Patent Publication Number: US-6903632-B2

Title: Band pass filter

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2003-142239, filed May 20, 2003, the entire contents of which are incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a band pass filter, and more particularly to a band pass filter for use in communication devices. 
   2. Description of the Related Art 
   A band pass filter is a component which is needed to prevent interference of signals and effectively utilize a frequency. In the field of communications, performance of a filter is particularly important, as it determines an effective use of a frequency which is an important resource. That is, in regard to an electromagnetic wave transmitted/received by an antenna, an out-of-band signal is cut by a reception filter or a transmission filter, thereby greatly reducing interferences with an adjacent signal. In order to most effectively cut the out-of-band signal, a filter which can clearly separate each signal is desirable. However, in a high frequency band in particular, a super sharp cut filter is desirable in order to cut an adjacent signal in a very narrow band, but realization of such a very narrow band super sharp cut filter is very difficult. 
   Usually, a band pass filter on an RF stage is constituted by using many resonators. In the band pass filter constituted by many resonators, types of filter characteristics to be realized are determined by a value given to each coupling between the resonators. Further, whether the resonators are correctly coupled with each other determines whether the designed characteristic can be realized. In particular, in a narrow band filter that coupling between the resonators is very weak, coupling between the resonators is important. 
   There has been conventionally known a filter using a planar structure circuit as typified by a microstrip line, a strip line and others. For example, IEEE Microwave Theory and Techniques Symposium Digest (1998), p. 379 discloses a Chebychev filter that the number of path which couples the resonators is determined as one. In such a filter, realization of a narrow band is achieved by spatially increasing a distance between the resonators. Furthermore, IEEE Transactions on Microwave Theory and Techniques, Vol. 44 (1996), p. 2099 discloses a pseudo-elliptic function type which can suppress an insertion loss and constitute a sharp cut filter. This type of filter can be realized by introducing non-adjacent coupling to a filter such as a Chebychev filter having one path of signals and bringing in a shortcut path. Moreover, there has been developed a filter which adopts not only simple spatial coupling as strong non-adjacent coupling between resonators but carries out coupling through a transmission line path coupled with a resonator by using a short-length section such as disclosed in IEEE Microwave Theory and Techniques Symposium Digest (2000), p. 661, and a sharp cut type high-quality filter with a relatively broad band is realized. However, achieving both the very narrow band and the super sharp cut is difficult. 
   As described above, realization of a very narrow band super sharp cut filter is very difficult, by using a conventional filter. The reason will be described hereinafter as problems in the prior art. 
   There are two problems when realizing the super sharp cut filter. For example, in a Chebychev filter or the like which adopts a structure that coupling between resonators based on a gap is used and the number of path of couplings is one, such as disclosed in IEEE Microwave Theory and Techniques Symposium Digest (1998) p. 379, all the couplings become weak when each distance between the resonators is increased, but coupling of the resonators other than adjacent resonators does not become sufficiently weak. Therefore, the characteristic is disadvantageously disrupted when the coupling is adjusted by using the distance between the resonators to obtain a very narrow bandwidth filter. Additionally, since the distance between the resonators must be largely increased, the filter itself becomes large in size, a problem of a limitation in size of a substrate and the like restricts the design. Also, the sufficient number of resonators cannot be assured, and hence the sharp cut cannot be realized. 
   Another important problem becomes apparent when configuring the very narrow band sharp cut filter with a low insertion loss. In the regular Chebychev type filter, the number of resonators is increased in order to realize the sharp cut, but this is very disadvantageous in terms of the loss in case of the narrow band, and the insertion loss is greatly increased. 
