12 , wherein there are two series resonators BX and two shunt resonators BY in the compensation circuit  44 . The frequency response has two well-defined passbands, which are separated by a stop band. The frequency response abs(VG) of the filter circuit generally corresponds to the inverse of the overall series impedance ZAs, which again represents the series impedance ZS in parallel with the series equivalent impedance ZA, as provided in  FIG. 16 . 
     Notably, the parallel resonance frequencies f p (ZS) of the series impedance ZS, in isolation, fall in the middle of the passbands of frequency response abs(VG) of the filter circuit. If the parallel resonance frequencies f p (ZS) of the series impedance ZS remained at these locations, the passbands would be severely affected. However, the negative capacitive behavior of the series equivalent impedance ZA functions to shift these parallel resonance frequencies f p (ZS) of the series impedance ZS to a higher frequency and, in this instance, above the respective passbands. This is manifested in the resulting overall series impedance ZAs, in which the only parallel resonance frequencies f p (ZAs) occur above and outside of the respective passbands. An additional benefit to having the parallel resonance frequencies f p (ZAs) occur outside of the respective passbands is the additional cancellation of frequencies outside of the passbands. Plus, the overall series impedance ZAs is lower than the series impedance ZS within the respective passbands. 
     A further contributor to the exemplary frequency response abs(VG) of the filter circuit is the presence of the additional series resonance frequencies f s , which are provided through the series equivalent impedance ZA. These series resonance frequencies f s  are offset from each other and from those provided through the series impedance ZS. The series resonance frequencies f s  for the series equivalent impedance ZA in the series impedance ZS occur when the magnitudes of the respective impedances approach zero. The practical results are wider passbands, steeper skirts for the passbands, and greater rejection outside of the passbands, as evidenced by the frequency response abs(VG) of the filter circuit. 
     Turning now to  FIG. 20 , another embodiment is provided wherein the compensation circuit  44  is placed in parallel with one or more series resonators BX. In this embodiment, shunt resonator B 2  is permanently coupled between the common node CN and ground. Shunt resonators B 3 , B 5 , and B 6  can be selectively coupled between the common node CN and ground via respective switches S 1 , S 2 , and S 3 . By using control circuitry (not shown) to selectively switch the various shunt resonators B 3 , B 5 , and B 6  into and out of the compensation circuit  44 , the passbands and stop bands provided by the filter circuit can be dynamically adjusted for different modes of operation. Again, the series resonance frequencies f s  of the shunt resonators B 2 , B 3 , B 5 , and B 6  will generally differ from one another. Resistors R 1  and R 2  are illustrated and may be coupled between the input node I/P and ground and the output node O/P and ground, respectively. In one embodiment, the series resonance frequency f s  of the series equivalent impedance ZA is greater than the series resonance frequency f s  of the series impedance ZS. The series resonance frequency f s  of at least one of the shunt resonators B 2 , B 3 , B 5 , and B 6  is greater than the series resonance frequency f s  of the series impedance ZS. As with any of these embodiments, the number of shunt resonators BY and series resonators BX may vary from embodiment to embodiment. The number illustrated is merely for illustrative purposes. 
       FIG. 21  illustrates yet another embodiment, which is similar to that illustrated in  FIG. 20 . The difference is that the series resonators BX are replaced with a lumped series L-C circuit, which is formed from a series capacitor CS and a series inductor LS that are coupled in series between the input node I/P and the output node O/P. 
       FIG. 22  illustrates an embodiment similar to that of  FIG. 9 , except that at least one inductor L 6  is coupled in series with shunt resonator B 3 . As such, shunt resonator B 2  is coupled between the common node CN and ground without a series inductor, and shunt resonator B 2  and inductor L 6  are coupled in series with one another and between the common node CN and ground. In one embodiment, the series resonance frequency f s  of the series equivalent impedance ZA is greater than the lowest series resonance frequency f s  of the series impedance ZS.  FIG. 23  illustrates a further modification to the embodiment of  FIG. 22 , wherein an inductor L 7  is placed in series with the series resonators BX, such that the inductor L 7  and the series resonators BX are coupled in series with one another between the input node I/P and the output node O/P. 
