Patent Publication Number: US-9837984-B2

Title: RF ladder filter with simplified acoustic RF resonator parallel capacitance compensation

Description:
RELATED APPLICATIONS 
     The present application claims the benefits of U.S. provisional patent application No. 62/106,901 filed Jan. 23, 2015, and U.S. provisional patent application No. 62/107,852, filed Jan. 26, 2015. 
     The present application claims the benefit of and is a continuation-in-part of U.S. patent application Ser. No. 14/757,651 filed Dec. 23, 2015, entitled “SIMPLIFIED ACOUSTIC RF RESONATOR PARALLEL CAPACITANCE COMPENSATION,” which claims priority to U.S. provisional patent application No. 62/096,801 filed Dec. 24, 2014, and U.S. provisional patent application No. 62/109,693 filed Jan. 30, 2015. 
     All of the applications listed above are hereby incorporated herein by reference in their entireties. 
    
    
     FIELD OF THE DISCLOSURE 
     Embodiments of the present disclosure relate to radio frequency (RF) communications systems, which may include RF front-end circuitry, RF transceiver circuitry, RF transmit circuitry, RF receive circuitry, RF diplexers, RF duplexers, RF filters, RF antennas, RF switches, RF combiners, RF splitters, the like, or any combination thereof. 
     BACKGROUND 
     As wireless communications technologies evolve, wireless communications systems become increasingly sophisticated. As such, wireless communications protocols continue to expand and change to take advantage of the technological evolution. As a result, to maximize flexibility, many wireless communications devices must be capable of supporting any number of wireless communications protocols, each of which may have certain performance requirements, such as specific out of band emissions requirements, linearity requirements, or the like. Further, portable wireless communications devices are typically battery powered and need to be relatively small, and have low cost. As such, to minimize size, cost, and power consumption, an RF ladder filter in such a device needs to be as simple, small, flexible, high performance, and efficient as is practical. Thus, there is a need for an RF ladder filter in a communications device that is low cost, small, simple, flexible, high performance, and efficient. 
     SUMMARY 
     An RF ladder filter having a parallel capacitance compensation circuit is disclosed. The parallel capacitance compensation circuit is made up of a first inductive element with a first T-terminal and a first end coupled to a first ladder terminal and a second inductive element with a second T-terminal that is coupled to the first T-terminal of the first inductive element and a second end coupled to a second ladder terminal. Further included is a compensating acoustic RF resonator (ARFR) having a fixed node terminal and a third T-terminal that is coupled to the first T-terminal of the first inductive element and the second T-terminal of the second inductive element, and a finite number of series-coupled ladder ARFRs, wherein the parallel capacitance compensation circuit is coupled across one of the finite number of series-coupled ARFRs by way of the first ladder terminal and the second ladder terminal. 
     Those skilled in the art will appreciate the scope of the disclosure and realize additional aspects thereof after reading the following detailed description in association with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings 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. 1A  shows a first acoustic RF resonator (ARFR) and a load resistive element according to the prior art. 
         FIG. 1B  illustrates a simplified behavioral model of the first ARFR illustrated in  FIG. 1  according to the prior art. 
         FIG. 2A  is a graph illustrating an electrical impedance of the first ARFR over an operating frequency ranges of the first ARFR according to the prior art. 
         FIG. 2B  is a graph illustrating a preferred electrical impedance of the first ARFR over the operating frequency ranges of the first ARFR according to one embodiment of the present disclosure. 
         FIG. 3  shows RF circuitry according to one embodiment of the RF circuitry. 
         FIG. 4  shows the RF circuitry according to an alternate embodiment of the RF circuitry. 
         FIG. 5  shows details of a capacitance circuit illustrated in  FIG. 4  according to one embodiment of the capacitance circuit. 
         FIG. 6  shows details of the capacitance circuit illustrated in  FIG. 4  according to an alternate embodiment of the capacitance circuit. 
         FIG. 7  shows details of the capacitance circuit illustrated in  FIG. 4  according to an additional embodiment of the capacitance circuit. 
         FIG. 8  shows the RF circuitry according to an additional embodiment of the RF circuitry. 
         FIG. 9  shows the RF circuitry according to another embodiment of the RF circuitry. 
         FIG. 10  shows the RF circuitry according to a further embodiment of the RF circuitry. 
         FIG. 11A  shows the first ARFR and the load resistive element according to the prior art. 
         FIG. 11B  shows the first ARFR, the load resistive element, and a first parallel capacitance compensation circuit according to one embodiment of the first ARFR, the load resistive element, and the first parallel capacitance compensation circuit. 
         FIG. 12A  is a graph illustrating a magnitude of an RF output signal illustrated in  FIG. 11A  according to the prior art. 
         FIG. 12B  is a graph illustrating a magnitude of the RF output signal illustrated in  FIG. 11B  according to one embodiment of the first ARFR, the load resistive element, and the first parallel capacitance compensation circuit. 
         FIG. 13  shows the RF circuitry according to one embodiment of the RF circuitry. 
         FIG. 14  shows the RF circuitry according to an alternate embodiment of the RF circuitry. 
         FIG. 15  shows details of the RF TX/RX multiplexer illustrated in  FIG. 13  according to one embodiment of the RF TX/RX multiplexer. 
         FIG. 16  shows details of the RF TX/RX multiplexer illustrated in  FIG. 14  according to an alternate embodiment of the RF TX/RX multiplexer. 
         FIG. 17A  shows details of the first antenna, first RF RX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter. 
         FIG. 17B  shows details of the first antenna, second RF RX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, second RF RX bandpass filter. 
         FIG. 18A  shows details of the first antenna, first RF RX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter. 
         FIG. 18B  shows details of the first antenna, second RF RX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF TX bandpass filter. 
         FIG. 19A  shows details of the first antenna, first RF RX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter. 
         FIG. 19B  shows details of the second antenna, first RF RX bandpass filter illustrated in  FIG. 16  according to one embodiment of the second antenna, first RF RX bandpass filter. 
         FIG. 20A  shows details of the first antenna, first RF TX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF TX bandpass filter. 
         FIG. 20B  shows details of the first antenna, second RF TX bandpass filter illustrated in  FIG. 15  according to one embodiment of the first antenna, second RF TX bandpass filter. 
         FIG. 21A  shows a portion of the RF circuitry according to one embodiment of the RF circuitry. 
         FIG. 21B  shows a portion of the RF circuitry according to one embodiment of the RF circuitry. 
         FIG. 22A  is a reproduction of the RF circuitry illustrated in  FIG. 10 . 
         FIG. 22B  shows the RF circuitry of  FIG. 22A  modeled using a wye-delta transform. 
         FIG. 23  is a schematic of a related art ladder filter that includes a finite number of ARFRs coupled in series. 
         FIG. 24  is a schematic of a related art ladder filter that uses an inductor to compensate for the parallel capacitance for one of the ARFRs that comprise the related art ladder filter. 
         FIG. 25  is a schematic of an embodiment of a ladder filter  94  that is in accordance with the present disclosure. 
         FIG. 26  is a simulation plot of out of band improvements realized by the ladder filter. 
         FIG. 27  is a simulation plot of in band insertion loss associated with the ladder filter  94  as configured for an 8 th  order B7 RX filter. 
         FIG. 28A  is a schematic of RF circuitry in which the first inductor L 1  and the second inductor L 2  are negatively magnetically coupled. 
         FIG. 28B  is a schematic of RF circuitry that is transformed to an equivalent bridged T network. 
         FIG. 28C  is a schematic of RF circuitry that has been transformed from the equivalent bridged T network to an equivalent PI network. 
         FIG. 29A  depicts a schematic model of a ladder filter that is similar to a traditional ladder filter. 
         FIG. 29B  is a schematic of a ladder filter according to an embodiment of the present disclosure that replaces two shunt resonators of  FIG. 29A . 
     
    
    
     DETAILED DESCRIPTION 
     The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the disclosure and illustrate the best mode of practicing the disclosure. Upon reading the following description in light of the accompanying drawings, 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. 
     RF circuitry, which includes a first acoustic RF resonator (ARFR), a first compensating ARFR, and a second compensating ARFR, is disclosed according to one embodiment of the present disclosure. The first compensating ARFR is coupled between a first inductive element and a first end of the first ARFR. The second compensating ARFR is coupled between a second inductive element and a second end of the first ARFR. The first inductive element and the second inductive element are negatively coupled to one another. The first compensating ARFR, the second compensating ARFR, the first inductive element, and the second inductive element at least partially compensate for a parallel capacitance of the first ARFR. 