   In order to reduce the insertion loss, it is necessary to constitute such a pseudo-elliptic function type which can suppress the insertion loss and configure the sharp cut filter as disclosed in IEEE Transactions on Microwave Theory and Techniques, Vol. 44(1996), p. 2099. This type of filter can be realized by introducing non-adjacent coupling to a filter, such as a Chebychev filter, having one path of signals and bringing in a shortcut path. Therefore, when a narrow band filter is tried to be realized, since weak non-adjacent coupling is introduced to the resonators which are originally connected by weak coupling, parasitic coupling is also generated to resonators other that those which should be coupled. This considerably disrupts the characteristic, and there occurs a problem that the sharp cut pseudo-elliptic function type filter cannot be successfully realized in the narrow band. 
   On the other hand, there has been developed such a filter which performs not only spatial coupling as strong non-adjacent coupling between the resonators, but also coupling through a transmission line path connected with the resonators via short-length sections, as disclosed in IEEE Microwave Theory and Techniques Symposium Digest (2000), p. 661. With this filter, a relatively-broad band sharp-cut high-quality filter can be realized. In this filter, however, spatial coupling between the resonators is also used for coupling between the adjacent resonators, but all the designed weak couplings are hard to be taken, thereby making it difficult to realize the very narrow band filter successfully. Additionally, in regard to non-adjacent coupling based on this transmission line path, there is a serious problem. This is a problem that an original resonance frequency of the resonators deviates by adding a transmission line path for coupling. In the very narrow band filter, since the band is originally very narrow, the filter is very sensitive to spatial distribution or the like of material parameters, adding such a deviation of the resonance frequency to this property results in a serious problem. For example, in the case of coupling the resonators, when a center frequency of each resonator is out of this band, which is assumed to be very narrow, realization of the band pass filter becomes very difficult. 
   As described above, the very narrow band sharp cut filter using a planar structure circuit is hard to realize based on only the prior art. 
   BRIEF SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide a narrow band sharp cut band pass filter by stabilizing weak coupling between resonators. 
   According to an aspect of the invention, there is provided a band pass filter for passing a frequency band having a central wavelength which is corresponding to a center frequency, comprising: 
   a substrate; 
   input/output portions formed on the substrate; 
   a plurality of resonators provided between the input/output portions; and 
   transmission line paths, each having coupling portions at both ends, the coupling portion being faced to one of the resonators with a gap, each of the transmission line paths having a length which is (1+2m)/4-fold (m: natural number) of the central wavelength, and each of the coupling portion having a length of a ¼ of the central wavelength. 
   Here, in this specification, it is determined that a wavelength means a wavelength in a transmission line formed by using a dielectric substrate, and a central wavelength means a wavelength corresponding to a center frequency. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       FIG. 1  is a cross-sectional view schematically showing a structure of a band pass filter according to an embodiment of the present invention; 
       FIG. 2  is a plane view showing a first resonator pattern for illustrating a basic structure of the band pass filter according to the embodiment of the present invention; 
       FIG. 3  is a graph showing a resonance characteristic of a filter having the resonator pattern depicted in  FIG. 2 ; 
       FIG. 4  shows a relationship between a length of a coupling part and a frequency deviation in a filter having the resonator pattern shown in  FIG. 2 ; 
       FIG. 5  is a plane view showing a second resonator pattern for illustrating a basic structure of a band pass filter according to another embodiment of the present invention; 
       FIG. 6  is a graph showing a resonance characteristic of a filter having the resonator pattern depicted in  FIG. 5 ; 
       FIG. 7  shows a relationship between a length of a coupling part and a frequency deviation in the filter having the resonator pattern depicted in  FIG. 5 ; 
       FIG. 8  is a plane view showing a third resonator pattern for illustrating a basic structure of a band pass filter according to another embodiment of the present invention; 
       FIG. 9  is a plane view showing a fourth resonator pattern for illustrating a basic structure of a band pass filter according to a further embodiment of the present invention; 
       FIG. 10  is a plane view showing a Chebychev type band pass filter according to an embodiment of the present invention; 
       FIG. 11  is a graph showing a filter characteristic of the Chebychev type filter depicted in  FIG. 10 ; 
       FIG. 12  is a plane view showing a Chebychev type band pass filter according to a further embodiment of the present invention; 
       FIG. 13  is a graph showing a filter characteristic of the Chebychev type filter depicted in  FIG. 12 ; 
       FIG. 14  is a plane view showing a pseudo-elliptic function type band pass filter according to a still further embodiment of the present invention; 
       FIG. 15  is a graph showing a filter characteristic of the pseudo-elliptic function type filter illustrated in  FIG. 14 ; 
       FIG. 16  is a plane view showing a pseudo-elliptic function type band pass filter according to a yet further embodiment of the present invention; and 
       FIG. 17  is a graph showing a filter characteristic of the pseudo-elliptic function type filter illustrated in FIG.  16 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A band pass filter according to an embodiment of the present invention will now be described hereinafter with reference to the accompanying drawings. 
