Abstract:
This invention provides a reflection-type bandpass filter for ultra-wideband wireless data communication, in which are provided, on the surface of a dielectric substrate, a center conductor and side conductors, provided on both sides of the center conductor, securing a prescribed distance between conductors with non-conducting portions intervening therebetween. The center conductor width or the distances between conductors, or both, are distributed non-uniformly in a length direction of the center conductor.

Description:
This application claims priority from Japanese Patent Application No. 2006-274323, filed on Oct. 5, 2006, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a reflection-type bandpass filter for use in ultra-wideband (UWB) wireless data communication. 
     2. Description of the Related Art 
     This invention relates to a reflection-type bandpass filter for use in ultra-wideband (hereafter “UWB”) wireless data communication. By using this UWB reflection-type bandpass filter, U.S. Federal Communications Commission requirements for spectrum masks can be satisfied. 
     As technology of the prior art related to this invention, for example, the technology disclosed in the following references 1 through 10 is known.
     Reference 1: Specification of U.S. Pat. No. 2,411,555   Reference 2: Japanese Unexamined Patent Application No. 56-64501   Reference 3: Japanese Unexamined Patent Application No. 9-172318   Reference 4: Japanese Unexamined Patent Application No. 9-232820   Reference 5: Japanese Unexamined Patent Application No. 10-65402   Reference 6: Japanese Unexamined Patent Application No. 10-242746   Reference 7: Japanese Unexamined Patent Application No. 2000-4108   Reference 8: Japanese Unexamined Patent Application No. 2000-101301   Reference 9: Japanese Unexamined Patent Application No. 2002-43810   Reference 10: A. V. Oppenheim and R. W. Schafer, “Discrete-time signal processing,” pp. 465-478, Prentice Hall, 1998.   Reference 11: G-B. Xiao, K. Yashiro, N. Guan, and S. Ohokawa, “An effective method for designing nonuniformly coupled transmission-line filters,” IEEE Trans. Microwave Theory Tech., vol. 49, pp. 1027-1031, June 2001.   Reference 12: Y. Konishi, “Microwave integrated circuits”, pp. 19-21, Marcel Dekker, 1991   

     However, the bandpass filters proposed in the prior art may not satisfy the FCC specifications, due to manufacturing tolerances and other reasons. 
     Further, bandpass filters which use coplanar strips do not use wide ground strips, and so are not suitable for coupling with transmission lines such as slot lines. 
     This invention was devised in light of the above circumstances, and has as an object the provision of a high-performance UWB reflection-type bandpass filter which has excellent coupling characteristics with transmission lines such as slot lines, and which satisfies FCC specifications. 
     SUMMARY OF THE INVENTION 
     This invention provides a reflection-type bandpass filter for ultra-wideband wireless data communication, in which are provided on the surface of a dielectric substrate a center conductor and side conductors provided on both sides of the center conductor securing a prescribed distance between conductors with non-conducting portions intervening, and in which the center conductor width or the distances between conductors, or both, are distributed non-uniformly in a length direction of the center conductor. 
     In a reflection-type bandpass filter of this invention, the center conductor width may be constant, and the distances between conductors may be distributed non-uniformly. 
     Alternately, the distances between conductors may be constant, and the center conductor width may be distributed non-uniformly. 
     In a reflection-type bandpass filter of this invention, a difference of 10 dB or higher may exist between a reflectance in a ranges of frequencies f for which f&lt;3.1 GHz and f&gt;10.6 GHz, and a reflectance in a range of frequencies 3.9 GHz≦f≦9.8 GHz, and in a range 3.9 GHz≦f≦9.8 GHz a group delay variation may be within ±0.1 ns. 
     In a reflection-type bandpass filter of this invention, alternately, a difference of 10 dB or higher may exist between a reflectance in a range of frequencies f for which f&lt;3.1 GHz and f&gt;10.6 GHz, and a reflectance in a range of frequencies 3.7 GHz≦f≦10.0 GHz, and in a range 3.7 GHz≦f≦10.0 GHz a group delay variation may be within ±0.1 ns. 
     In a reflection-type bandpass filter of this invention, alternately, a difference of 10 dB or higher may exist between a reflectance in a range of frequencies f for which f&lt;3.1 GHz and f&gt;10.6 GHz, and a reflectance in a range of frequencies 4.1 GHz≦f≦9.5 GHz, and in a range 4.1 GHz≦f≦9.5 GHz a group delay variation may be within ±0.1 ns. 
     In a reflection-type bandpass filter of this invention, a characteristic impedance Zc of an input terminal transmission line may be in the range 10Ω≦Zc≦300Ω. 
     In a reflection-type bandpass filter of this invention, a resistance having the same impedance as the above characteristic impedance value, or a non-reflecting terminator, may be provided on the terminating side. 
     In a reflection-type bandpass filter of this invention, the center conductor and the side conductors may comprise metal plates of thickness equal to or greater than a skin depth of the metal plates at f=1 GHz. 
     In a reflection-type bandpass filter of this invention, the dielectric substrate may have a thickness h in a range 0.1 mm≦h≦10 mm, a relative permittivity ∈r in a range 1≦∈r≦500, a width W in a range 2 mm≦W≦100 mm, and a length L in a range 2 mm≦L≦500 mm. 
     In a reflection-type bandpass filter of this invention, length-direction distributions of the center conductor width and of the distances between conductors may satisfy a design method based on the inverse problem of deriving a potential from spectral data in the Zakharov-Shabat equation. 
     In a reflection-type bandpass filter of this invention, length-direction distributions of the center conductor width and of the distances between conductors may satisfy a window function method. 
     In a reflection-type bandpass filter of this invention, length-direction distributions of the center conductor width and of the distances between conductors may satisfy a Kaiser window function method. 
     In a reflection-type bandpass filter of this invention, by applying a window function technique to design a reflection-type bandpass filter comprising non-uniform coplanar strips, the pass band can be made extremely broad and variation in group delay within the pass band can be made extremely small compared with filters of the related art, even when manufacturing tolerances are large. As a result, a UWB bandpass filter can be provided which satisfies FCC specifications. 
     Further, ground strips can be made wide, so that easy coupling with transmission lines such as slot lines is achieved. Here, “ground strips” refers to the conductors on both sides, which are connected together on the input end. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view showing one aspect of a reflection-type bandpass filter of the invention; 
         FIG. 2  is a graph showing the conductor-to-conductor distance dependence of the characteristic impedance in the coplanar strips; 
         FIG. 3  is a graph showing the center conductor width dependence of the characteristic impedance in the coplanar strips; 
         FIG. 4  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter fabricated in Embodiment 1; 
         FIG. 5  is a graph showing the distribution of the distance between conductors of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 1; 
         FIG. 6  is a graph showing the shape of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 1; 
         FIG. 7  is a graph showing the reflected wave amplitude characteristic in the reflection-type bandpass filter fabricated in Embodiment 1; 
         FIG. 8  is a graph showing the reflected wave group delay characteristic in the reflection-type bandpass filter fabricated in Embodiment 1; 
         FIG. 9  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter fabricated in Embodiment 2; 
         FIG. 10  is a graph showing the distribution of the center conductor width of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 2; 
         FIG. 11  is a graph showing the shape of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 2; 
         FIG. 12  is a graph showing the reflected wave amplitude characteristic in the reflection-type bandpass filter fabricated in Embodiment 2; 
         FIG. 13  is a graph showing the reflected wave group delay characteristic in the reflection-type bandpass filter fabricated in Embodiment 2; 
         FIG. 14  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter fabricated in Embodiment 3; 
         FIG. 15  is a graph showing the distribution of the distance between conductors of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 3; 
         FIG. 16  is a graph showing the shape of the coplanar strip in the reflection-type bandpass filter fabricated in Embodiment 3; 
         FIG. 17  is a graph showing the reflected wave amplitude characteristic in the reflection-type bandpass filter fabricated in Embodiment 3; 
         FIG. 18  is a graph showing the reflected wave group delay characteristic in the reflection-type bandpass filter fabricated in Embodiment 3; and, 
         FIG. 19  is an equivalent circuit of a non-uniform transmission line. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Below, exemplary aspects of the invention are explained referring to the drawings. 
       FIG. 1  is a perspective view showing, in summary, the configuration of a reflection-type bandpass filter of an exemplary aspect of this invention. In the figure, the symbol  1  is the reflection-type bandpass filter,  2  is a dielectric substrate,  3  is a center conductor,  4   a  and  4   b  are non-conducting portions, and  5   a  and  5   b  are side conductors. 
     In the reflection-type bandpass filter  1  of this aspect, the center conductor  3  and side conductors  5   a ,  5   b  provided on either side of the center conductor  3 , maintaining a prescribed distance between conductors and with non-conducting portions  4   a ,  4   b  intervening, are formed on the surface of the dielectric substrate  2 ; the non-uniform coplanar strips are such that the center conductor width or the distances between conductors, or both, are distributed non-uniformly in the length direction of the center conductor  3 . 
     As shown in  FIG. 1 , the z axis is taken along the length direction of the center conductor  3 , the y axis is taken in the direction perpendicular to the z axis and parallel to the surface of the substrate  2 , and the x axis is taken in the direction perpendicular to the y axis and to the z axis. The length extending in the z axis direction from the end face on the input end is z. In the reflection-type bandpass filter  1 , the conductor-to-conductor distance between the side conductor  5   a  and the center conductor  3 , and the conductor-to-conductor distance between the side conductor  5   b  and the center conductor  3 , are the same at each place where z is equal (hereafter the “distance between conductors s”). In this reflection-type bandpass filter, the side conductors  5   a  and  5   b  are semi-infinite: in other words, the widths of the side conductors  5   a  and  5   b  are ten times or greater than the width of the center conductor  3  and the non-conducting portions  4   a ,  4   b . Hence the side conductors  5   a ,  5   b  can be used in configuring a slot line, slot antenna, or the like. Moreover, compared with symmetric-type two-conductor coplanar strips (coplanar strips in which two conductors of equal width are arranged symmetrically), the characteristic impedance of this reflection-type bandpass filter is low, so that the substrate  2  can be fabricated from material with a low permittivity. 
     A reflection-type bandpass filter of this aspect of the invention adopts a configuration in which stop band rejection (the difference between the reflectance in the pass band, and the reflectance in the stop band) is increased, by using a window function method (see Reference 10) employed in digital filter design. By this means, instead of expansion of the transition frequency region (the region between the pass band boundary and the stop band boundary), the stop band rejection can be increased. As a result, manufacturing tolerances can be increased. Also, variation in the group delay within the pass band is decreased. 
     The transmission line of a reflection-type bandpass filter  1  of this aspect of the invention can be represented by a non-uniformly distributed constant circuit such as in  FIG. 19 . 
     From  FIG. 19 , the following equation (1) is obtained for the line voltage v(z,t) and the line current i(z,t). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               - 
                               
                                 
                                   ∂ 
                                   
                                     υ 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   z 
                                 
                               
                             
                             = 
                             
                               
                                 L 
                                 ⁡ 
                                 
                                   ( 
                                   z 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   ∂ 
                                   
                                     i 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             - 
                             
                               
                                 ∂ 
                                 
                                   i 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       z 
                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                           
                           = 
                           
                             
                               C 
                               ⁡ 
                               
                                 ( 
                                 z 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   ∂ 
                                   