     RF circuitry, which includes the first ARFR and the first compensating ARFR, is disclosed according to an alternate embodiment of the present disclosure. The first inductive element is coupled between the first compensating ARFR and a first end of the first ARFR. The second inductive element is coupled between the first compensating ARFR and a second end of the first ARFR. The first compensating ARFR, the first inductive element, and the second inductive element at least partially compensate for the parallel capacitance of the first ARFR. In one embodiment of the first inductive element and the second inductive element, the first inductive element and the second inductive element are negatively coupled to one another. 
       FIG. 1A  shows a first ARFR  10  and a load resistive element RL according to the prior art. The first ARFR  10  and the load resistive element RL are coupled in series to ground to form an RF filter, which has RF bandpass filtering characteristics. The first ARFR  10  receives an RF input signal RFN and a connection between the first ARFR  10  and the load resistive element RL provides an RF output signal RFT. 
       FIG. 1B  illustrates a simplified behavioral model of the first ARFR  10  illustrated in  FIG. 1  according to the prior art. According to the simplified behavioral model, the first ARFR  10  has a series resistance RS, a series inductance LS, and a series capacitance CS coupled in series with one another. Additionally, the first ARFR  10  has a parallel capacitance CP coupled in parallel with a series combination of the series capacitance CS and the series inductance LS. As a result, the first ARFR  10  has a series resonant frequency F S  ( FIG. 2A ) and a parallel resonant frequency F P  ( FIG. 2A ). 
       FIG. 2A  is a graph illustrating an electrical impedance of the first ARFR  10  ( FIG. 1A ) over an operating frequency range of the first ARFR  10  ( FIG. 1A ) according to the prior art. When using the first ARFR  10  ( FIG. 1A ) as a series element in an RF bandpass filter, preferably the series resonant frequency F S  falls within a passband of the RF bandpass filter and the parallel resonant frequency F P  falls outside of the passband of the RF bandpass filter. However, if the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10  is large, then a bandwidth of the RF bandpass filter may be too narrow to meet design requirements. Additionally, since the parallel capacitance CP ( FIG. 1B ) appears primarily across the first ARFR  10  ( FIG. 1A ), as frequency increases, impedance of the parallel capacitance CP ( FIG. 1B ) drops, thereby degrading RF bandpass filtering performance at higher frequencies. Reducing the parallel capacitance CP ( FIG. 1B ) drives the parallel resonant frequency F P  to higher values. However, the power handling capabilities of the first ARFR  10  (FIG.  1 A) may be reduced below requirements. Thus, there is a need to reduce the effects of the parallel resonant frequency F P , particularly in RF bandpass filtering applications. 
     One metric for quantifying bandpass filter effectiveness of the first ARFR  10  ( FIG. 1A ) is an RF coupling factor (k2e), which is defined as shown in EQ. 1 below.
 
 k 2 e =[(π/2)*( F   S   /F   P )]/[tan((π/2)*( F   S   /F   P ))].  EQ. 1:
 
     As the parallel resonant frequency F P  increases relative to the series resonant frequency F S , k2e increases, thereby improving the bandpass filter effectiveness of the first ARFR  10  ( FIG. 1A ). One way to increase the parallel resonant frequency F P  of the first ARFR  10  ( FIG. 1A ) is decrease a net parallel capacitance CP ( FIG. 1A ) of the first ARFR  10  ( FIG. 1A ). 
       FIG. 2B  is a graph illustrating a preferred electrical impedance of the first ARFR  10  ( FIG. 1A ) over the operating frequency ranges of the first ARFR  10  ( FIG. 1A ) according to one embodiment of the present disclosure. As such, a first parallel capacitance compensation circuit  12  ( FIG. 3 ) is coupled across the first ARFR  10  ( FIG. 1A ) to at least partially compensate for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10  ( FIG. 1A ), thereby increasing the parallel resonant frequency F P  and increasing k2e. 
       FIG. 3  shows RF circuitry  12  according to one embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 3  includes the first ARFR  10  and a first parallel capacitance compensation circuit  14 , which includes a first compensating ARFR  16 , a second compensating ARFR  18 , a first inductive element L 1 , and a second inductive element L 2 . 
     The first compensating ARFR  16  is coupled between the first inductive element L 1  and a first end of the first ARFR  10 . The second compensating ARFR  18  is coupled between the second inductive element L 2  and a second end of the first ARFR  10 . The first inductive element L 1  and the second inductive element L 2  have mutual coupling M between them as illustrated in  FIG. 3 . Further, the first inductive element L 1  and the second inductive element L 2  are negatively coupled to one another as illustrated in  FIG. 3 . The first compensating ARFR  16 , the second compensating ARFR  18 , the first inductive element L 1 , and the second inductive element L 2  at least partially compensate for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . In general, in one embodiment of the RF circuitry  12 , the first parallel capacitance compensation circuit  14  at least partially compensate for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . 
     The first inductive element L 1  is coupled between the first compensating ARFR  16  and ground. The second inductive element L 2  is coupled between the second compensating ARFR  18  and the ground. In general, in one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is a passive circuit, which includes no active components. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , an absolute value of a coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than zero. In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than 0.1. In an additional embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than 0.2. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.7. In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.6. In an additional embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.5. In another embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.4. In a further embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.3. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , an inductance of the first inductive element L 1  is essentially equal to an inductance of the second inductive element L 2 . In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the inductance of the first inductive element L 1  is not equal to the inductance of the second inductive element L 2 . 
     In one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  augments RF bandpass filtering behavior of the first ARFR  10 . In one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  increases a ratio of the parallel resonant frequency F P  ( FIG. 2B ) to the series resonant frequency F S  ( FIG. 2B ). 
     In one embodiment of the first parallel capacitance compensation circuit  14  and the first ARFR  10 , the first parallel capacitance compensation circuit  14  and the first ARFR  10  function as an RF bandpass filtering element, such that the parallel resonant frequency F P  ( FIG. 2B ) falls outside of a passband of the RF bandpass filtering element. 
     In one embodiment of the first parallel capacitance compensation circuit  14  and the first ARFR  10 , the first parallel capacitance compensation circuit  14  is coupled across the first ARFR  10 , such that the first parallel capacitance compensation circuit  14  presents a positive reactance across the first ARFR  10 . A magnitude of the positive reactance is inversely related to frequency. Since the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10  presents a negative reactance across the first ARFR  10 , such that the negative reactance is inversely related to frequency, the positive reactance at least partially cancels the negative reactance, thereby at least partially compensating for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . 
     In one embodiment of the first ARFR  10 , the first compensating ARFR  16 , and the second compensating ARFR  18 , each of the first ARFR  10 , the first compensating ARFR  16 , and the second compensating ARFR  18  is a surface acoustic wave (SAW) RF resonator. In an alternate embodiment of the first ARFR  10 , the first compensating ARFR  16 , and the second compensating ARFR  18 , each of the first ARFR  10 , the first compensating ARFR  16 , and the second compensating ARFR  18  is a bulk acoustic wave (BAW) RF resonator. 
       FIG. 4  shows the RF circuitry  12  according to an alternate embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 4  is similar to the RF circuitry  12  illustrated in  FIG. 3 , except in the RF circuitry  12  illustrated in  FIG. 4 , the first parallel capacitance compensation circuit  14  further includes a capacitance circuit  20 . In general, the capacitance circuit  20  is coupled between the first inductive element L 1  and the ground and is further coupled between the second inductive element L 2  and the ground. In one embodiment of the capacitance circuit  20 , the capacitance circuit  20  is used to optimize the first parallel capacitance compensation circuit  14  for improved compensation of the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . 
       FIG. 5  shows details of the capacitance circuit  20  illustrated in  FIG. 4  according to one embodiment of the capacitance circuit  20 . In the capacitance circuit  20  illustrated in  FIG. 5 , a first end of the first inductive element L 1  is coupled to a first end of the second inductive element L 2 , such that the capacitance circuit  20  presents a shunt capacitance CN between ground and both of the first inductive element L 1  and the second inductive element L 2 . 