   In the following embodiments, description will be given based on a band pass filter having a function to pass through a signal in a narrow band or a very narrow band. Here, the narrow band and the very narrow band can be represented by a specific band Δ/f 0  which is a ratio of a center frequency f 0  of a signal to be passed with respect to a band width Δ corresponding to a wavelength of the signal to be passed and, in this specification, it is determined that the narrow band is not more than 2% in the specific band and the very narrow band is not more than 0.5% in the specific band. 
     FIG. 1  is a cross-sectional view schematically showing a basic structure of a superconducting filter according to an embodiment of the present invention. 
   A distribution constant circuit type resonator shown in  FIG. 1  is a superconducting microstrip line path resonator, and there is formed a planar structure circuit by providing a pattern  4  of that resonator metal layer on an upper surface of a substrate  2  and excitation lines  8 - 1  and  8 - 2  on both sides of the pattern  4 , and a thin film, e.g., a Y-based copper oxide superconducting film  6  is formed on a lower surface of this substrate  2 . This substrate  2  has, e.g., a diameter of approximately 50 mm and a thickness of 0.43 mm, and it is formed of MgO having a relative dielectric constant of, e.g., 10. Further, as the superconducting film  6  of this microstrip line, for example, a Y-based copper oxide high-temperature superconducting thin film having a thickness of approximately 500 nm is used, and a line width of a strip conductor is approximately 0.4 mm. This superconducting thin film  6  can be formed by a laser deposition method, a sputtering method, a codeposition method and the like. The pattern  4  of the resonator is arranged in an area between the excitation lines  8 - 1  and  8 - 2 . The pattern  4  of the resonator, the excitation lines  8 - 1  and  8 - 2  and the like are likewise formed of thin films, e.g., YBCO thin films of Y-based copper oxide superconducting films. A lower surface thin film  6  of the substrate is grounded. 
   Here, although description will be given taking the resonator that the microstrip line is formed into a predetermined shape as an example, it is apparent that a resonator in which a strip line is formed into a predetermined shape can be likewise applied. Furthermore, although there is known, e.g., a strip line such that the pattern  4  of the resonator is formed between a pair of substrates, a pattern structure of the resonator can be also adopted for the strip line, as will be described below. 
     FIG. 2  is a plane view showing a first resonator pattern for illustrating the basic structure of a filter according to an embodiment of the present invention. The resonators  21  and  22  constituting the first resonator pattern  4 , which is shown in  FIG. 1 , are half-wavelength resonators, and their resonance frequency is determined as 5 GHz. That is, if the resonator  21  or  22  solely exists, when a signal frequency is gradually increased from 0 Hz to 5 GHz, the resonator  21  or  22  is firstly exited to generate a resonance at a resonance frequency of 5 GHz. A wavelength corresponding to this resonance frequency is twofold of a length of the resonator. Further, the resonators  21  and  22  are coupled through a transmission line path  23  having a length of a ¾ wavelength. The resonators  21  and  22  are opposed to the transmission line path  23  formed on the substrate  2  through gaps  24  and  25  by each predetermined length x, and extended in the same direction along the transmission  23  on the substrate  2 . Therefore, the transmission line path  23  and the resonator  21 , or the transmission line path  23  and the resonator  22  are respectively coupled through the gap  24  or  25 . As a result, the resonators  21  and  22  are coupled through the gaps  24  and  25  and the transmission line path  23 . 