                                     υ 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     Here L(z) and C(z) are the inductance and capacitance respectively per unit length in the transmission line. Here, the function of equation (2) is introduced. 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 ∂ 
                                 
                                   
                                     ϕ 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       z 
                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
                                       c 
                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     ∂ 
                                     
                                       
                                         ϕ 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           z 
                                           , 
                                           t 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     ∂ 
                                     t 
                                   
                                 
                               
                               - 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       ⅆ 
                                       
                                           
                                       
                                       ⁢ 
                                       ln 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       Z 
                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                   
                                     ⅆ 
                                     z 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     ϕ 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       z 
                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 
                                   ϕ 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
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                                   ) 
                                 
                               
                             
                             
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                           = 
                           
                             
                               
                                 1 
                                 
                                   c 
                                   ⁡ 
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                   ∂ 
                                   
                                     
                                       ϕ 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                             
                             - 
                             
                               
                                 1 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   
                                     ⅆ 
                                     
                                         
                                     
                                     ⁢ 
                                     ln 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Z 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 
                                   ⅆ 
                                   z 
                                 
                               
                               ⁢ 
                               
                                 
                                   
                                     ϕ 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                                 . 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Here Z(z)=√{L(z)/C(z)} is the local characteristic impedance, and φ 1 , φ 2  are the power wave amplitudes propagating in the +z and −z directions respectively. 
     Substitution into equation (1) yields equation (3). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 ∂ 
                                 
                                   
                                     ϕ 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
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                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
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                                         ϕ 
                                         1 
                                       
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                                         ( 
                                         
                                           z 
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                                           t 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     ∂ 
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                               - 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       ⅆ 
                                       
                                           
                                       
                                       ⁢ 
                                       ln 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       Z 
                                       ⁡ 
                                       
                                         ( 
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                                         ) 
                                       
                                     
                                   
                                   
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                                 ⁢ 
                                 
                                   
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                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                                       , 
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                                     ) 
                                   
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 
                                   ϕ 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     z 
                                     , 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             
                               ∂ 
                               z 
                             
                           
                           = 
                           
                             
                               
                                 1 
                                 
                                   c 
                                   ⁡ 
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                   ∂ 
                                   
                                     
                                       ϕ 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                             
                             - 
                             
                               
                                 1 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   
                                     ⅆ 
                                     
                                         
                                     
                                     ⁢ 
                                     ln 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Z 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 
                                   ⅆ 
                                   z 
                                 
                               
                               ⁢ 
                               
                                 
                                   
                                     ϕ 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       z 
                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                                 . 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     Here c(z)=1/√{L(z)/C(z)}. If the time factor is set to exp(jωt), and a variable transformation is performed as in equation (4) below, then the Zakharov-Shabat equation of equation (5) is obtained. 
     
       
         
           
             
               
                 
                   
                     x 
                     ⁡ 
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     
                       ∫ 
                       0 
                       z 
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         s 
                       
                       
                         c 
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   ∂ 
                                   
                                     
                                       ϕ 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       x 
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   x 
                                 
                               
                               + 
                               
                                 
                                   jωϕ 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                             = 
                             
                               
                                 - 
                                 
                                   q 
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                   ϕ 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 ∂ 
                                 
                                   
                                     ϕ 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 x 
                               
                             
                             - 
                             
                               
                                 jωϕ 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                           
                           = 
                           
                             
                               - 
                               
                                 q 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   ϕ 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     Here q(x) is as given by equation (6) below. 
     
       
         
           
             
               
                 
                   
                     q 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       
                         
                           
                             ⅆ 
                             
                                 
                             
                             ⁢ 
                             ln 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Z 
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         
                           ⅆ 
                           x 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     The Zakharov-Shabat inverse problem involves synthesizing the potential q(x) from spectral data which is a solution satisfying the above equations (see Reference 11). If the potential q(x) is found, the local characteristic impedance Z(x) is determined as in equation (7) below. 
     
       
         
           
             
               
                 
                   
                     Z 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       Z 
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             
                               
                                 ∫ 
                                 0 
                                 x 
                               
                               ⁢ 
                               
                                 
                                   q 
                                   ⁡ 
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ⅆ 
                                   s 
                                 
                               
                             
                           
                           ] 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, normally in a process to determine the potential q(x), the reflectance coefficient r(x) in x space is calculated from the spectra data reflectance coefficient R(ω) using the following equation (8), and q(x) are obtained from r(x). 
     
       
         
           
             
               
                 
                   
                     r 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         ∫ 
                         
                           - 
                           ∞ 
                         
                         ∞ 
                       
                       ⁢ 
                       
                         
                           R 
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             
                               - 
                               jω 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                           
                         
                         ⁢ 
                         
                           ⅆ 
                           ω 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     In this invention, in place of obtaining r(x) from the R(ω) for ideal spectral data, a window function is applied as in equation (9) to determine r′(x).
 
 r ′( x )= w ( x ) r ( x ).  (equation 9)
 
     Here ω(x) is the window function. If the window function is selected appropriately, the stop band rejection level can be appropriately controlled. Here, a Kaiser window is used as an example. The Kaiser window is defined as in equation (10) below (see Reference 10). 
     
       
         
           
             
               
                 
                   
                     w 
                     ⁡ 
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   I 
                                   0 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       β 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           
                                             
                                               [ 
                                               
                                                 
                                                   ( 
                                                   
                                                     n 
                                                     - 
                                                     α 
                                                   
                                                   ) 
                                                 
                                                 / 
                                                 α 
                                               
                                               ] 
                                             
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       2 
                                     
                                   
                                   ] 
                                 
                               
                               
                                 
                                   I 
                                   0 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   β 
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               0 
                               ≤ 
                               n 
                               ≤ 
                               M 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     Here α=M/s, and β is determined empirically as in equation (11) below. 
     
       
         
           
             
               
                 
                   β 
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               0.1102 
                               ⁢ 
                               
                                 ( 
                                 
                                   A 
                                   - 
                                   8.7 
                                 
                                 ) 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               A 
                               &gt; 
                               50 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             
                               
                                 0.5842 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       A 
                                       - 
                                       21 
                                     
                                     ) 
                                   
                                   0.4 
                                 
                               
                               + 
                               
                                 0.07886 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     A 
                                     - 
                                     21 
                                   
                                   ) 
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               21 
                               ≤ 
                               A 
                               ≤ 
                               50 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           
                             A 
                             &lt; 
                             21 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
     Here A=−20 log 10 δ. where δ is the peak approximation error in the pass band and in the stop band. 
     In this way q(x) is determined, and from equation (7) the local characteristic impedance Z(x) is determined. 
     Here, when either the width w of the center conductor  6  (hereafter the “center conductor width w”) or the distance between conductors s, or both, of the coplanar strips are varied, the characteristic impedance can be changed (see Reference 12). 
       FIG. 2  shows the dependence of the characteristic impedance on the distance between conductors s, when the center conductor width w=1 mm, the thickness of the substrate  2  is 1 mm, and the relative permittivity ∈ r  of the substrate  2  is 4.  FIG. 3  shows the dependence of the characteristic impedance on the center conductor width w, when the distance between conductors s=1 mm, h=1 mm, and ∈ r =4. 
     In this invention, the center conductor width w or distance between conductors s was calculated based on the local characteristic impedance obtained from equation (7), and a bandpass filter  1  was manufactured so as to satisfy the calculated center conductor width w or distance between conductors s. By this means, reflection-type bandpass filters  1  having the desired pass band were obtained. 
     Below, the invention is explained in further detail referring to embodiments. Each of the embodiments described below is merely an illustration of the invention, and the invention is in no way limited to these embodiment descriptions. 
     Embodiment 1 
     A Kaiser window was used for which the reflectance is 0.9 at frequencies f in the range 3.4 GHz≦f≦10.3 GHz, and is 0 elsewhere, and for which A=30. Design was performed using one wavelength of signals at a frequency f=1 GHz propagating in the coplanar strip as the waveguide length, and setting the system characteristic impedance to 75Ω. Here, the characteristic impedance is set so as to match the impedance of the system being used. In general, in a circuit which handles high-frequency signals, a system impedance of 50Ω, 75Ω, 300Ω, or similar is used. It is desirable that the characteristic impedance Zc be in the range 10Ω≦Zc≦300Ω. If the characteristic impedance is smaller than 10Ω, then losses due to the conductor and dielectric become comparatively large. If the characteristic impedance is higher than 300Ω, matching with the system impedance is not possible. 
       FIG. 4  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. The horizontal axis is z divided by one wavelength at f=1 GHz; similar axes are used in  FIG. 9  and  FIG. 14  below. 
       FIG. 5  shows the distribution in the z-axis direction of the distance between conductors s, when using a substrate  2  with a thickness h=1 mm and relative permittivity ∈ r =4, and when the center conductor width w=2 mm. Tables 1 through 3 list the distances between conductors s. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Distances between conductors (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.21 
                 0.41 
                 0.62 
                 0.83 
                 1.04 
                 1.24 
                 1.45 
                 1.66 
                 1.87 
                 2.07 
                 2.28 
               
             
          
           
               
                   
                 s[mm] 
               
             
          
           
               
                   
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 2.49 
                 2.70 
                 2.90 
                 3.11 
                 3.32 
                 3.53 
                 3.73 
                 3.94 
                 4.15 
                 4.36 
                 4.56 
                 4.77 
               
               
                 — 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.71 
               
               
                  #3 
                 4.98 
                 5.19 
                 5.39 
                 5.60 
                 5.81 
                 6.02 
                 6.23 
                 6.43 
                 6.64 
                 6.85 
                 7.06 
                 7.26 
               
               
                 — 
                 0.71 
                 0.71 
                 0.71 
                 0.72 
                 0.72 
                 0.72 
                 0.72 
                 0.72 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
               
               
                  #4 
                 7.47 
                 7.68 
                 7.89 
                 8.10 
                 8.31 
                 8.51 
                 8.72 
                 8.93 
                 9.14 
                 9.35 
                 9.55 
                 9.76 
               
               
                 — 
                 0.73 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
               
               
                  #5 
                 9.97 
                 10.18 
                 10.39 
                 10.59 
                 10.80 
                 11.01 
                 11.22 
                 11.43 
                 11.63 
                 11.84 
                 12.05 
                 12.26 
               
               
                 — 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
               
               
                  #6 
                 12.47 
                 12.67 
                 12.88 
                 13.09 
                 13.30 
                 13.51 
                 13.71 
                 13.92 
                 14.13 
                 14.34 
                 14.55 
                 14.75 
               
               
                 — 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
               
               
                  #7 
                 14.96 
                 15.17 
                 15.38 
                 15.58 
                 15.79 
                 16.00 
                 16.21 
                 16.42 
                 16.62 
                 16.83 
                 17.04 
                 17.25 
               
               
                 — 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
               
               
                  #8 
                 17.46 
                 17.66 
                 17.87 
                 18.08 
                 18.29 
                 18.50 
                 18.70 
                 18.91 
                 19.12 
                 19.33 
                 19.54 
                 19.74 
               
               
                 — 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.73 
                 0.72 
                 0.72 
                 0.72 
                 0.72 
                 0.71 
                 0.71 
                 0.71 
               
               
                  #9 
                 19.95 
                 20.16 
                 20.37 
                 20.57 
                 20.78 
                 20.99 
                 21.19 
                 21.40 
                 21.61 
                 21.82 
                 22.02 
                 22.23 
               
