Patent Publication Number: US-6700459-B2

Title: Dual-mode bandpass filter with direct capacitive couplings and far-field suppression structures

Description:
GOVERNMENT LICENSE RIGHTS 
     The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Contract MDA972-00-C-0010 awarded by the Defense Advanced Research Projects Agency (DARPA). 
    
    
     FIELD OF THE INVENTION 
     The present inventions generally relate to microwave filters, and more particularly, to microwave filters designed for narrow-band applications. 
     BACKGROUND OF THE INVENTION 
     Filters have long been used in the processing of electrical signals. For example, in communications applications, such as microwave applications, it is desirable to filter out the smallest possible passband and thereby enable dividing a fixed frequency spectrum into the largest possible number of bands. 
     Such filters are of particular importance in the telecommunications field (microwave band). As more users desire to use the microwave band, the use of narrow-band filters will increase the actual number of users able to fit in a fixed spectrum. Of most particular importance is the frequency range from approximately 800-2,200 MHz. In the United States, the 800-900 MHz range is used for analog cellular communications. Personal communication services are used for the 1,800 to 2,200 MHz range. 
     Historically, filters have been fabricated using normal, that is, non-superconducting materials. These materials have inherent lossiness, and as a result, the circuits formed from them having varying degrees of loss. For resonant circuits, the loss is particularly critical. The quality factor (Q) of a device is a measure of its power dissipation or lossiness. Resonant circuits fabricated from normal metals in a microstrip or stripline configuration have Q&#39;s at best on the order of four hundred. See, e.g., F. J. Winters, et al., “High Dielectric Constant Strip Line Band Pass Filters,” IEEE Transactions On Microwave. Theory and Techniques, Vol. 39, No. 12, December 1991, pp. 2182-87. 
     With the discovery of high temperature superconductivity in 1986, attempts have been made to fabricate electrical devices from high temperature superconductor (HTSC) materials. The microwave properties of HTSC&#39;s have improved substantially since their discovery. Epitaxial superconductive thin films are now routinely formed and commercially available. See, e.g., R. Hammond et al., “Epitaxial Tl 2  Ba 2 Ca 1 Cu 2 O 8  Thin Films With Low 9.6 GHz Surface Resistance at High Power and Above 77° K,” Applied Physics Letters, Vol. 57, pp. 825-27 (1990). Various filter structures and resonators have been formed from HTSC&#39;s. Other discrete circuits for filters in the microwave region have been described. See, e.g., S. H. Talisa, et al., “Low- and High-Temperature Superconducting Micro-wave filters,” IEEE Transactions on Microwave Theory and Techniques, Vol. 39, No. 9, September 1991, pp. 1448-1554, and “High Temperature Superconductor Staggered Resonator Array Bandpass Filter,” U.S. Pat. No. 5,616,538. 
     Currently, there are numerous applications where microstrip narrow-band filters that are as small as possible are desired. One such application involves the use of dual-mode filters (DMF&#39;s), which generate two orthogonal modes that occur at the resonant frequency. DMF&#39;s include patch dual-mode microstrip patterned structures, like circles and squares. These structures, however, take up a relatively large area on the substrate. More compact dual-mode microstrip ring structures, which occupy a smaller area on the substrate than do patch structures, have been designed. 
     For example, FIG. 1 shows a two-pole dual-mode filter structure  40 , which includes an electrically conductive meander loop resonator  42  and a dielectric substrate  44  on which the resonator  42  is disposed. The resonator  42  includes a resonator line  46  that is formed into a loop that has a square envelope. The resonator line  46  is routed, such that it forms four arms  48 , each with a single meander  50 . The filter structure  40  further includes orthogonal ports  52  and  54 , which are used to couple to the resonator  42 . The filter structure  40  also includes a small patch  56 , which is attached to an inner corner of one of the meanders  50  for perturbing the electric field pattern. As a result, a pair of degenerative modes will be coupled when either of the ports  52  and  54  is excited. The degree of coupling will depend on the size of the patch  56 . Without the patch  56 , no perturbation will result, and thus only the single mode will be excited. In this case, when the port  52  is used, only one of the degenerate modes will be excited, and when the other port  54  is used, the field pattern is rotated 90° for the associated degenerate mode. As illustrated, the resonator  42  generally exhibits four-quadrant symmetry to maintain orthogonality between the two degenerative modes. See J. S. Hong, “Microstrip Bandpass Filter Using Degenerate Modes of a Novel Meander Loop Resonator,” IEEE Microwave and Guided Wave Letters, vol. 5, no. 11, pp. 371-372, November 1995. 