       FIG. 6  shows details of the capacitance circuit  20  illustrated in  FIG. 4  according to an alternate embodiment of the capacitance circuit  20 . In the capacitance circuit  20  illustrated in  FIG. 6 , the second inductive element L 2  is coupled between the second compensating ARFR  18  and ground, and the capacitance circuit  20  presents the shunt capacitance CN between ground and the first inductive element L 1 . 
       FIG. 7  shows details of the capacitance circuit  20  illustrated in  FIG. 4  according to an additional embodiment of the capacitance circuit  20 . In the capacitance circuit  20  illustrated in  FIG. 7 , the first inductive element L 1  is coupled between the first compensating ARFR  16  and ground, and the capacitance circuit  20  presents the shunt capacitance CN between ground and the second inductive element L 2 . 
       FIG. 8  shows the RF circuitry  12  according to an additional embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 8  is similar to the RF circuitry  12  illustrated in  FIG. 4 , except in the RF circuitry  12  illustrated in  FIG. 8 , the capacitance circuit  20  is replaced with a variable capacitance circuit  22 . In one embodiment of the variable capacitance circuit  22 , the variable capacitance circuit  22  is used to vary the shunt capacitance CN illustrated in  FIG. 5 . In an alternate embodiment of the variable capacitance circuit  22 , the variable capacitance circuit  22  is used to vary the shunt capacitance CN illustrated in  FIG. 6 . In an additional embodiment of the variable capacitance circuit  22 , the variable capacitance circuit  22  is used to vary the shunt capacitance CN illustrated in  FIG. 7 . 
     In one embodiment of the variable capacitance circuit  22 , the variable capacitance circuit  22  receives the first function configuration signal FCS 1 , such that the shunt capacitance CN is adjusted based on the first function configuration signal FCS 1 . 
       FIG. 9  shows the RF circuitry  12  according to another embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 9  includes the first ARFR  10  and the first parallel capacitance compensation circuit  14 , which includes the first compensating ARFR  16 , the first inductive element L 1 , and the second inductive element L 2 . 
     The first inductive element L 1  is coupled between the first compensating ARFR  16  and a first end of the first ARFR  10 . The second inductive element L 2  is coupled between the first compensating ARFR  16  and a second end of the first ARFR  10 . The first inductive element L 1  and the second inductive element L 2  have mutual coupling M between them as illustrated in  FIG. 9 . Further, the first inductive element L 1  and the second inductive element L 2  are negatively coupled to one another as illustrated in  FIG. 9 . The first compensating ARFR  16 , the first inductive element L 1 , and the second inductive element L 2  at least partially compensate for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . In general, in one embodiment of the RF circuitry  12 , the first parallel capacitance compensation circuit  14  at least partially compensate for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . 
     The first compensating ARFR  16  is coupled between the first inductive element L 1  and ground. Additionally, the first compensating ARFR  16  is further coupled between the second inductive element L 2  and the ground. In general, in one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is a passive circuit, which includes no active components. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , an absolute value of a coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than zero. In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than 0.1. In an additional embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is greater than 0.2. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.7. In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.6. In an additional embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.5. In another embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.4. In a further embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is less than 0.3. 
     In one embodiment of the first inductive element L 1  and the second inductive element L 2 , an inductance of the first inductive element L 1  is essentially equal to an inductance of the second inductive element L 2 . In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the inductance of the first inductive element L 1  is not equal to the inductance of the second inductive element L 2 . 
     In one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  augments RF bandpass filtering behavior of the first ARFR  10 . In one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  increases a ratio of the parallel resonant frequency F P  ( FIG. 2B ) to the series resonant frequency F S  ( FIG. 2B ). 
     In one embodiment of the first parallel capacitance compensation circuit  14  and the first ARFR  10 , the first parallel capacitance compensation circuit  14  and the first ARFR  10  function as an RF bandpass filtering element, such that the parallel resonant frequency F P  ( FIG. 2B ) falls outside of a passband of the RF bandpass filtering element. 
     In one embodiment of the first parallel capacitance compensation circuit  14  and the first ARFR  10 , the first parallel capacitance compensation circuit  14  is coupled across the first ARFR  10 , such that the first parallel capacitance compensation circuit  14  presents a positive reactance across the first ARFR  10 . A magnitude of the positive reactance is inversely related to frequency. Since the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10  presents a negative reactance across the first ARFR  10 , such that the negative reactance is inversely related to frequency, the positive reactance at least partially cancels the negative reactance, thereby at least partially compensating for the parallel capacitance CP ( FIG. 1B ) of the first ARFR  10 . 
     In one embodiment of the first ARFR  10  and the first compensating ARFR  16 , each of the first ARFR  10  and the first compensating ARFR  16  is a SAW RF resonator. In an alternate embodiment of the first ARFR  10  and the first compensating ARFR  16 , each of the first ARFR  10  and the first compensating ARFR  16  is a BAW RF resonator. 
       FIG. 10  shows the RF circuitry  12  according to a further embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 10  is similar to the RF circuitry  12  illustrated in  FIG. 9 , except in the RF circuitry  12  illustrated in  FIG. 10 , there is no intended mutual coupling M ( FIG. 9 ) between the first inductive element L 1  and the second inductive element L 2 . As such, the absolute value of the coefficient of coupling between the first inductive element L 1  and the second inductive element L 2  is essentially equal to zero. 
       FIG. 11A  shows the first ARFR  10  and the load resistive element RL according to the prior art. The first ARFR  10  and the load resistive element RL illustrated in  FIG. 11A  are similar to the first ARFR  10  and the load resistive element RL illustrated in  FIG. 1A . 
       FIG. 11B  shows the first ARFR  10 , the load resistive element RL, and the first parallel capacitance compensation circuit  14  according to one embodiment of the first ARFR  10 , the load resistive element RL, and the first parallel capacitance compensation circuit  14 . The first ARFR  10  and the load resistive element RL illustrated in  FIG. 11B  is similar to the first ARFR  10  and the load resistive element RL illustrated in  FIG. 1A , except in  FIG. 11B , the first parallel capacitance compensation circuit  14  is coupled across the first ARFR  10 . 
     The first parallel capacitance compensation circuit  14  illustrated in  FIG. 11B  may include any of the embodiments of the first parallel capacitance compensation circuit  14  illustrated in  FIGS. 3, 4, 5, 6, 7, 8, 9, 10 , or any combination thereof. 
       FIG. 12A  is a graph illustrating a magnitude of the RF output signal RFT illustrated in  FIG. 11A  according to the prior art. The magnitude of the RF output signal RFT is shown versus frequency of the RF output signal RFT. A preferred passband is illustrated. The RF output signal RFT illustrated in  FIG. 12A  has insufficient bandwidth to support the preferred passband. Additionally, an out of band magnitude of the RF output signal RFT increases as the frequency of the RF output signal RFT increases due to the parallel capacitance CP ( FIG. 1B ). As such, the first ARFR  10  and the load resistive element RL illustrated in  FIG. 11A  do not provide good out of band rejection of the RF output signal RFT. 
       FIG. 12B  is a graph illustrating a magnitude of the RF output signal RFT illustrated in  FIG. 11B  according to one embodiment of the first ARFR  10 , the load resistive element RL, and the first parallel capacitance compensation circuit  14 . By adding the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  at least partially compensates for the parallel capacitance CP ( FIG. 1B ). 
     As a result, the RF output signal RFT has adequate bandwidth to support the preferred passband. Also, while the out of band magnitude of the RF output signal RFT illustrated in  FIG. 12B  increases as the frequency of the RF output signal RFT increases, the out of band magnitude of the RF output signal RFT illustrated in  FIG. 12B  is significantly less than the out of band magnitude of the RF output signal RFT illustrated in  FIG. 12A . 
       FIG. 13  shows the RF circuitry  12  according to one embodiment of the RF circuitry  12 . The RF circuitry  12  includes RF system control circuitry  24 , RF front-end circuitry  26 , and a first RF antenna  28 . The RF front-end circuitry  26  includes an RF TX/RX multiplexer  30 , RF receive circuitry  32 , and RF transmit circuitry  34 . The RF TX/RX multiplexer  30  has a first common connection node CN 1 , which is coupled to the first RF antenna  28 . In one embodiment of the RF TX/RX multiplexer  30 , the first common connection node CN 1  is directly coupled to the first RF antenna  28 . The RF system control circuitry  24  provides a first function configuration signal FCS 1  to the RF front-end circuitry  26 . As such, in one embodiment of the RF front-end circuitry  26 , the RF system control circuitry  24  configures any or all of the RF TX/RX multiplexer  30 , the RF receive circuitry  32 , and the RF transmit circuitry  34  using the first function configuration signal FCS 1 . 