               
                 — 
                 0.70 
                 0.70 
                 0.70 
                 0.69 
                 0.69 
                 0.69 
                 0.68 
                 0.68 
                 0.68 
                 0.67 
                 0.67 
                 0.67 
               
               
                 #10 
                 22.44 
                 22.64 
                 22.85 
                 23.06 
                 23.27 
                 23.47 
                 23.68 
                 23.89 
                 24.09 
                 24.30 
                 24.51 
                 24.71 
               
               
                 — 
                 0.67 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
               
               
                 #11 
                 24.92 
                 25.13 
                 25.33 
                 25.54 
                 25.75 
                 25.96 
                 26.16 
                 26.37 
                 26.58 
                 26.78 
                 26.99 
                 27.20 
               
               
                 — 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.66 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
               
               
                 #12 
                 27.41 
                 27.61 
                 27.82 
                 28.03 
                 28.23 
                 28.44 
                 28.65 
                 28.86 
                 29.06 
                 29.27 
                 29.48 
                 29.68 
               
               
                 — 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
               
               
                 #13 
                 29.89 
                 30.10 
                 30.31 
                 30.51 
                 30.72 
                 30.93 
                 31.13 
                 31.34 
                 31.55 
                 31.75 
                 31.96 
                 32.17 
               
               
                 — 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.66 
                 0.67 
                 0.67 
               
               
                 #14 
                 32.38 
                 32.58 
                 32.79 
                 33.00 
                 33.20 
                 33.41 
                 33.62 
                 33.83 
                 34.03 
                 34.24 
                 34.45 
                 34.65 
               
               
                 — 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.67 
                 0.68 
                 0.68 
                 0.68 
                 0.69 
                 0.69 
                 0.69 
               
               
                 #15 
                 34.86 
                 35.07 
                 35.28 
                 35.49 
                 35.69 
                 35.90 
                 36.11 
                 36.32 
                 36.53 
                 36.73 
                 36.94 
                 37.15 
               
               
                 — 
                 0.70 
                 0.70 
                 0.71 
                 0.71 
                 0.72 
                 0.72 
                 0.73 
                 0.74 
                 0.74 
                 0.75 
                 0.75 
                 0.76 
               
               
                 #16 
                 37.36 
                 37.57 
                 37.78 
                 37.98 
                 38.19 
                 38.40 
                 38.61 
                 38.82 
                 39.03 
                 39.24 
                 39.44 
                 39.65 
               
               
                 — 
                 0.76 
                 0.76 
                 0.77 
                 0.77 
                 0.77 
                 0.78 
                 0.78 
                 0.78 
                 0.78 
                 0.78 
                 0.78 
                 0.78 
               
               
                 #17 
                 39.86 
                 40.07 
                 40.28 
                 40.49 
                 40.70 
                 40.90 
                 41.11 
                 41.32 
                 41.53 
                 41.74 
                 41.95 
                 42.16 
               
               
                 — 
                 0.78 
                 0.78 
                 0.78 
                 0.78 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.76 
                 0.76 
                 0.76 
               
               
                 #18 
                 42.36 
                 42.57 
                 42.78 
                 42.99 
                 43.20 
                 43.41 
                 43.61 
                 43.82 
                 44.03 
                 44.24 
                 44.45 
                 44.66 
               
               
                 — 
                 0.76 
                 0.76 
                 0.76 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.76 
                 0.76 
               
               
                 #19 
                 44.86 
                 45.07 
                 45.28 
                 45.49 
                 45.70 
                 45.91 
                 46.11 
                 46.32 
                 46.53 
                 46.74 
                 46.95 
                 47.16 
               
               
                 — 
                 0.76 
                 0.76 
                 0.76 
                 0.76 
                 0.76 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
               
               
                 #20 
                 47.37 
                 47.57 
                 47.78 
                 47.99 
                 48.20 
                 48.41 
                 48.62 
                 48.82 
                 49.03 
                 49.24 
                 49.45 
                 49.66 
               
               
                 — 
                 0.77 
                 0.77 
                 0.77 
                 0.76 
                 0.76 
                 0.76 
                 0.76 
                 0.75 
                 0.75 
                 0.74 
                 0.73 
                 0.73 
               
               
                 #21 
                 49.86 
                 50.07 
                 50.28 
                 50.49 
                 50.70 
                 50.90 
                 51.11 
                 51.32 
                 51.52 
                 51.73 
                 51.94 
                 52.14 
               
               
                 — 
                 0.72 
                 0.71 
                 0.71 
                 0.70 
                 0.69 
                 0.68 
                 0.68 
                 0.67 
                 0.66 
                 0.66 
                 0.65 
                 0.64 
               
               
                 #22 
                 52.35 
                 52.56 
                 52.76 
                 52.97 
                 53.18 
                 53.38 
                 53.59 
                 53.79 
                 54.00 
                 54.21 
                 54.41 
                 54.62 
               
               
                 — 
                 0.64 
                 0.63 
                 0.63 
                 0.62 
                 0.62 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.60 
                 0.60 
                 0.60 
               
               
                 #23 
                 54.83 
                 55.03 
                 55.24 
                 55.44 
                 55.65 
                 55.86 
                 56.06 
                 56.27 
                 56.48 
                 56.68 
                 56.89 
                 57.09 
               
               
                 — 
                 0.60 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.62 
                 0.62 
                 0.62 
                 0.62 
                 0.63 
               
               
                 #24 
                 57.30 
                 57.51 
                 57.71 
                 57.92 
                 58.13 
                 58.33 
                 58.54 
                 58.75 
                 58.95 
                 59.16 
                 59.37 
                 59.57 
               
               
                 — 
                 0.63 
                 0.63 
                 0.63 
                 0.63 
                 0.64 
                 0.64 
                 0.64 
                 0.64 
                 0.64 
                 0.64 
                 0.63 
                 0.63 
               
               
                 #25 
                 59.78 
                 59.99 
                 60.19 
                 60.40 
                 60.61 
                 60.81 
                 61.02 
                 61.23 
                 61.43 
                 61.64 
                 61.84 
                 62.05 
               
               
                 — 
                 0.63 
                 0.63 
                 0.63 
                 0.63 
                 0.62 
                 0.62 
                 0.62 
                 0.62 
                 0.62 
                 0.62 
                 0.61 
                 0.61 
               
               
                 #26 
                 62.26 
                 62.46 
                 62.67 
                 62.88 
                 63.08 
                 63.29 
                 63.49 
                 63.70 
                 63.91 
                 64.11 
                 64.32 
                 64.53 
               
               
                 — 
                 0.61 
                 0.61 
                 0.62 
                 0.62 
                 0.62 
                 0.62 
                 0.63 
                 0.63 
                 0.64 
                 0.65 
                 0.65 
                 0.66 
               
               
                 #27 
                 64.74 
                 64.94 
                 65.15 
                 65.36 
                 65.57 
                 65.77 
                 65.98 
                 66.19 
                 66.40 
                 66.61 
                 66.82 
                 67.02 
               
               
                 — 
                 0.67 
                 0.68 
                 0.69 
                 0.70 
                 0.71 
                 0.73 
                 0.74 
                 0.75 
                 0.76 
                 0.78 
                 0.79 
                 0.80 
               
               
                 #28 
                 67.23 
                 67.44 
                 67.65 
                 67.86 
                 68.07 
                 68.28 
                 68.49 
                 68.70 
                 68.91 
                 69.12 
                 69.33 
                 69.54 
               
               
                 — 
                 0.81 
                 0.83 
                 0.84 
                 0.85 
                 0.86 
                 0.86 
                 0.87 
                 0.88 
                 0.88 
                 0.89 
                 0.89 
                 0.89 
               
               
                 #29 
                 69.75 
                 69.96 
                 70.17 
                 70.38 
                 70.59 
                 70.80 
                 71.01 
                 71.22 
                 71.43 
                 71.64 
                 71.85 
                 72.06 
               
               
                 — 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.88 
                 0.88 
                 0.87 
                 0.87 
                 0.86 
                 0.86 
                 0.85 
                 0.85 
               
               
                 #30 
                 72.27 
                 72.48 
                 72.69 
                 72.90 
                 73.11 
                 73.32 
                 73.53 
                 73.74 
                 73.95 
                 74.16 
                 74.37 
                 74.58 
               
               
                 — 
                 0.84 
                 0.84 
                 0.84 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Distances between conductors (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 74.78 
                 74.99 
                 75.20 
                 75.41 
                 75.62 
                 75.83 
                 76.04 
                 76.25 
                 76.46 
                 76.67 
                 76.88 
                 77.09 
               
               
                 — 
                 0.84 
                 0.84 
                 0.84 
                 0.85 
                 0.85 
                 0.86 
                 0.86 
                 0.87 
                 0.87 
                 0.87 
                 0.88 
                 0.88 
               
               
                 #32 
                 77.30 
                 77.51 
                 77.72 
                 77.93 
                 78.14 
                 78.35 
                 78.56 
                 78.77 
                 78.98 
                 79.19 
                 79.40 
                 79.61 
               
               
                 — 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.87 
                 0.86 
                 0.86 
                 0.85 
                 0.84 
                 0.82 
                 0.81 
                 0.79 
               
               
                 #33 
                 79.82 
                 80.03 
                 80.23 
                 80.44 
                 80.65 
                 80.86 
                 81.06 
                 81.27 
                 81.48 
                 81.68 
                 81.89 
                 82.09 
               
               
                 — 
                 0.78 
                 0.76 
                 0.74 
                 0.72 
                 0.70 
                 0.68 
                 0.66 
                 0.64 
                 0.62 
                 0.60 
                 0.58 
                 0.56 
               
               
                 #34 
                 82.30 
                 82.50 
                 82.71 
                 82.91 
                 83.12 
                 83.32 
                 83.53 
                 83.73 
                 83.93 
                 84.14 
                 84.34 
                 84.54 
               
               
                 — 
                 0.55 
                 0.53 
                 0.52 
                 0.50 
                 0.49 
                 0.48 
                 0.47 
                 0.46 
                 0.46 
                 0.45 
                 0.45 
                 0.44 
               
               
                 #35 
                 84.75 
                 84.95 
                 85.16 
                 85.36 
                 85.56 
                 85.77 
                 85.97 
                 86.17 
                 86.38 
                 86.58 
                 86.79 
                 86.99 
               
               
                 — 
                 0.44 
                 0.44 
                 0.44 
                 0.44 
                 0.45 
                 0.45 
                 0.45 
                 0.46 
                 0.46 
                 0.47 
                 0.48 
                 0.48 
               
               
                 #36 
                 87.20 
                 87.40 
                 87.60 
                 87.81 
                 88.01 
                 88.22 
                 88.42 
                 88.63 
                 88.83 
                 89.04 
                 89.24 
                 89.45 
               
               
                 — 
                 0.49 
                 0.49 
                 0.50 
                 0.50 
                 0.51 
                 0.51 
                 0.51 
                 0.52 
                 0.52 
                 0.51 
                 0.51 
                 0.51 
               
               
                 #37 
                 89.65 
                 89.86 
                 90.06 
                 90.27 
                 90.47 
                 90.67 
                 90.88 
                 91.08 
                 91.29 
                 91.49 
                 91.69 
                 91.90 
               
