Radio frequency filtering circuitry with resonators

RF multiplexer circuitry includes a first signal path coupled between a first intermediate node and a common node, a second signal path coupled between a second intermediate node and the common node, first resonator circuitry coupled between the first signal path and ground, and second resonator circuitry coupled between the second signal path and ground. The first resonator circuitry is configured to allow signals within a first frequency pass band to pass between the first intermediate node and the common node, while attenuating signals outside of the first frequency pass band. The first resonator circuitry includes a first LC resonator. The second resonator circuitry is configured to allow signals within a second frequency pass band to pass between the second intermediate node and the common node, while attenuating signals outside of the second frequency pass band.

FIELD OF THE DISCLOSURE

The present disclosure relates to radio frequency (RF) filtering circuitry, and specifically to RF filtering circuitry including one or more resonators.

BACKGROUND

Radio frequency (RF) filtering circuitry is essential to the operation of modern wireless communications devices. In addition to reducing distortion present in RF transmit and receive signals, RF filtering circuitry is also used to separate and combine RF signals in different frequency bands such that multiple RF signals can be simultaneously transmitted and received from a single antenna. One type of RF filtering circuitry often used for this task is RF multiplexer circuitry.FIG. 1shows a conventional RF multiplexer10. The conventional RF multiplexer10includes a common node12, a number of input/output nodes14, and RF filtering circuitry16coupled between the common node12and the input/output nodes14. Generally, the common node12of the conventional RF multiplexer10is coupled to an antenna, while each one of the input/output nodes14are coupled to RF front end circuitry. RF receive signals from the antenna are provided at the common node12, where they are separated by the RF filtering circuitry16and passed to one of the input/output nodes14. Each one of the input/output nodes14is associated with a particular frequency band such that each one of the input/output nodes14receives only the portion of the RF receive signals falling within their associated frequency band from the common node12. This allows RF receive signals to be routed to low noise amplifier (LNA) circuitry in the RF front end circuitry that is optimized to operate within the particular frequency band, which improves the performance thereof. RF transmit signals provided from the RF front end circuitry to each one of the input/output nodes14are combined and passed to the common node12, where they can then be transmitted from the antenna.

Generally, RF filtering circuitry can be divided into two categories:

acoustic filtering circuitry and electromagnetic filtering circuitry (that can be either lumped or distributed).FIG. 2shows the conventional RF multiplexer10wherein the RF filtering circuitry16is acoustic filtering circuitry18. Specifically, the RF filtering circuitry16is shown as a bulk acoustic wave (BAW) or a surface acoustic wave (SAW) filter.

To implement the conventional RF multiplexer10, the acoustic filtering circuitry18must provide a filter response configured to pass the particular frequency bands associated with each input/output node14. For the RF multiplexer10shown inFIG. 1, this means providing a filter response with a bandpass for six different frequency bands. Due to size constraints associated with mobile devices, the acoustic filtering circuitry18is generally implemented on a single module. As the number of desired pass bands gets larger and stop bands are needed to ensure good isolation between bands, the complexity of the acoustic filtering circuitry18increases substantially. The number of frequency bands that can be separated by conventional acoustic circuitry18is therefore limited.

Acoustic filtering circuitry generally has a relatively high quality factor (Q), however, the bandwidth thereof is generally limited. This is due to the fact that as the bandwidth of acoustic filtering circuitry is increased, an undesirable filter response known as “flyback” is also increased. To illustrate this effect,FIG. 3is a graph showing an exemplary portion of a filter response of acoustic filtering circuitry. As shown inFIG. 3, the acoustic filtering circuitry exhibits a bandpass response20with very steep roll-off (due to the high quality factor thereof). However, even for a relatively narrow bandpass response, the filter response shows significant flyback22. This amount of flyback is generally proportional to the number of acoustic filters sharing a common node. The flyback associated with acoustic filtering circuitry with a large number of filter responses therefore generally limits the achievable bandwidth thereof. As wireless communications standards continue to incorporate additional bands that span across a wide range of frequencies, and as carrier aggregation configurations in which wireless communications circuitry is required to simultaneously utilize these different bands, become more widely accepted, the constrained bandwidth of acoustic filtering circuitry has become problematic.