     In one embodiment of the RF system control circuitry  24 , the RF system control circuitry  24  provides a first antenna, first upstream RF transmit signal T 1 U 1 , a first antenna, second upstream RF transmit signal T 1 U 2 , and up to and including a first antenna, M TH  upstream RF transmit signal T 1 UM to the RF transmit circuitry  34 . In general, the RF system control circuitry  24  provides a group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM to the RF transmit circuitry  34 . 
     The RF transmit circuitry  34  processes the first antenna, first upstream RF transmit signal T 1 U 1  to provide a first antenna, first downstream RF transmit signal T 1 D 1  to the RF TX/RX multiplexer  30 , the first antenna, second upstream RF transmit signal T 1 U 2  to provide a first antenna, second downstream RF transmit signal T 1 D 2  to the RF TX/RX multiplexer  30 , and up to and including the first antenna, M TH  upstream RF transmit signal T 1 UM to provide a first antenna, M TH  downstream RF transmit signal T 1 DM to the RF TX/RX multiplexer  30 . In general, the RF transmit circuitry  34  provides a group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM to the RF TX/RX multiplexer  30 . 
     In one embodiment of the RF system control circuitry  24 , the RF system control circuitry  24  provides at least one of the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM to the RF transmit circuitry  34 , which processes and forwards any or all of the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM to provide a corresponding any or all of the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM to the RF TX/RX multiplexer  30 . The RF TX/RX multiplexer  30  receives, bandpass filters, and forwards the corresponding any or all of the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM to provide a corresponding any or all of a first antenna, first RF antenna transmit signal T 1 A 1 , a first antenna, second RF antenna transmit signal T 1 A 2 , and up to and including a first antenna, M TH  RF antenna transmit signal T 1 AM to the first RF antenna  28  via the first common connection node CN 1 . 
     The RF transmit circuitry  34  may include up-conversion circuitry, amplification circuitry, power supply circuitry, filtering circuitry, switching circuitry, combining circuitry, splitting circuitry, dividing circuitry, clocking circuitry, the like, or any combination thereof to process any or all of the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM. In one embodiment of the RF transmit circuitry  34 , the RF transmit circuitry  34  includes circuitry to reduce interference of RF receive signals in the RF TX/RX multiplexer  30  by processing the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM in the RF TX/RX multiplexer  30 . 
     In one embodiment of the RF TX/RX multiplexer  30 , the RF TX/RX multiplexer  30  receives any or all of a first antenna, first RF receive signal R 1 A 1 ; a first antenna, second RF receive signal R 1 A 2 ; and up to and including a first antenna, N TH  RF receive signal R 1 AN; which are received via the first RF antenna  28 . In general, the RF TX/RX multiplexer  30  receives any or all of a group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN from the first common connection node CN 1 . In one embodiment of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN, any or all of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN are received simultaneously, such that the RF TX/RX multiplexer  30  supports receive downlink carrier aggregation (RXDLCA). 
     The RF TX/RX multiplexer  30  processes and forwards any or all of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN from the first common connection node CN 1  to provide any or all of a first antenna, first upstream RF receive signal R 1 U 1 , a first antenna, second upstream RF receive signal R 1 U 2 , and up to and including a first antenna, N TH  upstream RF receive signal R 1 UN. In general, the RF TX/RX multiplexer  30  provides any or all of a group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN to the RF receive circuitry  32 . 
     In one embodiment of the RF receive circuitry  32 , the RF receive circuitry  32  receives and processes any or all of the group of the first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN to provide a corresponding any or all of a group of first antenna, downstream RF receive signals R 1 D 1 , R 1 D 2 , R 1 DN. 
     In an additional embodiment of the RF receive circuitry  32 , the RF receive circuitry  32  simultaneously receives and processes any or all of the group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN. As such, the RF receive circuitry  32  supports RXDLCA. The RF receive circuitry  32  may include down-conversion circuitry, amplification circuitry, low noise amplification circuitry, power supply circuitry, filtering circuitry, switching circuitry, combining circuitry, splitting circuitry, dividing circuitry, clocking circuitry, the like, or any combination thereof. 
     In one embodiment of the RF front-end circuitry  26 , any or all of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN, any or all of the group of first antenna, RF antenna transmit signals T 1 A 1 , T 1 A 2 , T 1 AM, any or all of the group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN, any or all of the group of first antenna, downstream RF receive signals R 1 D 1 , R 1 D 2 , R 1 DN, any or all of the group of upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM, and any or all of the group of downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM are omitted. 
     In one embodiment of the RF system control circuitry  24 , the RF system control circuitry  24  provides the first function configuration signal FCS 1  to the RF TX/RX multiplexer  30 , the RF receive circuitry  32 , and the RF transmit circuitry  34 . As such, the RF system control circuitry  24  may configure, tune, adjust, enable, disable, vary, or any combination thereof, circuits within the RF TX/RX multiplexer  30 , the RF receive circuitry  32 , the RF transmit circuitry  34 , or any combination thereof, as necessary, using the first function configuration signal FCS 1 . 
       FIG. 14  shows the RF circuitry  12  according to an alternate embodiment of the RF circuitry  12 . The RF circuitry  12  illustrated in  FIG. 14  is similar to the RF circuitry  12  illustrated in  FIG. 13 , except the RF circuitry  12  illustrated in  FIG. 14  further includes a second RF antenna  36 . Additionally, the RF TX/RX multiplexer  30  further has a second common connection node CN 2 , which is coupled to the second RF antenna  36 . 
     In one embodiment of the RF system control circuitry  24 , the RF system control circuitry  24  further provides a second antenna, first upstream RF transmit signal T 2 U 1 , a second antenna, second upstream RF transmit signal T 2 U 2 , and up to and including a second antenna, T TH  upstream RF transmit signal T 2 UT to the RF transmit circuitry  34 . In general, the RF system control circuitry  24  provides the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM and a group of second antenna, upstream RF transmit signals T 2 U 1 , T 2 U 2 , T 2 UT to the RF transmit circuitry  34 . 
     The RF transmit circuitry  34  further processes the second antenna, first upstream RF transmit signal T 2 U 1  to provide a second antenna, first downstream RF transmit signal T 2 D 1  to the RF TX/RX multiplexer  30 , the second antenna, second upstream RF transmit signal T 2 U 2  to provide a second antenna, second downstream RF transmit signal T 2 D 2  to the RF TX/RX multiplexer  30 , and up to and including the second antenna, T TH  upstream RF transmit signal T 2 UT to provide a second antenna, T TH  downstream RF transmit signal T 2 DT to the RF TX/RX multiplexer  30 . In general, the RF transmit circuitry  34  provides the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM to the RF TX/RX multiplexer  30  and further provides a group of second antenna, downstream RF transmit signals T 2 D 1 , T 2 D 2 , T 2 DT to the RF TX/RX multiplexer  30 . 
     In one embodiment of the RF system control circuitry  24 , the RF system control circuitry  24  further provides at least one of the group of second antenna, upstream RF transmit signals T 2 U 1 , T 2 U 2 , T 2 UT to the RF transmit circuitry  34 , which processes and forwards any or all of the group of second antenna, upstream RF transmit signals T 2 U 1 , T 2 U 2 , T 2 UT to provide a corresponding any or all of the group of second antenna, downstream RF transmit signals T 2 D 1 , T 2 D 2 , T 2 DT to the RF TX/RX multiplexer  30 . The RF TX/RX multiplexer  30  receives, bandpass filters, and forwards the corresponding any or all of the group of second antenna, downstream RF transmit signals T 2 D 1 , T 2 D 2 , T 2 DT to provide a corresponding any or all of a second antenna, first RF antenna transmit signal T 2 A 1 ; a second antenna, second RF antenna transmit signal T 2 A 2 ; and up to and including a second antenna, T TH  RF antenna transmit signal T 2 AT to the second RF antenna  36  via the second common connection node CN 2 . 