               
                 — 
                 0.51 
                 0.50 
                 0.49 
                 0.49 
                 0.48 
                 0.47 
                 0.47 
                 0.46 
                 0.45 
                 0.45 
                 0.44 
                 0.44 
               
               
                 #38 
                 92.10 
                 92.30 
                 92.51 
                 92.71 
                 92.91 
                 93.12 
                 93.32 
                 93.53 
                 93.73 
                 93.93 
                 94.14 
                 94.35 
               
               
                 — 
                 0.43 
                 0.43 
                 0.43 
                 0.44 
                 0.44 
                 0.45 
                 0.46 
                 0.47 
                 0.49 
                 0.51 
                 0.53 
                 0.56 
               
               
                 #39 
                 94.55 
                 94.76 
                 94.96 
                 95.17 
                 95.38 
                 95.59 
                 95.80 
                 96.01 
                 96.23 
                 96.44 
                 96.66 
                 96.88 
               
               
                 — 
                 0.59 
                 0.63 
                 0.68 
                 0.73 
                 0.79 
                 0.86 
                 0.93 
                 1.02 
                 1.11 
                 1.22 
                 1.34 
                 1.47 
               
               
                 #40 
                 97.09 
                 97.32 
                 97.54 
                 97.76 
                 97.99 
                 98.21 
                 98.44 
                 98.67 
                 98.91 
                 99.14 
                 99.37 
                 99.61 
               
               
                 — 
                 1.61 
                 1.76 
                 1.92 
                 2.09 
                 2.27 
                 2.45 
                 2.63 
                 2.81 
                 2.99 
                 3.15 
                 3.30 
                 3.42 
               
               
                 #41 
                 99.84 
                 100.08 
                 100.32 
                 100.55 
                 100.79 
                 101.02 
                 101.26 
                 101.49 
                 101.72 
                 101.95 
                 102.18 
                 102.41 
               
               
                 — 
                 3.51 
                 3.57 
                 3.60 
                 3.58 
                 3.53 
                 3.44 
                 3.32 
                 3.16 
                 2.98 
                 2.78 
                 2.56 
                 2.34 
               
               
                 #42 
                 102.63 
                 102.85 
                 103.07 
                 103.29 
                 103.51 
                 103.72 
                 103.93 
                 104.14 
                 104.35 
                 104.55 
                 104.76 
                 104.96 
               
               
                 — 
                 2.12 
                 1.90 
                 1.69 
                 1.49 
                 1.30 
                 1.13 
                 0.97 
                 0.83 
                 0.70 
                 0.59 
                 0.49 
                 0.41 
               
               
                 #43 
                 105.16 
                 105.36 
                 105.56 
                 105.76 
                 105.96 
                 106.16 
                 106.36 
                 106.56 
                 106.75 
                 106.95 
                 107.15 
                 107.34 
               
               
                 — 
                 0.34 
                 0.28 
                 0.23 
                 0.19 
                 0.15 
                 0.13 
                 0.10 
                 0.09 
                 0.07 
                 0.06 
                 0.05 
                 0.05 
               
               
                 #44 
                 107.54 
                 107.73 
                 107.93 
                 108.13 
                 108.32 
                 108.52 
                 108.71 
                 108.91 
                 109.10 
                 109.30 
                 109.50 
                 109.69 
               
               
                 — 
                 0.04 
                 0.04 
                 0.04 
                 0.03 
                 0.03 
                 0.04 
                 0.04 
                 0.04 
                 0.04 
                 0.05 
                 0.06 
                 0.07 
               
               
                 #45 
                 109.89 
                 110.09 
                 110.29 
                 110.48 
                 110.68 
                 110.88 
                 111.08 
                 111.29 
                 111.49 
                 111.69 
                 111.90 
                 112.10 
               
               
                 — 
                 0.08 
                 0.09 
                 0.11 
                 0.14 
                 0.17 
                 0.21 
                 0.25 
                 0.30 
                 0.37 
                 0.44 
                 0.53 
                 0.63 
               
               
                 #46 
                 112.31 
                 112.52 
                 112.73 
                 112.95 
                 113.16 
                 113.38 
                 113.60 
                 113.82 
                 114.05 
                 114.27 
                 114.50 
                 114.73 
               
               
                 — 
                 0.74 
                 0.87 
                 1.01 
                 1.16 
                 1.32 
                 1.50 
                 1.68 
                 1.87 
                 2.07 
                 2.26 
                 2.45 
                 2.62 
               
               
                 #47 
                 114.96 
                 115.19 
                 115.42 
                 115.65 
                 115.89 
                 116.12 
                 116.35 
                 116.59 
                 116.82 
                 117.05 
                 117.28 
                 117.51 
               
               
                 — 
                 2.78 
                 2.92 
                 3.03 
                 3.12 
                 3.17 
                 3.19 
                 3.18 
                 3.14 
                 3.07 
                 2.98 
                 2.87 
                 2.74 
               
               
                 #48 
                 117.74 
                 117.97 
                 118.19 
                 118.42 
                 118.64 
                 118.86 
                 119.09 
                 119.30 
                 119.52 
                 119.74 
                 119.95 
                 120.17 
               
               
                 — 
                 2.60 
                 2.45 
                 2.30 
                 2.15 
                 2.00 
                 1.86 
                 1.72 
                 1.59 
                 1.47 
                 1.36 
                 1.25 
                 1.16 
               
               
                 #49 
                 120.38 
                 120.59 
                 120.80 
                 121.01 
                 121.22 
                 121.43 
                 121.64 
                 121.84 
                 122.05 
                 122.26 
                 122.46 
                 122.67 
               
               
                 — 
                 1.07 
                 1.00 
                 0.93 
                 0.87 
                 0.81 
                 0.77 
                 0.73 
                 0.69 
                 0.66 
                 0.63 
                 0.61 
                 0.59 
               
               
                 #50 
                 122.88 
                 123.08 
                 123.29 
                 123.49 
                 123.70 
                 123.90 
                 124.11 
                 124.31 
                 124.52 
                 124.72 
                 124.93 
                 125.14 
               
               
                 — 
                 0.58 
                 0.57 
                 0.56 
                 0.56 
                 0.55 
                 0.55 
                 0.55 
                 0.55 
                 0.55 
                 0.56 
                 0.56 
                 0.56 
               
               
                 #51 
                 125.34 
                 125.55 
                 125.75 
                 125.96 
                 126.16 
                 126.37 
                 126.57 
                 126.78 
                 126.99 
                 127.19 
                 127.40 
                 127.60 
               
               
                 — 
                 0.57 
                 0.57 
                 0.57 
                 0.57 
                 0.57 
                 0.57 
                 0.57 
                 0.56 
                 0.56 
                 0.55 
                 0.54 
                 0.53 
               
               
                 #52 
                 127.81 
                 128.01 
                 128.22 
                 128.42 
                 128.62 
                 128.83 
                 129.03 
                 129.23 
                 129.44 
                 129.64 
                 129.84 
                 130.05 
               
               
                 — 
                 0.52 
                 0.51 
                 0.50 
                 0.49 
                 0.47 
                 0.46 
                 0.44 
                 0.43 
                 0.42 
                 0.41 
                 0.40 
                 0.38 
               
               
                 #53 
                 130.25 
                 130.45 
                 130.65 
                 130.86 
                 131.06 
                 131.26 
                 131.46 
                 131.66 
                 131.87 
                 132.07 
                 132.27 
                 132.47 
               
               
                 — 
                 0.38 
                 0.37 
                 0.36 
                 0.35 
                 0.35 
                 0.35 
                 0.34 
                 0.34 
                 0.35 
                 0.35 
                 0.35 
                 0.36 
               
               
                 #54 
                 132.68 
                 132.88 
                 133.08 
                 133.28 
                 133.49 
                 133.69 
                 133.90 
                 134.10 
                 134.30 
                 134.51 
                 134.71 
                 134.92 
               
               
                 — 
                 0.37 
                 0.38 
                 0.39 
                 0.40 
                 0.42 
                 0.43 
                 0.45 
                 0.47 
                 0.50 
                 0.52 
                 0.54 
                 0.57 
               
               
                 #55 
                 135.13 
                 135.33 
                 135.54 
                 135.75 
                 135.95 
                 136.16 
                 136.37 
                 136.58 
                 136.79 
                 137.00 
                 137.21 
                 137.42 
               
               
                 — 
                 0.60 
                 0.62 
                 0.65 
                 0.68 
                 0.71 
                 0.74 
                 0.76 
                 0.79 
                 0.82 
                 0.84 
                 0.86 
                 0.88 
               
               
                 #56 
                 137.63 
                 137.84 
                 138.05 
                 138.26 
                 138.47 
                 138.68 
                 138.89 
                 139.10 
                 139.31 
                 139.53 
                 139.74 
                 139.95 
               
               
                 — 
                 0.90 
                 0.91 
                 0.93 
                 0.94 
                 0.94 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.94 
                 0.94 
               
               
                 #57 
                 140.16 
                 140.37 
                 140.58 
                 140.79 
                 141.00 
                 141.21 
                 141.42 
                 141.63 
                 141.84 
                 142.05 
                 142.26 
                 142.47 
               
               
                 — 
                 0.93 
                 0.93 
                 0.92 
                 0.91 
                 0.90 
                 0.90 
                 0.89 
                 0.88 
                 0.88 
                 0.87 
                 0.87 
                 0.87 
               
               
                 #58 
                 142.68 
                 142.89 
                 143.10 
                 143.31 
                 143.52 
                 143.73 
                 143.94 
                 144.15 
                 144.36 
                 144.57 
                 144.78 
                 144.99 
               
               
                 — 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.88 
                 0.88 
                 0.89 
                 0.89 
                 0.90 
                 0.91 
                 0.91 
                 0.92 
               
               
                 #59 
                 145.20 
                 145.42 
                 145.63 
                 145.84 
                 146.05 
                 146.26 
                 146.47 
                 146.68 
                 146.89 
                 147.10 
                 147.32 
                 147.53 
               
               
                 — 
                 0.93 
                 0.94 
                 0.95 
                 0.95 
                 0.96 
                 0.96 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.96 
                 0.96 
               
               
                 #60 
                 147.74 
                 147.95 
                 148.16 
                 148.37 
                 148.58 
                 148.79 
                 149.00 
                 149.21 
                 149.42 
                 149.63 
                 149.84 
                 150.05 
               
               
                 — 
                 0.95 
                 0.94 
                 0.93 
                 0.92 
                 0.91 
                 0.89 
                 0.87 
                 0.86 
                 0.84 
                 0.82 
                 0.80 
                 0.78 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Distances between conductors (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 150.26 
                 150.46 
                 150.67 
                 150.88 
                 151.09 
                 151.29 
                 151.50 
                 151.71 
                 151.91 
                 152.12 
                 152.32 
                 152.53 
               
               
                 — 
                 0.76 
                 0.74 
                 0.72 
                 0.70 
                 0.68 
                 0.66 
                 0.65 
                 0.63 
                 0.61 
                 0.60 
                 0.59 
                 0.58 
               
               
                 #62 
                 152.74 
                 152.94 
                 153.15 
                 153.35 
                 153.56 
                 153.76 
                 153.97 
                 154.17 
                 154.38 
                 154.58 
                 154.79 
                 154.99 
               
               
                 — 
                 0.57 
                 0.56 
                 0.55 
                 0.55 
                 0.54 
                 0.54 
                 0.53 
                 0.53 
                 0.53 
                 0.53 
                 0.53 
                 0.54 
               
