Patent Publication Number: US-7904129-B2

Title: Superconducting device with a disk shape resonator pattern that is adjustable in bandwidth

Description:
RELATED ART 
     This application is a divisional application of U.S. patent application Ser. No. 11/233,074, filed on Sep. 23, 2005, which issued as U.S. Pat. No. 7,558,608 and claims priority of Japanese Application No. 2004-284670, filed on Sep. 29, 2004; Japanese Application No. 2004-0303301, filed on Oct. 18, 2004; and Japanese Application No. 2005-233037, filed on Aug. 11, 2005, the entire contents of each are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a superconducting high-frequency device, and more particularly, to a dual-mode superconducting device applied to front end devices, such as transmission filters or transmission antennas, in mobile Communications systems or broadcast systems. 
     2. Description of the Related Art 
     Along with recent spread and progress of mobile (cellular) phones, high-rate high-capacity signal transmission techniques are becoming indispensable. Application of superconductors to base station filters for mobile communications is greatly expected, being promised as providing low loss and high Q value resonance, because superconductors have very small surface resistance as compared with ordinary electric conductors, even at a high-frequency region. 
     For example, as illustrated in  FIG. 1C , the RF signal received at the antenna (ANT)  151  is subjected to baseband processing at the baseband processing unit  156 , after having passed through the bandpass filter (BPF)  152 R, the low-noise amp (LNA)  153 , the down converter (D/C)  154 , and the demodulator (DEMOD)  155 . 
     In the transmission system, the signal processed by the baseband processing unit  156  passes through the modulator (MOD)  157 , the up converter (U/C)  158 , the high-power amp (HPA)  159 , and the bandpass filter (BPF)  152 T, and is finally transmitted from the antenna  151 . 
     When applying a superconductive filter as the receiving-end bandpass filter  152 R, a steep frequency cutoff characteristic can be expected with less transmission loss. On the other hand, application to the transmission-end bandpass filter  152 T leads to the effect for removing distortion caused by the high-power amp  159 . However, the transmission end requires high power to transmit a radio signal, and therefore, simultaneous pursuit of compactness and a satisfactory power characteristic is the present issue. 
     Conventionally, a resonator is provided with a superconducting filter pattern (signal layer)  102  of a hairpin type illustrated in  FIG. 1A , or a straight-line type illustrated in  FIG. 1B . See, for example, JP 2001-308603A and JP 3-194979A. The bottom of a dielectric substrate  101  is covered with a superconducting ground film (blanket film)  104 , while the top face is furnished with a hairpin or straight-line superconducting filter pattern  102  and a feeder  103 . 
     Conventional filters with the above-described microstrip structure have a problem in that transmission loss increases especially at the transmission end when high RF power is input. This is because a high-frequency wave, such as a microwave, is likely to concentrate on the edge of the conductor pattern, causing concentration of electric current on the edge or the corner of the microstrip line, and because the electric current density exceeds the critical current density of the superconductor. 
     To overcome this problem, a disk pattern has been proposed to reduce concentration of electric current, as illustrated in  FIG. 2A . In this example, a superconducting disk pattern  112  with fewer corners or edges is formed on the dielectric substrate  101  in order to realize a high power response as the transmission filter. 
     When the filter pattern is formed as a TM 11  mode disk resonator, the electric current flows uniformly along the symmetric arcs with respect to the diameter of the disk in the presence of an electric field, as illustrated in  FIG. 2B . The magnetic field points in a direction perpendicular to the electric current. 
     However, a multistage filter or a multistage array antenna with several disk resonators arranged in it has a drawback of increasing the device size. 
     Then, a superconducting disk pattern  122  with a notch  125  formed on a portion of the circumference of the disk is proposed. By forming the notch  125 , the degeneracy of the mutually orthogonal electric and magnetic fields of the mode is lifted to separate the resonate frequency so as to allow the resonator to function as a dual-mode filter. In the example shown in  FIG. 3 , two types of resonance at lower frequency f 1  (with electric current flow in direction A) and higher frequency f 2  (with electric current flow in direction B) with respect to the center frequency f 0  are generated. 
     However, the notch  125  formed in the superconducting disk pattern  122  causes the electric current to concentrate on the corners of the notch  125  on the lower frequency f 1  side, as illustrated in  FIG. 3 , resulting in exceeding the maximum electric current density of the basic disk resonator without a notch. In  FIG. 3 , concentration of electric current occurs in the shaded areas indicated by the arrows. Electric current concentration is conspicuous especially at the bottom edge and the bottom corners of the square-shaped notch  125 . In contrast, the area along the circumference of the superconducting disk pattern  122  has less electric current concentration. Frequencies f 1  and f 2  are 45 degrees out of phase at the maximum electric current density. 
     Electric current concentration on the corners and edges of the notch  125  will cause a decrease of the maximum allowable power and an increase of distortion in the bandpass filter or the antenna using a superconducting resonator. 
     Concerning a microstrip type high-frequency transmission line, it is proposed to form a straight groove along the edge of the electrode formed on the dielectric substrate to disperse the electric current concentration on the edge. See, for example, JP 11-177310. 
     SUMMARY OF THE INVENTION 
     The present invention is conceived in view of the above-described problems in the prior art, and it is an object of the invention to provide a superconducting device with improved power tolerance and reduced distortion, which can be suitably used for a transmission filter or an antenna. 
     It is another object of the invention to provide a tuning method for finely tuning the characteristic of a resonant filter of a plane-figure type (e.g., a disk type) formed with a superconductive material. 
     To achieve the above-described object, in a superconducting resonator pattern of a plane-figure type (such as a disk, an oval figure, or a polygon), at least a portion of the notch, especially an area on which electric current is likely to concentrate, is curved or arc-shaped. The plane-figure type resonator pattern has a two-dimensional expanse, and is distinguished from a line type resonator pattern, such as a hairpin type or a microstrip type. 
     Depending on the shape of the arced portion, the degree of mutual interference between the electric field and the magnetic field (e.g., the degree of coupling) varies. As the radius of the curvature or the arc increases, concentration of electric current can be reduced more efficiently; however, the coupling of the mode changes and the bandwidth becomes broader. Accordingly, it is desired to set the radius of the curvature of the arced portion of the notch to be at or below a quarter of the effective wavelength (λ/4). 