Electromagnetic filtering circuitry has thus been used to achieve wider bandwidths in wireless communications circuitry.FIG. 4shows the conventional RF multiplexer10wherein the RF filtering circuitry16is electromagnetic in the form of lumped LC filtering circuitry24. The LC filtering circuitry24includes a number of inductors26and a number of capacitors28coupled between the common node12and the input/output nodes14. While the LC filtering circuitry24provides a much wider bandwidth than the acoustic filtering circuitry18, a wide bandwidth is generally associated with higher loading along the signal path of the filtering circuitry. This generally results in a significant reduction in the quality factor of the LC filtering circuitry24. Such a reduction in quality factor can result in relatively poor isolation between adjacent bands to be separated by the LC filtering circuitry. This is illustrated inFIG. 5.FIG. 5shows a first bandpass filter response30and a second bandpass filter response32that are adjacent to one another. Within each bandpass filter response, a number of sub-bands are shown, labeled A through N. While each one of the first bandpass filter response30and the second bandpass filter response32has a relatively wide bandwidth, due to the relatively low quality factor associated with active filtering devices, the roll-off of each bandpass filter response is quite gradual. This results in significant overlap between the first bandpass filter response30and the second bandpass filter response32, which translates to poor isolation between the pass bands. Specifically, this overlap often results in leakage of undesirable signals into a signal path in wireless communications circuitry, which can cause distortion, desensitization, and even damage to one or more components therein. This may be especially problematic in carrier aggregation applications in which two bordering sub-bands from each filter response are used. For example, in a carrier aggregation application in which signals are transmitted on band G and received on band H, a significant portion of the band G signals will likely leak into the signal path for band H, and vice versa.

In light of the above, there is a need for RF filtering circuitry with improved performance. Specifically, there is a need for RF filtering circuitry with improvements to the quality factor and bandwidth thereof.

SUMMARY

The present disclosure relates to radio frequency (RF) filtering circuitry, and specifically to RF filtering circuitry including one or more resonators. In one embodiment, RF multiplexer circuitry includes a first signal path coupled between a first intermediate node and a common node, a second signal path coupled between a second intermediate node and the common node, first resonator circuitry coupled between the first signal path and ground, and second resonator circuitry coupled between the second signal path and ground. The first resonator circuitry is configured to allow signals within a first frequency pass band to pass between the first intermediate node and the common node, while attenuating signals outside of the first frequency pass band. The first resonator circuitry includes a first LC resonator and a second LC resonator. The second resonator circuitry is configured to allow signals within a second frequency pass band to pass between the second intermediate node and the common node, while attenuating signals outside of the second frequency pass band. The second resonator circuitry includes a third LC resonator and a fourth LC resonator. The first LC resonator and the second LC resonator are electromagnetically coupled such that a coupling factor between the first LC resonator and the second LC resonator is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.4). The third LC resonator and the fourth LC resonator are electromagnetically coupled such that a coupling factor between the third LC resonator and the fourth LC resonator is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.4). Providing the first LC resonator and the second LC resonator such that they are electromagnetically coupled as discussed above results in a sharper roll-off and increased bandwidth of the first frequency pass band and the second frequency pass band.

In one embodiment, the quality factor of the first resonator circuitry and the second resonator circuitry is between about 10 and 300.

The first LC resonator may be electromagnetically coupled to the third LC resonator such that a coupling factor between the first LC resonator and the third LC resonator is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.04). Providing the first LC resonator and the third LC resonator such that they are electromagnetically coupled as discussed above results in re-combination of leakage signals within a secondary signal path with the primary signal path, thereby increasing isolation in the RF multiplexer circuitry.

Coupling capacitors may be coupled between the various resonators and the nodes of the RF multiplexer circuitry.

In one embodiment, the resonator control circuitry is configured to adjust the capacitances of the various capacitors in the RF multiplexer circuitry such that the first frequency pass band and the second frequency pass band overlap in a carrier aggregation mode, and do not overlap in a standard mode.

DETAILED DESCRIPTION

FIG. 6shows RF filtering circuitry34according to one embodiment of the present disclosure. The RF filtering circuitry34includes resonator multiplexer circuitry36and supplemental filtering circuitry38. The resonator multiplexer circuitry36is coupled between a common node40, a first intermediate node42A, and a second intermediate node42B. The supplemental filtering circuitry38is coupled between the first intermediate node42A, the second intermediate node42B, a first input/output node44A, a second input/output node44B, a third input/output node44C, and a fourth input/output node44D. Specifically, the supplemental filtering circuitry38includes a first supplemental filter46A coupled between the first intermediate node42A, the first input/output node44A, and the second input/output node44B, and a second supplemental filter46B coupled between the second intermediate node42B, the third input/output node44C, and the fourth input/output node44D. Notably, the particular number of intermediate nodes42, input/output nodes44, and supplemental filters46are merely exemplary. The RF filtering circuitry34may include any number of intermediate nodes42, input/output nodes44, and supplemental filters46without departing from the principles of the present disclosure.

