RELATED APPLICATIONS DATA

[0001] This application is a continuation-in-part of U.S. Patent Application Serial No. 13/282,289, filed October 26, 201 1 , which is a continuation of U.S. Patent

Application Serial No.12/959,237, filed December 2, 2010, now issued as U.S.

Patent No. 8,063,714, which is a continuation of U.S. Patent Application Serial No. 12/620,455, filed November 17, 2009, now issued as U.S. Patent No. 7,863,999, which is a continuation of U.S. Patent Application Serial No. 12/163,814, filed June 27, 2008, now issued as U.S. Patent No. 7,639,101 , which claims priority from U.S. Provisional Patent Application Ser. No. 60/937,462, filed June 27, 2007, and is a continuation-in-part of U.S. Patent Application Ser. No. 1 1/561 ,333, filed November 17, 2006, now issued as U.S. Patent No. 7,719,382, which applications are all incorporated herein by reference.

FIELD OF THE INVENTION

[0002] The present inventions generally relate to microwave circuits, and in particular, microwave band-pass filters.

BACKGROUND OF THE INVENTION

[0003] Electrical filters have long been used in the processing of electrical signals. In particular, such electrical filters are used to select desired electrical signal frequencies from an input signal by passing the desired signal frequencies, while blocking or attenuating other undesirable electrical signal frequencies. Filters may be classified in some general categories that include low-pass filters, high-pass filters, band-pass filters, and band-stop filters, indicative of the type of frequencies that are selectively passed by the filter. Further, filters can be classified by type, such as Butterworth, Chebyshev, Inverse Chebyshev, and Elliptic, indicative of the type of bandshape frequency response (frequency cutoff characteristics) the filter provides relative to the ideal frequency response.

[0004] The type of filter used often depends upon the intended use. In

communications applications, band-pass filters are conventionally used in cellular base stations and other telecommunications equipment to filter out or block RF signals in all but one or more predefined bands. For example, such filters are typically used in a receiver front-end to filter out noise and other unwanted signals that would harm components of the receiver in the base station or

telecommunications equipment. Placing a sharply defined band-pass filter directly at the receiver antenna input will often eliminate various adverse effects resulting from strong interfering signals at frequencies near the desired signal frequency. Because of the location of the filter at the receiver antenna input, the insertion loss must be very low so as to not degrade the noise figure. In most filter technologies, achieving a low insertion loss requires a corresponding compromise in filter steepness or selectivity.

[0005] In commercial telecommunications applications, it is often desirable to filter out the smallest possible pass band using narrow-band filters to enable a fixed frequency spectrum to be divided into the largest possible number of frequency bands, thereby increasing the actual number of users capable of being fit in the fixed spectrum. With the dramatic rise in wireless communications, such filtering should provide high degrees of both selectivity (the ability to distinguish between signals separated by small frequency differences) and sensitivity (the ability to receive weak signals) in an increasingly hostile frequency spectrum. Of most particular importance is the frequency ranges of 800-900 MHz range for analog cellular communications, and 1 ,800-2,200 MHz range for personal communication services (PCS).

[0006] Of particular interest to the present invention is the need for a high-quality factor Q (i.e., measure of the ability to store energy, and thus inversely related to its power dissipation or lossiness), low insertion loss, tunable filter in a wide range of microwave and RF applications, in both military (e.g., RADAR), communications, and electronic intelligence (ELINT), and the commercial fields, such as in various communications applications, including cellular. In many applications, a receiver filter must be tunable to either select a desired frequency or to trap an interfering signal frequency. Thus, the introduction of a linear, tunable, band-pass filter between the receiver antenna and the first non-linear element (typically a low-noise amplifier or mixer) in the receiver, offers substantial advantages in a wide range of RF microwave systems, providing that the insertion loss is very low.

[0007] For example, in commercial applications, the 1 ,800-2,200 MHz frequency range used by PCS can be divided into several narrower frequency bands (A-F bands), only a subset of which can be used by a telecommunications operator in any given area. Thus, it would be beneficial for base stations and hand-held units to be capable of being reconfigured to operate with any selected subset of these frequency bands. As another example, in RADAR systems, high amplitude interfering signals, either from "friendly" nearby sources, or from jammers, can desensitize receivers or intermodulate with high-amplitude clutter signal levels to give false target indications. Thus, in high-density signal environments, RADAR warning systems frequently become completely unusable, in which case, frequency hopping would be useful.

[0008] Microwave filters are generally built using two circuit building blocks: a plurality of resonators, which store energy very efficiently at one frequency, fo; and couplings, which couple electromagnetic energy between the resonators to form multiple stages or poles. For example, a four-pole filter may include four resonators. The strength of a given coupling is determined by its reactance (i.e., inductance and/or capacitance). The relative strengths of the couplings determine the filter shape, and the topology of the couplings determines whether the filter performs a band-pass or a band-stop function. The resonant frequency fo is largely determined by the inductance and capacitance of the respective resonator. For conventional filter designs, the frequency at which the filter is active is determined by the resonant frequencies of the resonators that make up the filter. Each resonator must have very low internal resistance to enable the response of the filter to be sharp and highly selective for the reasons discussed above. This requirement for low resistance tends to drive the size and cost of the resonators for a given technology.

[0009] Typically, fixed frequency filters are designed to minimize the number of resonators required to achieve a certain shape as the size and cost of a conventional filter will increase linearly with the number of resonators required to realize it. As is the case for semiconductor devices, photolithographically defined filter structures (such as those in high-temperature superconductor (HTS), micro electro-mechanical systems (MEMS), and film bulk acoustic resonator (FBAR) filters are much less sensitive to this kind of size and cost scaling than conventional combline or dielectric filters.

[0010] The approaches used to design tunable filters today follow the same approach as described above with respect to fixed frequency filters. Thus, they lead to very efficient, effective, and simple circuits; i.e., they lead to the simplest circuit necessary to realize a given filter response. In prior art tuning techniques, all the resonant frequencies of the filter are adjusted to tune the filter's frequency. For example, if it is desired to increase the operating frequency band of the device by 50 MHz, all of the resonant frequencies of the narrow-band filter must be increased by 50 MHz. While this prior art technique has been generally successful in adjusting the frequency band, it inevitably introduces resistance into the resonators, thereby disadvantageously increasing the insertion loss of the filter.

[001 1] Although HTS filters may be tuned without introducing significant resistance into the resonators by mechanically moving an HTS plate above each resonator in the filter to change its resonant frequency, such technique is inherently slow (on the order of seconds) and requires relative large three-dimensional tuning structures. Insertion loss can be reduced in so-called switched filter designs; however, these designs still introduce a substantial amount of loss between switching times and require additional resonators. For example, the insertion-loss of a filter system can be reduced, by providing two filters and a pair of single-pole double-throw (SP2T) switches to select between the filters, thus effectively reducing the tuning range requirement, but increasing the number of resonators by a factor of two and introducing loss from the switch. The loss of the filter system can further be reduced by introducing more switches and filters, but each additional filter will require the same number of resonators as the original filter and will introduce more loss from the required switches.

[0012] There, thus, remains a need to provide a band-pass filter that can be tuned quickly with a decreased insertion loss.

SUMMARY OF THE INVENTION

[0013] In accordance with a first aspect of the present inventions, a radio frequency (RF) filter is provided. The RF filter comprises a signal transmission path having an input and an output, a plurality of resonant elements disposed along the signal transmission path between the input and the output, and a plurality of non-resonant elements coupling the resonant elements together. The resonant elements are coupled together to form a stop band having a plurality of transmission zeroes corresponding to respective frequencies of the resonant elements, and at least one sub-band between the transmission zeroes. The non-resonant elements have susceptance values that locate at least one reflection zero within the stop band to create a pass band in one of the at least one sub-bands. [0014] The non-resonant elements comprise at least one variable non-resonant element for selectively introducing at least one reflection zero within the stop band to create a pass band in one of the sub-bands(s). In one embodiment, a plurality of sub-bands is provided, in which case, the variable non-resonant element(s) may be for displacing the reflection zero(es) along the stop band to create the pass band within selected ones of the sub-bands. The pass band may have a substantially different bandwidths within the selected sub-bands. In another embodiment, the variable non-resonant element(s) is for displacing at least another reflection zero within the stop band to create another pass band within another one of the sub- bands.