     As another example, FIG. 2 shows a two-pole dual-mode filter structure  60 , which includes an electrically conductive meander loop resonator  62  and a dielectric substrate  64  on which the resonator  62  is disposed. The resonator  62  includes a resonator line  66  that is formed into a loop with a square envelope. The resonator line  66  is routed, such that it forms four arms  68 , each with three meanders  70 . The filter structure  60  further includes orthogonal fork-shaped coupling structures  72  and  74 , which are distributed between the arms  68  and meanders  70 . The filter structure  60  also includes a patch  76 , which is attached to the inner corner of one of the meanders  70  to effect the dual-mode coupling as previously described in the filter structure  40  of FIG.  1 . See, e.g., Z. M. Hejazi, “Compact Dual-Mode Filters for HTS Satellite Communication System,” IEEE Microwave and Guided Wave Letters, vol. 8, no. 8, pp. 1113-1117, June 2001. 
     As still another example, FIG. 3 shows two-pole dual-mode filter structure  80 , which includes an electrically conductive meander loop resonator  82  and a dielectric substrate  84  on which the resonator  82  is disposed. The resonator  82  is similar to the resonator  62  shown in FIG. 2, with exception that it includes a resonator line  86  that is routed, such that it forms four arms  88 , each with five meanders  90 . The filter-structure  80  further includes orthogonal fork-shaped coupling structures  92  and  94 , which are distributed between the arms  88  and meanders  90 . The filter structure  80  also includes a patch  96 , which is attached to the inner corner of one of the meanders  90  to effect the dual-mode coupling as previously described in the filter structure  40  of FIG.  1 . See, e.g., Z. M. Hejazi, “Compact Dual-Mode Filters for HTS Satellite Communication System,” IEEE Microwave and Guided Wave Letters, vol. 8, no. 8, pp. 1113-1117, June 2001. 
     At lower frequencies, however, even these ring structures can become quite large, since resonance occurs when the ring is approximately a full electrical wavelength long. In addition, these ring structures do not necessarily address the problems associated with parasitic coupling, which becomes more prevalent as circuits are squeezed into smaller spaces. When coupling multiple resonators to make more complex narrow-band filters, the area required to accommodate the filter can grow undesirably large in order to minimize unwanted parasitic coupling between resonators and to test the package. This is particularly an issue for narrow bandwidth filters, where the desired coupling between resonators is very small, making the spacing between resonators greater. Thus, the overall size of the filter becomes even larger. For very high Q structures, like thin film HTS, significant Q degradation can occur due to the normal metal housing. 
     Another issue that arises in the design of narrow-band filter structures is the ability to accurately model these structures in the presence of unknown parameters, such as parasitic coupling and the introduction of mode exciting perturbations within the electrical field. In addition, computer models often use ideal capacitors to model the external capacitive coupling of dual-mode microstrip resonators. Because of the parasitic nature of physical capacitors, low quality, and effects of mounting, however, they often become undesirable when fabricating state-of-the-art HTS microstrip circuits. In order to eliminate the physical capacitors, the computer capacitor models are often replaced by distributed structures (i.e., by using the coupling between a length of the resonator and an input/output line running parallel to it). This replacement usually introduces degradation in frequency response, which is most noticeable in the shape and depth of the transmission zeros and poor alignment of the filter poles. This adverse effect can be seen in FIGS. 4 and 5, which plot the measured (dashed lines) and computed (solid lines) of the frequency responses for the resonators  60  and  80  illustrated in FIGS. 2 and 3. As shown, the transmission zeros are not well-defined, at least in part, because the coupling structures used to couple to these resonators act as distributed or quasi-distributed structures. 
     SUMMARY OF THE INVENTION 
     The present inventions are directed to novel dual-mode resonating filter structures. The filter structures contemplated by the present inventions may be planar structures, such as microstrip, stripline and suspended stripline. In preferred embodiments, the resonators may be composed of HTSC material. The broadest aspects of the invention, however, should not be limited to HTSC material, and contemplate the use of non-HTSC material as well. 