     The RF transmit circuitry  34  may include up-conversion circuitry, amplification circuitry, power supply circuitry, filtering circuitry, switching circuitry, combining circuitry, splitting circuitry, dividing circuitry, clocking circuitry, the like, or any combination thereof to process any or all of the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM and the group of second antenna, upstream RF transmit signals T 2 U 1 , T 2 U 2 , T 2 UT. In one embodiment of the RF transmit circuitry  34 , the RF transmit circuitry  34  includes circuitry to reduce interference of RF receive signals in the RF TX/RX multiplexer  30  by processing the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM and the group of second antenna, downstream RF transmit signals T 2 D 1 , T 2 D 2 , T 2 DT in the RF TX/RX multiplexer  30 . 
     In one embodiment of the RF TX/RX multiplexer  30 , the RF TX/RX multiplexer  30  further receives any or all of a second antenna, first RF receive signal R 2 A 1 ; a second antenna, second RF receive signal R 2 A 2 ; and up to and including a second antenna, P TH  RF receive signal R 2 AP; which are received via the second RF antenna  36 . In general, the RF TX/RX multiplexer  30  further receives any or all of a group of second antenna, RF receive signals R 2 A 1 , R 2 A 2 , R 2 AP from the second common connection node CN 2 . In one embodiment of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN and the group of second antenna, RF receive signals R 2 A 1 , R 2 A 2 , R 2 AP, any or all of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN and the group of second antenna, RF receive signals R 2 A 1 , R 2 A 2 , R 2 AP are received simultaneously, such that the RF TX/RX multiplexer  30  supports receive downlink carrier aggregation (RXDLCA). 
     The RF TX/RX multiplexer  30  processes and forwards any or all of the group of second antenna, RF receive signals R 2 A 1 , R 2 A 2 , R 1 AP from the second common connection node CN 2  to provide any or all of a second antenna, first upstream RF receive signal R 2 U 1 , a second antenna, second upstream RF receive signal R 2 U 2 , and up to and including a second antenna, P TH  upstream RF receive signal R 2 UP. In general, the RF TX/RX multiplexer  30  provides any or all of the group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN and the group of second antenna, upstream RF receive signals R 2 U 1 , R 2 U 2 , R 2 UP to the RF receive circuitry  32 . 
     In one embodiment of the RF receive circuitry  32 , the RF receive circuitry  32  receives and processes any or all of the group of the first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN and the group of second antenna, upstream RF receive signals R 2 U 1 , R 2 U 2 , R 2 UP to provide a corresponding any or all of the group of first antenna, downstream RF receive signals R 1 D 1 , R 1 D 2 , R 1 DN and a group of second antenna, downstream RF receive signals R 2 D 1 , R 2 D 2 , R 2 DP. 
     In an additional embodiment of the RF receive circuitry  32 , the RF receive circuitry  32  simultaneously receives and processes any or all of the group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN and the group of second antenna, upstream RF receive signals R 2 U 1 , R 2 U 2 , R 2 UP. As such, the RF receive circuitry  32  supports RXDLCA. The RF receive circuitry  32  may include down-conversion circuitry, amplification circuitry, low noise amplification circuitry, power supply circuitry, filtering circuitry, switching circuitry, combining circuitry, splitting circuitry, dividing circuitry, clocking circuitry, the like, or any combination thereof. 
     In one embodiment of the RF front-end circuitry  26 , any or all of the group of first antenna, RF receive signals R 1 A 1 , R 1 A 2 , R 1 AN, any or all of the group of second antenna, RF receive signals R 2 A 1 , R 2 A 2 , R 1 AP, any or all of the group of first antenna, RF antenna transmit signals T 1 A 1 , T 1 A 2 , T 1 AM, any or all of the group of second antenna, RF antenna transmit signals T 2 A 1 , T 2 A 2 , T 2 AT, any or all of the group of first antenna, upstream RF receive signals R 1 U 1 , R 1 U 2 , R 1 UN, any or all of the group of second antenna, upstream RF receive signals R 2 U 1 , R 2 U 2 , R 2 UP, any or all of the group of first antenna, downstream RF receive signals R 1 D 1 , R 1 D 2 , R 1 DN, any or all of the group of second antenna, downstream RF receive signals R 2 D 1 , R 2 D 2 , R 2 DP, any or all of the group of first antenna, upstream RF transmit signals T 1 U 1 , T 1 U 2 , T 1 UM, any or all of the group of second antenna, upstream RF transmit signals T 2 U 1 , T 2 U 2 , T 2 UT, any or all of the group of first antenna, downstream RF transmit signals T 1 D 1 , T 1 D 2 , T 1 DM, and any or all of the group of second antenna, downstream RF transmit signals T 2 D 1 , T 2 D 2 , T 2 DT are omitted. 
       FIG. 15  shows details of the RF TX/RX multiplexer  30  illustrated in  FIG. 13  according to one embodiment of the RF TX/RX multiplexer  30 . The RF TX/RX multiplexer  30  includes a first antenna, first RF RX bandpass filter  38 , a first antenna, second RF RX bandpass filter  40 , and up to and including a first antenna, N TH  RF RX bandpass filter  42 , a first antenna, first RF TX bandpass filter  44 , a first antenna, second RF TX bandpass filter  46 , and up to and including a first antenna, M TH  RF TX bandpass filter  48 . Each of the first antenna, RF bandpass filters  38 ,  40 ,  42 ,  44 ,  46 ,  48  illustrated in  FIG. 15  is coupled to the first common connection node CN 1 . 
     In one embodiment of the first antenna, RF RX bandpass filters  38 ,  40 ,  42 , each of the first antenna, RF RX bandpass filters  38 ,  40 ,  42  has a corresponding passband that is associated with a corresponding RF receive communications band. In one embodiment of the first antenna, RF TX bandpass filters  44 ,  46 ,  48 , each of the first antenna, RF TX bandpass filters  44 ,  46 ,  48  has a corresponding passband that is associated with a corresponding RF transmit communications band. In one embodiment of the RF TX/RX multiplexer  30 , any or all of the first antenna, RF bandpass filters  38 ,  40 ,  42 ,  44 ,  46 ,  48  is omitted. 
     In one embodiment of the first antenna, first RF RX bandpass filter  38 , the first antenna, first RF RX bandpass filter  38  receives and filters the first antenna, first RF receive signal R 1 A 1  ( FIG. 13 ) via the first RF antenna  28  ( FIG. 13 ) and the first common connection node CN 1  to provide the first antenna, first upstream RF receive signal R 1 U 1 . In one embodiment of the first antenna, second RF RX bandpass filter  40 , the first antenna, second RF RX bandpass filter  40  receives and filters the first antenna, second RF receive signal R 1 A 2  ( FIG. 13 ) via the first RF antenna  28  ( FIG. 13 ) and the first common connection node CN 1  to provide the first antenna, second upstream RF receive signal R 1 U 2 . In one embodiment of the first antenna, N TH  RF RX bandpass filter  42 , the first antenna, N TH  RF RX bandpass filter  42  receives and filters the first antenna, N TH  RF receive signal R 1 AN ( FIG. 13 ) via the first RF antenna  28  ( FIG. 13 ) and the first common connection node CN 1  to provide the first antenna, N TH  upstream RF receive signal R 1 UN. 
     In one embodiment of the first antenna, first RF TX bandpass filter  44 , the first antenna, first RF TX bandpass filter  44  receives and filters the first antenna, first downstream RF transmit signal T 1 D 1  to provide the first antenna, first RF antenna transmit signal T 1 A 1  ( FIG. 13 ) via first common connection node CN 1  and the first RF antenna  28  ( FIG. 13 ). In one embodiment of the first antenna, second RF TX bandpass filter  46 , the first antenna, second RF TX bandpass filter  46  receives and filters the first antenna, second downstream RF transmit signal T 1 D 2  to provide the first antenna, second RF antenna transmit signal T 1 A 2  ( FIG. 13 ) via first common connection node CN 1  and the first RF antenna  28  ( FIG. 13 ). In one embodiment of the first antenna, M TH  RF TX bandpass filter  48 , the first antenna, M TH  RF TX bandpass filter  48  receives and filters the first antenna, M TH  downstream RF transmit signal T 1 DM to provide the first antenna, M TH  RF antenna transmit signal T 1 AM ( FIG. 13 ) via first common connection node CN 1  and the first RF antenna  28  ( FIG. 13 ). 