     Alternatively, a second conductor pattern is arranged above the superconducting resonator pattern of the plane-figure type (such as a disk type, an oval type, or a polygonal type) so as to cause a coupling corresponding to the desired bandwidth. Preferably, the second conductor pattern has a curved shape, such as round or oval. 
     Depending on the size and the position of the second conductor pattern, and on the dielectric constant of a dielectric material between the second conductor pattern and the superconducting resonator pattern, the center frequency and the degree of mutual interference of the electric and magnetic fields of the mode (coupling) vary, causing the bandwidth to change. As the size of the second conductor pattern increases, electric current concentration can be reduced more efficiently; however, coupling of the mode changes and ripple in the pass band increases. Accordingly, it is desired to set the diameter of the round shape or the major axis of the oval shape less than or equal to a quarter of the effective wavelength (λ/4). 
     As still another alternative, a ladder pattern is formed in the plane-figure type (such as a disk, an oval, or a polygon) superconducting resonator pattern. The ladder pattern is defined by a notch formed from the periphery of the resonator pattern, and a line-and-space section extending from the notch toward the center of the resonator pattern. The direction of each line of the line-and-space section of the ladder pattern is consistent with direction A in which electric current of lower frequency f 1  flows. 
     Depending on the cutaway amount of the notch, the filter characteristic can be roughly determined. Depending on the line width, the number of lines and the end position of the ladder pattern, the center frequency and the degree of mutual interference of the electric and magnetic fields of the mode (coupling) and the bandwidth can be finely tuned, while reducing electric current concentration. 
     The conductor pattern may have a thickness greater than a skin depth or a magnetic penetration depth. 
     To be more precise, in one aspect of the invention, a superconducting device includes:
     (a) a dielectric substrate; and   (b) a plane-figure type resonator pattern made of a superconductive material and formed on the dielectric substrate, the resonator pattern having a notch at least a portion of which is made round or arc-shaped.   

     By shaping a portion of the notch round or arc-shaped, electric current concentration can be reduced, while maintaining the power characteristic and the frequency characteristic of the device satisfactory. 
     This superconducting device can operate in two resonant modes in a high-frequency range. 
     In another aspect of the invention, a superconducting device includes:
     (a) a first dielectric substrate;   (b) a plane-figure type resonator pattern formed of a superconductive material on the first dielectric substrate; and   (c) a conductor pattern positioned above the resonator pattern so as to generate coupling of a prescribed bandwidth in the resonator pattern.   

     In still another aspect of the invention, a superconducting device includes:
     (a) a dielectric substrate; and   (b) a plane-figure type resonator pattern formed of a superconducting material on the dielectric substrate,   

     wherein the resonator pattern has a ladder pattern consisting of a notch formed in portion of a periphery of the resonator pattern and a line-and-space section extending from the notch. 
     In yet another aspect of the invention, a filter adjusting method for a dual-mode superconducting filter device having a plane-figure type resonator pattern with a notch formed in a periphery of the resonator pattern is provided. The method includes the steps of:
     (a) forming a line-and-space section by laser trimming in the resonator pattern such that the line-and-space section extends from the notch and that each line of the line-and-space section extends in a tangential direction of the resonator pattern; and   (b) making fine adjustment of a filtering characteristic of the superconducting filter device by controlling a line width of the line-and-space section and/or an end position of the line-and-space section.   

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other objects, features, and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings, in which: 
         FIG. 1A  through  FIG. 1C  illustrate conventional superconducting filters used in the RF front end of a base station in a mobile communications system; 
         FIG. 2A  illustrates a conventional disk resonator, and  FIG. 2B  illustrates the current flow and the distribution of the electric and magnetic fields in the TM 11  mode; 
         FIG. 3  illustrates concentration of electric current density in a conventional notched disk resonator; 
         FIG. 4A  and  FIG. 4B  are schematic diagrams of a superconducting device according to the first embodiment of the invention; 
         FIG. 5A  and  FIG. 5B  are schematic diagrams illustrating examples of the notch formed in the resonator pattern of the superconducting device according to the first embodiment of the invention; 
         FIG. 6A  through  FIG. 6C  are modifications of the notch formed in the resonator pattern; 
         FIG. 7  illustrates the effect of reducing concentration of electric current density according to the first embodiment of the invention; 
         FIG. 8  is a graph showing the effect of the first embodiment in comparison with a conventional notched disk resonator; 
         FIG. 9  is a graph showing the power characteristic and the distortion of the superconducting device of the first embodiment in comparison with the conventional device; 
         FIG. 10  is a schematic diagram illustrating a superconducting device according to the second embodiment of the invention; 
         FIG. 11  is a schematic diagram of the packaged superconducting device according to the second embodiment of the invention; 
         FIG. 12  is a schematic diagram illustrating the positional relation between the resonator pattern and the conductive pattern arranged above the resonator pattern; 
         FIG. 13  illustrates the effect of reducing concentration of electric current density according to the second embodiment of the invention; 
         FIG. 14  is a graph showing the effect of the second embodiment in comparison with a conventional notched disk resonator; 
         FIG. 15  is a graph showing the maximum tolerable power of the superconducting device according to the second embodiment in comparison with a conventional notched disk resonator; 
         FIG. 16  is a graph showing the improvement in third order intermodulation distortion (IPD3) according to the second embodiment of the invention, in comparison with a conventional notched resonator; 
         FIG. 17A  and  FIG. 17B  are schematic diagrams illustrating a superconducting device according to the third embodiment of the invention; 
         FIG. 18  is a top view of the resonator pattern with a ladder pattern according to the third embodiment of the invention; 
         FIG. 19  is a schematic diagram illustrating an example of the ladder pattern (Pattern  1 ) formed in the disk resonator; 
         FIG. 20  is a graph showing the filter characteristics of the disk resonator with ladder pattern  1 ; 
         FIG. 21  is a schematic diagram illustrating the distribution of electric current density in the disk resonator with ladder pattern  1 ; 
         FIG. 22  is a schematic diagram illustrating another example of the ladder pattern (pattern  2 ) formed in the disk resonator; 
         FIG. 23  is a graph showing the filter characteristics of the disk resonator with ladder pattern  2 ; 
         FIG. 24  is a schematic diagram illustrating distribution of electric current density in the disk resonator with ladder pattern  2 ; 
         FIG. 25A  and  FIG. 25B  are modifications of the ladder pattern formed in the disk resonator; 
         FIG. 26  is a schematic diagram illustrating still another example of the ladder pattern (pattern  3 ) formed in the disk resonator; 
         FIG. 27  is a graph showing the filter characteristics of the disk resonator with ladder pattern  3 ; and 
         FIG. 28  is a schematic diagram illustrating distribution of electric current density in the disk resonator with ladder pattern  3 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The preferred embodiments of the present invention are described below with reference to the attached drawings. 