[0015] The variable non-resonant element may have, e.g., an adjustable susceptance, and may include one or more of a variable capacitor, a loss-loss switch, a varactor, and a switched capacitor. In one embodiment, each of the resonant elements comprises a thin-film lumped element structure (such as, e.g., a high temperature superconductor (HTS)), although a resonant element can take the form of any structure that resonates at a desired frequency.

[0016] The RF filter further comprises an electrical controller configured for receiving an operating temperature, and adjusting the variable non-resonant element(s) based on the received operating temperature, thereby selectively moving the reflection zero(es) along the stop band to move the pass band within the selected sub-band. In one embodiment, the electrical controller is configured for adjusting the variable non-resonant element(s) to selectively introduce the reflection zero(es) within the stop band to create the pass band in the one sub-band. For example, each of the non-resonant element(s) may have a plurality of capacitors coupled in parallel to each other to form a capacitive circuit and at least one switch coupled to at least one of the capacitors. The electrical controller may then be configured for varying the reactance of the respective non-resonant element by operating the switch(es) to selectively include or exclude at least one capacitor from the capacitive circuit to vary the capacitance of the capacitive circuit, thereby selectively moving the reflection zero within the stop band to move the pass band in the selected sub-band.

[0017] The electrical controller may be configured for adjusting the variable non- resonant element(s), thereby selectively moving the reflection zero(es) along the stop band to return the pass band back to a nominal as-designed location within a frequency range. In this case, the electrical controller may be configured for adjusting at least one of the resonant elements based on the received operating temperature, thereby selectively moving the transmission zero corresponding to each frequency of the resonant element(s) along the stop band to return the pass band back to the nominal as-designed location within the frequency range.

[0018] In one embodiment, the RF filter further comprises a temperature sensor configured for measuring the operating temperature, in which case, the electrical controller is configured for receiving the measured operating temperature from the temperature sensor. The RF filter may further comprises memory storing a look up table containing a plurality of reference operating temperatures and a plurality of sets of adjustment settings respectively corresponding to the different operating temperatures. In this case, electrical controller is configured for comparing the measured operating temperature to the plurality of reference operating temperatures in the look-up table, selecting the set of adjustment settings corresponding to the reference operating temperature closest to the measured operating temperature, and adjusting the variable non-resonant element(s) in accordance with the set of adjustment settings.

[0019] Other and further aspects and features of the invention will be evident from reading the following detailed description of the preferred embodiments, which are intended to illustrate, not limit, the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The drawings illustrate the design and utility of preferred embodiments of the present invention, in which similar elements are referred to by common reference numerals. In order to better appreciate how the above-recited and other advantages and objects of the present inventions are obtained, a more particular description of the present inventions briefly described above will be rendered by reference to specific embodiments thereof, which are illustrated in the accompanying drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:

[0021] Fig. 1 is a block diagram of a tunable radio frequency (RF) filter constructed in accordance with one embodiment of the present inventions; [0022] Fig. 2 is a plot of a modeled frequency response of an exemplary wide stop band using eight resonant elements;

[0023] Fig. 3 is a plot of the frequency response of Fig. 2, wherein a pass band has been introduced within a sub-band of the stop band;

[0024] Figs. 4(a)-4(g) are plots of the frequency response of Fig. 2, wherein a pass band has been introduced within selected sub-bands of the stop band;

[0025] Figs. 5(a)-5(d) are plots of the frequency response of Fig. 2, wherein the stop band has been shifted in frequency and a pass band has been introduced at various locations of a sub-band of the shifted stop band;

[0026] Fig. 6 is a plot illustrating the simultaneous shifting of transmission zeroes of the frequency response of Fig. 2 to extend the range of the pass band introduced within the selected sub-bands of the stop band of Figs. 4(a)-4(g);

[0027] Figs. 7(a)-7(f) are plots of a modeled frequency response of an exemplary wide stop band using nine resonant elements, wherein a pass band has been introduced within selected sub-bands of the stop band to cover the personal communications services (PCS) frequency range;

[0028] Fig. 8 are plots illustrating the independent shifting of transmission zeroes of the frequency response of Figs. 7(a)-7(f) to accommodate the introduction of the pass band within the selected sub-bands of the stop band;

[0029] Figs. 9(a)-9(f) are plots of a modeled frequency response of Fig. 2, wherein multiple pass bands have been introduced within selected sub-bands of the stop band;

[0030] Fig. 10 is a block diagram of a tunable RF filter constructed in accordance with another embodiment of the present inventions;

[0031] Fig. 1 1 is a plot of a modeled frequency response of the filter of Fig. 10, wherein a pass band has been introduced at various locations of the sub-band of the shifted stop band;

[0032] Fig. 12 is a plot illustrating the variation of coupling values of non-resonant elements used in the tunable RF filter of Fig. 10 versus a frequency shift in the pass- band of Fig. 11 ;

[0033] Figs. 13(a)-13(d) illustrate circuit representations of the tunable RF filter of Fig. 1 ;

[0034] Fig. 14 is a table illustrating component values used in modeling the RF filter of Fig. 14 for three filter states; [0035] Figs. 15(a)-15(c) is a circuit implementation of the tunable RF filter of Fig. 1 , particularly illustrating various filter states and corresponding frequency responses;

[0036] Figs. 16(a)-16(c) are plots of the frequency response of the RF filter of Fig. 14 in the three states;

[0037] Fig. 17 is a plot illustrating the tuning of the RF filter of Fig. 14 versus insertion loss of the filter;

[0038] Fig. 18 is a plot comparing the insertion loss of the RF filter of Fig. 14 versus the insertion loss of a conventional filter when tuned over the same frequency range;

[0039] Fig. 19 is a plot comparing the insertion loss of the filter of Fig. 1 versus the insertion loss of a switched filter when tuned over the same frequency range;

[0040] Fig. 20 is a plot comparing frequency responses between two-resonator, four-resonator, and six-resonator tunable filters constructed in accordance with the present inventions and a frequency response of a standard band-pass filter;

[0041] Fig. 21 illustrates another circuit representation of the tunable RF filter of Fig. 1 ;

[0042] Fig. 22 illustrates a coupling matrix of the circuit representation of Fig. 21 ;

[0043] Figs. 23(a)-23(c) are plots of the frequency responses of the RF filter of Fig. 21 and corresponding coupling matrices;

[0044] Fig. 24 is a plot graphically showing the coupling values in the coupling matrices of Figs. 23(a)-23(c) used to tune the RF filter of Fig. 21 ;

[0045] Fig. 25 is a plot graphically showing another set of coupling values that can be used to tune the RF filter of Fig. 21 ;

[0046] Fig. 26 is a plot graphically showing still another set of coupling values that can be used to tune the RF filter of Fig. 21 ;

[0047] Fig. 27 is a plan view layout of one resonator of the tunable RF filter of Fig.

1 , particularly illustrating tuning forks for tuning the resonator;

[0048] Fig. 28 is a plan view layout of one resonator of the tunable RF filter of Fig.