In operation, signals provided at the common node40are separated into a first frequency pass band and a second frequency pass band and separately delivered to the first intermediate node42A and the second intermediate node42B, respectively. Signals within the first frequency pass band are then separated again into a first sub-band and a second sub-band by the first supplemental filter46A. Signals within the second frequency pass band are similarly separated again into a third sub-band and a fourth sub-band by the second supplemental filter46B. In one embodiment, the first frequency pass band and the second frequency pass band include multiple operating bands, while the first sub-band, the second sub-band, the third sub-band, and the fourth sub-band include only a single operating band, where an operating band is a single band used for communication (e.g., a single long term evolution (LTE) operating band). Accordingly, the resonator multiplexer circuitry36provides filtering having a coarse granularity, while the supplemental filtering circuitry38provides filtering at a finer granularity.

In one embodiment, the resonator multiplexer circuitry36is configured to provide a relatively wide bandwidth, while the supplemental filtering circuitry38provides high selectivity (e.g., via a higher quality factor). To accomplish this, the resonator multiplexer circuitry36may include multiple resonators (including a number of inductors and capacitors), while the supplemental filtering circuitry38may include a number of acoustic filters. In particular, the resonator multiplexer circuitry36may include at least two resonators, which are coupled to one another such that a coupling factor between the at least two resonators is between about 0.1% and 40.0% (i.e., between about 0.01 and 0.4). As discussed in detail below, this improves the loaded quality factor of the resonator multiplexer circuitry36, such that the quality factor of the resonator multiplexer circuitry36may be between about 10 and 300. However, further improvements may be made by using acoustic filters for the first supplemental filter46A and the second supplemental filter46B. The present disclosure is not limited to the use of acoustic filters in the supplemental filtering circuitry38. Any suitable filters may be used for the first supplemental filter46A and the second supplemental filter46B without departing from the principles of the present disclosure.

FIG. 7shows details of the resonator multiplexer circuitry36according to one embodiment of the present disclosure. The resonator multiplexer circuitry36includes a first signal path48coupled between the first intermediate node42A and the common node40, a second signal path50coupled between the second intermediate node42B and the common node40, first resonator circuitry52coupled between the first signal path48and ground, and second resonator circuitry54coupled between the second signal path50and ground. The first resonator circuitry52includes a first LC resonator56and a second LC resonator58coupled between the first signal path48and ground. The second resonator circuitry54includes a third LC resonator60and a fourth LC resonator62coupled between the second signal path50and ground. The first LC resonator56includes a first resonator inductor64and a first resonator capacitor66coupled in parallel between the first signal path48and ground. The second LC resonator58includes a second resonator inductor68and a second resonator capacitor70coupled between the first signal path48and ground. The first signal path48includes a first coupling capacitor72coupled between the common node40and the first LC resonator56, a second coupling capacitor74coupled between the first intermediate node42A and the second LC resonator58, and a third coupling capacitor76coupled between the common node40and the first intermediate node42A. The third LC resonator60includes a third resonator inductor78and a third resonator capacitor80coupled between the second signal path50and ground. The fourth LC resonator62includes a fourth resonator inductor82and a fourth resonator capacitor84coupled between the second signal path50and ground. The second signal path50includes a fourth coupling capacitor86coupled between the common node40and the third LC resonator60, a fifth coupling capacitor88coupled between the second intermediate node42B and the fourth LC resonator62, and a sixth coupling capacitor90coupled between the common node40and the third LC resonator60.

In operation, the first LC resonator56, the second LC resonator58, the third LC resonator60, and the fourth LC resonator62are configured to resonate at different frequencies. When resonating, the resonators present a very high impedance to their respective signal paths. This effectively allows signals within a first frequency band to pass between the common node40and the first intermediate node42A, and signals within a second frequency band to pass between the common node40and the second intermediate node42B. When the resonators are not resonating, the impedance presented thereby is significantly lower, thereby shunting signals outside of the first frequency band and the second frequency band, respectively, to ground.