     First Embodiment 
     A superconducting high-frequency device (which may be referred to simply as a “superconducting device”) according to the first embodiment of the invention is described in conjunction with  FIG. 4A ,  4 B,  5 A,  5 B,  6 A to  6 C,  7  to  9 . 
       FIG. 4A  is a schematic diagram of the superconducting device, and  FIG. 4B  illustrates an application of the superconducting device to a transmission filter used at a base station in a mobile communications system, which device is accommodated in a metal package  30  ( FIG. 4B ). 
     The superconducting device comprises a dielectric substrate (such as a single-crystal MgO substrate)  11 , ( FIG. 4A ) a superconducting resonator pattern (or filter pattern)  12  formed in a prescribed shape on the top face of the MgO dielectric substrate  11 , signal input/output lines (feeders)  13  extending toward the superconducting resonator pattern  12 , and a ground electrode  14  ( FIG. 4A ) covering the rear face of the MgO dielectric substrate  11 . In this example, a YBCO (Y—Ba—Cu—O) based material is used as the superconductive material. 
     The superconducting resonator pattern  12  is a plane-figure pattern (disk pattern) with a notch  20 . At least a portion of the notch  20  is shaped in an arc. The notch  20  produces resonant frequencies of two modes through coupling. In this context, the “plane-figure” pattern is a circuit pattern for defining a basic shape of the resonator and extending in a two-dimensional plane, such as a disk pattern, an oval pattern, or a polygonal pattern. The plane-figure pattern is distinguished from a line pattern (or a linear pattern). 
     As the dielectric substrate  11 , an arbitrary dielectric substrate may be used, other than the single-crystal MgO substrate, as long as it has a dielectric constant ranging from 8 to 10 in the frequency range of 3 GHz to 5 GHz. One of the feeders  13  extending from the signal input/output electrode  15  toward the superconducting resonator pattern  12  is used for signal input, and the other is used for signal output. 
     In  FIG. 4B , the plane-figure type superconducting device is mounted in the metal package  30  coated with gold, and covered with a top plate (not shown). Input/output connectors  31  are fixed to the metal package  30 , and the center conductor of the input/output connector  31  is electrically connected to the electrode  15  coupled to the end of the corresponding feeder  13 . The electric connection is realized using any suitable technique, such as wire bonding, tape-automated bonding, or solder bonding. The ground electrode (or ground coat)  14  ( FIG. 4A ) covering the rear face of the MgO dielectric substrate  11  improves the electric connection with the metal package  30 . 
       FIG. 5A  and  FIG. 5B  are examples of the notch shape formed in the superconducting resonator pattern  12 . In  FIG. 5A , the notch  20  is U-shaped with round corners. Preferably, the radius R of curvature of the round (or arced) portion is at or below a quarter of the effective wavelength (λ/4). 
     In the example shown in  FIG. 5B , the notch  20  is defined only by an arc, without a straight portion. Again, the radius R of curvature is at or below λ/4. These notches  20  are characterized in round cut, in comparison with the conventional square notch. 
     In fabrication of the superconducting device, for example, a YBCO (Y—Ba—Cu—O) based thin film is formed by laser evaporation on both faces of a MgO substrate, which substrate is to be cut into pieces with dimensions of 20×20×0.5 (mm) in a later process. The thickness of the YBCO-based thin film is appropriately selected according to the filter characteristic, and it is set to, for example, 0.5 μm. The YBCO-based thin film on one side of the MgO substrate  11  is patterned by photolithography to form a resonator disk pattern  12  with a round notch  20  and feeders  13 . The diameter of the disk pattern  12  is about 14 mm. Then, a metal electrode  15  is formed at the end of each of the feeders  13 . The YBCO-based thin film on the other side of the MgO substrate  11  is left as it is, and used as a ground electrode  14 . 
     The thus-fabricated superconducting device is mounted in the metal package  30  to comprise a resonator. The superconducting device illustrated in  FIGS. 4A and 4B  has resonant frequencies of two modes orthogonal to each other in the 4 GHz band, and it can be applied to the fourth generation mobile communications systems. 
       FIG. 6A  through  FIG. 6C  are modifications of the notch shape formed in the superconducting resonator pattern. In these examples, the radius R (e.g., see  FIG. 6B ) of curvature is at or below λ/4, and more preferably, at or below λ/8. 
       FIG. 7  is a schematic diagram illustrating the effect of the superconducting resonator pattern of the first embodiment for reducing concentration of electric current density for lower frequency f 1 , center frequency f 0 , and higher frequency f 2 . As indicated by the arrow, concentration of electric current density is greatly reduced around the notch  20  especially on the low frequency (f 1 ) side, as compared with the conventional disk resonator with a squared-shaped notch illustrated in  FIG. 3 . In the other portion of the disk edge, concentration of electric current density is sufficiently low, as in the conventional disk resonator. Resonant frequencies f 1  and f 2  are out of phase by 45 degrees. 
       FIG. 8  is a graph showing the reduction of electric current density concentration J max  [A/m], together with the frequency in GHz characteristics of the superconducting device of the first embodiment. In  FIG. 8 , the maximum electric current density J max  of the conventional disk resonator with a square cut is plotted by white squares as a function of frequency, and the maximum electric current density J max  . of the disk resonator with a round cut of the first embodiment is plotted by white circles as a function of frequency. The solid line and the dashed line represent the transmission characteristic (S 21 ) in dB and the input reflection characteristic (S 11 ) in dB, respectively, of the superconducting device of the first embodiment. 