     With reference to  FIG. 24 , a more complex filter arrangement is illustrated. In particular, resonators B 7 , B 8 , and B 9  are coupled in series between the input node I/P and the output node O/P. The compensation circuits  44  of  FIG. 22  are coupled across resonator B 7  and resonator B 9 . The resonators B 7 , B 8 , and B 9  may each represent a single acoustic resonator or multiple acoustic resonators in parallel. Notably, the shunt resonators B 2 , B 3 , B 5 , B 6  in the embodiments of  FIGS. 21 through 24 and 30  are considered to be in parallel with one another between the common node CN and ground, even if an additional switch, inductive, capacitive, or like element is provided in series with one or more of the shunt resonators. 
       FIG. 25  illustrates yet another embodiment wherein resonators B 10  and B 11  are coupled in series between the input node I/P and the output node O/P. An inductor L 8  is coupled between node N 1  and ground. The compensation circuit  44  is coupled across both of the resonators B 10  and B 11 . Accordingly, the compensation circuit  44  may be coupled across one or more acoustic resonators along the series path that extends between the input node I/P and the output node O/P. 
       FIG. 26  illustrates a modification to the embodiment of  FIG. 25 , wherein the inductor L 8  is replaced with a shunt resonator B 12 . 
       FIG. 27  illustrates an embodiment wherein the compensation circuit  44  is tunable, such that the bandwidth of the passband for the filter circuit can be varied, or tuned, in a dynamic fashion. As illustrated, the compensation circuit  44  is provided in parallel with the series resonator BX. The compensation circuit  44  differs from the above-described embodiments in that a variable capacitor C 1 , or varactor, is placed in parallel with at least two of the shunt resonators B 2 , B 3  between the common node CN and ground. As the capacitance of the variable capacitor C 1  varies, the bandwidth of the passband for the filter circuit will vary. In this embodiment, the upper skirt of the passband will remain relatively constant, while the location of the lower skirt will vary. In particular, as the capacitance of the variable capacitor C 1  increases, the location of the lower skirt of the passband increases, and vice versa. 
     The graph of  FIG. 28  illustrates the frequency responses of the filter circuit of  FIG. 27  at three different capacitance levels for the variable capacitor C 1 . Frequency response FR 1  has the broadest passband bandwidth and corresponds to the lower of the three capacitance levels. Frequency response FR 2  provides an intermediate passband bandwidth and corresponds to an intermediate capacitance level for the variable capacitor C 1 . Frequency response FR 3  provides the narrowest passband bandwidth and corresponds to a higher capacitance level for the variable capacitor C 1 . As depicted, the upper skirts of the three passbands remain relatively constant, and the location of the lower skirts for the three passbands progressively increase as the capacitance provided by the variable capacitor C 1  increases. The result is that the bandwidth of the passbands decrease as the capacitance provided by the variable capacitor C 1  increases. 
     As illustrated in  FIG. 28 , the three frequency responses FR 1 - 3  exhibit flat passbands, steep side skirts, and excellent out-of-band rejection above and below the passbands. A further benefit of the described circuitry is that the return losses of RL 1 - 3  are excellent within the passband for each of the three corresponding frequency responses FR 1 - 3 , especially for the two wider-bandwidth passbands (RL 1  and RL 2 ). 
       FIG. 29  illustrates a modified version of the filter circuit of  FIG. 28 . In this example, an additional variable capacitor C 2  is provided in parallel with at least two series resonators B 1 , B 4 . The additional variable capacitor C 2  provides additional tunability of the overall frequency response. 