The first LC resonator56is electromagnetically coupled to the second LC resonator58such that a coupling factor between the first LC resonator56and the second LC resonator58is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.40). The third LC resonator60is electromagnetically coupled to the fourth LC resonator62such that a coupling factor between the third LC resonator60and the fourth LC resonator62is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.40). The first LC resonator56and the third LC resonator60are electromagnetically coupled such that a coupling factor between the first LC resonator56and the third LC resonator60is between about 1.0% and 40.0% (i.e., between about 0.01 and 0.40). The second LC resonator58and the fourth LC resonator62are not electromagnetically coupled such that a coupling factor between the second LC resonator58and the fourth LC resonator62is less than about 1.0%. Similarly, the first LC resonator56and the fourth LC resonator62are not electromagnetically coupled such that a coupling factor between the first LC resonator56and the fourth LC resonator62is less than about 1.0%.

As discussed above, providing coupling between the first LC resonator56and the second LC resonator58, and providing coupling between the third LC resonator60and the fourth LC resonator62effectively widens the bandwidth of the resonator multiplexer circuitry36along each signal path, and further increases the sharpness of the roll-off thereof. Providing coupling between the first LC resonator56and the third LC resonator60allows a portion of leakage signals coupled into each secondary signal path to be effectively re-combined with the primary signal path, thereby increasing the isolation of the resonator multiplexer circuitry36.

While only four LC resonators are shown in the resonator multiplexer circuitry36, any number of LC resonators may be used without departing from the principles of the present disclosure. Adding additional LC resonators to the resonator multiplexer circuitry36may widen the pass band of each signal path by adding a resonant response at a nearby frequency to pass additional signals. As discussed above, due to the weak coupling between the LC resonators, the bandwidth and roll-off of the filter response thereof is sharpened, which increases the performance thereof.

FIG. 8shows the resonator multiplexer circuitry36according to an additional embodiment of the present disclosure. The resonator multiplexer circuitry36shown inFIG. 8is substantially similar to that shown inFIG. 7, but further includes resonator control circuitry92. Further, the first resonator capacitor66, the second resonator capacitor70, the third resonator capacitor80, the fourth resonator capacitor84, the first coupling capacitor72, the second coupling capacitor74, the third coupling capacitor76, the fourth coupling capacitor86, the fifth coupling capacitor88, and the sixth coupling capacitor90are adjustable. The resonator control circuitry92is coupled to the first resonator capacitor66, the second resonator capacitor70, the third resonator capacitor80, the fourth resonator capacitor84, the first coupling capacitor72, the second coupling capacitor74, the third coupling capacitor76, the fourth coupling capacitor86, the fifth coupling capacitor88, and the sixth coupling capacitor90in order to adjust a capacitance thereof. Adjusting a capacitance of one or more of the first resonator capacitor66, the second resonator capacitor70, the third resonator capacitor80, the fourth resonator capacitor84, the first coupling capacitor72, the second coupling capacitor74, the third coupling capacitor76, the fourth coupling capacitor86, the fifth coupling capacitor88, and the sixth coupling capacitor90adjusts the resonant frequency of the first LC resonator56, the second LC resonator58, the third LC resonator60, and the fourth LC resonator62, as well as the coupling factors between the resonators. Accordingly, the filter response of the resonator multiplexer circuitry36may be adjusted as desired.

FIG. 9shows the resonator multiplexer circuitry36according to an additional embodiment of the present disclosure. The resonator multiplexer circuitry36shown inFIG. 9is substantially similar to that shown inFIG. 8, but further includes a fifth LC resonator96coupled between the first signal path48and ground and a sixth LC resonator98coupled between the second signal path50and ground. The fifth LC resonator96includes a fifth resonator capacitor100and a fifth resonator inductor102coupled in parallel between the first signal path48and ground. The sixth LC resonator98includes a sixth resonator capacitor104and a sixth resonator inductor106coupled in parallel between the second signal path50and ground. A seventh coupling capacitor108may couple the first LC resonator56to the fifth LC resonator96. An eighth coupling capacitor110may couple the second LC resonator58to the fifth LC resonator96. A ninth coupling capacitor112may couple the third LC resonator60to the sixth LC resonator98. A tenth coupling capacitor114may couple the fourth LC resonator62to the sixth LC resonator98. The resonator control circuitry92may be coupled to each one of the first resonator capacitor66, the second resonator capacitor70, the third resonator capacitor80, the fourth resonator capacitor84, the fifth resonator capacitor100, the sixth resonator capacitor104, the first coupling capacitor72, the second coupling capacitor74, the third coupling capacitor76, the fourth coupling capacitor86, the fifth coupling capacitor88, the sixth coupling capacitor90, the seventh coupling capacitor108, the eighth coupling capacitor110, the ninth coupling capacitor112, and the tenth coupling capacitor114to adjust the response of the resonator multiplexer circuitry36as described above.