     The dual-mode resonator contemplated by the present inventions comprises a dielectric substrate having a region divided into four quadrants, and a resonator line forming quadrangularly symmetrical configurations within the four quadrants of the region. In this manner, the orthogonality of the degenerative modes is maintained. In preferred embodiments, the resonator line has a nominal length of one full-wavelength at the resonant frequency, and forms an outer envelope in the form of a square. Input and output couplings are used to couple to the resonator line, e.g., in a quadrangularly asymmetrical manner. In this manner, the orthogonal degenerative modes are excited without the use of electrical field perturbing patches. 
     The dual-mode resonators of the present inventions can be used as building blocks for a more complex filter structure. This complex filter structure comprises a dielectric substrate having a plurality of regions, each of which is divided into four quadrants, and a plurality of the resonators associated with the plurality of regions in the manner described above. In the preferred embodiment, an input coupling is coupled to a first one of the plurality of resonators, and an output coupling coupled to the last one of the plurality of resonators. One or more couplings can be used to interconnect the plurality of resonators. 
     In accordance with a first aspect of the present inventions, the quadrangularly symmetrical configurations are formed from four folded sections of the ring resonator line. The quadrangularly symmetrical configurations can be any one of a variety of configurations, e.g., a unidirectional bending configuration, spiraled configuration, or a meandering configuration. These configurations can be either rectilinear or curvilinear. 
     Although the present inventions should not necessarily be limited to this, these symmetrical configurations provide for a more compact structure. In addition, the electrical currents within parallel line segments of each folded section are in opposite directions. As a result, the far-field radiation is minimized, thereby allowing for tighter packing of multiple resonators and minimum performance degradation due to the tighter packaging. The minimized far-field radiation also limits the amount of energy coupled to lossy test packages thereby resulting in minimal impact to the resonator quality factor. 
     In accordance with a second aspect of the present inventions, each of the quadrangularly symmetrical configurations is symmetrical about an imaginary line and comprises a plurality of meanders (e.g., four, six, or more meanders) and a plurality of interconnecting segments. Each of the interconnecting segments on one side of the imaginary line is parallel to and opposes an interconnecting segment on another side of the imaginary line. 
     Although the present inventions should not necessarily be limited to this, the meandered configurations provide for a more compact structure. In addition, the electrical currents within parallel line segments of each meander, as well as the electrical currents within opposing interconnecting segments, are in opposite directions. As a result, the far-field radiation is minimized, thereby allowing for tighter packing of multiple resonators and minimum performance degradation due to the tighter packaging. 
     In accordance with a third aspect of the present inventions, input and output couplings are coupled to the resonator line, wherein one or both of the input and output couplings comprises a capacitor (e.g., an interdigitated, parallel plate, or discrete capacitor) that is coupled to the resonator line through a transmission line. The transmission line is directly connected to the resonator line to provide a point of contact with the resonator line. The input or output coupling can also have another transmission line for coupling to external circuitry. By way of non-limiting example, the first transmission line can be a narrow high impedance line, and the second transmission line can be a broad low impedance (e.g., 50 ohm) line connected to the external circuitry. Although the present inventions should not necessarily be limited by this, the direct coupling of the capacitor to the resonator line more accurately represent ideal lumped element capacitor connections from the computer modeling than do distributed coupling structures. If the filter structure comprises a plurality of resonator lines, one or more couplings can interconnect the plurality of resonator lines. Each of these interconnecting couplings can include a common coupling segment, first and second capacitors respectively coupled to the ends of the common coupling segment, and first and second transmission line segments directly connected to the respective resonant lines. In this manner, the resonator lines are coupled together at points of contact, rather than in a distributed capacitive manner between the lengths of the resonators. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     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: 
     FIG. 1 illustrates a prior art two-pole dual-mode filter structure having four arms, each of which have one meander; 
     FIG. 2 illustrates another prior art two-pole dual-mode filter structure having four arms, each of which have three meanders; 
     FIG. 3 illustrates another prior art two-pole dual-mode filter structure having four arms, each of which have five meanders; 
     FIG. 4 illustrates the measured and computed frequency responses of the filter structure of FIG. 2; 