1 , particularly illustrating trimming tabs for tuning the resonator; and

[0049] Fig. 29 is a block diagram of another tunable RF filter constructed in accordance with one embodiment of the present inventions.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] Referring to Fig. 1 , a tunable radio frequency (RF) filter 10 constructed in accordance with the present inventions will now be described. In the illustrated embodiment, the RF filter 10 is a band-pass filter having pass band tunable within a desired frequency range, e.g., 800-900 MHz or 1 ,800-2,220 MHz. In a typical scenario, the RF filter 10 is placed within the front-end of a receiver (not shown) behind a wide pass band filter that rejects the energy outside of the desired frequency range. The RF filter 10 generally comprises a signal transmission path 12 having an input 14 and an output 16, a plurality of nodes 17 disposed along the signal transmission path 12, a plurality of resonant branches 19 respectively extending from the nodes 17, and a plurality of non-resonant branches 21

respectively extending from the nodes 17. The RF filter 10 further comprises a plurality of resonant elements 18 (in this case, four) between the input 14 and output 16, and in particular coupled between the resonant branches 21 and ground, a plurality of tuning elements 20 for adjusting the frequencies of the resonant elements 18, a plurality of non-resonant elements 22 coupling the resonant elements 18 together, four of which are coupled between the non-resonant branches 21 and ground. The RF filter 10 further comprises an electrical controller 24 configured for tuning the RF filter 10 to a selected narrow-band within the frequency range.

[0051] The signal transmission path 12 may comprise a physical transmission line to which the non-resonant elements 22 are directly or indirectly coupled to, although in alternative embodiments, a physical transmission line is not used. In the illustrated embodiment, the resonant elements 18 includes lumped element electrical components, such as inductors and capacitors, and in particular, thin-film lumped structures, such as planar spiral structures, zig-zag serpentine structures, single coil structures, and double coil structures. Such structures may include thin film epitaxial high temperature superconductors (HTS) that are patterned to form capacitors and inductors on a low loss substrate. Further details discussing high temperature superconductor lumped element filters are set forth in U.S. Patent No. 5,616,539, which is expressly incorporated herein by reference.

[0052] In the illustrated embodiment, the resonant elements 18 are represented by susceptance B ^R , and the non-resonant elements 22 are represented by susceptance B ^N , which are coupled in parallel with the resonant elements 18, and admittance inverters J, which are coupled between the resonant elements 18. Selected ones of the non-resonant elements 22 can be varied, while any remaining ones of the non- resonant elements 22 remained fixed. [0053] As will be described in greater detail below, the non-resonant elements 22 may be varied to tune the pass band substantially over the entire frequency range, with the frequencies of the resonant elements 18, if necessary, only slightly adjusted to accommodate and/or move the pass band within a relatively portion of the frequency range. In this manner, the insertion loss of the filter 10 is significantly reduced, since it is the non-resonant elements 22, rather than the resonant elements 18, that are used as the primary means for tuning the filter 10. That is, because adjustment of the non-resonant elements 22 contributes less to the loss of the filter 10 than does the adjustment of the significantly loss sensitive resonant elements 18, the filter 10 will have less loss than prior art filters that utilize resonant elements as the main means for tuning the filter 10. In addition, since the frequencies of the resonant elements 18 are adjusted very little, if at all, the tuning speed of the filter 10 is increased.

[0054] The RF filter 10 accomplishes the foregoing by introducing a narrow pass band with selected regions of a wide stop band. That is, although the RF filter 10 is ultimately used as a pass band filter, the resonant elements 18 are actually coupled together by the non-resonant elements 22— not to create a pass band, but rather to create a wide stop band response having transmission zeroes (in this case, numbering four) corresponding to the respective frequencies of the resonant elements 18. The electrical controller 24 then adjusts the non-resonant elements 22 to introduce and displace reflection zeroes along the stop band to move a narrow pass band within the desired frequency range. The electrical controller 24 may also adjust the frequencies of the resonating elements 18 via the tuning elements 20 to move the transmission zeroes along the frequency range to optimize the filter response. In the illustrated embodiment, the electrical controller 24 including memory (not shown) for storing the values of the non-resonant elements 22 necessary to effect the desired location of the pass band within the frequency range.

[0055] This technique will now be described with reference to various exemplary filter responses modeled in accordance with the following equations: 511(5) = ^ ^), 52 ) = , \E\ ² = \F\ ² , where S-n is the input reflection

E(s) sE\s) ε

coefficient of the filter, S21 is the forward transmission coefficient, s is the normalized frequency, F and P are N-order polynomial (where N is the number of resonant elements) of the generalized complex frequency s, and ε is a constant that defines equal ripple return loss. Each of the coefficients S-n and S ₂ i is capable of having up to an N number of zero-points, since the numerator has an Nth order. When both of the coefficients Sn , S21 have all N zero-points, the filter response is considered fully elliptic. Further details discussing the modeling of filters are set forth in "Microstrip Filters for RF/Microwave Application," Jia-Shen G. Hong and M.J. Lancaster, Wiley- Interscience 2001 . The normalized frequency, s=iw can be mapped into real

fi (£ _ fc

frequency in accordance with the equation: w ^■ ■ where f is the real

BW \ fi fi

frequency, f _c is the center frequency, and BW is the bandwidth of the filter. Further details discussing the transformation of normalized frequency into real frequency are set forth in "Microwave Filters, Impedance-Matching Networks, and Coupling Structures," G. Matthaei, L. Young and E.M.T. Jones, McGraw-Hill (1964).

[0056] Fig. 2 illustrates an exemplary wide band stop filter response, which was modeled using eight resonant elements, thereby creating eight corresponding transmission zeroes 30 (only six shown) at the respective resonant element frequencies (as best shown in the right side view of Fig. 2) to form a stop band 32, and eight reflection zeroes 34 (only six shown) that fall outside of this stop band 32 (as best shown in the left side view of Fig. 2). In this particular example, the transmission zeroes 30 are positioned at -1 .05, -0.75, -0.45, -0.15, 0.15, 0.45, 0.75, and 1 .05 in the normalized frequency range, thereby creating a stop band having a normalized frequency range between -1 .05 and 1 .05. As shown in right side view of Fig. 2, the filter response includes seven "bounce-backs" in regions 36 between the transmission zeroes 30 that are respectively located at -0.90, -0.60, -0.30, 0.0, 0.30, 0.60, and 0.90. Thus, in general, a stop band filter includes an N number of transmission zeroes (corresponding to the N number of resonant elements), up to N number of reflection zeroes, and an N-1 number of bounce-back regions 36.

[0057] Significantly, a pass band can be formed from any one of the bounce-backs in regions 36 illustrated in Fig. 2 (herein after referred to as "sub-bands") by displacing at least one of the reflection zeroes 34 into the stop band 32 (i.e., by adjusting the values of the non-resonant elements). For example, Fig. 3 illustrates an exemplary filter response where four of the reflection zeroes 34 have been introduced into the stop band of Fig. 2 to create a pass band 38 within the center sub-band 36(4) (i.e., at 0). The reflection zeroes 34 can be displaced along the stop band 32 (i.e., by adjusting the values of the non-resonant elements), thereby creating the pass band 38 within selected ones of the sub-bands 36. That is, the reflection zeroes 34 can be displaced along the stop band 32 to "hop" the pass band 38 between sub-bands 36.

[0058] For example, Figs. 4(a)-4(g) illustrate exemplary filter responses where the four reflection zeroes 34 have been displaced within the stop band 32 to selectively create the pass band 38 in the centers of all seven of the sub-bands 36. That is, going sequentially through Figs. 4(a)-4(g), the pass band 38 hops from the first sub- band 36(1 ) (Fig. 4(a)), to the second sub-band 36(2) (Fig. 4(b)), to the third sub- band 36(3) (Fig. 4(c)), to the fourth sub-band 36(4) (Fig. 4(d)), to the fifth sub-band 36(5) (Fig. 4(e)), to the sixth sub-band 36(6) (Fig. 4(f)), and then finally to the seventh sub-band 36(7) (Fig. 4(g)). Thus, in the illustrated embodiment, the center of the pass band 38 can hop between -0.90, -0.60, -0.30, 0.0, 0.30, 0.60, and 0.90. It should be noted that while the sequence of Figs. 4(a)-4(g) implies that the pass band 38 is hopped between adjacent sub-bands 36, the pass band 38 may be hopped between non-adjacent sub-bands 36; for example, from the second sub- band 36(2) to the fifth sub-band 36(5).