FIG. 10Ashows an exemplary filter response of the resonator multiplexer circuitry36according to one embodiment of the present disclosure. As shown inFIG. 10A, a first frequency pass band116and a second frequency pass band118are provided adjacent to one another. A number of sub-bands in each one of the first frequency pass band116and the second frequency pass band118are labeled A through N. Notably, the roll-off of the first frequency pass band116and the second frequency pass band118are significantly sharper than those shown above inFIG. 5. This is due to the weak coupling between the LC resonators therein, and in particular the coupling between the first LC resonator56and the second LC resonator58and the coupling between the third LC resonator60and the fourth LC resonator62, as well as the third coupling capacitor76and the sixth coupling capacitor90, which create a number of notches in the filter response. Due to the steeper roll-off, there is less overlap between the first frequency pass band116and the second frequency pass band118. However, due to inherent limitations in electromagnetic filtering circuitry, there is still some overlap. In some situations, this overlap may reduce the performance of a wireless communications device by introducing distortion from undesired frequency bands into a particular signal path. In particular, this may result in leakage of powerful transmission signals into a relatively low-power receive path, which may in turn desensitize receiver circuitry in the signal path. Such a scenario is especially prevalent when, for example, band G and band H are used together in a carrier aggregation configuration. As discussed above, due to the overlap in the first frequency pass band116and the second frequency pass band118, a portion of signals from band G and band H will be cross-coupled. When both of band G and band H must be used simultaneously, such a result may be unavoidable. However, for all other configurations, the likelihood of distortion may be reduced.

FIG. 10Bthus shows a filter response of the resonator multiplexer circuitry36according to an additional embodiment of the present disclosure. In particular,FIG. 10Bshows a filter response in which the components in the resonator multiplexer circuitry36have been adjusted to reduce the bandwidth of the first frequency pass band116to increase the isolation between the first frequency pass band116and the second frequency pass band118. In such an embodiment, the first frequency pass band116and the second frequency pass band118no longer overlap. The increased isolation afforded by such an approach comes at the cost of significantly reduced performance in band G due to a much higher insertion loss. However, such an approach will generally be used when, for example, band G is not in use. The resonator control circuitry discussed above with respect toFIG. 8andFIG. 9can dynamically change between the filter response shown inFIG. 10Aand the filter response shown inFIG. 10Bas desired.

FIG. 10Cshows a filter response of the resonator multiplexer circuitry36according to an additional embodiment of the present disclosure. The frequency response shown inFIG. 10Cis similar to that shown inFIG. 10B, except that the bandwidth of the second frequency pass band118is reduced to increase isolation between the first frequency pass band116and the second frequency pass band118. As discussed above, this may come at the cost of significantly decreased performance in band H due to increased insertion loss. However, the resonator control circuitry discussed above with respect toFIG. 8andFIG. 9can dynamically change between the filter responses inFIG. 10A,FIG. 10B, andFIG. 10Cin order to implement the increased isolation response only when band G or band H is not in use.

FIG. 11shows a wireless communications device120including the RF filtering circuitry34according to one embodiment of the present disclosure. The wireless communications device120may be a mobile telephone, personal digital assistant (PDA), or the like. The basic architecture of the wireless communications device120may include the resonator multiplexer circuitry36, the supplemental filtering circuitry38, a receiver front end122, an RF transmitter section124, an antenna126, a baseband processor128, a control system130, a frequency synthesizer132, and an interface134. The receiver front end122receives information bearing RF signals from one or more remote transmitters provided by a base station via the resonator multiplexer circuitry36and the supplemental filtering circuitry38. A low noise amplifier (LNA)136amplifies the signal. While only one LNA136is shown to avoid obscuring the drawings, multiple LNAs136are generally provided, each designed to process signals within a specific frequency range. Accordingly, signals from different outputs of the resonator multiplexer circuitry36and the supplemental filtering circuitry38(also not shown for purposes of clarity) will generally be provided to different LNAs136in the receiver front end122. Additional filtering circuitry138minimizes broadband interference in the received signal, while a down-converter140down-converts the filtered received signal to an intermediate or baseband frequency signal, which is then digitized into one or more digital streams. The receiver front end122typically uses one or more mixing frequencies generated by the frequency synthesizer132.