               
                 #63 
                 155.20 
                 155.40 
                 155.61 
                 155.81 
                 156.02 
                 156.22 
                 156.43 
                 156.64 
                 156.84 
                 157.05 
                 157.25 
                 157.46 
               
               
                 — 
                 0.54 
                 0.54 
                 0.55 
                 0.55 
                 0.56 
                 0.56 
                 0.57 
                 0.57 
                 0.58 
                 0.58 
                 0.59 
                 0.59 
               
               
                 #64 
                 157.66 
                 157.87 
                 158.08 
                 158.28 
                 158.49 
                 158.70 
                 158.90 
                 159.11 
                 159.31 
                 150.52 
                 159.73 
                 159.93 
               
               
                 — 
                 0.60 
                 0.60 
                 0.60 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
                 0.61 
               
               
                 #65 
                 160.14 
                 160.35 
                 160.55 
                 160.76 
                 160.96 
                 161.17 
                 161.38 
                 161.58 
                 161.79 
                 161.99 
                 162.20 
                 162.41 
               
               
                 — 
                 0.61 
                 0.61 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
               
               
                 #66 
                 162.61 
                 162.82 
                 163.02 
                 163.23 
                 163.44 
                 163.64 
                 163.85 
                 164.06 
                 164.26 
                 164.47 
                 164.68 
                 164.88 
               
               
                 — 
                 0.60 
                 0.60 
                 0.60 
                 0.61 
                 0.61 
                 0.62 
                 0.63 
                 0.63 
                 0.64 
                 0.65 
                 0.66 
                 0.67 
               
               
                 #67 
                 165.09 
                 165.30 
                 165.51 
                 165.71 
                 165.92 
                 166.13 
                 166.34 
                 166.55 
                 166.75 
                 166.96 
                 167.17 
                 167.38 
               
               
                 — 
                 0.68 
                 0.69 
                 0.70 
                 0.72 
                 0.73 
                 0.74 
                 0.75 
                 0.77 
                 0.78 
                 0.79 
                 0.80 
                 0.81 
               
               
                 #68 
                 167.59 
                 167.80 
                 168.01 
                 168.22 
                 168.43 
                 168.64 
                 168.85 
                 169.06 
                 169.27 
                 169.48 
                 169.69 
                 169.90 
               
               
                 — 
                 0.82 
                 0.83 
                 0.84 
                 0.85 
                 0.85 
                 0.86 
                 0.86 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
               
               
                 #69 
                 170.11 
                 170.32 
                 170.53 
                 170.74 
                 170.95 
                 171.16 
                 171.37 
                 171.58 
                 171.78 
                 171.99 
                 172.20 
                 172.41 
               
               
                 — 
                 0.86 
                 0.86 
                 0.86 
                 0.85 
                 0.85 
                 0.84 
                 0.83 
                 0.83 
                 0.82 
                 0.81 
                 0.81 
                 0.80 
               
               
                 #70 
                 172.62 
                 172.83 
                 173.04 
                 173.25 
                 173.46 
                 173.66 
                 173.87 
                 174.08 
                 174.29 
                 174.50 
                 174.71 
                 174.91 
               
               
                 — 
                 0.79 
                 0.79 
                 0.78 
                 0.78 
                 0.77 
                 0.77 
                 0.76 
                 0.76 
                 0.76 
                 0.75 
                 0.75 
                 0.75 
               
               
                 #71 
                 175.12 
                 175.33 
                 175.54 
                 175.75 
                 175.95 
                 176.16 
                 176.37 
                 176.58 
                 176.79 
                 177.00 
                 177.20 
                 177.41 
               
               
                 — 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
               
               
                 #72 
                 177.62 
                 177.83 
                 178.04 
                 178.25 
                 178.45 
                 178.66 
                 178.87 
                 179.08 
                 179.29 
                 179.49 
                 179.70 
                 179.91 
               
               
                 — 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.74 
                 0.74 
                 0.74 
                 0.73 
                 0.73 
                 0.72 
                 0.72 
                 0.71 
               
               
                 #73 
                 180.12 
                 180.32 
                 180.53 
                 180.74 
                 180.95 
                 181.15 
                 181.36 
                 181.57 
                 181.77 
                 181.98 
                 182.19 
                 182.39 
               
               
                 — 
                 0.71 
                 0.70 
                 0.69 
                 0.69 
                 0.68 
                 0.67 
                 0.66 
                 0.66 
                 0.65 
                 0.64 
                 0.64 
                 0.63 
               
               
                 #74 
                 182.60 
                 182.81 
                 183.01 
                 183.22 
                 183.43 
                 183.63 
                 183.84 
                 184.04 
                 184.25 
                 184.46 
                 184.66 
                 184.87 
               
               
                 — 
                 0.62 
                 0.62 
                 0.61 
                 0.61 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.59 
                 0.59 
                 0.59 
                 0.59 
               
               
                 #75 
                 185.07 
                 185.28 
                 185.49 
                 185.69 
                 185.90 
                 186.10 
                 186.31 
                 186.52 
                 186.72 
                 186.93 
                 187.14 
                 187.34 
               
               
                 — 
                 0.59 
                 0.60 
                 0.60 
                 0.60 
                 0.60 
                 0.61 
                 0.61 
                 0.62 
                 0.62 
                 0.62 
                 0.63 
                 0.64 
               
               
                 #76 
                 187.55 
                 187.76 
                 187.96 
                 188.17 
                 188.38 
                 188.58 
                 188.79 
                 189.00 
                 189.20 
                 189.41 
                 189.62 
                 189.83 
               
               
                 — 
                 0.64 
                 0.65 
                 0.65 
                 0.66 
                 0.66 
                 0.67 
                 0.67 
                 0.67 
                 0.68 
                 0.68 
                 0.68 
                 0.69 
               
               
                 #77 
                 190.03 
                 190.24 
                 190.45 
                 190.66 
                 190.86 
                 191.07 
                 191.28 
                 191.49 
                 191.69 
                 191.90 
                 192.11 
                 192.32 
               
               
                 — 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
               
               
                 #78 
                 192.52 
                 192.73 
                 192.94 
                 193.15 
                 193.35 
                 193.56 
                 193.77 
                 193.98 
                 194.18 
                 194.30 
                 194.60 
                 194.81 
               
               
                 — 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.70 
                 0.71 
                 0.71 
               
               
                 #79 
                 195.01 
                 195.22 
                 195.43 
                 195.64 
                 195.85 
                 196.05 
                 196.26 
                 196.47 
                 196.68 
                 196.89 
                 197.09 
                 197.30 
               
               
                 — 
                 0.71 
                 0.72 
                 0.72 
                 0.72 
                 0.73 
                 0.73 
                 0.74 
                 0.74 
                 0.75 
                 0.75 
                 0.76 
                 0.76 
               
               
                 #80 
                 197.51 
                 197.72 
                 197.93 
                 198.14 
                 198.35 
                 198.55 
                 198.76 
                 198.97 
                 199.18 
                 199.39 
                 199.60 
                 199.81 
               
               
                 — 
                 0.76 
                 0.77 
                 0.77 
                 0.78 
                 0.78 
                 0.78 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
               
               
                 #81 
                 200.02 
                 200.23 
                 200.43 
                 200.64 
                 200.85 
                 201.06 
                 201.27 
                 201.48 
                 201.69 
                 201.90 
                 202.10 
                 202.31 
               
               
                 — 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.78 
                 0.78 
                 0.78 
                 0.77 
                 0.77 
                 0.76 
                 0.76 
               
               
                 #82 
                 202.52 
                 202.73 
                 202.94 
                 203.14 
                 203.35 
                 203.56 
                 203.77 
                 203.98 
                 204.18 
                 204.39 
                 204.60 
                 204.81 
               
               
                 — 
                 0.75 
                 0.75 
                 0.74 
                 0.74 
                 0.73 
                 0.73 
                 0.72 
                 0.72 
                 0.71 
                 0.71 
                 0.71 
                 0.70 
               
               
                 #83 
                 205.01 
                 205.22 
                 205.43 
                 205.64 
                 205.84 
                 206.05 
                 206.26 
                 206.47 
                 206.67 
                 206.88 
                 207.09 
                 207.30 
               
               
                 — 
                 0.70 
                 0.70 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
               
               
                 #84 
                 207.50 
                 207.71 
                 207.92 
                 208.12 
                 208.33 
               
               
                 — 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
                 0.69 
               
               
                   
               
             
          
         
       
     
       FIG. 6  shows the shape of the coplanar strip in the reflection-type bandpass filter  1  of Embodiment 1. In the figure, the lightly shaded portion represents the center conductor  3  and the side conductors  5   a  and  5   b , and the heavily shaded lines represent the non-conducting portions  4   a  and  4   b . A non-reflecting terminator, or an R=75Ω resistance, is provided on the terminating side (the face at z=208.33 mm) of this reflection-type bandpass filter  1 . The non-reflecting terminator or resistance may be connected directly to the terminating end of the reflection-type bandpass filter  1 . The thicknesses of the metal films of the center conductor  3  and of the side conductors  5   a ,  5   b  are to be thick compared with the skin depth at f=1 GHz, δs=√{2/(ωμ 0 σ)}. Here ω, μ 0 , and σ are respectively the angular frequency, permittivity in a vacuum, and the conductivity of the metal. For example, when using copper, the thickness of the center conductor  3  and of the side conductors  5   a ,  5   b  may be 2.1 μm or greater. This bandpass filter  1  is used in a system with a characteristic impedance of 75Ω. 
       FIG. 7  and  FIG. 8  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter  1  of Embodiment 1. As shown in the figures, in the range of frequencies f for which 3.9 GHz≦f≦9.8 GHz, the reflectance is −2 dB or greater, and the group delay variation is within ±0.1 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −15 dB or lower. 
     Embodiment 2 
     A Kaiser window was used for which the reflectance is 0.8 at frequencies f in the range 3.4 GHz≦f≦10.3 GHz, and is 0 elsewhere, and for which A=30. Design was performed using one wavelength of signals at a frequency f=1 GHz propagating in the coplanar strip as the waveguide length, and setting the system characteristic impedance to 75Ω.  FIG. 9  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 10  shows the distribution in the z-axis direction of the center conductor width w, when using a substrate  2  with a thickness h=1 mm and relative permittivity ∈ r =10, and when the distance between conductors s=0.5 mm. Tables 4 through 6 list the center conductor widths w. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Center conductor widths (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.13 
                 0.26 
                 0.39 
                 0.52 
                 0.65 
                 0.78 
                 0.92 
                 1.05 
                 1.18 
                 1.31 
                 1.44 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 1.57 
                 1.70 
                 1.83 
                 1.96 
                 2.09 
                 2.22 
                 2.35 
                 2.48 
                 2.62 
                 2.75 
                 2.88 
                 3.01 
               
               
                 — 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.28 
                 0.28 
                 0.28 
               
               
                  #3 
                 3.14 
                 3.27 
                 3.40 
                 3.53 
                 3.66 
                 3.79 
                 3.92 
                 4.05 
                 4.18 
                 4.31 
                 4.45 
                 4.58 
               