   In such a resonator pattern, each predetermined length x at the coupling parts between the resonators  21  and  22  and the coupling transmission line path  23  coupled via the gaps  24  and  25  is important, and this predetermined length x is substantially set to a ¼ wavelength.  FIG. 3  shows a resonance characteristic of a filter having the resonator pattern  4  constituted by the resonators  21  and  22  and the transmission line path  23  illustrated in FIG.  2 . In the resonance characteristic of the filter depicted in  FIG. 3 , there are two resonance points in the vicinity of the center frequency, and an average value of their frequencies matches with 5.00 GHz, which corresponds to the resonance frequency when the resonator is solely used. It can be understood that the resonance frequency of each resonator is not deviated by this coupling. As a value of coupling of the resonators, 10 −4  or a lower value can be realized. Therefore, in the filter having the resonator pattern shown in  FIG. 2 , the frequency characteristic of the narrow band can be realized. 
     FIG. 4  shows a relationship between the predetermined length x at the coupling part of the resonators  21  and  22  and frequency deviation. As apparent from  FIG. 4 , it can be understood that when the predetermined length x of the coupling part substantially corresponding to the ¼ wavelength falls within a range of 0.22 to 0.28 wavelengths, or more strictly a range of 0.24 to 0.27 wavelengths, a deviation of the resonance frequency becomes minimum in that range. That is because the resonator part is changed from the opened state to the short-circuited state or from the short-circuited state to the opened state with the ¼ wavelength, and positions of a node and an anti-node are substantially the same as those when the resonator is solely used, even if the coupling line path is coupled, since coupling through the gaps  24  and  25  is weak. Furthermore, when the predetermined length x of the coupling part is substantially set to the ¼ wavelength, a deviation of the frequency can be suppressed from being generated. 
     FIG. 5  is a plane view showing a second resonator pattern for illustrating a basic structure of a filter according to another embodiment of the present invention. 
   In a filter structure shown in  FIG. 1 , a superconducting microstrip line path is formed on an MgO substrate having a thickness of approximately 0.43 mm and a relative dielectric constant of approximately 10. Here, a Y-based copper oxide high-temperature superconducting thin film having a thickness of approximately 500 nm is used as a superconductor of the microstrip line, and a line width of a strip conductor is formed to approximately 0.4 mm. The superconducting thin film is formed by a laser evaporation method, a sputtering method, a codeposition method or the like. 
   As shown in  FIG. 5 , resonators  27  and  28  constituting the second resonator pattern  4  are. one-wavelength resonators, and their resonance frequency is determined as 5 GHz. Each of the resonators  27  and  28  is opposed to a transmission line  29  formed on a substrate  2  by a predetermined length x through each of gaps  26  and  30 , and extended in the same direction along the transmission  29  on the substrate  2 . Therefore, the transmission line path  29  and the resonator  27 , or the transmission line path  29  and the resonator  28  are respectively coupled through the gap  26  or  30 . As a result, the resonators  27  and  28  are coupled through the transmission line path  29  having a length of a {fraction (5/4)} wavelength. 
   In such a resonator pattern, the predetermined length x of each of coupling parts  26  and  30  between the resonators  27  and  28  and the coupling transmission line path  29  which are coupled through the gaps  26  and  30  is set to a ¼ wavelength.  FIG. 6  shows a resonance characteristic of a filter having the resonator pattern  4  constituted by the resonators  27  and  28  and the transmission line path  29  illustrated in FIG.  5 . In the resonance characteristic of the filter depicted in  FIG. 5 , there are two resonance points in the vicinity of the center frequency, and an average value of their frequencies matches 5.0 GHz, which corresponds to the resonance frequency when the resonator is solely used. It can be understood that the resonance frequency of each resonator is not deviated by this coupling. In the filter having the resonator pattern shown in  FIG. 5 , therefore, it is possible to realize the frequency characteristic of the narrow band. 