[0059] While the pass band 38 can be hopped between sub-bands 36 to discretely cover the desired frequency range, the transmission zeroes 30 can be

simultaneously moved in concert from their nominal positions (i.e., by adjusting the frequencies of the resonating elements) to displace the entire stop band 32, and thus the pass band 38, within the normalized frequency range. Thus, the pass band 38 can be moved from the centers of the sub-bands 36 (i.e., -0.90, -0.60, -0.30, 0.0, 0.30, 0.60, and 0.90) to cover the continuum of the desired frequency range. Thus, if all of the transmission zeroes 30 can be displaced by +/-0.15 from their nominal positions (i.e., resonant elements tuned together in a frequency range of +/- 0.15), each pass band 38 illustrated in Figs. 4(a)-4(g) would cover 15% of the normalized frequency range from -1 .05 to 1 .05.

[0060] By way of example, if it is desired to center the pass band 38 at -0.20, the pass band 38 can be located in the third sub-band 36(3) (centered at -0.30 in Fig. 4(c)), and the transmission zeroes 30 can be displaced 0.10 from their nominal positions to move the pass band 38 from -0.30 to -0.20. If it is desired to center the pass band 38 at 0.85, the pass band 38 can be located in the seventh sub-band 36(7) (centered at 0.90 in Fig. 4(g)), and the transmission zeroes 30 can be displaced -0.05 from their nominal positions to move the pass band 38 from 0.90 to 0.85.

[0061] While the pass band 38 is illustrated in Figs. 4(a)-4(g) as being centered within the sub-bands 36, the reflection zeroes 34 can be displaced within the stop band 32 (i.e., by adjusting the values of the non-resonant elements) to selectively move the pass band 38 within a selected sub-band 36. In this case, the pass band 38 can be hopped between sub-bands 36, as well as moved within each sub-band 36, thereby decreasing the amount the transmission zeroes 30 needed to be adjusted for the pass band 38 to cover the continuum of the desired frequency range. For example, Figs. 5(a)-5(d) illustrate exemplary filter responses, with respect to the center sub-band 36(4), where all of the transmission zeroes 30 are displaced 0.05 from their nominal positions (i.e., by increasing the frequencies of the resonant elements 18 by 0.05), and the reflection zeroes 34 are incrementally displaced by 0.05 (i.e., by adjusting the non-resonant elements 22) from their nominal positions.

[0062] In particular, going sequentially through Figs. 5(a)-5(d), the transmission zeroes 30 are displaced 0.05 from their nominal positions, thereby moving the pass band 38 from 0 (Fig. 5(a)) to 0.05 (Fig. 5(b)). Then, after fixing the transmission zeroes 30 in place, the reflection zeroes 34 are incrementally displaced 0.05 from their nominal positions to move the pass band 38 from the center of the sub-band 36(4) (0.05 in Fig. 5(b)) to a position 0.05 to the right of the center of the sub-band 36(4) (0.10 in Fig. 5(c)), and then to a position 0.10 to the right of the center of the sub-band 36(4) (0.15 in Fig. 5(d)).

[0063] While this modality may disrupt the symmetry of the rejection slope of the band-pass filter, in this case, it reduces the needed displacement of the transmission zeroes 30, and thus, the tuning range of the resonant elements, from 15% to 5%, to obtain the same tuning range as the case where the reflection zeroes 34 are not displaced within a sub-band 36. As a result, the loss of filter is further reduced.

[0064] Notably, while the transmission zeroes 30 may theoretically be displaced within the entirety of a sub-band 36, in which case, each pass band 38 can cover approximately 15% of the entire stop band 32 without having to tune the resonant elements, in reality, the filter loss significantly increases as a reflection zero 34 closely approaches a transmission zero 30. As such, it is preferable that the transmission zeroes 30 be displaced, along with the reflection zeroes 34, to allow the pass band 38 to move within the entire frequency range without significant loss.

[0065] For example, referring to Fig. 6, the transmission zeroes 30 are displaced in a range of +/- 0.05 relative to their nominal positions (shown by horizontal dashed lines) to allow the pass band 38 to be located anywhere within the nominal frequency range of -1 .05 to 1 .05 (as represented by the diagonal dashed line). As the frequency of pass band 38 moves from -1 .05 to 1 .05, the reflection zeroes 34 hop from one sub-band 36 to the next, with the reflection zeroes 34 being displaced along a sub-band 36 within a range of +/- 0.10, and the transmission zeroes 30 being displaced within range of +/- 0.05, for a total range of 0.30 between hops.

[0066] In particular, at the beginning of the tuning range, the transmission zeroes 30 will initially be positioned -0.05 relative to their nominal positions (i.e., -1 .05, -0.75, -0.45, -0.15, 0.15, 0.45, 0.75, 1 .05), which places the center the first sub-band 36(1 ) at -0.95, in which case, the reflection zeroes 34 will be initially positioned -0.10 relative to their nominal positions in the first sub-band 36(1 ) to place the pass band 38 at -1 .05. While the transmission zeroes 30 are fixed, the reflection zeroes 34 can be displaced to their nominal positions in the first sub-band 36(1 ) to move the pass band 38 from -1 .05 to -0.95. While the reflection zeroes 34 are fixed, the

transmission zeroes 30 can then be displaced 0.05 relative to their nominal positions, which moves the center of the first sub-band 36(1 ) to -0.85, thereby moving the pass band from -0.95 to -0.85. While the transmission zeroes 30 are again fixed, the reflection zeroes 34 can be displaced 0.10 relative to their nominal positions to move the pass band 38 from -0.85 to -0.75.

[0067] Once the pass band 38 reaches -0.75, the reflection zeroes 34 will then hop from the first sub-band 36(1 ) to the second sub-band 36(2), and the transmission zeroes 30 will then again be displaced -0.05 relative to their nominal positions, which moves the center of the second sub-band 36(2) to -0.65, in which case, the reflection zeroes 34 will be initially positioned -0.10 relative to their nominal positions to maintain the pass band 38 at -0.75. The transmission zeroes 30 and reflection zeroes 34 are then moved in coordination with each other in the same manner described above with respect to the first sub-band 36(1 ) to move the pass band 38 from -0.75 to -0.45. Once the pass band 38 reaches -0.45, the reflection zeroes 34 will then hop from the second sub-band 36(2) to the third sub-band 36(3), and so forth, until the pass band 38 reaches 1 .05. [0068] While the RF filter 10 has been described above as being capable of tuning a narrow pass band within a continuum of the desired frequency range (i.e., the RF filter 10 can be reconfigured in a continuous manner), the RF filter 10 may be reconfigurable in a discrete manner, such that the pass band 38 can be discretely centered at selected regions of the frequency band. For example, in PCS applications, the RF filter 10 may be reconfigured to operate in any of the six A-F frequency bands by locating the narrow pass band at a selected one of these frequency bands.

[0069] Figs. 7(a)-7(f) illustrate exemplary filter responses corresponding to six different reconfigured states of an RF filter. In this case, the modeled filter has nine transmission zeroes 30 (only seven shown) to create a stop band 32 with eight sub- bands 36 located between the respective transmission zeroes 30, and seven reflection zeroes 34 that can be displaced into the stop band 32 to create a pass band 38 within selected ones of the six middle sub-bands 36. Thus, the RF filter can be reconfigured to operate in the A-Band (Fig. 7(a)), D-Band (Fig. 7(b)), B-Band (Fig. 7(c)), E-Band (Fig. 7(d)), F-Band (Fig. 7(e)), or C-Band (Fig. 7(f)) of the PCS communications protocol. As shown, the width of the pass band 38 differs within the sub-bands 36, as dictated by the separation of adjacent transmission zeroes 30. In particular, the widths of the A-, B-, and C-Bands are approximately two-and-half greater than the widths of the D-, E-, and F-Bands.