     FIG. 5 illustrates the measured and computed frequency responses of the filter structure of FIG. 3; 
     FIG. 6 illustrates a two-pole dual-mode folded filter structure constructed in accordance with one preferred embodiment of the present inventions, wherein each folded section is arranged to form a quadrangularly symmetrical rectilinear bending configuration; 
     FIG. 7 illustrates the folded sections of the ring resonator used in the filter structure of FIG. 6 prior to arranging them into the rectilinear bending configuration; 
     FIG. 8 illustrates a close-up of one of the rectilinear bending configurations of the filter structure of FIG. 6; 
     FIG. 9 illustrates another folded ring resonator that can be used by the filter structure of FIG. 6, wherein the folded sections are arranged in quadrangularly symmetrical curvilinear bending configurations; 
     FIG. 10 illustrates another folded ring resonator that can be used by the filter structure of FIG. 6, wherein the folded sections are arranged in quadrangularly symmetrical rectilinear spiraling configurations; 
     FIG. 11 illustrates another folded ring resonator that can be used by the filter structure of FIG. 6, wherein the folded sections are arranged in quadrangularly symmetrical curvilinear spiraling configurations; 
     FIG. 12 illustrates another folded ring resonator that can be used by the filter structure of FIG. 6, wherein the folded sections are arranged in quadrangularly symmetrical rectilinear meandering configurations; 
     FIG. 13 illustrates another folded ring resonator that can be used by the filter structure of FIG. 6, wherein the folded sections are arranged in quadrangularly symmetrical curvilinear meandering configurations; 
     FIG. 14 illustrates a close-up of one of the interdigitated couplings used in the filter structure of FIG. 6; 
     FIG. 15 illustrates a computer simulated filter structure designed in accordance with the filter structure of FIG. 6; 
     FIG. 16 illustrates the measured and computed frequency responses of a filter structure fabricated in accordance with the filter structure of FIG. 6; 
     FIG. 17 illustrates a four-pole dual-mode folded filter structure constructed in accordance with another preferred embodiment of the present inventions, wherein two folded ring resonators similar to those used in the filter structure of FIG. 6 are used; 
     FIG. 18 illustrates the measured frequency responses of a filter structure fabricated in accordance with the filter structure of FIG. 17; 
     FIG. 19 illustrates a four-pole dual-mode folded filter structure similar to the filter structure of FIG. 17, wherein two substrates are used; 
     FIG. 20 illustrates a two-pole dual-mode meandered filter structure constructed in accordance with still another preferred embodiment of the present inventions, wherein each quadrangularly meandering configuration is formed with six meanders; 
     FIG. 21 illustrates a close-up of one of the meandered configurations of the filter structure of FIG. 13; 
     FIG. 22 illustrates a computer simulated filter structure designed in accordance with the filter structure of FIG. 21; 
     FIG. 23 illustrates the computed frequency response of the computer simulated filter structure of FIG. 21; 
     FIG. 24 illustrates another meandered ring resonator that can be used in the filter structure of FIG. 20, wherein shorter meanders are used; 
     FIG. 25 illustrates another meandered ring resonator that can be used in the filter structure of FIG. 20, wherein longer meanders are used; 
     FIG. 26 illustrates another meandered ring resonator that can be used in the filter structure of FIG. 20, wherein each quadrangularly meandering configuration is formed with four meanders; 
     FIG. 27 illustrates another meandered ring resonator that can be used in the filter structure of FIG. 20, wherein each quadrangularly meandering configuration is formed with four longer meanders; 
     FIG. 28 illustrates a four-pole dual-mode meandered filter structure constructed in accordance with yet another preferred embodiment of the present inventions, wherein two meandered ring resonators similar to those used in the filter structure of FIG. 20 are used; and 
     FIG. 29 illustrates the computed frequency responses of a computer simulated filter structure of FIG.  28 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to FIG. 6, a two-pole dual-mode folded filter structure  100  constructed in accordance with one preferred embodiment of the present inventions will now be described. The folded filter structure  100  generally comprises a folded ring resonator  102  and a substrate  104  with a region  108  on which the resonator  102  is disposed. In the illustrated embodiment, the folded filter structure  100  is formed using microstrip. The resonator  102  is composed of a suitable HTS material, and the substrate  104  is composed of a suitable dielectric material. 
     The resonator  102  comprises a resonator line  106 , which in the illustrated embodiment, has a nominal length of one full wavelength at the resonant frequency. The region  108  is divided into four imaginary quadrants  110 ( 1 )-( 4 ), and the resonator line  106  is arranged with respect to these imaginary quadrants  110  to maintain orthogonality between the two degenerative modes, while minimizing the space occupied by the resonator  102 , as well as the far-field radiation generated by the resonator  102 . 