               
                 — 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                  #4 
                 4.71 
                 4.84 
                 4.97 
                 5.10 
                 5.23 
                 5.36 
                 5.49 
                 5.62 
                 5.75 
                 5.88 
                 6.01 
                 6.14 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                  #5 
                 6.27 
                 6.41 
                 6.54 
                 6.67 
                 6.80 
                 6.93 
                 7.06 
                 7.19 
                 7.32 
                 7.45 
                 7.58 
                 7.71 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                  #6 
                 7.84 
                 7.97 
                 8.10 
                 8.23 
                 8.37 
                 8.50 
                 8.63 
                 8.76 
                 8.89 
                 9.02 
                 9.15 
                 9.28 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                  #7 
                 9.41 
                 9.54 
                 9.67 
                 9.80 
                 9.93 
                 10.06 
                 10.20 
                 10.33 
                 10.46 
                 10.59 
                 10.72 
                 10.85 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                  #8 
                 10.98 
                 11.11 
                 11.24 
                 11.37 
                 11.50 
                 11.63 
                 11.76 
                 11.89 
                 12.02 
                 12.16 
                 12.29 
                 12.42 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
               
               
                  #9 
                 12.55 
                 12.68 
                 12.81 
                 12.94 
                 13.07 
                 13.20 
                 13.33 
                 13.46 
                 13.59 
                 13.72 
                 13.86 
                 13.99 
               
               
                 — 
                 0.28 
                 0.28 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #10 
                 14.12 
                 14.25 
                 14.38 
                 14.51 
                 14.64 
                 14.77 
                 14.90 
                 15.03 
                 15.16 
                 15.30 
                 15.43 
                 15.56 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #11 
                 15.69 
                 15.82 
                 15.95 
                 16.08 
                 16.21 
                 16.34 
                 16.47 
                 16.60 
                 16.73 
                 16.87 
                 17.00 
                 17.13 
               
               
                 — 
                 0.31 
                 0.31 
                 0.31 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #12 
                 17.26 
                 17.39 
                 17.52 
                 17.65 
                 17.78 
                 17.91 
                 18.04 
                 18.17 
                 18.30 
                 18.44 
                 18.57 
                 18.70 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #13 
                 18.83 
                 18.96 
                 19.09 
                 19.22 
                 19.35 
                 19.48 
                 19.61 
                 19.74 
                 19.88 
                 20.01 
                 20.14 
                 20.27 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #14 
                 20.40 
                 20.53 
                 20.66 
                 20.79 
                 20.92 
                 21.05 
                 21.18 
                 21.31 
                 21.45 
                 21.58 
                 21.71 
                 21.84 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
               
               
                 #15 
                 21.97 
                 22.10 
                 22.23 
                 22.36 
                 22.49 
                 22.62 
                 22.75 
                 22.88 
                 23.01 
                 23.14 
                 23.28 
                 23.41 
               
               
                 — 
                 0.29 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.26 
                 0.26 
               
               
                 #16 
                 23.54 
                 23.67 
                 23.80 
                 23.93 
                 24.06 
                 24.19 
                 24.32 
                 24.45 
                 24.58 
                 24.71 
                 24.84 
                 24.97 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
               
               
                 #17 
                 25.10 
                 25.23 
                 25.36 
                 25.49 
                 25.63 
                 25.76 
                 25.89 
                 26.02 
                 26.15 
                 26.28 
                 26.41 
                 26.54 
               
               
                 — 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #18 
                 26.67 
                 26.80 
                 26.93 
                 27.06 
                 27.19 
                 27.32 
                 27.45 
                 27.58 
                 27.71 
                 27.85 
                 27.98 
                 28.11 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #19 
                 28.24 
                 28.37 
                 28.50 
                 28.63 
                 28.76 
                 28.89 
                 29.02 
                 29.15 
                 29.28 
                 29.41 
                 29.54 
                 29.67 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #20 
                 29.80 
                 29.93 
                 30.07 
                 30.20 
                 30.33 
                 30.46 
                 30.59 
                 30.72 
                 30.85 
                 30.98 
                 31.11 
                 31.24 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                 #21 
                 31.37 
                 31.50 
                 31.63 
                 31.76 
                 31.89 
                 32.03 
                 32.16 
                 32.29 
                 32.42 
                 32.55 
                 32.68 
                 32.81 
               
               
                 — 
                 0.28 
                 0.28 
                 0.28 
                 0.29 
                 0.29 
                 0.29 
                 0.30 
                 0.39 
                 0.30 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #22 
                 32.94 
                 33.07 
                 33.20 
                 33.33 
                 33.47 
                 33.60 
                 33.73 
                 33.86 
                 33.99 
                 34.12 
                 34.25 
                 34.38 
               
               
                 — 
                 0.32 
                 0.32 
                 0.32 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.34 
                 0.34 
               
               
                 #23 
                 34.51 
                 34.65 
                 34.78 
                 34.91 
                 35.04 
                 35.17 
                 35.30 
                 35.43 
                 35.56 
                 35.69 
                 35.82 
                 35.96 
               
               
                 — 
                 0.34 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.32 
                 0.32 
               
               
                 #24 
                 36.09 
                 36.22 
                 36.35 
                 36.48 
                 36.61 
                 36.74 
                 36.87 
                 37.00 
                 37.13 
                 37.27 
                 37.40 
                 37.53 
               
               
                 — 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
               
               
                 #25 
                 37.66 
                 37.79 
                 37.92 
                 38.05 
                 38.18 
                 38.31 
                 38.44 
                 38.58 
                 38.71 
                 38.84 
                 38.97 
                 39.10 
               
               
                 — 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
               
               
                 #26 
                 39.23 
                 39.36 
                 39.49 
                 39.62 
                 39.75 
                 39.89 
                 40.02 
                 40.15 
                 40.28 
                 40.41 
                 40.54 
                 40.67 
               
               
                 — 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.33 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.31 
                 0.31 
                 0.30 
               
               
                 #27 
                 40.80 
                 40.93 
                 41.06 
                 41.19 
                 41.33 
                 41.46 
                 41.59 
                 41.72 
                 41.85 
                 41.98 
                 42.11 
                 42.24 
               
               
                 — 
                 0.30 
                 0.29 
                 0.29 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
                 0.26 
                 0.26 
                 0.25 
                 0.25 
                 0.24 
               
               
                 #28 
                 42.37 
                 42.50 
                 42.63 
                 42.76 
                 42.89 
                 43.02 
                 43.15 
                 43.28 
                 43.41 
                 43.54 
                 43.67 
                 43.80 
               
               
                 — 
                 0.24 
                 0.24 
                 0.23 
                 0.23 
                 0.23 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
               
               
                 #29 
                 43.93 
                 44.06 
                 44.20 
                 44.33 
                 44.46 
                 44.59 
                 44.72 
                 44.85 
                 44.98 
                 45.11 
                 45.24 
                 45.37 
               
               
                 — 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.23 
                 0.23 
                 0.23 
               
               
                 #30 
                 45.50 
                 45.63 
                 45.76 
                 45.89 
                 46.02 
                 46.15 
                 46.28 
                 46.41 
                 46.54 
                 46.67 
                 46.80 
                 46.93 
               
               
                 — 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.23 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 Center conductor widths (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                  47.06 
                  47.19 
                  47.32 
                  47.46 
                  47.59 
                  47.72 
                  47.85 
                  47.98 
                  48.11 
                  48.24 
                  48.37 
                  48.50 
               
               
                 — 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
                 0.23 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
               
               
                 #32 
                 48.63 
                 48.76 
                 48.89 
                 49.02 
                 49.15 
                 49.28 
                 49.41 
                 49.54 
                 49.67 
                 49.80 
                 49.93 
                 50.06 
               
               
                 — 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.23 
                 0.23 
                 0.23 
                 0.24 
                 0.24 
                 0.25 
               
               
                 #33 
                 50.19 
                 50.32 
                 50.45 
                 50.59 
                 50.72 
                 50.85 
                 50.98 
                 51.11 
                 51.24 
                 51.37 
                 51.50 
                 51.63 
               
               
                 — 
                 0.25 
                 0.26 
                 0.27 
                 0.28 
                 0.29 
                 0.30 
                 0.31 
                 0.32 
                 0.33 
                 0.34 
                 0.35 
                 0.36 
               
               
                 #34 
                 51.76 
                 51.90 
                 52.03 
                 52.16 
                 52.29 
                 52.42 
                 52.55 
                 52.69 
                 52.82 
                 52.95 
                 53.08 
                 53.21 
               
               
                 — 
                 0.37 
                 0.39 
                 0.40 
                 0.41 
                 0.42 
                 0.43 
                 0.44 
                 0.44 
                 0.45 
                 0.46 
                 0.46 
                 0.46 
               
               
                 #35 
                 53.35 
                 53.48 
                 53.61 
                 53.74 
                 53.87 
                 54.01 
                 54.14 
                 54.27 
                 54.40 
                 54.53 
                 54.66 
                 54.80 
               
               
                 — 
                 0.47 
                 0.47 
                 0.47 
                 0.46 
                 0.46 
                 0.46 
                 0.45 
                 0.45 
                 0.44 
                 0.44 
                 0.43 
                 0.42 
               
               
                 #36 
                 54.93 
                 55.06 
                 55.19 
                 55.32 
                 55.45 
                 55.58 
                 55.72 
                 55.85 
                 55.98 
                 56.11 
                 56.24 
                 56.37 
               
               
                 — 
                 0.42 
                 0.41 
                 0.41 
                 0.41 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
               
               
                 #37 
                 56.51 
                 56.64 
                 56.77 
                 56.90 
                 57.03 
                 57.16 
                 57.30 
                 57.43 
                 57.56 
                 57.69 
                 57.82 
                 57.95 
               
               
                 — 
                 0.41 
                 0.41 
                 0.41 
                 0.42 
                 0.43 
                 0.43 
                 0.44 
                 0.45 
                 0.45 
                 0.46 
                 0.47 
                 0.47 
               
               
                 #38 
                 58.09 
                 58.22 
                 58.35 
                 58.48 
                 58.61 
                 58.75 
                 58.88 
                 59.01 
                 59.14 
                 59.27 
                 59.40 
                 59.54 
               
               
                 — 
                 0.47 
                 0.48 
                 0.47 
                 0.47 
                 0.47 
                 0.46 
                 0.45 
                 0.44 
                 0.42 
                 0.40 
                 0.39 
                 0.36 
               
               
                 #39 
                 59.67 
                 59.80 
                 59.93 
                 60.06 
                 60.19 
                 60.32 
                 60.45 
                 60.58 
                 60.71 
                 60.84 
                 60.97 
                 61.10 
               
               
                 — 
                 0.34 
                 0.32 
                 0.30 
                 0.27 
                 0.25 
                 0.23 
                 0.20 
                 0.18 
                 0.16 
                 0.15 
                 0.13 
                 0.12 
               
               
                 #40 
                 61.23 
                 61.36 
                 61.49 
                 61.62 
                 61.75 
                 61.88 
                 62.01 
                 62.14 
                 62.26 
                 62.39 
                 62.52 
                 62.65 
               
               
                 — 
                 0.10 
                 0.09 
                 0.08 
                 0.07 
                 0.06 
                 0.05 
                 0.05 
                 0.04 
                 0.04 
                 0.04 
                 0.03 
                 0.03 
               
               
                 #41 
                 62.78 
                 62.91 
                 63.04 
                 63.17 
                 63.30 
                 63.43 
                 63.55 
                 63.68 
                 63.81 
                 63.94 
                 64.07 
                 64.20 
               