[0070] Notably, because, in this reconfigurable implementation, the pass band 38 need not be moved within a continuum of the desired frequency range, but rather is designed to be broad enough to cover the desired frequency range, the transmission zeroes 30 are not displaced to extend the range of the pass band 38. Rather, as illustrated in Fig. 8, the transmission zeroes 30 are independently displaced from their nominal positions to make room for the pass band 38 or otherwise improve rejection performance. For example, the second and third transmission zeroes 30(2), 30(3) are moved away from each other to make room for the reflection zeroes 34 at the A-Band; the fourth and fifth transmission zeroes 30(4), 30(5) are moved away from each other to make room for the reflection zeroes at the B-Band, the seventh and eighth transmission zeroes 30(7), 30(8) are moved away from each other to make room for the reflection zeroes 34 at the C-Band; the third and fourth transmission zeroes 30(3), 30(4) are moved away from each other to make room for the reflection zeroes 34 at the D-Band, the fifth and sixth transmission zeroes 30(5), 30 (6) are moved away from each other to make room for the reflection zeroes 34 at the E-Band; and the sixth and seventh transmission zeroes 30(6), 30(7) are moved away from each other to make room for the reflection zeroes 34 at the F-Band.

[0071] Although the foregoing techniques have been described as introducing a single pass band 38 (i.e., one pass band at a time) within the stop band 32, multiple pass bands can be introduced within the stop band 32. For example, Figs. 9(a)-9(f) illustrate exemplary filter responses where two sets of four reflection zeroes 34 have been displaced within the stop band 32 to selectively create two pass bands 38(1 ), 38(2) in the centers of selected pairs of the sub-bands 36. That is, going

sequentially through Figs. 9(a)-9(f), the pass bands 38(1 ), 38(2) are introduced into the second and third sub-bands 36(2), 36(3) (Fig. 9(a)), into the third and fifth sub- bands 36(3), 36(5) (Fig. 9(b)), into the third and fourth sub-bands 36(3), 36(4) (Fig. 9(c)), into the second and fourth sub-bands 36(2), 36(4) (Fig. 9(d)), into the second and sixth sub-bands 36(2), 36(6) (Fig. 9(e)), and second and fifth sub-bands 36(2), 36(5) (Fig. 9(f)).

[0072] Referring now to Figs. 10 and 11 , a basic tunable filter 50 will be described for the purposes of explaining the correlation between the values of variable non- resonant elements (in terms of coupling values) and the movement of a resulting narrow pass band within a wide stop band. As shown in Fig. 10, the RF filter 50 generally comprises a signal transmission path 52 having an input 54 and an output 56, a plurality of resonant elements 58 (in this case two) between the input 54 and output 56, and a plurality of non-resonant elements 62 coupling the resonant elements 58 together. Tuning elements (not shown) can be used to adjust the frequencies of the resonant elements 58, and an electrical controller (not shown) can be used to tune the RF filter 50 to a selected narrow-band within the frequency range. Like the filter 10 illustrated in Fig. 1 , the resonant elements 58 of the filter 50 are represented by susceptance B ^R , and the non-resonant elements 62 are represented by susceptance B ^N , which are coupled in parallel with the resonant elements 58, and admittance inverters J, which are coupled between the resonant elements 58. Selected ones of the non-resonant elements 22 can be varied (in this case, the susceptances B ^N ), while any remaining ones of the non-resonant elements 22 remained fixed (in this case, the admittance inverters J).

[0073] The filter 50 was modeled to create the exemplary filter response illustrated in Fig. 11. The frequencies of the two resonant elements 58, and thus two transmission zeroes 70, were set at 0.95 GHz and 1 .05 GHz, thereby creating a stop band (not shown) having a normalized frequency range between 0.95 GHz and 1 .05 GHz. In this case, because there are only two resonant elements 58, a single sub- band 76 is centered between the transmission zeroes 70 at 1 .00 GHz. Thus, reflection zeroes (not shown) are introduced and displaced along the stop-band only to move a pass-band 78 within the single sub-band 76 (five positions of the pass- band 78 shown)

[0074] As further illustrated in Figs. 11 and 12, the variable non-resonant elements 66 (designated in Fig. 12 as B ^N (L) and B ^N (S)) can be adjusted to move the pass band 78 about the nominal frequency of 1 .00 GHz by changing their coupling values. In particular, the pass band 78 will decrease in frequency (move left) as the percentage coupling value of the load-side non-resonant element B ^N (L) increases and the percentage coupling value of the source-side non-resonant element B ^N (S) decreases, and will increase in frequency (move right) as the percentage coupling value of the load-side non-resonant element B ^N (L) decreases and the percentage coupling value of the source-side non-resonant element B ^N (S) increase.

[0075] Referring to Figs. 13(a)-13(c), the non-resonant elements 22 of the filter 10 of Fig. 1 can be replaced with actual components, so that the filter 10 can be modeled and implemented. As shown in Fig. 13(a), the circuit was first reduced to the constituent components necessary to reconfigure the filter 10 using only the non- resonant elements 22. In this case, the tuning elements 20 were not necessary to simulate (model) reconfiguration of the filter 10, and were thus, removed from the circuit representation in Fig. 13(a). As shown in Fig. 13(b), the block components of the circuit representation of Fig. 13(a) have been replaced with actual circuit components. The non-resonant elements 22 represented by B ^N were replaced with capacitors, the non-resonant elements 22 represented by J were replaced with capacitive pi networks, and the resonant elements 20 represented by B ^R were replaced with parallel capacitor-inductor combinations. The circuit representation of Fig. 13(b) was further reduced to the circuit representation of Fig. 13(c), the non- resonant elements 22 of which can be varied to effect reconfiguration of the filter 10.

[0076] The filter 10 of Fig. 13(c) was emulated using actual circuit component values. The circuit of Fig. 13(c) was modeled in accordance with the polynomial equations discussed above, with the exception that component values relate to the coefficient of the polynomials. As discussed above, the filter 10 has four resonating elements 18, and therefore, four transmission zeroes with three sub-bands formed therebetween, in its frequency response. Thus, the values of the capacitors non- resonant elements 22 in the circuit representation of Fig. 13(c) can be adjusted in accordance with one of the three sets of values illustrated in Fig. 14 to hop a pass band between the three sub-bands to place the filter 10 in a selected one of the three states. Each of the capacitors in the circuit representation of Fig. 13(c) was modeled in accordance with the circuit representation of Fig. 13(d). In particular, each capacitor C was represented as a circuit having a fixed capacitor Co in parallel with a variable capacitor Cd, and a resistor R (representing a switch) in series with the variable capacitor C _d .

[0077] Referring now to Figs. 15(a)-15(c), the filter 10, using the basic architecture illustrated in Fig. 13(c), can be reconfigured between one of three states by adjusting selected ones of the non-resonant elements 22. As shown, all of the frequency responses of the filter 10 have four transmission zeroes 30 corresponding to the frequencies of the four resonant elements 18, and three sub-bands 36 formed between the transmission zeroes 30. Thus, a pass band 38 can be created in each of the three sub-bands 36 to enable a total of three different states: a left state where the pass band 38 is created in the first sub-band 36(1 ); a middle state where the pass band 38 is created in the second sub-band 36(2); and a right state where the pass band 38 is created in the third sub-band 36(3).

[0078] As shown, each non-resonant element 22 has three capacitors C1-C3 in parallel, with the outer two capacitors Ci and C ₂ having respective switched capacitances in series with resistors Ri and R ₂ stimulating resistive loss of the switches Si and S ₂ . Thus, the capacitors Ci and C ₂ may be included within the circuit by closing the switches S ₂ and S3, and excluded from the circuit by independently opening the switches Si and S ₂ . Thus, assuming that capacitors Ci- C3 have equal values, each non-resonant element 22 can have a selected one of the three values: Ci (neither switch S-i , S ₂ closed), C ₂ +C ₃ (one of the switches S-i , S ₂ closed), or Ci +C ₂ +C ₃ (both switches S-i , S ₂ closed). The switches Si and S ₂ can be any suitable loss-switch, such as, e.g., a low-loss GaAs switch. Alternatively, other variable elements capable of adjusting a capacitance value, such as a variable capacitor, GaAs varactor, or switch capacitor, can be used.