       FIG. 16  shows details of the RF TX/RX multiplexer  30  illustrated in  FIG. 14  according to an alternate embodiment of the RF TX/RX multiplexer  30 . The RF TX/RX multiplexer  30  illustrated in  FIG. 16  is similar to the RF TX/RX multiplexer  30  illustrated in  FIG. 15  further includes a second antenna, first RF RX bandpass filter  50 , a second antenna, second RF RX bandpass filter  52 , a second antenna, P TH  RF RX bandpass filter  54 , a second antenna, first RF TX bandpass filter  56 , a second antenna, second RF TX bandpass filter  58 , and a second antenna, T TH  RF TX bandpass filter  60 . 
     Each of the first antenna, RF bandpass filters  38 ,  40 ,  42 ,  44 ,  46 ,  48  illustrated in  FIG. 16  is coupled to the first common connection node CN 1  and each of the second antenna, RF bandpass filters  50 ,  52 ,  54 ,  56 ,  58 ,  60  illustrated in  FIG. 16  is coupled to the second common connection node CN 2 . 
     In one embodiment of the second antenna, RF RX bandpass filters  50 ,  52 ,  54 , each of the second antenna, RF RX bandpass filters  50 ,  52 ,  54  has a corresponding passband that is associated with a corresponding RF receive communications band. In one embodiment of the second antenna, RF TX bandpass filters  56 ,  58 ,  60 , each of the second antenna, RF TX bandpass filters  56 ,  58 ,  60  has a corresponding passband that is associated with a corresponding RF transmit communications band. In one embodiment of the RF TX/RX multiplexer  30 , any or all of the second antenna, RF bandpass filters  50 ,  52 ,  54 ,  56 ,  58 ,  60  is omitted. 
     In one embodiment of the second antenna, first RF RX bandpass filter  50 , the second antenna, first RF RX bandpass filter  50  receives and filters the second antenna, first RF receive signal R 2 A 1  ( FIG. 14 ) via the second RF antenna  36  ( FIG. 14 ) and the second common connection node CN 2  to provide the second antenna, first upstream RF receive signal R 2 U 1 . In one embodiment of the second antenna, second RF RX bandpass filter  52 , the second antenna, second RF RX bandpass filter  52  receives and filters the second antenna, second RF receive signal R 2 A 2  ( FIG. 14 ) via the second RF antenna  36  ( FIG. 14 ) and the second common connection node CN 2  to provide the second antenna, second upstream RF receive signal R 2 U 2 . In one embodiment of the second antenna, P TH  RF RX bandpass filter  54 , the second antenna, P TH  RF RX bandpass filter  54  receives and filters the second antenna, P TH  RF receive signal R 2 AP ( FIG. 14 ) via the second RF antenna  36  ( FIG. 14 ) and the second common connection node CN 2  to provide the second antenna, P TH  upstream RF receive signal R 2 UP. 
     In one embodiment of the second antenna, first RF TX bandpass filter  56 , the second antenna, first RF TX bandpass filter  56  receives and filters the second antenna, first downstream RF transmit signal T 2 D 1  to provide the second antenna, first RF antenna transmit signal T 2 A 1  ( FIG. 14 ) via second common connection node CN 2  and the second RF antenna  36  ( FIG. 14 ). In one embodiment of the second antenna, second RF TX bandpass filter  58 , the second antenna, second RF TX bandpass filter  58  receives and filters the second antenna, second downstream RF transmit signal T 2 D 2  to provide the second antenna, second RF antenna transmit signal T 2 A 2  ( FIG. 14 ) via second common connection node CN 2  and the second RF antenna  36  ( FIG. 13 ). In one embodiment of the second antenna, T TH  RF TX bandpass filter  60 , the second antenna, T TH  RF TX bandpass filter  60  receives and filters the second antenna, T TH  downstream RF transmit signal T 2 DT to provide the second antenna, T TH  RF antenna transmit signal T 2 AT ( FIG. 14 ) via second common connection node CN 2  and the second RF antenna  36  ( FIG. 14 ). 
       FIG. 17A  shows details of the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter  38 . The first antenna, first RF RX bandpass filter  38  includes the first ARFR  10 , the first parallel capacitance compensation circuit  14 , a first group  62  of series-coupled ARFRs  64 , and a first group  66  of shunt-coupled ARFRs  68 . The first parallel capacitance compensation circuit  14  is coupled across the first ARFR  10 . 
     The series-coupled ARFRs  64  of the first group  62  of series-coupled ARFRs  64  are coupled in series between the first ARFR  10  and the first RF antenna  28  ( FIG. 13 ) via the first common connection node CN 1 . In one embodiment of the first group  66  of shunt-coupled ARFRs  68 , each shunt-coupled ARFR  68  of the first group  66  of shunt-coupled ARFRs  68  is coupled between a corresponding pair of the first group  62  of series-coupled ARFRs  64  and ground. The first antenna, first RF RX bandpass filter  38  receives and filters the first antenna, first RF receive signal R 1 A 1  ( FIG. 15 ) via the first RF antenna  28  ( FIG. 13 ) and the first common connection node CN 1  to provide the first antenna, first upstream RF receive signal R 1 U 1  via the first ARFR  10 . 
     In one embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 , such that the first parallel capacitance compensation circuit  14  includes the first compensating ARFR  16  ( FIG. 3 ), the second compensating ARFR  18  ( FIG. 3 ), the first inductive element L 1  ( FIG. 3 ), and the second inductive element L 2  ( FIG. 3 ). 
     In an alternate embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 , such that the first parallel capacitance compensation circuit  14  includes the first compensating ARFR  16  ( FIG. 4 ), the first inductive element L 1  ( FIG. 4 ), the second inductive element L 2  ( FIG. 4 ), and the capacitance circuit  20  ( FIG. 4 ). 
     In an additional embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 , such that the first parallel capacitance compensation circuit  14  includes the first compensating ARFR  16  ( FIG. 9 ), the first inductive element L 1  ( FIG. 9 ), and the second inductive element L 2  ( FIG. 9 ). 
     In another embodiment of the first parallel capacitance compensation circuit  14 , the first parallel capacitance compensation circuit  14  is the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 , such that the first parallel capacitance compensation circuit  14  includes the first compensating ARFR  16  ( FIG. 10 ), the first inductive element L 1  ( FIG. 10 ), and the second inductive element L 2  ( FIG. 10 ). 
       FIG. 17B  shows details of the first antenna, second RF RX bandpass filter  40  illustrated in  FIG. 15  according to one embodiment of the first antenna, second RF RX bandpass filter  40 . The first antenna, second RF RX bandpass filter  40  includes a second ARFR  70 , a second parallel capacitance compensation circuit  72 , a second group  74  of series-coupled ARFRs  64 , and a second group  76  of shunt-coupled ARFRs  68 . The second parallel capacitance compensation circuit  72  is coupled across the second ARFR  70 . In one embodiment of the second ARFR  70 , the second ARFR  70  is similar to the first ARFR  10  illustrated in  FIG. 17A . In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 17A . 
     The series-coupled ARFRs  64  of the second group  74  of series-coupled ARFRs  64  are coupled in series between the second ARFR  70  and the first RF antenna  28  ( FIG. 13 ) via the first common connection node CN 1 . In one embodiment of the second group  76  of shunt-coupled ARFRs  68 , each shunt-coupled ARFR  68  of the second group  76  of shunt-coupled ARFRs  68  is coupled between a corresponding pair of the second group  74  of series-coupled ARFRs  64  and ground. The first antenna, second RF RX bandpass filter  40  receives and filters the first antenna, second RF receive signal R 1 A 2  ( FIG. 15 ) via the first RF antenna  28  ( FIG. 13 ) and the first common connection node CN 1  to provide the first antenna, second upstream RF receive signal R 1 U 2  via the first ARFR  10 . 
     In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 . In an alternate embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 . In an additional embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 . In another embodiment of the second parallel capacitance compensation circuit  72 , the first parallel capacitance compensation circuit  14  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 . 
       FIG. 18A  shows details of the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter  38 . The first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 18A  is similar to the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 17A . 
       FIG. 18B  shows details of the first antenna, first RF TX bandpass filter  44  illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF TX bandpass filter  44 . The first antenna, first RF TX bandpass filter  44  includes the second ARFR  70 , the second parallel capacitance compensation circuit  72 , the second group  74  of series-coupled ARFRs  64 , and the second group  76  of shunt-coupled ARFRs  68 . The second parallel capacitance compensation circuit  72  is coupled across the second ARFR  70 . In one embodiment of the second ARFR  70 , the second ARFR  70  is similar to the first ARFR  10  illustrated in  FIG. 18A . In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 18A . 