     Specifically, the resonator line  106  comprises a four folded sections  112 ( 1 )-( 4 ), each characterized by a pair of generally parallel line segments  114  and  116 , as illustrated in FIG.  7 . These four folded sections  112  are arranged to respectively form four quadrangularly symmetrical configurations  118 ( 1 )-( 4 ). For the purposes of this specification, the term “quadrangularly symmetrical” means that the configuration of the resonator line  106  in all four quadrants  110  are generally the same as seen from a center  120  of the region  108 . This feature helps maintain well-defined transmission zeros within the frequency response. In the embodiment illustrated in FIG. 6, the symmetrical configurations  118  are characterized as rectilinear unidirectional bending configurations. 
     Specifically referring to FIG. 8, each folded section  112  (shown as folded section  112 ( 2 ) in FIG. 7) is bent in the same direction at angles  122  (here, 90 degrees) to form a plurality of rectilinear segments  124 . In general, the more times the folded section  112  is bend, the more compact the resonator  102  will be. In the illustrated embodiment, the folded section  112  is bent three times at 90 degree angles to effect a 270 degree bending configuration. It should be noted, however, that the folded section  112  can have less bends to effect a lesser bending configuration, e.g., two bends for a 180 degree bending configuration, or can have more bends to effect a greater bending configuration, e.g., four bends for a 360 degree bending configuration. 
     Thus, the bending configurations  118  reduce the footprint of the resonator  102 . In addition, since the electrical currents in the adjacent parallel line segments  114  and  116  of each folded section  112  are in the opposite directions (as illustrated in FIG.  7 ), far-field radiation is minimized, thereby allowing for tighter packing of multiple resonators and minimum performance degradation due to the tighter packaging. Another feature provided by the resonator  102  is that its electrical field is localized within each of the bending configurations  118 . As a result, the two degenerate modes can be tuned nearly independently by positioning tuning elements over adjacent quadrants  110  of the region  108  where the peak electrical fields are located. This tuning can be done using low loss dielectric rotors in order to preserve the quality factor of the resonator  102 . 
     The folded sections  112  of the resonator line  106  can be arranged into other types of quadrangularly symmetrical configurations. For example, FIG. 9 illustrates a folded filter structure  130  wherein the folded sections  112  are respectively arranged into 270 degree curvilinear unidirectional bending configurations  132 . FIG. 10 illustrates a folded filter structure  134  wherein the folded sections  112  are respectively arranged into rectilinear spiraling configurations  136 . FIG. 11 illustrates a folded filter structure  138  wherein the folded sections  112  are respectively arranged into curvilinear spiraling configurations  140 . FIG. 12 illustrates a folded filter structure  142  wherein the folded sections  112  are respectively arranged into rectilinear meandering configurations  144 . FIG. 13 illustrates a folded filter structure  146  wherein the folded sections  112  are respectively arranged into curvilinear meandering configurations  148 . 
     Referring back to FIG. 6, input and output couplings  125  and  126  are coupled to the resonator  102 . Specifically, the input coupling  125  is coupled to the portion of the resonator  102  at the bottom of quadrant  110 ( 4 ), and the output coupling  126  is coupled to the portion of the resonator  102  at the bottom of quadrant  110 ( 3 ). The tap locations of the couplings  125 / 126  play a key role in coupling to the orthogonal modes of the resonator  102  as well as defining the transmission zeros. As can be seen, the couplings  125 / 126  are coupled to the resonator  102  in a quadrangularly asymmetrical manner, so that the orthogonal degenerate modes are excited within the electrical field generated by the resonator  102 . Thus, no patches are required to be placed within the resonator  102  to perturb the electrical field. 
     The couplings  125 / 126  advantageously use capacitive couplings that are directly connected to the resonator  102 , which more accurately represent ideal lumped element capacitor connections from the computer modeling than do distributed coupling structures. As best shown in FIG. 14, the input coupling  125  comprises first and second transmission line segments  127  and  128 , and a capacitor  129  (in this case, an interdigitated capacitor) formed therebetween. Other types of capacitors can also be used, such as discrete or parallel plate capacitors. In the illustrated embodiment, the first transmission line segment  127  is a broad low impedance transmission line (in the illustrated embodiment 50 ohms) that connects to the external circuitry, and the second transmission line segment  128  is a narrow high impedance transmission line that is directly connected to the resonator  102 , thereby acting as a point of contact. The output coupling  126  similarly includes two transmission line segments and an interdigitated capacitor. 