[0079] It has been determined that the pass band 38 can be placed in the first sub- band 36(1 )(left state) when the non-resonant elements 22 have the values dictated by the switch states illustrated in Fig. 15(a); in the second sub-band 36(2)(middle state) when the non-resonant elements 22 have the values dictated by the switch states illustrated in Fig. 15(b); and in the third sub-band 36(3)(middle state) when the non-resonant elements 22 have the values dictated by the switch states illustrated in Fig. 15(c). The filter 10 can be tuned using the parameter extraction and analysis techniques disclosed in U.S. Patent Application Ser. No. 1 1/289,463, entitled "Systems and Methods for Tuning Filters," which is expressly incorporated herein by reference. For purposes of illustration, light bulbs adjacent switches in closed states have been shown lit (colored in), and light bulbs adjacent switches in open states have been shown unlit (not colored in). While the filter 10 has been described with respect to Figs. 15(a)-15(c) as only having the capability of hopping the pass band 38 between sub-bands 36, the resolution of the circuit can be increased by adding more switched capacitors in order to enable movement of the pass band 38 within a selected sub-band 36. Also, because the pass band 38 is positioned in the centers of the sub-bands 36, no tuning elements are shown coupled to the resonant elements 18.

[0080] Referring now to Fig. 17, the emulated filter 10 illustrated in Fig. 13(c) is shown being tuned along the frequency range of 770 MHz to 890 MHz to minimize insertion loss. In this scenario, the filter 10 was tuned by adjusting the non-resonant elements 22 to hop the pass band 38 between the centers of the sub-bands 36 (as illustrated in Figs. 16(a)-16(c)), and varying the frequencies of the resonant elements 18 to move the pass band 38 within the sub-bands 36 (i.e., to cover the frequency range between the centers of the sub-bands 36). As shown, the pass band 38 is moved from the center of the third sub-band 36(3)(shown in Fig. 15(c)) at 890 MHz to the left side of the third sub-band 36(3) at 850 MHz, increasing the insertion loss of the filter 10 from approximately -0.2 dB to approximately -1 .5 dB. Once it reaches 850 MHz, the pass band 38 hops from the third sub-band 36(3) to the center of the second sub-band 36(2)(shown in Fig. 15(b)), thereby decreasing the insertion loss from approximately -1 .5 dB to approximately -0.25 dB. The pass band 38 is then moved from the center of the second sub-band 36(2) at 850 MHz to the left side of the second sub-band 36(2) at 810 MHz, increasing the insertion loss of the filter 10 from approximately -0.25 to approximately -1 .5 dB. Once it reaches 810 MHz, the pass band 38 hops from the second sub-band 36(2) to the center of the first sub-band 36(1 )(shown in Fig. 15(a)), decreasing the insertion loss from approximately -1 .5 dB to -0.7 dB. The pass band 38 is then moved from the center of the first sub-band 36(1 ) at 810 MHz to the left side of the first sub-band 36(1 ) at 770 MHz, increasing the insertion loss of the filter 10 from approximately -0.7 dB to - 1 .9 dB. Thus, it can be appreciate that the full range of the frequency range 770 MHz to 890 MHz can be covered by the filter 10 by moving the pass band 38 along the frequency range, while hopping between sub-bands 36 to minimize insertion loss.

[0081] Using the modeled parameters illustrated in Fig. 15, it has been

demonstrated that the insertion loss is significantly decreased across a frequency range when using non-resonant elements 22, as opposed to only resonant elements 18, to tune a filter. For example, as shown in Fig. 18, the worst case insertion loss of the filter 10 when the non-resonant elements 22 are adjusted, along with the frequencies of the resonant elements 18, to tune the filter 10 over the frequency range 770 MHz to 890 MHz is approximately 8 dB less than the insertion loss of the filter 10 when only the frequencies of the resonant elements are adjusted to tune the filter 10 over the same frequency range.

[0082] It has also been demonstrated that the filter 10, as modeled in accordance with the parameters illustrated in Fig. 15, has an insertion loss that is significantly less than prior art switched filtered tuning techniques. For example, as shown in Fig. 19, the worst case insertion loss of the filter 10 when the variable non-resonant elements are adjusted, along with the frequencies of the resonant elements, to tune the filter 10 over the frequency range 770 MHz to 890 MHz is significantly less than the insertion loss of a switched filter tuned over the same frequency range (assuming small insertion loss from the addition of a switch and adjusting the frequencies of the resonant elements to cover half of the total tuning range between switching).

[0083] Notably, while it has been the conventional thinking that the insertion loss of pass-band filter increases with an increase in the number of resonant elements, it has been demonstrated that the insertion loss does not increase with the number of resonant elements used in a filter utilizing the design techniques described herein. For example, as illustrated in Fig. 20, the frequency response of 2-resonator, 4- resonator and 6-resonator filter designs using the techniques described herein, and a standard filter design, are plotted along the frequency range from 750 GHz to 950 GHz. As there shown, the Q of the closest resonant elements— not the number of resonant elements— dominates the insertion loss. [0084] It should be noted that varying the values of the non-resonant elements 22 that are coupled to the resonant elements 18 in series may slightly vary the transmission zeroes. It is preferred that these transmission zeroes not inadvertently move in order to provide the filter with an optimal performance.

[0085] In particular, as shown in Fig. 21 , the circuit was again reduced to the constituent components necessary to reconfigure the filter 10 using only the non- resonant elements 22. In this case, the tuning elements 20 were not necessary to simulate (model) reconfiguration of the filter 10, and were thus, removed from the circuit representation in Fig. 21.

[0086] In the illustrated embodiment, there are four resonant elements 18 represented by susceptance B ^R (in particular, Bi ^R , B ₂ ^R , B ₃ ^R , and B ^R ) and fifteen non- resonant elements 22, which can be arranged into six non-resonant elements 22(1 ) (also referred to as NRN-ground (shunt non-resonant element)) represented by susceptance B ^N (in particular, B _S ^N , Β B ₂ ^N , B ₃ ^N , B ₄ ⁿ and B _L ^N ), five non-resonant elements 22(2) (also referred to as NRN-NRN (series non-resonant element) represented by admittance inverters J (in particular, J ₀ i , Ji ₂ , J ₂ 3, J3 ₄ , and J ₅ ), and four non-resonant elements 22(3) (also referred to as NRN-resonator (resonator coupling)) represented by admittance inverters J (in particular, J-i, J ₂ , J ₃ , and J ). The non-resonant elements 22(1 ), 22(2) are coupled in parallel to the respective resonant elements 18, while the non-resonant elements 22(3) are coupled in series to the respective resonant elements 18. Selected ones of the non-resonant elements 22 can be varied, while any remaining ones of the non-resonant elements 22 remained fixed. In the illustrated embodiment, the non-resonant elements 22 that are coupled in series to the resonant elements 18 (i.e., the non-resonant elements 22(3)), which tend to "pull" the resonant frequencies when implemented in a practical solution, remain fixed.

[0087] It should be noted that in designs where the resonant elements 18 are realized using acoustic resonators, such as surface acoustic wave (SAW), film bulk acoustic resonator (FBAR), microelectromechanical system (MEMS) resonators, the non-resonant elements 22 may be realized as either electrical or mechanical coupling elements. In this case, it may be advantageous to realize non-resonant elements 22(3) as electromechanical transducers to allow the non-resonant elements 22(3) and acoustic resonant elements 18 of the circuit to remain fixed, while still allowing for electronic tuning using only the non-resonant elements 22(1 ), 22(2).

[0088] Fig. 22 illustrates the coupling matrix representation of the filter 10. As there shown, the nodes S, 1 -4, L, and 5-8 (shown in Fig. 20) are on the left side of the matrix representation, and the nodes S, NRN1 -NRN4 (non-resonant nodes), L, and resonant nodes R1 -R4 are on the top side of the matrix representation. As also shown in Fig. 22, the coupling values between the nodes are the susceptance values and admittance inverter values of the resonant elements 18 and non-resonant elements 22.