     The series-coupled ARFRs  64  of the second group  74  of series-coupled ARFRs  64  are coupled in series between the second ARFR  70  and the first RF antenna  28  ( FIG. 13 ) via the first common connection node CN 1 . In one embodiment of the second group  76  of shunt-coupled ARFRs  68 , each shunt-coupled ARFR  68  of the second group  76  of shunt-coupled ARFRs  68  is coupled between a corresponding pair of the second group  74  of series-coupled ARFRs  64  and ground. 
     The first antenna, first RF TX bandpass filter  44  receives and filters the first antenna, first downstream RF transmit signal T 1 D 1  via the second ARFR  70  to provide the first antenna, first RF antenna transmit signal T 1 A 1  ( FIG. 13 ) via the first common connection node CN 1  and the first RF antenna  28  ( FIG. 13 ). 
     In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 . In an alternate embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 . In an additional embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 . In another embodiment of the second parallel capacitance compensation circuit  72 , the first parallel capacitance compensation circuit  14  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 . 
       FIG. 19A  shows details of the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF RX bandpass filter  38 . The first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 19A  is similar to the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 17A . 
       FIG. 19B  shows details of the second antenna, first RF RX bandpass filter  50  illustrated in  FIG. 16  according to one embodiment of the second antenna, first RF RX bandpass filter  50 . The second antenna, first RF RX bandpass filter  50  includes the second ARFR  70 , the second parallel capacitance compensation circuit  72 , the second group  74  of series-coupled ARFRs  64 , and the second group  76  of shunt-coupled ARFRs  68 . The second parallel capacitance compensation circuit  72  is coupled across the second ARFR  70 . In one embodiment of the second ARFR  70 , the second ARFR  70  is similar to the first ARFR  10  illustrated in  FIG. 19A . 
     The series-coupled ARFRs  64  of the second group  74  of series-coupled ARFRs  64  are coupled in series between the second ARFR  70  and the second RF antenna  36  ( FIG. 14 ) via the second common connection node CN 2 . In one embodiment of the second group  76  of shunt-coupled ARFRs  68 , each shunt-coupled ARFR  68  of the second group  76  of shunt-coupled ARFRs  68  is coupled between a corresponding pair of the second group  74  of series-coupled ARFRs  64  and ground. 
     The second antenna, first RF RX bandpass filter  50  receives and filters the second antenna, first RF antenna receive signal R 2 A 1  via the second RF antenna  36  ( FIG. 14 ) and the second common connection node CN 2  to provide the second antenna, first upstream RF receive signal R 2 U 1 . 
     In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 . In an alternate embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 . In an additional embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 . In another embodiment of the second parallel capacitance compensation circuit  72 , the first parallel capacitance compensation circuit  14  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 . 
     In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 . In an alternate embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 . In an additional embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 . In another embodiment of the second parallel capacitance compensation circuit  72 , the first parallel capacitance compensation circuit  14  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 . 
       FIG. 20A  shows details of the first antenna, first RF TX bandpass filter  44  illustrated in  FIG. 15  according to one embodiment of the first antenna, first RF TX bandpass filter  44 . The first antenna, first RF TX bandpass filter  44  illustrated in  FIG. 20A  is similar to the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 19A . However, the first antenna, first RF TX bandpass filter  44  receives and filters the first antenna, first downstream RF transmit signal T 1 D 1  via the first ARFR  10  to provide the first antenna, first RF antenna transmit signal T 1 A 1  ( FIG. 13 ) via the first common connection node CN 1  and the first RF antenna  28  ( FIG. 13 ). 
       FIG. 20B  shows details of the first antenna, second RF TX bandpass filter  46  illustrated in  FIG. 15  according to one embodiment of the first antenna, second RF TX bandpass filter  46 . The first antenna, second RF TX bandpass filter  46  includes the second ARFR  70 , the second parallel capacitance compensation circuit  72 , the second group  74  of series-coupled ARFRs  64 , and the second group  76  of shunt-coupled ARFRs  68 . The second parallel capacitance compensation circuit  72  is coupled across the second ARFR  70 . In one embodiment of the second ARFR  70 , the second ARFR  70  is similar to the first ARFR  10  illustrated in  FIG. 18A . In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 18A . 
     The series-coupled ARFRs  64  of the second group  74  of series-coupled ARFRs  64  are coupled in series between the second ARFR  70  and the first RF antenna  28  ( FIG. 13 ) via the first common connection node CN 1 . In one embodiment of the second group  76  of shunt-coupled ARFRs  68 , each shunt-coupled ARFR  68  of the second group  76  of shunt-coupled ARFRs  68  is coupled between a corresponding pair of the second group  74  of series-coupled ARFRs  64  and ground. 
     The first antenna, second RF TX bandpass filter  46  receives and filters the first antenna, second downstream RF transmit signal T 1 D 2  via the second ARFR  70  to provide the first antenna, second RF antenna transmit signal T 1 A 2  ( FIG. 13 ) via the first common connection node CN 1  and the first RF antenna ( FIG. 13 ). 
     In one embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 3 . In an alternate embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 4 . In an additional embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 9 . In another embodiment of the second parallel capacitance compensation circuit  72 , the second parallel capacitance compensation circuit  72  is similar to the first parallel capacitance compensation circuit  14  illustrated in  FIG. 10 . 
       FIG. 21A  shows a portion of the RF circuitry  12  according to one embodiment of the RF circuitry  12 . The RF circuitry  12  includes an acoustic substrate  78 , which includes portions of the first antenna, first RF RX bandpass filter  38  illustrated in  FIG. 17A . The acoustic substrate  78  includes the first ARFR  10 , the first compensating ARFR  16 , the second compensating ARFR  18 , the first group  62  of series-coupled ARFRs  64 , and the first group  66  of shunt-coupled ARFRs  68 . 
       FIG. 21B  shows a portion of the RF circuitry  12  according to one embodiment of the RF circuitry  12 . The RF circuitry  12  includes the acoustic substrate  78 . The acoustic substrate  78  illustrated in  FIG. 21B  is similar to the acoustic substrate  78  Illustrated in  FIG. 21A , except in the acoustic substrate  78  illustrated in  FIG. 21B , the second compensating ARFR  18  is omitted. 
       FIG. 22A  is a schematic of the RF circuitry  12  first illustrated in  FIG. 10 . The RF circuitry  12  includes the ARFR  10  and the first parallel capacitance compensation circuit  14 , which includes the first compensating ARFR  16 , the first inductive element L 1 , and the second inductive element L 2 . 
       FIG. 22B  shows the RF circuitry  12  modeled by performing a wye-delta transformation on the first parallel capacitance compensation circuit  14  that is a bridged T resonator network. The wye-delta transformation yields a wye-delta model that includes a first shunt branch made up of a first impedance ZA 1  in series with a first shunt ARFR  16 ′. A second shunt branch is made up of a second impedance ZB 1  that is in series with a second shunt ARFR  16 ″. A third impedance ZC 1  is coupled in parallel across the ARFR  10 . The third impedance ZC 1  tends to raise a net out of band series impedance when placed in parallel with the parallel capacitance CP ( FIG. 1B ) of the ARFR  10 . Moreover, the third impedance ZC 1  provides higher broadband cancellation of the parallel capacitance CP relative to placing an inductor in parallel with the ARFR  10 . 
     Additionally, the first shunt branch made up of the first impedance ZA 1  in series with the first shunt ARFR  16 ′ and the second shunt branch made up of the second impedance ZB 1  in series with the second shunt ARFR  16 ″ provides stop band zeros and improves attenuation outside a desired passband. The first shunt ARFR  16 ′ and the second shunt ARFR  16 ″ are models of the first compensating ARFR  16 . 
       FIG. 23  is a schematic of a related art ladder filter  80  that includes a finite number of the ARFRs  10  coupled in series. In this series-coupled configuration, each ARFR  10  is referred to as a ladder ARFR  10 . The related art ladder filter  80  further includes a group of shunt branches  82  each of which are made up of a shunt ARFR  84  coupled in series with a shunt inductor  86 . The shunt branches  82  are coupled between ladder nodes  88  and a fixed voltage node that is typically ground. 