     FIG. 7  shows a relationship between the length x of the coupling part of the resonator and a frequency deviation. As apparent from  FIG. 7 , it can be understood that when the predetermined length x of the coupling part substantially corresponding to the ¼ wavelength falls within a range of 0.22 to 0.28 wavelengths, or more strictly a range of 0.24 to 0.27 wavelengths, the frequency deviation becomes minimum in that range. That is because the resonator part is changed from the opened state to the short-circuited state or from the short-circuited state to the opened state with the ¼ wavelength and positions of a node and an anti-node are substantially the same as those when the resonator is solely used. 
   Incidentally, in regard to this coupling position, as shown in  FIG. 8 , coupling can be performed at positions obtained by substantially partitioning off the resonators  27  and  28  in units of the ¼ wavelength like the example shown in FIG.  5 . That is, a part of the transmission line path  29  other than coupling parts  29   a  and  29   b  is bent into a U-shape so as to be away from the resonators  27  and  28 , and there is formed a transmission line path  29  having a shape that the coupling parts are added to the U-shaped portion. Each of the coupling parts  29   a  and  29   b  has a predetermined length x of the substantial ¼ wavelength, and a section of each of the resonators  27  and  28  is partitioned off by the predetermined length x of the substantial ¼ wavelength. Each of the coupling portions  29   a  and  29   b  with the predetermined length x in the partitioned section is opposed to a corresponding resonator in closest proximity thereto. In such a case, the coupling part  29   a  or  29   b  may be opposed at any position of the resonator  27  or  28 . When the transmission line path  29  is bent in this manner, a deviation of coupling can be reduced as compared with a case that the transmission path  29  is linearly formed. 
   Moreover, coupling can be performed on a side opposite to the resonator as shown in FIG.  9 . That is, one resonator  27  may be arranged on one side of an area partitioned off by the transmission line path  29 , and the other resonator  28  may be arranged on the opposite side. 
   Additionally, the resonators  27  and  28  are not restricted to the one-wavelength resonators. Even if (n+2)/2 (n: natural number) wavelength resonators longer than one wavelength are used, coupling of the resonators  27  and  28  can be likewise established by using the transmission line  29 . 
   Further, in the filter according to the embodiment of the present invention, resonators longer than a half wavelength and a coupling transmission line path longer than a half wavelength are used. In the filter having such a structure, these members resonate in frequency region lower than a pass band in theory and a cutoff characteristic is deteriorated in some cases. However, this deterioration in characteristic can be avoided by setting a band pass filter for a broad band, a low pass filter, a wide pass filter or the like on front and rear stages. 
   Various embodiments of the filter according to the present invention will now be described hereinafter with reference to  FIGS. 10  to  17 . 
   Embodiment 1 
     FIG. 10  is a plane view for illustrating one pattern of a filter according to an embodiment 1 of the present invention. 
   Like the description based on  FIG. 1 , a superconducting microstrip line is formed on an MgO substrate  2  having a thickness of approximately 0.43 mm and a relative dielectric constant of approximately 10. Here, a Y-based copper oxide high-temperature superconducting thin film having a thickness of approximately 500 nm is used as a superconductor of the microstrip line, and a line width of a strip conductor is approximately 0.4 mm. The superconducting thin film  4  is manufactured by a laser evaporation method, a sputtering method, a codeposition method or the like. 