     As is clearly shown in the graph, by making at least a portion of the notch  20  arced, the maximum electric current density can be reduced greatly, as compared with the conventional disk resonator with a square notch. As indicated by the S 11  characteristic, the resonant frequencies of the two modes are clearly shown in the 4 GHz band. This means that the disk resonator of the first embodiment is suitably used as a dual-mode filter or a double filter with satisfactory frequency characteristics. 
       FIG. 9  is a graph showing the power characteristic and the distortion characteristic of the superconducting device of the first embodiment. To measure the power characteristic and the distortion characteristic, a sample of a disk resonator with a round-cut notch illustrated in  FIG. 5B  is prepared, and the sample resonator is mounted in a metal dewar. The dewar is filled with helium gas, and the temperature is varied in the temperature range from -203° C. (70K) to -193° C. (80K). The resonant curves measured at each temperature are ones (S 11  and S 21 ) shown in the graph of  FIG. 8 . Under this condition, output power level of the fundamental wave Pout in dBm is measured as a function of input power level Pin to evaluate tolerable (or allowable) power as the RF power characteristic. In addition, the third-order intermodulation distortion (IMD 3 ) is also measured to evaluate the distortion characteristic. 
     As the power level is increased in the dual mode at resonant frequencies f 1  and f 2 , the quench phenomenon occurs at -195.9° C. (77.3K) in the conventional prior art disk resonator with a square-notched superconductor pattern. That is, the output power level abruptly falls near 33.6 dBm at the lower frequency f 1  as the input power level is increased, as plotted by the dark diamonds, and loss increases greatly. 
     In contrast, with the round-cut resonant pattern of embodiment 1, tolerable power level at or above 40 dBm can be achieved, without causing quench, as plotted by the dark circles. 
     As to the measurement of IDM 3, two waves are applied near the resonant frequencies f 1  and f 2  within as close range as 1 MHz to measure the third-order intermodulation distortion caused by the non-linear response of the resonator. The IDM3 of the conventional square-notched superconductor pattern is indicated by white diamonds, and that of the round-cut resonant pattern of embodiment  1  is indicated by the white circles. As is clearly shown in the graph, by shaping at least a portion of the notch formed in the superconducting resonator pattern in the form of arc, the third-order intermodulation distortion can be reduced by about 10 dBm, as compared with the conventional square-notched superconducting resonant pattern. 
     With the first embodiment, the maximum tolerable (or allowable) power is improved, while reducing distortion, in a superconducting device. Such a superconducting device is suitably applied to transmission resonators, transmission filters, antennas, or other types of front end devices, and a high-performance transmission/receiving front end can be provided in the fields of mobile communications and broadcasting. 
     Although it is preferable for the plane-figure type superconductor pattern to be a disk or a round shape from the viewpoint of reducing corners or edges as much as possible, a polygonal pattern may be used. By making at least a portion of the notch round, a dual-mode resonator can be realized, while reducing electric current concentration. 
     Second Embodiment 
     The second embodiment of the invention is described in conjunction with  FIG. 10  through  FIG. 16 .  FIG. 10  is a schematic diagram of a superconducting device according to the second embodiment, and  FIG. 11  illustrates a packaged device in which the superconducting device shown in  FIG. 10  is mounted in a metal package  30  ( FIG. 11 ) for application to a transmission superconducting filter used at a base station of a mobile communications system. 
     The superconducting device comprises a dielectric base substrate (such as a single crystal MgO substrate)  11  ( FIG. 10 ), a superconducting resonator pattern (or filter pattern)  12  formed in a prescribed shape on the top face of the MgO dielectric substrate  11 , signal input/output lines (feeders)  13  extending toward the superconducting resonator pattern  12 , a ground electrode  14  ( FIG. 10 ) covering the rear face of the MgO dielectric substrate  11 , a second dielectric substrate  16  ( FIGS. 10 ,  11 ) placed over the dielectric base substrate  11 , and a disk shaped or oval shaped conductor pattern  17  formed on the second dielectric substrate  16  ( FIGS. 10 ,  11 ). 
     In this example, a YBCO (Y—Ba—Cu—O) based material is used as the superconductive material, and the superconducting resonator pattern  12  is of a plane-figure type formed in a disk pattern. 
     As in the first embodiment, the plane-figure pattern includes a disk, an ellipse, and a polygon, and is distinguished from a line (or a linear) pattern. 
     For the dielectric base substrate  11 , an arbitrary dielectric substrate may be used, other than the single-crystal MgO substrate, as long as it has a dielectric constant ranging from 8 to 10 in the frequency range of 3 GHz to 5 GHz. 
     One of the feeders  13  extending from the signal input/output electrode  15  ( FIGS. 10 ,  11 ) toward the superconducting resonator pattern  12  is used for signal input, and the other is used for signal output. 
     It is preferable for the dielectric upper substrate  16  ( FIGS. 10 ,  11 ) to be made of a material with a relatively high dielectric constant and less dielectric loss. For example, MgO, LaAlO 3 , sapphire, CeO 2 , and TiO 2  may be used. When using a material with a dielectric constant greater than that of the dielectric base substrate  11  for the dielectric upper substrate  16 , the effective dielectric constant increases, and the resonant frequency of the superconductor pattern shifts to the lower frequency f 1  side. To maintain the original resonant frequency, the superconducting resonator pattern has to be made smaller. In other words, the superconducting device can be made compact at the same frequency. It is desired that the size of the dielectric upper substrate  16  be the same as that of the dielectric base substrate  11 . 
     In  FIG. 11 , the superconducting device with a plane-figure pattern is mounted in the metal package  30  coated with gold, and covered with a top plate (not shown). Input/output connectors  31  are fixed to the metal package  30 , and the center conductor of the input/output connector  31  is electrically connected to the electrode  15  coupled to the end of the corresponding feeder  13 . The electric connection is realized using any suitable technique, such as wire bonding, tape-automated bonding, or solder bonding. The ground electrode (or ground coat)  14  ( FIG. 10 ) covering the rear face of the MgO dielectric substrate  11  improves the electric connection with the metal package  30 . The dielectric base substrate  11  and the dielectric upper substrate  16  (FIGS.  10 , 11 ) are fixed by a presser bar spring  32  in the metal package  30 . 