     Turning now to  FIG. 30 , another embodiment is provided where the additional variable capacitor C 2  is provided in parallel with at least two series resonators B 1 , B 4 . In this embodiment, shunt resonator B 2  is permanently coupled between the common node CN and ground. Shunt resonators B 3  and B 5  can be selectively coupled between the common node CN and ground via respective switches S 1  and S 2 . Variable capacitor C 1  is provided in parallel with the shunt resonators B 3  and B 5  between the common node CN and ground. By using control circuitry  46  to selectively switch the various shunt resonators B 3  and B 5  into and out of the compensation circuit  44  using switches S 1  and S 2  as well as varying the capacitance of the variable capacitors C 1  and C 2 , the bandwidths and locations of the passbands provided by the filter circuit can be dynamically adjusted for different modes of operation. Again, the series resonance frequencies f s  of the shunt resonators B 2 , B 3  and B 5  will generally differ from one another. In one embodiment, the series resonance frequency f s  of at least one of the shunt resonators B 2 , B 3 , and B 5  is greater than the series resonance frequency f s  of the series impedance ZS. As with any of these embodiments, the number of shunt resonators BY and series resonators BX may vary from embodiment to embodiment. The number illustrated is merely for illustrative purposes. 
       FIGS. 31 and 32  are graphs of frequency responses and return losses for an exemplary configuration of the filter circuit of  FIG. 30 . Assume that the shunt resonator B 2  has a series resonance frequency of 2.700 GHz, shunt resonator B 3  has a series resonance frequency of 2.470 GHz, and shunt resonator B 5  as a series resonance frequency of 2.490 GHz. For the filter circuit of  FIG. 30 , shunt resonator B 2  is permanently coupled between the common node CN and ground, and the shunt resonators B 3  and B 5  are alternately switched into and out of the circuit using switches S 1  and S 2 , respectively. The total inherent, or parasitic, capacitance for either of the shunt resonators B 3  or B 5  in parallel with shunt resonator B 2  is approximately 0.65 pF. Assume that the variable capacitor C 1  has a capacitance that can vary between 0 pF and at least 0.20 pF. 
     The frequency response FR 4  and the return loss RL 4  illustrated in  FIG. 31  corresponds to the shunt resonator B 3  being switched into the circuit, shunt resonator B 5  being switched out of the circuit, and the capacitance for the variable capacitor C 1  being set to zero. The passband provided by the frequency response FR 4  corresponds to the requisite passband for downlink band  41  (B 41 ) of the LTE (Long Term Evolution) standard for cellular communications. The passband for downlink LTE band B 41  is 2.496 GHz to 2.690 GHz. 
     The frequency response can be dynamically modified to the requisite passband for downlink band  38 X (B 38 X) of the LTE standard by switching the shunt resonator B 3  out of the circuit, switching the shunt resonator B 5  into the circuit, and adjusting the capacitance for the variable capacitor C 1  to approximately 0.20 pF, such that the total capacitance between the common node CN and ground is approximately 0.85 pF (0.20 pF+0.65 pF). The passband for downlink LTE band B 38 X is 2.545 GHz to 2.655 GHz, wherein the upper end of the passband is only 35 MHz lower that required for LTE band B 41 . In  FIG. 32 , the frequency response FR 5  and the return loss RL 5  for LTE band B 38 X is illustrated along with the frequency response FR 4  and the return loss RL 4  for LTE band B 41 . As illustrated, LTE bands B 41  and B 38 X have similar upper skirts but have significantly different locations for the lower skirts. Notably, the return losses RL 4  and RL 5  within the passbands are exceptionally low, and in this example, less than −13 dB throughout a vast majority of the passbands. In this example, assume that variable capacitor C 2  is not used or is set to approximately 0 pF. 