     By way of non-limiting example, an actual embodiment of a two-pole dual-mode folded filter structure was modeled and fabricated in accordance with the folded filter structure  100  illustrated in FIG.  6 . The resonator was composed of an epitaxial Tl 2  Ba 2 Ca 1 Cu 2 O 8  thin film, and the substrate was composed of 20 mil thick Magnesium Oxide material (e r =9.7). Using a full-wave electromagnetic simulator, specifically SONNET software, the filter structure was modeled with ten de-embedded tap points (as illustrated in FIG. 15) to create a multi-port network. This network was then used in a 2-pole lumped element model in a proprietary linear circuit analysis program to determine the coupling values needed to produce the desired frequency response. Other standard linear circuit analysis programs can be used as well. With the ideal coupling values known, the SONNET software was used again to create a 2-port network that represents the interdigitated coupling sections. This network was then used in the linear circuit analysis program to generate the final computed frequency response of the filter structure. 
     FIG. 16 shows the passband response of both the modeled and fabricated two-pole dual-mode folded filter structure, with the dashed lines representing the response computed using the linear circuit analysis software incorporating the Sonnet networks, and the solid lines representing the response measured at 77° K. As can be seen, there is very good agreement between the measured and modeled responses. The well-defined transmission zeros illustrated in FIG. 16 are a result of the implementation of the coupling technique and the four-quadrant symmetrical layout. In order to measure the unloaded quality factor (Q) of the dual-mode resonator, the input and output couplings were greatly decoupled, allowing the natural modes of the resonator to be measured. This was accomplished by scribing away part of the input and output transmission lines. The measured unloaded Q at 77° K and 2.14 GHz was approximately 36,000, which included the effects of the normal metal package and lid. 
     The dual-mode resonator of FIGS.  6  and  9 - 13  are building blocks that can be utilized to create more complex filters. Referring now to FIG. 17, a four-pole dual-mode folded filter structure  150  constructed in accordance with another preferred embodiment of the present inventions will now be described. The folded filter structure  150  generally comprises two folded ring resonators  152 ( 1 ) and  152 ( 2 ) and a substrate  154 , which has two regions  158 ( 1 ) and  158 ( 2 ) on which the two resonators  152  are respectively disposed. The composition and configuration of the resonators  152  and substrate  154  are identical to the previously discussed resonator  102  and substrate  104 , and thus, will not be described in further detail. Although the resonators  152  use rectilinear bending configurations  118  as shown, they can use other types of symmetrical configurations, such as the symmetrical configurations illustrated in FIGS. 9-13. 
     Input and output couplings  175  and  176 , which are similar to the previously described input and output couplings  125  and  126 , are respectively coupled to the resonators  152 ( 1 ) and  152 ( 2 ). In the illustrated embodiment, rather than coupling the resonators  152  by placing them in a relatively close relationship, which would result in a distributed capacitance, an interconnecting coupling  180  is coupled between the two resonators  152  to provide for a point capacitance. To this end, the interconnecting coupling  180  includes interdigitated capacitors to more accurately represent ideal lumped element capacitor connections from the computer modeling. Specifically, the interconnecting coupling  180  comprises a common high impedance transmission line segment  181 , a first high impedance transmission line segment  182  that is coupled to end of the common transmission line segment  181  via an interdigitated capacitor  183 , and a second high impedance transmission line segment  184  that is coupled to the other end of the common transmission line segment  181  via another interdigitated capacitor  185 . The high impedance transmission line segments  182  and  184  are directly connected to the resonators  152 ( 1 ) and  152 ( 2 ), thereby acting as points of contact. The interconnecting coupling  180  further comprises shunt capacitance structures  186  and  187  to provide additional shunt capacitance to the interconnecting coupling  180 . 
     By way of non-limiting example, an actual embodiment of a four-pole dual-mode folded filter structure was modeled and fabricated in accordance with the folded filter structure  150  illustrated in FIG.  17 . This filter structure was composed of the same material and modeled in the same manner as the fabricated two-pole folded filter structure. FIG. 18 shows the measured passband response of the fabricated four-pole dual-mode folded filter structure. As shown, the well-defined poles are, again, a result of the implementation of the coupling technique and four-quadrant symmetry layout. 