               
                 — 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.04 
                 0.04 
                 0.05 
                 0.05 
                 0.06 
               
               
                 #42 
                 64.33 
                 64.46 
                 64.59 
                 64.72 
                 64.85 
                 64.98 
                 65.11 
                 65.24 
                 65.37 
                 65.50 
                 65.63 
                 65.76 
               
               
                 — 
                 0.07 
                 0.08 
                 0.10 
                 0.11 
                 0.14 
                 0.16 
                 0.20 
                 0.24 
                 0.28 
                 0.34 
                 0.41 
                 0.50 
               
               
                 #43 
                 65.90 
                 66.03 
                 66.17 
                 66.30 
                 66.44 
                 66.58 
                 66.72 
                 66.86 
                 67.01 
                 67.15 
                 67.30 
                 67.45 
               
               
                 — 
                 0.60 
                 0.72 
                 0.86 
                 1.03 
                 1.24 
                 1.49 
                 1.79 
                 2.14 
                 2.54 
                 2.98 
                 3.44 
                 3.90 
               
               
                 #44 
                 67.61 
                 67.76 
                 67.91 
                 68.07 
                 68.22 
                 68.38 
                 68.53 
                 68.68 
                 68.83 
                 68.98 
                 69.13 
                 69.27 
               
               
                 — 
                 4.32 
                 4.66 
                 4.90 
                 5.02 
                 5.00 
                 4.84 
                 4.57 
                 4.20 
                 3.78 
                 3.33 
                 2.88 
                 2.46 
               
               
                 #45 
                 69.42 
                 69.56 
                 69.70 
                 69.83 
                 69.97 
                 70.10 
                 70.24 
                 70.37 
                 70.50 
                 70.63 
                 70.77 
                 70.90 
               
               
                 — 
                 2.08 
                 1.76 
                 1.48 
                 1.24 
                 1.05 
                 0.88 
                 0.75 
                 0.63 
                 0.54 
                 0.46 
                 0.39 
                 0.33 
               
               
                 #46 
                 71.03 
                 71.16 
                 71.29 
                 71.42 
                 71.55 
                 71.68 
                 71.81 
                 71.94 
                 72.07 
                 72.20 
                 72.33 
                 72.46 
               
               
                 — 
                 0.28 
                 0.24 
                 0.21 
                 0.18 
                 0.16 
                 0.14 
                 0.12 
                 0.11 
                 0.10 
                 0.09 
                 0.08 
                 0.08 
               
               
                 #47 
                 72.59 
                 72.71 
                 72.84 
                 72.97 
                 73.10 
                 73.23 
                 73.36 
                 73.49 
                 73.62 
                 73.75 
                 73.88 
                 74.01 
               
               
                 — 
                 0.07 
                 0.07 
                 0.07 
                 0.06 
                 0.06 
                 0.06 
                 0.06 
                 0.07 
                 0.07 
                 0.07 
                 0.07 
                 0.08 
               
               
                 #48 
                 74.14 
                 74.27 
                 74.40 
                 74.53 
                 74.66 
                 74.79 
                 74.92 
                 75.05 
                 75.18 
                 75.30 
                 75.43 
                 75.56 
               
               
                 — 
                 0.08 
                 0.09 
                 0.10 
                 0.10 
                 0.11 
                 0.12 
                 0.13 
                 0.13 
                 0.14 
                 0.15 
                 0.16 
                 0.17 
               
               
                 #49 
                 75.70 
                 75.83 
                 75.96 
                 76.09 
                 76.22 
                 76.35 
                 76.48 
                 76.61 
                 76.74 
                 76.87 
                 77.00 
                 77.13 
               
               
                 — 
                 0.18 
                 0.19 
                 0.20 
                 0.20 
                 0.21 
                 0.22 
                 0.22 
                 0.23 
                 0.23 
                 0.23 
                 0.24 
                 0.24 
               
               
                 #50 
                 77.26 
                 77.39 
                 77.52 
                 77.65 
                 77.78 
                 77.91 
                 78.04 
                 78.17 
                 78.30 
                 78.43 
                 78.56 
                 78.69 
               
               
                 — 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
               
               
                 #51 
                 78.82 
                 78.96 
                 79.09 
                 79.22 
                 79.35 
                 79.48 
                 79.61 
                 79.74 
                 79.87 
                 80.00 
                 80.13 
                 80.26 
               
               
                 — 
                 0.25 
                 0.25 
                 0.25 
                 0.26 
                 0.26 
                 0.27 
                 0.28 
                 0.29 
                 0.29 
                 0.30 
                 0.32 
                 0.33 
               
               
                 #52 
                 80.39 
                 80.53 
                 80.66 
                 80.79 
                 80.92 
                 81.05 
                 81.18 
                 81.31 
                 81.45 
                 81.58 
                 81.71 
                 81.84 
               
               
                 — 
                 0.34 
                 0.35 
                 0.37 
                 0.38 
                 0.40 
                 0.42 
                 0.43 
                 0.45 
                 0.46 
                 0.48 
                 0.49 
                 0.51 
               
               
                 #53 
                 81.98 
                 82.11 
                 82.24 
                 82.37 
                 82.50 
                 82.64 
                 82.77 
                 82.90 
                 83.03 
                 83.17 
                 83.30 
                 83.43 
               
               
                 — 
                 0.52 
                 0.53 
                 0.54 
                 0.54 
                 0.55 
                 0.55 
                 0.55 
                 0.55 
                 0.55 
                 0.54 
                 0.53 
                 0.52 
               
               
                 #54 
                 83.56 
                 83.70 
                 83.83 
                 83.96 
                 84.09 
                 84.22 
                 84.36 
                 84.49 
                 84.62 
                 84.75 
                 84.88 
                 85.01 
               
               
                 — 
                 0.51 
                 0.50 
                 0.49 
                 0.47 
                 0.46 
                 0.44 
                 0.43 
                 0.42 
                 0.40 
                 0.39 
                 0.38 
                 0.36 
               
               
                 #55 
                 85.14 
                 85.28 
                 85.41 
                 85.54 
                 85.67 
                 85.80 
                 85.93 
                 86.06 
                 86.19 
                 86.32 
                 86.45 
                 86.58 
               
               
                 — 
                 0.35 
                 0.34 
                 0.33 
                 0.32 
                 0.32 
                 0.31 
                 0.30 
                 0.30 
                 0.29 
                 0.29 
                 0.28 
                 0.28 
               
               
                 #56 
                 86.71 
                 86.85 
                 86.98 
                 87.11 
                 87.24 
                 87.37 
                 87.50 
                 87.63 
                 87.76 
                 87.89 
                 88.02 
                 88.15 
               
               
                 — 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
               
               
                 #57 
                 88.28 
                 88.41 
                 88.54 
                 88.68 
                 88.81 
                 88.94 
                 89.07 
                 89.20 
                 89.33 
                 89.46 
                 89.59 
                 89.72 
               
               
                 — 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.26 
                 0.26 
                 0.26 
                 0.25 
               
               
                 #58 
                 89.85 
                 89.98 
                 90.11 
                 90.24 
                 90.37 
                 90.50 
                 90.63 
                 90.76 
                 90.89 
                 91.02 
                 91.15 
                 91.28 
               
               
                 — 
                 0.25 
                 0.24 
                 0.24 
                 0.23 
                 0.23 
                 0.23 
                 0.22 
                 0.22 
                 0.21 
                 0.21 
                 0.21 
                 0.20 
               
               
                 #59 
                 91.41 
                 91.54 
                 91.68 
                 91.81 
                 91.94 
                 92.07 
                 92.20 
                 92.33 
                 92.46 
                 92.59 
                 92.72 
                 92.85 
               
               
                 — 
                 0.20 
                 0.20 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
                 0.19 
               
               
                 #60 
                 92.98 
                 93.11 
                 93.24 
                 93.37 
                 93.50 
                 93.63 
                 93.76 
                 93.89 
                 94.02 
                 94.15 
                 94.28 
                 94.41 
               
               
                 — 
                 0.20 
                 0.20 
                 0.20 
                 0.21 
                 0.21 
                 0.21 
                 0.22 
                 0.22 
                 0.23 
                 0.23 
                 0.24 
                 0.24 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Center conductor widths (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 94.54 
                 94.67 
                 94.80 
                 94.93 
                 95.06 
                 95.19 
                 95.32 
                 95.46 
                 95.59 
                 95.72 
                 95.85 
                 95.98 
               
               
                 — 
                 0.25 
                 0.25 
                 0.26 
                 0.26 
                 0.27 
                 0.27 
                 0.28 
                 0.28 
                 0.29 
                 0.29 
                 0.29 
                 0.30 
               
               
                 #62 
                 96.11 
                 96.24 
                 96.37 
                 96.50 
                 96.63 
                 96.76 
                 96.90 
                 97.03 
                 97.16 
                 97.29 
                 97.42 
                 97.55 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #63 
                 97.68 
                 97.81 
                 97.94 
                 98.07 
                 98.20 
                 98.33 
                 98.47 
                 98.60 
                 98.73 
                 98.86 
                 98.99 
                 99.12 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #64 
                 99.25 
                 99.38 
                 99.51 
                 99.64 
                 99.78 
                 99.91 
                 100.04 
                 100.17 
                 100.30 
                 100.43 
                 100.56 
                 100.69 
               
               
                 — 
                 0.31 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.33 
                 0.33 
                 0.33 
                 0.34 
                 0.34 
                 0.34 
                 0.35 
               
               
                 #65 
                 100.82 
                 100.96 
                 101.09 
                 101.22 
                 101.35 
                 101.48 
                 101.61 
                 101.74 
                 101.87 
                 102.01 
                 102.14 
                 102.27 
               
               
                 — 
                 0.35 
                 0.35 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
                 0.36 
               
               
                 #66 
                 102.40 
                 102.53 
                 102.66 
                 102.79 
                 102.92 
                 103.05 
                 103.19 
                 103.32 
                 103.45 
                 103.58 
                 103.71 
                 103.84 
               
               
                 — 
                 0.36 
                 0.36 
                 0.35 
                 0.35 
                 0.35 
                 0.34 
                 0.34 
                 0.33 
                 0.33 
                 0.32 
                 0.32 
                 0.31 
               
               
                 #67 
                 103.97 
                 104.10 
                 104.23 
                 104.36 
                 104.50 
                 104.63 
                 104.76 
                 104.89 
                 105.02 
                 105.15 
                 105.28 
                 105.41 
               
               
                 — 
                 0.31 
                 0.30 
                 0.30 
                 0.30 
                 0.29 
                 0.29 
                 0.28 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
                 0.27 
               
               
                 #68 
                 105.54 
                 105.67 
                 105.80 
                 105.93 
                 106.06 
                 106.19 
                 106.32 
                 106.46 
                 106.59 
                 106.72 
                 106.85 
                 106.98 
               
               
                 — 
                 0.27 
                 0.27 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #69 
                 107.11 
                 107.24 
                 107.37 
                 107.50 
                 107.63 
                 107.76 
                 107.89 
                 108.02 
                 108.15 
                 108.28 
                 108.41 
                 108.54 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #70 
                 108.68 
                 108.81 
                 108.94 
                 109.07 
                 109.20 
                 109.33 
                 109.46 
                 109.59 
                 109.72 
                 109.85 
                 109.98 
                 110.11 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
               