       FIG. 24  is a schematic of a related art ladder filter  90  that uses a resonance inductor  92  to compensate for the parallel capacitance of the rightmost ARFR  10 . In this case, the resonance inductor  92  is coupled across the rightmost ARFR  10 . The related art ladder filter  90  provides a relatively narrow band isolation around a frequency at which the resonance inductor  92  is resonant with the parallel capacitance CP ( FIG. 1B ) of the ARFR  10 . 
       FIG. 25  is a schematic of an embodiment of a ladder filter  94  that is in accordance with the present disclosure. In this embodiment, the first parallel capacitance compensation circuit  14  that was first introduced in  FIG. 10  is a type of bridged T network that is coupled across the rightmost ARFR  10  by way of a first ladder terminal  96  and a second ladder terminal  98 . In this particular case, the first parallel capacitance compensation circuit  14  includes the first inductive element L 1  that has a first T-terminal  100  and a first end  102  coupled to the first ladder terminal  96 . The second inductive element L 2  has a second T-terminal  104  that is coupled to the first T-terminal  100  of the first inductive element  1  and a second end  106  that is coupled to the second ladder terminal  98 . The first compensating ARFR  16  has a fixed node terminal  108  that is typically coupled to ground and a third T-terminal  110  that is coupled to both the first T-terminal  100  of the first inductive element L 1  and the second T-terminal  104  of the second inductive element L 2 . 
     In this particular embodiment there is negligible mutual coupling between the first inductive element L 1  and the second inductive element L 2 . Even so, the first parallel capacitance compensation circuit  14  provides between 10 dB and 20 dB improvement over the related art ladder filter  80 , and between 5 dB and 10 dB improvement over the related art ladder filter  90  that includes the resonance inductor  92 . 
       FIG. 26  is a simulation plot of out of band improvements realized by the ladder filter  94  as configured for an 8 th  order band 7 (B7) receive (RX) filter. In this exemplary case, the ladder filter  94  was simulated without any mutual coupling between the first inductive element L 1  and the second inductive element L 2 . A dashed trace in the simulation plot of  FIG. 26  represents isolation provided by the related art ladder filter  80  of  FIG. 23 , while a dotted and dashed trace represents isolation provided by the related art ladder filter  90  of  FIG. 24  that includes the inductive compensation available from the resonance inductor  92 . A solid trace in the simulation plot of  FIG. 26  represents isolation provided by the ladder filter  94  of the present embodiment depicted in  FIG. 25 . Note that isolation provided by the ladder filter  94  of the present disclosure is generally much improved relative to the isolation provided by the related art ladder filter  80  and the related art ladder filter  90  having inductance compensation  18 . This exemplary embodiment has an in band insertion loss that is no greater −1.8 dB over a frequency range of about 2.6 GHz to about 2.7 GHz. 
       FIG. 27  is a simulation plot of in band insertion loss associated with the ladder filter  94  as configured for an 8 th  order B7 RX filter. In this exemplary embodiment, the ladder filter  94  was simulated without any mutual coupling between the first inductive element L 1  and the second inductive element L 2 . A dashed trace in the simulation plot of  FIG. 27  represents in band insertion loss associated with the related art ladder filter  80  of  FIG. 23 , while a dotted and dashed trace represents in band insertion loss associated with the related art ladder filter  90  of  FIG. 24  that includes the inductive compensation available from the resonance inductor  92 . A solid trace in the simulation plot of  FIG. 26  represents in band insertion loss associated with the ladder filter  94  of the present embodiment depicted in  FIG. 25 . Note that in band insertion loss associated with the ladder filter  94  of the present disclosure is generally much improved relative to the in band insertion loss associated with the related art ladder filter  80  and the related art ladder filter  90  having inductance compensation  18 . The RF ladder filter  94  has an in band insertion loss is no greater −1.8 dB over a frequency range of about 2.6 GHz to about 2.7 GHz. This exemplary embodiment has an out of band isolation over a frequency range of 1.6 GHz to about 2.5 GHz that is less than about −50 dB and further has an out of band isolation over a frequency range of about 2.9 GHz to about 4.0 GHz that is less than about −60 dB. 
       FIG. 28A  is a schematic of RF circuitry  12  in which the first inductor L 1  and the second inductor L 2  are negatively magnetically coupled.  FIG. 28B  is a schematic of RF circuitry  12  that is transformed to an equivalent bridged T network.  FIG. 28C  is a schematic of RF circuitry  12  that has been transformed from the equivalent bridged T network to an equivalent PI network.  FIG. 28C  includes a first shunt branch made up of a first impedance ZA 1  in series with a first shunt ARFR  16 ′. A second shunt branch is made up of a second impedance ZB 1  that is in series with a second shunt ARFR  16 ″. A third impedance ZC 1  is coupled in parallel across the ARFR  10 . The third impedance ZC 1  tends to raise a net out of band series impedance when placed in parallel with the parallel capacitance CP ( FIG. 1B ) of the ARFR  10 . Moreover, the third impedance ZC 1  provides higher broadband cancellation of the parallel capacitance CP relative to placing an inductor in parallel with the ARFR  10 . 
     Additionally, the first shunt branch made up of the first impedance ZA 1  in series with the first shunt ARFR  16 ′ and the second shunt branch made up of the second impedance ZB 1  in series with the second shunt ARFR  16 ″ provides stop band zeros and improves attenuation outside a desired passband. The first shunt ARFR  16 ′ and the second shunt ARFR  16 ″ are models of the first compensating ARFR  16 . 
     While  FIGS. 28B and 28C  depict L 1  and L 2  as being equal, it is important to note that the first inductor L 1  and the second inductor L 2  do not necessarily need to be made equal in inductance value. In some instances, the inductance values for the first inductor L 1  and the second inductor L 2  will be required to be unequal in order to position poles and zeros for the first parallel capacitance compensation circuit  14  in order to realize a transfer function that yields maximum isolation and minimum insertion loss. 
     In all embodiments of  FIGS. 28A, 28B and 28C , a coefficient of coupling M between the first inductor L 1  and the second inductor L 2  is nonzero. In one embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling M between the first inductive element L 1  and the second inductive element L 2  is less than 0.7. In an alternate embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling M between the first inductive element L 1  and the second inductive element L 2  is less than 0.6. In an additional embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling M between the first inductive element L 1  and the second inductive element L 2  is less than 0.5. In another embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling M between the first inductive element L 1  and the second inductive element L 2  is less than 0.4. In a further embodiment of the first inductive element L 1  and the second inductive element L 2 , the absolute value of the coefficient of coupling M between the first inductive element L 1  and the second inductive element L 2  is less than 0.3. 
     The significance of the equivalent PI network depicted in  FIG. 28C  is that it shows that the RF circuitry  12  of  FIG. 28A  is usable to replace a number of shunt resonators, such as the shunt resonators  84  shown in the typical ladder filter  80  depicted in related art  FIG. 23 . For example an eight resonator ladder filter that has four shunt branches with four series-coupled resonators can be replaced by a six resonator ladder filter having two of the first parallel capacitance compensation circuit  14  ( FIG. 28A ). 
     In this regard,  FIG. 29A  depicts a schematic model of a ladder filter  112  that is similar to a traditional ladder filter, except in model ladder filter  112  in  FIG. 29A , mutual coupling coefficients M 1  and M 2  are employed during transformation of model ladder filter  112  into a realizable ladder filter  114  that is a further embodiment of the present disclosure as depicted in  FIG. 29B . In effect, the ladder filter  114  replaces one of the shunt resonators  16 ′ and one of the shunt resonators  16 ″ that are depicted in  FIG. 29A . Note that in the particular embodiment of  FIG. 29B , the first parallel capacitance compensation circuit  14  is coupled to every other one of the ladder resonators  10  due to shunt resonator reduction. 
     Some of the circuitry previously described may use discrete circuitry, integrated circuitry, programmable circuitry, non-volatile circuitry, volatile circuitry, software executing instructions on computing hardware, firmware executing instructions on computing hardware, the like, or any combination thereof. The computing hardware may include mainframes, micro-processors, micro-controllers, DSPs, the like, or any combination thereof. 
     None of the embodiments of the present disclosure are intended to limit the scope of any other embodiment of the present disclosure. Any or all of any embodiment of the present disclosure may be combined with any or all of any other embodiment of the present disclosure to create new embodiments of the present disclosure. 
     Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.