     It should be noted that the resonators of a four-pole dual-mode folded filter structure need not be disposed on a single substrate. For example, FIG. 19 shows a filter structure  190 , wherein the two resonators  152 ( 1 ) and  152 ( 2 ) disposed on two regions  158 ( 1 ) and  158 ( 2 ) located on separate substrates  154 ( 1 ) and  154 ( 2 ). A jumper  188  is used to interconnect the portions of the interconnecting coupling  180  residing on the respective substrates  154 ( 1 ) and  154 ( 2 ). 
     Referring to FIG. 20, a two-pole dual-mode meandered filter structure  200  constructed in accordance with another preferred embodiment of the present inventions will now be described. The meandered filter structure  200  generally comprises a meandered ring resonator  202  and a substrate  204  with a region  208  on which the resonator  202  is disposed. In the illustrated embodiment, the meandered filter structure  200  is formed using microstrip. The resonator  202  is composed of a suitable HTS material, and the substrate  204  is composed of a suitable dielectric material. 
     The resonator  202  comprises a resonator line  206 , which in the illustrated embodiment, has a nominal length of one full wavelength at the resonant frequency. The region  208  is divided into four imaginary quadrants  210 ( 1 )-( 4 ), and the resonator line  206  is arranged with respect to these imaginary quadrants  210  to maintain orthogonality between the two degenerative modes, while minimizing the space occupied by the resonator  202 , as well as the far-field radiation generated by the resonator  202 . 
     Specifically, the resonator line  206  arranged to form four meandered quadrangularly symmetrical configurations  218 ( 1 )-( 4 ). As with the previously described resonator line  106 , this feature helps maintain well-defined transmission zeros within the frequency response. The resonator line  206  is placed into the meandered configurations in that, for each quadrant  210 , there exists a plurality of meanders  220  (in this case, six meanders). 
     Specifically referring to FIG. 21, the meandered configuration  218  (shown as meandered configuration  218 ( 2 )) comprises a plurality of meanders  220  that are spaced from each other via interconnecting line segments  221  (which define a spacing s). Each meander  220  extends in a direction perpendicular to the imaginary line of symmetry  216 . Each meander  220  comprises parallel line segments  222  and  223  (which define a length l of the meander) that are interconnected via line segments  224  (which define a width w of the meander). In the illustrated embodiment, the lengths l of the meanders  220  gradually increase along the length of the meandered configuration  218 . 
     Thus, it can be seen that the meandered configurations  218  reduce the footprint of the resonator  202 . Like with the previously described folded configuration  118 , the two degenerate modes can be tuned nearly independently by positioning tuning elements over adjacent quadrants  210  of the region  208  where the peak electrical fields are located. In addition, since the electrical currents between adjacent parallel line segments  222 / 223  of each meander  220  are in the opposite directions, far-field radiation is minimized, thereby allowing for tighter packing of multiple resonators  202  and minimum performance degradation due to the tighter packaging. 
     To enhance this electrical current canceling effect, the electrical current between any given interconnecting line segment  221  is in a direction opposite to that of the electrical current between an adjacent interconnecting line segment  221 . To ensure that this occurs, the meandering configuration  218  is symmetrical about an imaginary line  216 , so that the interconnecting segments  221  disposed along one side of the imaginary line  216  are parallel to and oppose interconnecting segments  221  disposed along the other side of the imaginary line  216 . Thus, the directions of the electrical currents in any opposing pair of interconnecting segments  221  are opposite, and thus cancel each other. 
     Referring back to FIG. 20, input and output couplings  225  and  226  are coupled to the resonator  202 . Specifically, the input coupling  225  is coupled to the portion of the resonator  202  in quadrant  210 ( 4 ), and the output coupling  226  is coupled to the portion of the resonator  202  quadrant  210 ( 3 ). Like the couplings  125 / 126  of the folded filter structure  100 , the tap locations of the couplings  225 / 226  play a key role in coupling to the orthogonal modes of the resonator  202  as well as defining the transmission zeros, and are coupled to the resonator  202  in a quadrangularly asymmetrical manner. As a result, the orthogonal degenerate modes are excited within the electrical field generated by the resonator  202 , and thus, no patches are required to be placed within the resonator  202  to perturb the electrical field. Like-the couplings  125 / 126  of the folded filter structure  100 , each of the couplings  225 / 226  comprises first and second transmission line segments  227  and  228 , and an interdigitated capacitor  229  formed therebetween. The first transmission line segment  227  is low impedance transmission line, and the second transmission line segment  228  is a high impedance transmission line that is directly connected to the resonator  202  to provide a point of contact. The couplings  225 / 226  further comprise additional shunt capacitance structures  230  and  231  on opposing sides of the interdigitated capacitors  229  to provide the proper susceptance values for the couplings  225 / 226 . 