     In the example shown in  FIG. 10  and  FIG. 11 , the conductor pattern  17  may be overlapped directly on the superconducting resonator pattern  12 . However, inserting a dielectric between the superconducting resonator pattern  12  and the conductor pattern  17  will lead to more improvement in the operational characteristic. Although the embodiment employs a substrate with a high dielectric constant, the substrate may be replaced by an air layer. In this case, the conductor pattern  17  is formed in the top cover (not shown) of the metal package  30  so as to face the superconducting resonator pattern  12 . Alternatively, a second dielectric substrate with the conductor pattern  17  formed at the bottom may be held above the dielectric base substrate  11  such that the conductor pattern  17  faces the superconducting resonator pattern  12  via the air layer. 
       FIG. 12  is a plan view of the superconducting device, showing the positional relation between the superconducting resonator pattern  12  and the conductor pattern  17 . The conductor pattern  17  is arranged such that the two feeders  13  and the conductor pattern  17  are substantially symmetric with respect to the center of the resonator pattern  12 . The conductor pattern  17  is a disk or an ellipse, and the diameter (or the major axis when an ellipse) is at or below a quarter of the effective wavelength (λ/4). 
     As the diameter of the conductor pattern  17  increases, concentration of electric current can be reduced; however, if the diameter becomes too large, coupling between the resonant modes of the disk becomes strong, and ripples in the pass band are increased. In addition, the conductor pattern  17  generates resonance and such resonance disturbs the originally determined resonant modes of the disk. To avoid such situations, the diameter (or the major axis if an oval pattern) of the conductor pattern  17  is set less than or equal to a quarter of the effective wavelength (λ/4). 
     Depending on the position of the conductor pattern  17 , the center frequency and the degree of mutual interference of the modes of the electric/magnetic field (the degree of coupling, that is, the band width) vary. For example, if the conductor pattern  17  is separated from the resonator pattern  12  as indicated by the arrow A, coupling is enhanced and the band width is increased. On the other hand, if the conductor pattern  17  approaches the center of the resonator pattern  12 , then coupling is weakened and the band width is narrowed. In order to generate desired dual modes, the position of the conductor pattern  17  is adjusted appropriately so as not to be concentric with respect to the superconducting resonator pattern  12  and so as to produce desired coupling. 
     In fabrication of the superconducting device, for example, a YBCO (Y—Ba—Cu—O) based thin film is formed by laser evaporation on both faces of a MgO substrate  11 . The substrate  11  is to be cut into pieces with dimensions of  20  x  20  x  0 . 5  (mm) after all the necessary layers are formed. The thickness of the YBCO-based thin film is appropriately selected according to the filter characteristic, and it is set to, for example,  0 . 5  pm. The YBCO-based thin film on one side of the MgO base substrate  11  is patterned by photolithography to form a resonator disk pattern  12  and feeders  13 . The diameter of the disk pattern  12  is about 12.8 mm when a LaAIO 3  upper substrate  16  is placed over the MgO base substrate  11 . Then, a metal electrode  15  is formed at the end of each of the feeders  13 . The YBCO-based thin film on the other side of the MgO base substrate is left as it is, and used as a ground electrode  14  ( FIG. 10 ). 
     The conductor pattern  17  is formed using a lift-off method in one face of a LaAlO 3  single crystal substrate. Alternatively, the conductor pattern  17  may be formed by photolithography and etching after coating the LaAlO 3  substrate with a conductive film. Then the substrate is cut into pieces with dimensions of 18×18×0.5 (mm). 
     The thickness of the conductor pattern  17  is selected so as to reduce the surface resistance. If a metal material is used, a metal film is formed by vacuum evaporation or sputtering such that the thickness is at or above the skin depth. If a superconductive material is used, a superconducting film is formed by laser evaporation, sputtering, or an MBE method such that the thickness is at or above the magnetic penetration depth. When using a metal material, a conductor pattern  17  containing Ag, Cu or Au is formed on the dielectric upper substrate  16  via a glue layer (not shown) made of chromium (Cr) or titanium (Ti) in order to achieve satisfactory adhesiveness between the conductor pattern  17  and the dielectric substrate  16 . Since the surface resistance of the glue layer is greater than that of the conductor pattern  17 , the thickness of the glue layer is set to or below 0.1 μm. When using a superconductive material, it is desired to form the film under the same conditions as the disk resonator pattern  12  for consistency in characteristics. 
     The thus-fabricated superconducting device is mounted in the metal package  30  to comprise a resonator. Positioning marks (cross marks in this example)  18  are formed at four corners of the dielectric base substrate  11  and the dielectric upper substrate  16 , as illustrated in  FIG. 12 . By arranging the positioning marks  18  at the four corners, influence on the resonator pattern  12 , the conductor pattern  17 , and the feeders  13  can be minimized. The positioning marks  18  are formed in the same process as forming the resonator pattern  12 , the feeder  13 , or the conductor pattern  17 . If using a metal material, the positioning marks  18  are formed by a lift-off method on the dielectric base substrate  11 , and by lift-off or etching on the dielectric upper substrate  16 . 
     The superconducting device illustrated in  FIG. 10  through  FIG. 12  has resonant frequencies of two mutually orthogonal modes in the 4 GHz band, and it can be applied to the fourth generation mobile communications systems. Without the conductor pattern  17 , the resonator has a single mode with complete orthogonality. By arranging the conductor pattern  17  above the superconducting resonator pattern  12 , the orthogonality is partially released, and coupling modes are generated unless the conductor pattern  17  and the superconducting resonator pattern  12  are in the concentric relation. If, as shown in  FIG. 12 , the conductor pattern  17  is symmetric with respect to an x-axis and a y-axis projected on the pattern, such as an ellipse or a rectangle, dual modes are generated even if the center of the conductor pattern  17  is consistent with the center of the resonator pattern  12 . However, it is desired to shape the conductor pattern  17  as a disk or an ellipse for the purpose of preventing concentration of electric current. 
       FIG. 13  is a schematic diagram illustrating the effect for reducing concentration of electric current in the second embodiment. There is little concentration of electric current, and the current density is relatively low over the entire area of the disk pattern  12  at lower frequency f 1 , center frequency f 0 , and higher frequency f 2 . As compared with the conventional square-notched disk pattern (covered with a dielectric) shown in  FIG. 3 , concentration of electric current is reduced greatly. 