     For the example associated with graphs of  FIGS. 33 and 34 , the variable capacitor C 2  is employed along with the variable capacitor C 1 . Assume that the shunt resonator B 2  has a series resonance frequency of 2.700 GHz, shunt resonator B 3  has a series resonance frequency of 2.470 GHz, shunt resonator B 5  as a series resonance frequency of 2.550 GHz, and series resonator B 1  as a series resonance frequency of 2.552 GHz. Again, shunt resonator B 2  is permanently coupled between the common node CN and ground, and the shunt resonators B 3  and B 5  are alternately switched into and out of the circuit using switches S 1  and S 2 , respectively. The total inherent, or parasitic, capacitance for either of the shunt resonators B 3  or B 5  in parallel with shunt resonator B 2  is approximately 0.95 pF. Assume that the variable capacitor C 1  has a capacitance that can vary between 0 pF and at least 1.20 pF, and the variable capacitor C 1  has a capacitance that can vary between 0 pF and at least 0.35 pF. 
     The frequency response FR 6  and the return loss RL 6  illustrated in  FIG. 33  correspond to the shunt resonator B 3  being switched into the circuit, shunt resonator B 5  being switched out of the circuit, and the capacitances for the variable capacitor C 1  and the variable capacitor C 2  being set to zero. The passband provided by the frequency response FR 4  again corresponds to the requisite passband for LTE band B 41 , which is 2.496 GHz to 2.690 GHz. 
     The frequency response can be dynamically modified to the requisite passband for downlink LTE band  7  (B 7 RX) of the LTE standard by switching the shunt resonator B 3  out of the circuit, switching the shunt resonator B 5  into the circuit, and adjusting the capacitance for the variable capacitor C 1  to approximately 1.20 pF and the capacitance for the variable capacitor C 2  to approximately 0.35 pF. The total capacitance between the common node CN and ground is approximately 1.85 pF (1.20 pF+0.65 pF), and the capacitance across the series resonators B 1  and B 4  is approximately 1.3 pF (0.95 pF+0.35 pF). The passband for LTE band B 7 RX is 2.620 GHz to 2.690 GHz, wherein the upper end of the passband aligns precisely with that required for LTE band B 41 . 
     In  FIG. 34 , the frequency response FR 7  and the return loss RL 7  for LTE band B 7 RX is illustrated along with the frequency response FR 6  and the return loss RL 6  for LTE band B 41 . As illustrated, LTE bands B 41  and B 7 RX have upper skirts that align with one another, but have significantly different locations for the lower skirts. Notably, the return losses RL 6  and RL 7  within the passbands are exceptionally low, and this example, less than −13 dB throughout a vast majority of the passbands. While the above examples relate to LTE bands B 41 , B 41 RX, and B 38 X, the concepts above can apply to any bands in any communication standard. The concepts above are particularly beneficial when implemented in receive filters that rest between one or more antennas and downconversion or other receiver circuitry in virtually any wireless communication application. These concepts may also be implemented in transmit filters. 
     With reference to  FIG. 35 , other techniques may be applied to the compensation circuit  44  to facilitate tuning the passband for the associated filter circuitry. As illustrated, bias circuitry  48  may be used to apply one or more DC bias signals to one or more of the variable capacitor C 1 , shunt resonator B 2 , and shunt resonator B 3 . In this example, the DC bias signal is a DC voltage that is applied to the common node CN. Doing so adjusts the effective capacitance between the common node CN and ground, and thus, will shift at least the lower skirt of the passband up or down. 
     As illustrated in  FIG. 36 , the same DC bias signal or different DC bias signals may be provided to the variable capacitor C 2 , series resonator B 1 , and/or series resonator B 4 , to adjust the series capacitance presented between the input node VP and the output node O/P. Adjusting the series capacitance also impacts the center frequency, lower skirt, and/or upper skirt of the passband provided by the filter circuit. The bias circuitry  48  may also be applied to the embodiments of  FIG. 30 , wherein the DC bias signals provided to the variable capacitor C 1 , variable capacitor C 2 , and/or any of the series resonators B 1 , B 4  and shunt resonators B 2 , B 3 , and B 5 . 
     Those skilled in the art will recognize numerous modifications and other embodiments that incorporate the concepts described herein. These modifications and embodiments are considered to be within scope of the teachings provided herein and the claims that follow.