[0089] The filter representation illustrated in Fig. 21 was emulated using different sets of coupling coefficients to hop the pass band 38 between the centers of the sub- bands 36. In particular, Figs. 23(a)-23(c) illustrate exemplary filter responses (and their corresponding coupling matrix representation) where four reflection zeroes 34 have been displaced within the stop band 32 to selectively create the pass band 38 in the centers of all three of the sub-band 36. That is, going sequentially through Figs. 23(a)-23(c), the pass band 38 hops from the first sub-band 36(1 ) (Fig. 23(a)), to the second sub-band 36(2) (Fig. 23(b)), and then to the third sub-band 36(3) (Fig. 23(c)). Thus, the center of the pass band 38 hops between the nominal frequencies -0.80, 0.0, and 0.80. As can be appreciated from the corresponding matrix representations shown in Figs. 23(a)-23(c), the susceptance values for the serially coupled non-resonant elements 22(3)(i.e., Ji-J ₄ ) are fixed at -1 , while the

susceptance values and admittance inverter values for the parallel coupled non- resonant elements 22(1 ), 22(2) are varied to hop the pass band 38 between the sub- bands 36. The changes (and non-changes) in these values as the pass band 38 hops between the three nominal frequencies are graphically illustrated in Fig. 24. As there shown, the values for the parallel coupled non-resonant elements 22(1 ), (2) (i.e., Joi, Ji2, J23, J3 ₄ , J ₄ 5, Β B ₂ ^N , B ₃ ⁿ , and B ₄ ^N ) are varied, whereas the values for the serially coupled non-resonant elements 23(3) (i.e., J-i, J ₂ , J3, and J ) remain constant.

[0090] As discussed previously with respect to Figs. 4(a)-4(g), while the pass band 38 can be hopped between sub-bands 36 to discretely cover the desired frequency range, the transmission zeroes 30 can be simultaneously moved in concert from their nominal positions (i.e., by adjusting the frequencies of the resonating elements) to displace the entire stop band 32, and thus the pass band 38, within the normalized frequency range. Thus, with respect to Figs. 23(a)-23(c), the pass band 38 can be moved from the centers of the sub-bands 36 (i.e., -0.80, 0.0, and 0.80) to cover the continuum of the desired frequency range. Thus, if all of the transmission zeroes 30 can be displaced by +/-0.40 from their nominal positions (i.e., resonant elements tuned together in a frequency range of +/- 0.40), each pass band 38 illustrated in Figs. 23(a)-23(c) would cover 33% of the normalized frequency range from -1 .20 to 1 .20.

[0091] While the pass band 38 is illustrated in Figs. 23(a)-23(c) as being centered within the sub-bands 36, the reflection zeroes 34 can be displaced within the stop band 32 (i.e., by adjusting the values of the non-resonant elements) to selectively move the pass band 38 within a selected sub-band 36. In this case, the pass band 38 can be hopped between sub-bands 36, as well as moved within each sub-band 36, thereby decreasing the amount the transmission zeroes 30 need to be adjusted for the pass band 38 to cover the continuum of the desired frequency range. For example, Fig. 25 graphically shows the changes (and non-changes) in the values for the non-resonant elements 22 as the pass band 38 is moved within the continuum of the nominal frequency range of -1 .0 to 1 .0.

[0092] Notably, the coupling values set forth in Fig. 25 are entirely different from the coupling values set forth in Fig. 24, and therefore, it should be appreciated that more than one coupling matrix exists for each filter (i.e., the coupling matrix does not have a unique solution). For example, Fig. 26 graphically shows another set of changes (and non-changes) in the values for the non-resonant elements 22 as the pass band 38 is moved within the continuum of the nominal frequency range of -1 .0 to 1 .0.

[0093] Selecting the ideal coupling matrix from the family of coupling matrices that realize the same filter function may be driven by further analysis of the filter performance characteristics, such as power handling, intermodulation, or insertion loss. As demonstrated in co-pending Patent Application Ser. No. 12/163,837 (Attorney Docket No. STI-008), entitled "Electrical Filters with Improved

Intermodulation Distortion," which is expressly incorporated herein by reference, small changes to the internal structure of the filter can produce enhancement of the filter's terminal performance characteristics without changing the filter function, as seen in measured S-parameters at the input/output terminals. The techniques disclosed in U.S. Patent Application Ser. No. 12/163,837, including changing the order of transmission zeroes, can be applied to the filter circuits disclosed in this application.

[0094] As briefly described above, the filter 10 can be tuned using a parameter extraction and analysis technique, and then varying one of the non-resonant elements 22 to selectively displace the pass band 38 within the selected sub-band 36. In particular, the filter 10 may be operated at an expected operating temperature to determine various initial or pre-tuning performance characteristics. For example, an HTS filter may be operated at 77 degrees K and measurements taken.

Parameter extraction may then be performed by, for example, a network analyzer. For example, the measured S-parameter response (e.g., return loss) may be used to determine various parameters (e.g., the resonator frequencies and/or resonator-to- resonator coupling values) associated with the filter. Next, the filter response may be optimized by, for example, a computer. Then, a difference between the extracted filter characteristics and the optimized filter characteristics may be determined and used to provide a tuning recipe. The filter may then be tuned according to the tuning recipe. In various embodiments, this tuning may be done by, for example, selecting the capacitors that are switched on or off to adjust the pass band 38 within a selected sub-band 36 using the electrical controller 24. Once the filter has been tuned, it may be checked. For example, the filter may again be operated at its operating temperature and measured to determine the filter's new performance characteristics. If the new tuned performance characteristics, such as the frequency response and/or S-parameter response are acceptable, the filter may be packaged for operation.

[0095] Another tuning technique for high-performance planar filters involves using one or more tuning elements that enable filter tuning. For example, and with reference to Fig. 27, tuning elements in the form of tuning forks 40, 42 can be disposed on the same substrate 44 as resonant element 18, which in the illustrated case, takes the form of a spiral-in-spiral-out (SISO) shape half-wavelength structure. For the purposes of illustration, only one resonant element 18 is illustrated in Fig. 27, although a complete filter may include multiple resonant elements 18, as illustrated in Fig. 1. In a multi-resonator planar filter, each resonant element 18 may have tuning forks 40, 42. Portions of the tuning forks 40, 42 may be removed from the substrate 44, e.g., by scribing, to modify the frequency of the resonant element 18 to which it is coupled, thereby displaying the transmission zero corresponding to the frequency of the resonant element 18 along the stop band 32 relative to the reflection zero(es) 34. In the case of turning multiple resonant elements 18, the frequencies of the resonant elements 18 can be modified to simultaneously displace the stop band 32 with the pass band 38 along a frequency range. The tuning forks 40, 42 are capacitively coupled to one end of the resonant element 18 through a series inter-digitated capacitor 46.

[0096] Alternatively, the tuning forks 40, 42 may be directly coupled to the resonant element 18. However, the series capacitor can be designed to reduce the tuning sensitivity to approximately 10% of what would be seen if the tuning fork was directly connected to the resonator. This reduced sensitivity enables tuning by hand, e.g., with a mechanical device, such as a diamond scribe pen. The hand scribing may be performed with a diamond scribe pen under a microscope. Alternate means of scribing the tuning forks 40, 42, such as a laser scribing tool, focused ion beams, or photolithography, may also be employed. In any case, the resonator 18 may be tuned by physically disconnecting (e.g., scribing) part of the tuning forks 40, 42 in order to alter the capacitance of the filter circuit.

[0097] For accuracy and ease of tuning, the tuning forks 40, 42 may respectively include a coarse scale 48 and a fine scale 50 to provide ease of scribing for coarse and fine tuning. The scales 48, 50 may be related to a tuning recipe. Although two tuning forks 40, 42 are illustrated, any number of tuning forks may be used depending on the desired tuning range and tuning resolution.