       FIG. 14  is a graph showing the frequency characteristics and the current concentration reducing effect of the superconducting device of the second embodiment. The maximum current density (Jmax) [Am] of the superconducting device of the embodiment is plotted by the dark squares as a function of frequency in GHz. As a comparison, Jmax of the conventional square-cut resonator is plotted by white squares as a function of frequency. The input reflecting characteristic (S 11 ) in dB and the transmission characteristic (S 21 ) in dB are also indicated by the dashed line and the solid line, respectively. 
     As is clearly shown in the graph, with a disk conductor pattern  17  arranged above the superconducting resonator pattern  12 , the maximum electric current density can be reduced greatly, as compared with the conventional disk resonator with a square cut. As indicated by the S 11  characteristic, the resonant frequencies of the two modes are clearly shown in the  4  GHz band. This means that the disk resonator of the second embodiment is suitably used as a dual-mode filter or a double filter with satisfactory frequency characteristic. 
       FIG. 15  and  FIG. 16  are graphs respectively showing the power characteristic IP [dBm] and the distortion characteristic ΔIMD @ 40 dBm, 70K [dB] of the superconducting device vs. Frequency in [GHz]of the second embodiment. To measure the power characteristic and the distortion characteristic, a sample of a disk resonator with a round-cut notch illustrated in  FIG. 5B  is prepared, and the sample resonator is mounted in a metal dewar. The dewar is filled with helium gas, and the temperature is varied in the temperature range from -203° C. (70K) to -193° C. (80K). The resonant curves measured at each temperature are ones (S 11  and S 21 ) shown in the graph of  FIG. 14 . Under this condition, output power level is measured as a function of input power level to evaluate tolerable (or allowable) power level as the RF power characteristic. In addition, the third-order intermodulation distortion (IMD 3 ) is also measured to evaluate the distortion characteristic. 
     From  FIG. 15  indicating the IP value in dBm representing tolerable power level, it is understood that the power characteristic ΔIMD of the superconducting device with an overlapped conductor pattern of the second embodiment is improved greatly, as compared with the conventional square-cut disk resonator. 
     From  FIG. 16 , it can be understood that the third-order intermodulation distortion characteristic ΔIMD@40dBm, 70K[dB] indicated along the ordinate of the graph is improved greatly in the second embodiment, as compared with the conventional square-cut disk resonator. 
     With the second embodiment, the tolerable (or allowable) power level is improved, while reducing distortion, in a superconducting device. Such a superconducting device is suitably applied to transmission resonators, transmission filters, antennas, or other types of frontend devices, and a high-performance transmission/receiving frontend can be provided in the fields of mobile communications and broadcasting. 
     Third Embodiment 
     The third embodiment of the invention is described in conjunction with  FIGS. 17A ,  17 B,  18  to  24 ,  25 A,  25 B,  26  to  28 .  FIG. 17A  is a schematic diagrams of a superconducting device according to the third embodiment, and  FIG. 17B  illustrates a packaged device in which the superconducting device shown in  FIG. 17A  is mounted in a metal package  30  for application to a transmission superconducting filter used at a base station of a mobile communications system. 
     The superconducting device comprises a dielectric substrate (such as a single-crystal MgO substrate)  11  ( FIG. 17A ), a superconducting resonator pattern (or filter pattern)  12  formed in a prescribed shape on the top face of the MgO dielectric substrate  11 , signal input/output lines (feeders)  13  extending toward the superconducting resonator pattern  12 , and a ground electrode  14  ( FIG. 17A ) covering the rear face of the MgO dielectric substrate  11 . In this example, a YBCO (Y—Ba—Cu—O) based material is used as the superconductive material. 
     As shown in  FIG. 17A , the superconducting resonator pattern  12  is of a plane-figure type (a disk type in this example), and it has a ladder pattern  47  extending from the circumference of the disk. The ladder pattern  47  consists of a notch  47   a  cut by a prescribed amount from the circumference of the disk, and multiple lines and spaces (a line-and-space section)  47   b  extending from the end of the notch  47   a.    
     As in the previous embodiments, a “plane-figure” pattern defines the basic shape of the resonator extending in a two-dimensional plane, including a disk, an ellipse, and a polygon, and it is distinguished from a “line pattern (or a linear pattern)”. 
     For the dielectric base substrate  11 , an arbitrary dielectric substrate may be used, other than the single-crystal MgO substrate, as long as it has a dielectric constant ranging from 8 to 10 in the frequency range of 3 GHz to 5 GHz. 
     One of the feeders  13  extending from the signal input/output electrode  15  toward the superconducting resonator pattern  12  is used for signal input, and the other is used for signal output. 
     In  FIG. 17B , the plane-figure type superconducting device is mounted in the metal package  30  coated with gold, and covered with a top plate (not shown). Input/output connectors  31  are fixed to the metal package  30 , and the center conductor of the input/output connector  31  is electrically connected to the electrode  15  coupled to the end of the corresponding feeder  13 . The superconducting pattern  12  has a ladder pattern  47 . The electric connection is realized using any suitable technique, such as wire bonding, tape-automated bonding, or solder bonding. The ground electrode (or ground coat)  14  covering the rear face of the MgO dielectric substrate  11  improves the electric connection with the metal package  30 . 
       FIG. 18  is a top view of the superconducting resonant pattern  12  shown in  FIG. 17 . The ladder pattern  47  extends from the circumference of the disk pattern  12  toward the center. Each line of the line-and-space section  47   b  extends in direction A of current flow at lower frequency f 1 . The higher-frequency (f 2 ) current flow B is perpendicular to direction A. 
     The notch  47   a  of the ladder pattern  47  mainly contributes to coupling of two resonant frequencies, while the line-and-space section  47   b  mainly contributes to reducing concentration of current density and to fine adjustment of the filter characteristics. By controlling the line width and the end position of the line-and-space section  47   b , the center frequency and the degree of mutual interference of the electric/magnetic field modes (the degree of coupling, that is, the band width) can be adjusted finely. 
     In the example shown in  FIG. 18 , the notch  47   a  and the line-and-space section  47   b  are defined by straight lines; however, it is desired to make the corners of the notch  47   a  and the line-and-space section  47   b  arced at a prescribed radius of curvature. In this case, the radius of curvature of the arced portion is preferably at or below a quarter of the effective wavelength ( 8/4). As the radius of curvature increases, electric current concentration can be more reduced. However, the coupling of the two modes varies, and the band width increases. 