     By way of non-limiting example, an actual embodiment of a two-pole dual-mode meandered filter structure was modeled in accordance with the meandered filter structure  200  illustrated in FIG.  20 . This filter structure was composed of the same material and modeled in the same manner as the fabricated two-pole folded filter structure previously described, with the exception that the meandered filter structure was modeled with twenty-six de-embedded tap points (as illustrated in FIG. 22) to create the multi-port network. FIG. 23 shows the computed passband response of the modeled two-pole dual-mode meandered filter structure. 
     Other meandering configurations are contemplated. For example, FIG. 24 shows a two-pole dual-mode  300  that is similar to the previously described filter structure  200 , with the exception that it comprises meanders  330 , the lengths of which are shorter than the lengths of the meanders  220  of the meandered filter structure  200 . In contrast, FIG. 25 shows a two-pole dual-mode filter structure  350  that is similar to the previously described filter structure  200 , with the exception that it comprises meanders  380 , the lengths of which are longer than the lengths of the meanders  220  of the meandered filter structure  200 . FIGS. 26 and 27 respectively show two-pole dual-mode meandered filter structures  400 / 450  that are similar to the previously described filter structure  200 , with the exception that they comprise four meanders  430 / 480  of differing-lengths, rather than six meanders in each quadrant. 
     The dual-mode resonators of FIGS.  20  and  24 - 27  are building blocks that can be utilized to create more complex filters. Referring now to FIG. 28, a four-pole dual-mode meandered filter structure  250  constructed in accordance with another preferred embodiment of the present inventions will now be described. The meandered filter structure  250  generally comprises two meandered ring resonators  252 ( 1 ) and  252 ( 2 ) and a substrate  254 , which has two regions  258 ( 1 ) and  258 ( 2 ) on which the two resonators  252  are respectively disposed. The composition and configuration of the resonators  252  and substrate  254  are identical to the previously discussed resonator  202  and substrate  204 , and thus, will not be described in further detail. Although the resonators  252  use the meandering configuration  218  illustrated in FIG. 20 as shown, they can use other types of symmetrical configurations, such as the symmetrical configurations illustrated in FIGS. 24-27. Also, the resonators  252 ( 1 ) and  252 ( 2 ) can be disposed on two substrates similarly to that described with respect to FIG.  19 . 
     Input and output couplings  275  and  276 , which are similar to the previously described input and output couplings  175  and  176 , are respectively coupled to the resonators  252 ( 1 ) and  252 ( 2 ). An interconnecting coupling  280  is coupled between the two resonators  252 . The interconnecting coupling  280  includes interdigitated capacitors to more accurately represent ideal lumped element capacitor connections from the computer modeling. Specifically, the interconnecting coupling  280  comprises a common transmission line segment  281 , a first transmission line segment  282  that is coupled to end of the common transmission line segment  281  via an interdigitated capacitor  283 , and a second transmission line segment  284  that is coupled to the other end of the common transmission line segment  281  via another interdigitated capacitor  285 . The high impedance transmission line segments  282  and  284  are directly connected to the resonators  152 ( 1 ) and  152 ( 2 ), thereby acting as points of contact. The interconnecting coupling  280  further comprises shunt capacitance structures  285  and  286  to provide additional shunt capacitance to the interconnecting coupling  280 . 
     By way of non-limiting example, an actual embodiment of a four-pole dual-mode meandered filter structure was modeled in accordance with the meandered filter structure  250  illustrated in FIG.  28 . This filter structure was composed of the same material and modeled in the same manner as the fabricated two-pole meandered filter structure. FIG. 29 shows the simulated passband response of the modeled four-pole dual-mode meandered filter structure. As shown, the well-defined poles are, again, a result of the implementation of the interdigitated coupling technique and four-quadrant symmetry layout. 
     Although particular embodiments of the present inventions have been shown and described, it will be understood that it is not intended to limit the present inventions to the preferred embodiments,.and 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 inventions. Thus, the present inventions are intended to cover alternatives, modifications, and equivalents, which may be included within the spirit and scope of the present inventions as defined by the claims.