[0098] A parameter extraction based technique may be used to diagnose the filter couplings and resonant frequencies, and to provide a recipe for scribing the tuning forks. As such, a filter design is provided that realizes very accurate tuning without requiring any expensive tools.

[0099] As another example, tuning elements in the form of trimming tabs 52 can be disposed on the same substrate 44 as the resonant element 18, as illustrated in Fig. 28. The trimming tabs 52 on located a resonator edge that may be, for example, trimmed (i.e. disconnected from the circuit) to reduce the shunt capacitance of the resonant element 18. The trimming tabs 52 may have discrete values that shift a resonant frequency of the filter by different known amounts, and the amounts may be configured in a binary progression.

[00100] For example, the filter may have four trimming tabs 52 on each resonant element 18 that can shift the resonant frequency in a binary progression, such as 1500 KHz, 800 KHz, 400 KHz, 200 kHz, and 100 KHz. In the illustrated

embodiment, seven trimming tabs 52 of varying sizes are provided. In particular, the trimming tab 52(1 ) results in a 1500 KHz frequency shift to the resonant element 18 when trimmed; the trimming tab 52(2) results in an 800 KHz frequency shift to the resonant element 18 when trimmed; the trimming tab 52(3) results in a 400 KHz frequency shift to the resonant element 18 when trimmed; the trimming tab 52(4) results in an 200 KHz frequency shift to the resonant element 18 when trimmed; and each of the trimming tabs 52(5)-56(7) results in a 100 KHz frequency shift to the resonant element 18 when trimmed. Thus, as an example, if the resonant element 18 needs a 670 KHz frequency shift according to a tuning recipe, then the trimming tab 52(2) (400 KHz), the trimming tab 52(3) (200 KHz), and one of the trimming tabs 52(5)-56(7) may be removed from the substrate 44.

[00101] Further details discussing the use of tuning forks and trimming tabs to tune resonators are described in U.S. Patent Application Ser. No. 12/330,510, entitled "Systems and Methods for Tuning Filters," which is expressly incorporated herein by reference.

[00102] A parameter extraction based technique may be used to diagnose the filter couplings and resonant frequencies, and to provide a recipe indicating which of the trimming tabs 52 should be disconnected or trimmed from the resonator edges so as to produce a properly tuned filter.

[00103] Referring now to Fig. 29, another tunable RF filter 100 constructed in accordance with the present inventions will now be described. The RF filter 100 is capable of being dynamically tuned to compensate for changes in the operating temperature, which may otherwise cause the pass band 38 to inadvertently move within the frequency range away from its nominal as-designed position in a manner similar to the shifting of the pass band 78 shown in Fig. 11. That is, changes in operating temperature cause the coupling values of the resonant elements 18 and non-resonant elements 22 to change from their nominal values (i.e., the reactances of the elements at the operating temperature at which the RF filter 100 is initially tuned). For example, the reactances of the non-resonant elements 22 may change by ±1 % for each 10° change in the operating temperature. Accordingly, the RF filter 100 can dynamically adjust the reactances of the resonant elements 18 and non- resonant elements 22 to return the pass band 38 to its nominal position within the frequency range. [00104] The RF filter 100 is similar to the RF filter 10 illustrated in Fig. 13(a), with the exception that the RF filter 100 additionally includes an electrical controller 124, a temperature sensor 126, and memory 128. Like the electrical controller 24 illustrated in Fig. 1 , the electrical controller 124 is configured for adjusting the non-resonant elements 22 to introduce and displace reflection zeroes along the stop band 32 to move a narrow pass band 38 within the desired frequency range, and may also further adjust the frequencies of the resonant elements 18 via tuning elements (not shown) to move the transmission zeroes along the frequency range to optimize the filter response. Unlike the electrical controller 24, the electrical controller 124 is configured for dynamically adjusting the resonant elements 18 and non-resonant elements 22 to compensate for changes in the operating temperature.

[00105] To this end, the electrical controller 124 obtains a current operating temperature measurement from the temperature sensor 126, accesses a look-up table from memory 128, and adjusts the resonant elements 18 and non-resonant elements 22 based on the look-up table. In particular, the look-up table contains a plurality of reference operating temperatures, which may, e.g., range from -20°K to 100°K in increments of 10°, and for each reference operating temperature, a corresponding set of adjustment settings. Each adjustment setting controls the reactance of one of the resonant elements 18 or one of the non-resonant elements 22. A typical set of adjustment settings will include adjustment settings that control a multitude of resonant elements 18 and non-resonant elements 22.

[00106] The electrical controller 124 applies the adjustment settings to the resonant elements 18 and non-resonant elements 22 via electrical signals to adjust their respective reactances in a manner that returns the pass band 38 to its nominal location within the frequency range. In particular, the electrical controller 124 compares the measured operating temperature to the reference operating temperatures in the look-up table, selects the set of adjustment settings

corresponding to the reference operating temperature that best matches the measured operating temperature, and adjusts the reactances of the resonant elements 18 and non-resonant elements 22 in accordance with the selected set of adjustment settings.

[00107] In the preferred embodiment, similar to the tuning technique illustrated in Figs. 5(a)-5(d), the resonant elements 18 are adjusted in a manner that returns the selected sub-band 36 to its nominal position within the frequency range, and the non-resonant elements 22 are adjusted in a manner that returns the pass band 38 to its nominal position within the selected sub-band 36. Alternatively, the resonant elements 18 may be adjusted in a manner that does not return the sub-band 36 to its nominal position within the frequency range, or may not be adjusted at all, in which case, the non-resonant elements 22 may be adjusted in a manner that does not return the pass band 38 to its nominal position within the selected sub-band 36. In any event, the pass band 38 will be returned to its nominal position within the frequency range.

[00108] The nature of the adjustment settings will depend upon the mechanism that is used to adjust the reactances of the resonant elements 18 and non-resonant elements 22. For example, if each of the resonant elements 18 and non-resonant elements 22 comprises parallel capacitors with switches to form a variable capacitive circuit, each adjustment setting can include data indicating which of the capacitors are switched on to include the respective capacitor within the capacitive circuit or switched off to exclude the respective capacitor of the circuit, with the goal of varying the reactance of the respective resonant element 18 or non-resonant element 22 in a manner that locates the pass band 38 to its nominal position within the frequency range, or at least as near to its nominal position within the frequency range as possible given the resolution of the look-up table. Thus, in this case, for each measured operating temperature, the look-up table will have a set of on-off states of the switched capacitors for each resonant elements 18 and non-resonant element 22. The adjustment settings in the look-up table can be determined by exposing the filter 100 at each of the reference operating temperatures and using the afore- described parameter extraction and analysis technique to determine the adjustment settings for the resonant elements 18 and non-resonant elements 22.

[00109] Notably, the parallel capacitors that are turned on and off to compensate for changes in operating temperature for the non-resonant elements 18 may include at least some of the parallel capacitors used to move the pass band 38 between different sub-bands 36, as illustrated in Figs. 15(a)-15(c). Furthermore, although the look-up table has been described as including adjustment settings for only one of the sub-bands 36, the look-up table can include adjustment settings for more than one of the sub-bands 36. In this case, the adjustment settings for the particular sub-band 36 in which the pass band 38 is currently located in may be used to move the pass band 38 to its nominal position within the frequency range in response to a change in the operating temperature.

[001 10] Although particular embodiments of the present invention have been shown and described, it should be understood that the above discussion is not intended to limit the present invention to these embodiments. It will be obvious to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the present invention. For example, the present invention has applications well beyond filters with a single input and output, and particular embodiments of the present invention may be used to form duplexers, multiplexers, channelizers, reactive switches, etc., where low-loss selective circuits may be used. Thus, the present invention is intended to cover alternatives, modifications, and equivalents that may fall within the spirit and scope of the present invention as defined by the claims.