The baseband processor128processes the digitized received signal to extract the information or data bits conveyed in the received signal. This processing typically comprises demodulation, decoding, and error correction operations. As such, the baseband processor128is generally implemented in one or more digital signal processors (DSPs).

On the transmit side, the baseband processor128receives digitized data from the control system130, which it encodes for transmission. The encoded data is output to the RF transmitter section124where it is used by a modulator142to modulate a carrier signal that is at a desired transmit frequency. Power amplifier circuitry144amplifies the modulated carrier signal to a level appropriate for transmission from the antenna126. The signals are then provided through the supplemental filtering circuitry38and the resonator multiplexer circuitry36. Generally, the power amplifier circuitry144includes multiple power amplifiers, the signals from which may be simultaneously provided to the supplemental filtering circuitry38and the resonator multiplexer circuitry36simultaneously, where they are combined for transmission from the antenna126.

A user may interact with the wireless communications device120via the interface134which may include interface circuitry146associated with a microphone148, a speaker150, a keypad152, and a display154. The interface circuitry146typically includes analog-to-digital converters, digital-to-analog converters, amplifiers, and the like. Additionally, it may include a voice encoder/decoder, in which case it may communicate directly with the baseband processor128.

The microphone148will typically convert audio input, such as the user's voice, into an electrical signal, which is then digitized and passed directly or indirectly to the baseband processor128. Audio information encoded in the received signal is recovered by the baseband processor128and converted by the interface circuitry146into an analog signal suitable for driving the speaker150. The keypad152and the display154enable the user to interact with the wireless communications device120by inputting numbers to be dialed, address book information, or the like, as well as monitoring call progress information.

As discussed above, the coupling between the various LC resonators in the resonator multiplexer circuitry36may be achieved via specific placement of the inductors in the resonators.FIGS. 12A and 12Billustrate various configurations for the first resonator inductor64, the second resonator inductor68, the third resonator inductor78, and the fourth resonator inductor82shown inFIGS. 9 and 10. Specifically,FIG. 12Ashows two nested two-dimensional inductors such that the second resonator inductor68and the fourth resonator inductor82are shaped like a figure “8”, and the first resonator inductor64and the third resonator inductor78surround the second resonator inductor68and the fourth resonator inductor82, respectively. Because the second resonator inductor68is surrounded by the first resonator inductor64, and because the fourth resonator inductor82is surrounded by the third resonator inductor78, electromagnetic coupling occurs between the respective inductors. Further, because the first resonator inductor64and the third resonator inductor78are adjacent to one another, they are also electromagnetically coupled. This increases the isolation of the resonator multiplexer circuitry36as discussed above. However, due to shielding provided by the first resonator inductor64and the third resonator inductor78, the second resonator inductor68and the fourth resonator inductor82have minimal coupling with one another. Accordingly, the desired coupling factors between the first resonator inductor64, the second resonator inductor68, the third resonator inductor78, and the fourth resonator inductor82may be achieved with a minimal footprint.

FIG. 12Bshows the first resonator inductor64and the second resonator68as three-dimensional inductors wherein second resonator inductor68is nested inside of the first resonator inductor64. Further,FIG. 12Bshows the third resonator inductor78and the fourth resonator inductor82as three-dimensional inductors wherein the fourth resonator inductor82is nested inside of the third resonator inductor78. Due to the three-dimensional structure of the first resonator inductor64and the third resonator inductor78, the magnetic field of each inductor is substantially confined to an interior of the three-dimensional space bounded thereby. This results in coupling between the first resonator inductor64and the second resonator inductor68and coupling between the third resonator inductor78and the fourth resonator inductor82. Further, due to the fact that the first resonator inductor64and the third resonator inductor78are adjacent to one another, and that not all of the magnetic field of each is confined to the interior thereof, a small amount of coupling will also occur between the first resonator inductor64and the third resonator inductor78, which, as discussed above, results in cross-isolation between the first signal path48and the second signal path50. Providing the first resonator inductor64, the second resonator inductor68, the third resonator inductor78, and the fourth resonator inductor82as shown results in the ability to control the coupling factors there-between as desired while consuming minimal space with the inductors.