     In fabrication of the superconducting device, for example, a YBCO (Y—Ba—Cu—O) based thin film is formed by laser evaporation on both faces of a MgO substrate. The substrate is to be cut into pieces with dimensions of 20×20×0.5 (mm) after the formation of all the necessary layers. The thickness of the YBCO-based thin film is appropriately selected according to the filter characteristic, and it is set to, for example, 0.5 μm. The YBCO-based thin film on one side of the MgO substrate  11  is patterned by photolithography to form a resonator disk pattern  12  having the ladder pattern  47  and feeders  13 . The ladder pattern  47  may be formed simultaneously with the disk resonator pattern  12  using a mask, or alternatively, it may be formed after the formation of the disk resonator pattern  12 , by ion milling using argon (Ar) gas. The diameter of the disk pattern  12  is about 12.8 mm, and the line width of the ladder pattern  47  is about 100 μm. 
     Then, a metal electrode  15  is formed at the end of each of the feeders  13 . The YBCO-based thin film on the other side of the MgO substrate  11  is left as it is, and used as a ground electrode  14 . 
     The thus-fabricated superconducting device is mounted in the metal package  30  to comprise a resonator, as illustrated in  FIG. 17B . The superconducting device illustrated in  FIGS. 17A ,  17 B and  18  has resonant frequencies of two modes orthogonal to each other in the 4 GHz band, and it can be applied to the fourth generation mobile communications systems. 
     Even after the completion of the superconducting device (e.g., superconducting high-frequency filter) having the resonator pattern  12  with the ladder pattern  47 , the center frequency and the coupling characteristics of the device can be adjusted in a simple manner. For example, the line width or the corner shape of the ladder pattern  47  is changed finely by laser trimming, or one or more lines and spaces may be added by laser trimming after the test operation. 
       FIGS. 19 to 24 ,  25 A,  25 B,  26  to  28  show observation results of electric current concentration and the filter characteristics of disk resonator pattern  12  with different configurations of ladder patterns  47 . Signal input/output lines (feeders) are shown at  13 . A line-and-space section is shown at  47   b.    
       FIG. 19  illustrates a first example of ladder pattern  47  (Pattern  1 ) formed in the disk resonator pattern  12 . In this example, the diameter of the disk pattern  12  is 12.8 mm, the amount of cut from the circumference (that is, the size of the notch  47   a ) is 0.192 mm, and the length of the line-and-space section  47   b  extending from the notch  47   a  in the radial direction is 1.6 mm. Four lines are formed at a line width of 200 μm. The space width between adjacent lines is 200 μm, which width is set below a quarter of the effective wavelength (λ/4). The lateral width in the tangential direction of ladder pattern  47  is about 1 mm. 
       FIG. 20  is a graph showing the filter characteristics of the resonant filter having the ladder pattern  47  (Pattern  1 ) shown in  FIG. 19 , and  FIG. 21  is a schematic diagram illustrating distribution of electric current density in the resonant filter with the ladder pattern  47  shown in  FIG. 19 . The hatched area in  FIG. 21  is a region of high current density, in which the maximum current density Jmax is at or more than 30A/m. 
     Pattern  1  illustrated in  FIG. 19  can reduce electric current concentration very efficiently, as illustrated in  FIG. 21 ; however, this pattern cannot produce different frequencies of two modes, as is clearly illustrated in the graph of  FIG. 20 . This is because the cut amount (length from the circumference) of the notch  47   a  is insufficient, and therefore, there is little difference from an ordinary disk resonator. 
     In  FIG. 20 , the input reflection characteristic (S 11 ) and the transmission characteristic (S 21 ) are plotted as an example of the frequency characteristic in GHz of the superconducting resonant filter. The fine dotted line represents the input reflection characteristic (S 11 ) of the filter pattern with an ordinary square notch (without ladder pattern  47 ) whose size is the same as that of the ladder pattern  47 . The bold dashed line represents the input reflection characteristic (S  11 ) of the filter pattern with the ladder pattern  47  shown in  FIG. 19 . With a simple square notch, resonant frequencies of two modes are clearly indicated. In contrast, the ladder pattern  47  whose line-and-space section  47   b  starts near the circumference of the disk pattern cannot produce resonance. 
     The solid line represents the transmission characteristic (S 21 ) of the resonant filter with an ordinary square notch (without ladder pattern  47 ), and the dotted dashed line represents the transmission characteristic (S 21 ) of the resonant filter with the ladder pattern  47  shown in  FIG. 19 . When the amount of cut from the circumference (the size of the notch  47   a ) is insufficient, transmission loss becomes large, and a signal of a specific frequency band cannot be filtered. 
     It is understood from  FIG. 20  and  FIG. 21  that the resonator having a ladder pattern  47 , as shown in  FIG. 21 , with a small amount of cut from the circumference (with a small notch  47   a ) does not function as a dual-mode resonant filter though electric current concentration can be reduced efficiently. 
       FIG. 22  illustrates a second example of ladder pattern  47  (Pattern  2 ) formed in the disk resonator pattern  12 . In this example, the diameter of the disk pattern  12  is 12.8 mm, the amount of cut from the circumference (that is, the size of the notch  47   a ) is 1.789 mm, and the length of the line-and-space section  47   b  extending from the notch  47   a  in the radial direction is 0.8 mm. Four lines are formed at a line width of 100 μm. The space width between adjacent lines is 100 μm, which width is set below a quarter of the effective wavelength (λ/4). The lateral width in the tangential direction of ladder pattern  47  is about 1 mm. 
       FIG. 23  is a graph showing the filter characteristics (frequencies in GHz) of the resonant filter having the ladder pattern  47  (Pattern  2 ) shown in  FIG. 22 , and  FIG. 24  is a schematic diagram illustrating distribution of electric current density in the resonant filter with the ladder pattern  47  shown in  FIG. 22 . The shaded area in  FIG. 23  is a region of high current density, in which the maximum current density Jmax is at or more 30 A/m. In  FIG. 23 , Sll is the input reflection characteristic of the resonant filter pattern with and without the ladder pattern  47  shown in  FIG. 22 . S 21  is the transmission characteristic of the resonant filter pattern with and without the ladder pattern  47  shown in  FIG. 22 . 