   The filter shown in  FIG. 10  is a Chebychev type filter including six resonators  32 ,  34 ,  36 ,  38 ,  40  and  42  between input/output line paths  31  and  43  formed by excitation lines. The six half-wavelength hairpin type resonators  32 ,  34 ,  36 ,  38 ,  40  and  42  whose open sides are directed in the same direction are arranged in a line, and substantially-U-shaped coupling line paths  33 ,  35 ,  37 ,  39  and  41  each having a ¾ wavelength in order to couple resonators adjacent to each other, are arranged between the respective hairpin type resonators  32 ,  34 ,  36 ,  38 ,  40  and  42 . As apparent from the arrangement shown in  FIG. 10 , this filter is constituted as a Chebychev type that non-adjacent couplings are not intentionally adopted, and weak couplings are realized by using all coupling transmission lines between the half-wavelength resonators adjacent to each other. Here, a resonance frequency of each resonator is set to 5 GHz which is a center frequency of the filter, and a band width is set to 10 MHz. Furthermore, a wavelength corresponding to this resonance frequency is twofold a length of each resonator. Moreover, a length x of a coupling part of each of all the coupling line path and all the resonators is selected as 0.23 of a wavelength which is substantially a ¼ wavelength. 
     FIG. 11  shows a characteristic obtained by the filter having the arrangement depicted in FIG.  10 . As apparent from  FIG. 11 , irrespective of a very small specific band which is 0.20%, since small coupling can be stably achieved, it is revealed that disruption in the band is very small and the excellent characteristic can be obtained. Therefore, according to the filter having such a structure as shown in  FIG. 10 , it is possible to realize the very narrow band filter. 
   Embodiment 2 
     FIG. 12  is a plane view for illustrating one pattern of a filter according to another embodiment of the present invention. The filter shown in  FIG. 12  is a Chebychev filter including four resonators  51 ,  53 ,  55  and  57  between input/output line paths  50  and  58  formed by excitation lines. As the resonators, there are used one-wavelength linear type resonators  51 ,  53 ,  55  and  57 . Therefore, a wavelength corresponding to a resonance frequency matches a length of each resonator. Additionally, the resonators  51 ,  53 ,  55  and  57  adjacent to each other are coupled through line paths  52 ,  54  and  56  bent into such a shape as shown in  FIG. 8 , respectively. Each of the transmission line paths  52 ,  54  and  56  has a length of a {fraction (7/4)} wavelength, a length x of each coupling portion is substantially determined as a ¼ wavelength, and this coupling portion is arranged in closest proximity to a corresponding resonator. As described above, since the length of each resonator is determined as one wavelength, edges of the two coupling line paths coupled to the resonators can be sufficiently separated from each other, and it is revealed that an excellent narrow band characteristic can be obtained as shown in  FIG. 13  even if the linear resonators are used. 
   In the filters according to the embodiments depicted in  FIGS. 10 and 12 , although the linear type or hairpin type resonators are adopted as the resonators  32 ,  34 ,  36 ,  38 ,  40 ,  42 ,  51 ,  53 ,  55  and  57 , the present invention is not restricted thereto, and resonators having various shapes such as an open loop type can be used. 
   It is to be noted that the circuit is configured by the microstrip line in the embodiment shown in  FIG. 12 , but the circuit can be also constituted by a strip line. Further, when realizing the narrower band filter, metal partitions can be provided between the coupling line paths, between the resonators or between the resonators and the coupling line paths. 
   Embodiment 3 
     FIG. 14  is a plane view for illustrating one pattern of a filter according to still another embodiment of the present invention. 
   In the filter shown in  FIG. 14 , a superconducting microstrip line path is formed on an MgO substrate (not shown) having a thickness of approximately 0.43 mm and a relative dielectric constant of 10. Here, a Y-based copper oxide high-temperature superconducting thin film having a thickness of approximately 500 nm is used as a superconductor of the microstrip line, and a line width of a strip conductor is approximately 0.4 mm. The superconducting thin film is manufactured by a laser evaporation method, a sputtering method, a codeposition method or the like. 
   The filter shown in  FIG. 14  is a four-stage filter constituted by four linear resonators  61 ,  63 ,  65  and  67  provided between input/output line paths  60  and  68  formed by excitation lines. In the filter depicted in  FIG. 14 , a one-wavelength resonator is used as each resonator, and the adjacent resonators  61 ,  63 ,  65  and  67  are coupled by transmission lines  62 ,  64  and  66  each having a length of a {fraction (7/4)} wavelength through coupling parts each having a length x which is substantially a ¼ wavelength. Moreover, the resonators  61  and  67  are non-adjacently-coupled by a transmission line path  69 . Here, determining the resonators  61  and  67  as references, the coupled transmission line  62  and  66  are arranged in one area, and the transmission line path  69  having a {fraction (17/4)} wavelength is arranged in the other area provided on the opposite side. In the other area, the coupling parts of the transmission line path  69  each substantially having a ¼ wavelength are opposed to the resonators  61  and  67 . In design of this filter, a normalization low pass filter which sets a zero point of a transfer function to ±1.5j is used. Here, j is an imaginary number unit. 
     FIG. 15  shows a characteristic obtained in the filter having the arrangement depicted in  FIG. 14  by measurement in the vicinity of the center frequency. As apparent from  FIG. 14 , according to the filter having the structure depicted in  FIG. 14 , it is revealed that the frequency characteristic of the notched sharp cut narrow band can be obtained. 
   In the filter shown in  FIG. 14 , although each resonator is of a linear type, various kinds of resonators such as an open loop type can be also used. 
   It is to be noted that the circuit is configured by the microstrip line in the filter shown in  FIG. 14 , but the circuit can be constituted by the strip line. 
   Embodiment 4 
     FIG. 16  is a plane view for illustrating one pattern of a filter according to yet another embodiment of the present invention. In the filter shown in  FIG. 16 , a superconducting microstrip line path is formed on an MgO substrate  2  having a thickness of approximately 0.43 mm and a relative dielectric constant of approximately 10. Here, a Y-based copper oxide high-temperature superconducting thin film having a thickness of approximately 500 nm is used as a superconductor of the microstrip line path, and a line is path width of a strip conductor is approximately 0.4 mm. The superconducting thin film is manufactured by a laser evaporation method, a sputtering method, a codeposition method or the like. 
   In the filter shown in  FIG. 16 , there is arranged a six-stage filter constituted by six linear resonators  71 ,  73 ,  75 ,  79 ,  81  and  83  between input/output line paths  70  and  84  formed by excitation lines. Here, one-wavelength resonators are used as the resonators  71 ,  73 ,  75 ,  79 ,  81  and  83 , and transmission line paths  72 ,  74 ,  76 ,  80  and  82  each having a {fraction (7/4)} wavelength are used for coupling of the adjacent resonators through coupling parts each substantially having a ¼ wavelength. Moreover, for non-adjacent coupling, there are used transmission line paths  77  and  78  each of which is arranged on the opposite side of the line paths  72 ,  74 ,  80  and  82  for coupling the adjacent resonators  71 ,  73 ,  75 ,  79 ,  81  and  83 , pulled out through coupling portions each substantially having a length of a ¼ wavelength and has a {fraction (7/4)} wavelength. In design, a normalized low pass filter which sets a zero point of a transfer function to ±1.25j and ±2j is used. Here, j is an imaginary number unit. 
     FIG. 17  shows a characteristic obtained by the filter having the arrangement depicted in FIG.  16 . As apparent from  FIG. 17 , according to the filter having the structure illustrated in  FIG. 16 , it is revealed that the characteristic of the sharp cut narrow band with four notches can be obtained. 
   In the filter shown in  FIG. 16 , although each resonator is of a linear type, various kinds of resonators, such as an open loop type, can be likewise used. 
   It is to be noted that the circuit is configured by the microstrip line in this embodiment, but the circuit can be also constituted by the strip line. Further, the MgO substrate is used in this embodiment, but a sapphire substrate may also be used. 
   Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general invention concept as defined by the appended claims and their equivalents.