     The ladder pattern  47  (Pattern  2 ) shown in  FIG. 22  can produce resonant frequencies of two modes in a satisfactory manner, and has a transmission characteristic of an acceptable level so as to function as a bandpass filter. This is because the ladder pattern  47  has a notch  47   a  of an appropriate size. 
     It should be noted that in  FIG. 23  the center frequency of the device (resonant filter) with the ladder pattern  47  slightly shifts from the ordinary square-notched resonator pattern whose notch size is equivalent to that of the ladder pattern  47 . This means that the pass band width and the resonant frequencies can be adjusted finely by providing a ladder pattern. 
     As illustrated in  FIG. 24 , electric current tends to converge to the first line of the line-and-space section  47   b  (which is the closest to the circumference); however, the current concentration reducing effect can be achieved as a whole of the resonant filter pattern. The convergence of electric current on the first line can be reduced to some extent by making the corner of the notch  47   a  round with a radius of curvature less that a quarter of the effective wavelength (λ/4), or broadening the line width at both ends. 
       FIG. 25A  and  FIG. 25B  illustrate modifications of the ladder pattern  47  with variations of the line-and-space section  47   b . In  FIG. 25A , the bottom corners of the notch  47   a  and the corners of each space in the line-and-space section  47   b  are arced at a radius of curvature below 8/4. In  FIG. 25B , these corners of notch  47   a  are chamfered with straight lines. In either example, the end portions of each line are widened so as to prevent electric current from converging to the lines of the ladder pattern  47 . 
       FIG. 26  illustrates a third example of ladder pattern  47  (Pattern  3 ) formed in the disk resonator pattern  12 . In this example, the diameter of the disk pattern  12  is 12.8 mm, the amount of cut from the circumference (that is, the size of the notch  47   a ) is 1.0 mm, and the length of the line-and-space section  47   b  extending from the notch  47   a  in the radial direction is 3.2 mm. Sixteen (16) lines are formed at a line width of 100 μm. The space width between adjacent lines is 100 μm, which width is set below a quarter of the effective wavelength (λ/4). The lateral width in the tangential direction of ladder pattern  47  is about 1 mm. 
       FIG. 27  is a graph showing the filter characteristics (frequencies in GHz) of the resonant filter having the ladder pattern  47  (Pattern  3 ) shown in  FIG. 26 , and  FIG. 28  is a schematic diagram illustrating distribution of electric current density in the resonant filter with the ladder pattern  47  shown in  FIG. 26 . In  FIG. 27 , S 11  is the input reflection characteristic of the resonant filter pattern with and without the ladder pattern  48  shown in  FIG. 26 . S 21  is the transmission characteristic of the resonant filter pattern with and without the ladder pattern  47  shown in  FIG. 26 . 
     As illustrated in  FIG. 27 , when the ladder pattern  12  extends close to the center of the disk pattern  12 , as shown in  FIG. 26 , resonant frequencies of two modes cannot be produced. Although the filtering characteristics are satisfactory, the device functions only as a single-mode resonator, not a dual-mode resonator. 
     As illustrated in  FIG. 28 , electric current is more likely to converge on the lines located near the circumference, as well as on the end portions of each line of the line-and-space section  47   b . This means that if the line-and-space section  47   b  of the ladder pattern  47  is too long, the device does not function as a dual-mode resonator, and cannot reduce localized concentration of electric current. The hatched area is a region in which the maximum current density Jmax is at or more than 30 A/m. 
     From the observation of the first through third examples of the ladder pattern  47  (Patterns  1 - 3 ) described above in conjunction with  FIG. 19  through  FIG. 28 , the following points are derived.
     (1) The basic characteristics for a dual-mode filter are determined by the cut amount or the size of the notch  47   a  of the ladder pattern  47 ;   (2) Fine adjustment of the center frequency and/or the band width can be made by forming the line-and-space section  47   b ; and   (3) The effect for reducing electric current concentration is determined by the starting position and the end position of the line-and-space section  47   b.      

     In other words, by appropriately selecting the cut amount of the notch  47   a  and the size of the line-and-space section  47   b  of the ladder pattern  47   a , a dual-mode superconducting resonant filter with satisfactory filtering characteristic and tolerable power characteristic can be realized. 
     To be more precise, the notch  47   a  of the ladder pattern  47  needs to be deep enough to produce different resonant frequencies of two modes from comparison between Pattern  1  and Pattern  2 . The length of the ladder pattern  47  is preferably less than half (½), and more preferably, less than one third (⅓) of the distance between the circumference and the center (that is, the radius) of the disk resonator pattern  12  from comparison between Pattern  2  and Pattern  3 . These points apply not only to a disk pattern, but also to other shapes of resonator pattern, such as an oval or polygonal pattern. 
     The superconducting device of the third embodiment with an improved tolerable power characteristic is suitable for a dual-mode transmission resonant filter or an antenna, and can provide a high-performance transmission/receiving frontend in the field of mobile communications and broadcasting. 
     Although the preferred embodiments are described using specific examples, the invention is not limited to these examples. 
     For example, in place of the YBCO-based thin film, any suitable superconducting oxide, such as a RBCO (R—Ba—Cu—O) based thin film in which Nd, Gd, Sm, or Ho is used in place of Y (yttrium) as the R element, may be used as the superconductive material. Alternatively, a BSCCO (Bi—Sr—Ca—Cu—O) based material, a PBSCCO (Pb—Bi—Sr—Ca—Cu—O) based material, or CBCCO (Cu—Ba p —Ca q —Cu r —O x  where 1.5≦p≦2.5, 2.5≦q≦3.5, and 3.5≦r≦4.5) based material may be used as the superconductive material. 
     The dielectric substrate is not limited to the single crystal MgO substrate, and it may be replaced by another material, such a LaAlO 3  substrate or a sapphire substrate. 
     This patent application is based on and claims the benefit of the earlier filing dates of Japanese Patent Application Nos. 2004-284670 filed Sep. 29, 2004, 2004-303301 filed Oct. 18, 2004, and 2005-233037 filed Aug. 11, 2005, the entire contents of which are incorporated herein by reference.