               
                 #71 
                 110.24 
                 110.37 
                 110.50 
                 110.63 
                 110.76 
                 110.90 
                 111.03 
                 111.16 
                 111.29 
                 111.42 
                 111.55 
                 111.68 
               
               
                 — 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
                 0.24 
               
               
                 #72 
                 111.81 
                 111.94 
                 112.07 
                 112.20 
                 112.33 
                 112.46 
                 112.59 
                 112.72 
                 112.85 
                 112.98 
                 113.11 
                 113.24 
               
               
                 — 
                 0.24 
                 0.24 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.25 
                 0.26 
                 0.26 
                 0.26 
                 0.27 
               
               
                 #73 
                 113.38 
                 113.51 
                 113.64 
                 113.77 
                 113.90 
                 114.03 
                 114.16 
                 114.29 
                 114.42 
                 114.55 
                 114.68 
                 114.81 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.28 
                 0.28 
                 0.28 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.30 
                 0.30 
               
               
                 #74 
                 114.94 
                 115.08 
                 115.21 
                 115.34 
                 115.47 
                 115.60 
                 115.73 
                 115.86 
                 115.99 
                 116.12 
                 116.25 
                 116.38 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #75 
                 116.52 
                 116.65 
                 116.78 
                 116.91 
                 117.04 
                 117.17 
                 117.30 
                 117.43 
                 117.56 
                 117.69 
                 117.82 
                 117.95 
               
               
                 — 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #76 
                 118.09 
                 118.22 
                 118.35 
                 118.48 
                 118.61 
                 118.74 
                 118.87 
                 119.00 
                 119.13 
                 119.26 
                 119.39 
                 119.53 
               
               
                 — 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.31 
               
               
                 #77 
                 119.66 
                 119.79 
                 119.92 
                 120.05 
                 120.18 
                 120.31 
                 120.44 
                 120.57 
                 120.70 
                 120.83 
                 120.97 
                 121.10 
               
               
                 — 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
               
               
                 #78 
                 121.23 
                 121.36 
                 121.49 
                 121.62 
                 121.75 
                 121.88 
                 122.01 
                 122.14 
                 122.27 
                 122.41 
                 122.54 
                 122.67 
               
               
                 — 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.31 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 #79 
                 122.80 
                 122.93 
                 123.06 
                 123.19 
                 123.32 
                 123.45 
                 123.58 
                 123.71 
                 123.84 
                 123.97 
                 124.11 
                 124.24 
               
               
                 — 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.29 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.28 
                 0.27 
                 0.27 
               
               
                 #80 
                 124.37 
                 124.50 
                 124.63 
                 124.76 
                 124.89 
                 125.02 
                 125.15 
                 125.28 
                 125.41 
                 125.54 
                 125.67 
                 125.80 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
               
               
                 #81 
                 125.93 
                 126.06 
                 126.20 
                 126.33 
                 126.46 
                 126.59 
                 126.72 
                 126.85 
                 126.98 
                 127.11 
                 127.24 
                 127.37 
               
               
                 — 
                 0.26 
                 0.26 
                 0.26 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                 #82 
                 127.50 
                 127.63 
                 127.76 
                 127.89 
                 128.02 
                 128.16 
                 128.29 
                 128.42 
                 128.55 
                 128.68 
                 128.81 
                 128.94 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                 #83 
                 129.07 
                 129.20 
                 129.33 
                 129.46 
                 129.59 
                 129.72 
                 129.85 
                 129.98 
                 130.12 
                 130.25 
                 130.38 
                 130.51 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                 #84 
                 130.64 
                 130.77 
                 130.90 
                 131.03 
                 131.16 
               
               
                 — 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                   
               
             
          
         
       
     
       FIG. 11  shows the shape of the coplanar strip in the reflection-type bandpass filter  1  of Embodiment 2. In the figure, the lightly shaded portion represents the center conductor  3  and the side conductors  5   a  and  5   b , and the heavily shaded lines represent the non-conducting portions  4   a  and  4   b . A non-reflecting terminator, or an R=75Ω resistance, is provided on the terminating side (the face at z=131.16 mm) of this reflection-type bandpass filter  1 . The thicknesses of the metal films of the center conductor  3  and of the side conductors  5   a ,  5   b  are to be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the center conductor  3  and of the side conductors  5   a ,  5   b  may be 2.1 μm or greater. This bandpass filter  1  is used in a system with a characteristic impedance of 75Ω. 
       FIG. 12  and  FIG. 13  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter  1  of Embodiment 2. As shown in the figures, in the range of frequencies f for which 3.7 GHz≦f≦10.0 GHz, the reflectance is −5 dB or greater, and the group delay variation is within ±0.1 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −20 dB or lower. 
     Embodiment 3 
     A Kaiser window was used for which the reflectance is 1 at frequencies f in the range 3.7 GHz≦f≦10.0 GHz, and is 0 elsewhere, and for which A=30. Design was performed using 0.3 wavelength of signals at frequency f=1 GHz propagating in the coplanar strip as the waveguide length, and setting the system characteristic impedance to 50Ω.  FIG. 14  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 15  shows the distribution in the z-axis direction of the distance between conductors s, when using a substrate  2  with a thickness h=1 mm and relative permittivity ∈ r =24, and when the center conductor width w=1 mm. Table 7 lists the distances between conductors s. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Distances between conductors 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.09 
                 0.18 
                 0.27 
                 0.36 
                 0.45 
                 0.54 
                 0.63 
                 0.72 
                 0.81 
                 0.90 
                 0.99 
               
             
          
           
               
                   
                 s[mm] 
               
             
          
           
               
                   
                 1.54 
                 1.55 
                 1.55 
                 1.56 
                 1.57 
                 1.58 
                 1.58 
                 1.59 
                 1.61 
                 1.62 
                 1.63 
                 1.64 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 1.08 
                 1.17 
                 1.26 
                 1.35 
                 1.44 
                 1.53 
                 1.63 
                 1.72 
                 1.81 
                 1.90 
                 1.99 
                 2.08 
               
               
                 — 
                 1.65 
                 1.66 
                 1.67 
                 1.68 
                 1.69 
                 1.70 
                 1.71 
                 1.72 
                 1.72 
                 1.73 
                 1.73 
                 1.73 
               
               
                  #3 
                 2.17 
                 2.26 
                 2.35 
                 2.44 
                 2.53 
                 2.62 
                 2.71 
                 2.80 
                 2.89 
                 2.98 
                 3.07 
                 3.16 
               
               
                 — 
                 1.72 
                 1.72 
                 1.71 
                 1.70 
                 1.69 
                 1.67 
                 1.66 
                 1.64 
                 1.62 
                 1.59 
                 1.57 
                 1.54 
               
               
                  #4 
                 3.25 
                 3.34 
                 3.43 
                 3.52 
                 3.61 
                 3.70 
                 3.79 
                 3.88 
                 3.97 
                 4.06 
                 4.15 
                 4.23 
               
               
                 — 
                 1.51 
                 1.49 
                 1.46 
                 1.43 
                 1.40 
                 1.37 
                 1.34 
                 1.32 
                 1.29 
                 1.27 
                 1.24 
                 1.22 
               
               
                  #5 
                 4.32 
                 4.41 
                 4.50 
                 4.59 
                 4.68 
                 4.77 
                 4.85 
                 4.94 
                 5.03 
                 5.12 
                 5.21 
                 5.30 
               
               
                 — 
                 1.20 
                 1.18 
                 1.17 
                 1.15 
                 1.14 
                 1.13 
                 1.12 
                 1.11 
                 1.11 
                 1.10 
                 1.10 
                 1.10 
               
               
                  #6 
                 5.39 
                 5.47 
                 5.56 
                 5.65 
                 5.74 
                 5.83 
                 5.92 
                 6.00 
                 6.09 
                 6.18 
                 6.27 
                 6.36 
               
               
                 — 
                 1.10 
                 1.11 
                 1.11 
                 1.11 
                 1.12 
                 1.12 
                 1.13 
                 1.13 
                 1.13 
                 1.14 
                 1.14 
                 1.14 
               
               
                  #7 
                 6.45 
                 6.54 
                 6.62 
                 6.71 
                 6.80 
                 6.89 
                 6.98 
                 7.07 
                 7.15 
                 7.24 
                 7.33 
                 7.42 
               
               
                 — 
                 1.14 
                 1.13 
                 1.13 
                 1.12 
                 1.11 
                 1.10 
                 1.09 
                 1.07 
                 1.06 
                 1.04 
                 1.02 
                 1.00 
               
               
                  #8 
                 7.51 
                 7.59 
                 7.68 
                 7.77 
                 7.86 
                 7.95 
                 8.03 
                 8.12 
                 8.21 
                 8.30 
                 8.38 
                 8.47 
               
               
                 — 
                 0.98 
                 0.96 
                 0.94 
                 0.92 
                 0.90 
                 0.88 
                 0.86 
                 0.85 
                 0.84 
                 0.83 
                 0.82 
                 0.82 
               
               
                  #9 
                 8.56 
                 8.65 
                 8.73 
                 8.82 
                 8.91 
                 9.00 
                 9.08 
                 9.17 
                 9.26 
                 9.35 
                 9.44 
                 9.53 
               
               
                 — 
                 0.82 
                 0.83 
                 0.84 
                 0.85 
                 0.87 
                 0.90 
                 0.93 
                 0.97 
                 1.02 
                 1.08 
                 1.15 
                 1.23 
               
               
                 #10 
                 9.61 
                 9.70 
                 9.79 
                 9.88 
                 9.98 
                 10.07 
                 10.16 
                 10.25 
                 10.35 
                 10.44 
                 10.54 
                 10.64 
               
               
                 — 
                 1.32 
                 1.43 
                 1.55 
                 1.69 
                 1.85 
                 2.02 
                 2.22 
                 2.43 
                 2.67 
                 2.92 
                 3.19 
                 3.48 
               
               
                 #11 
                 10.74 
                 10.84 
                 10.94 
                 11.04 
                 11.15 
                 11.25 
                 11.36 
                 11.47 
                 11.57 
                 11.68 
                 11.79 
                 11.90 
               
               
                 — 
                 3.79 
                 4.11 
                 4.43 
                 4.76 
                 5.08 
                 5.40 
                 5.70 
                 5.97 
                 6.21 
                 6.41 
                 6.56 
                 6.65 
               
               
                 #12 
                 12.01 
                 12.12 
                 12.23 
                 12.34 
                 12.45 
                 12.56 
                 12.66 
                 12.77 
                 12.87 
                 12.97 
                 13.07 
                 13.17 
               
               
                 — 
                 6.69 
                 6.67 
                 6.58 
                 6.44 
                 6.23 
                 5.97 
                 5.67 
                 5.32 
                 4.95 
                 4.56 
                 4.16 
                 3.76 
               
               
                 #13 
                 13.27 
                 13.37 
                 13.46 
                 13.55 
                 13.65 
                 13.74 
                 13.83 
                 13.91 
                 14.00 
                 14.09 
                 14.18 
                 14.26 
               
               
                 — 
                 3.36 
                 2.97 
                 2.61 
                 2.27 
                 1.95 
                 1.66 
                 1.41 
                 1.19 
                 1.00 
                 0.83 
                 0.69 
                 0.58 
               
               
                 #14 
                 14.35 
                 14.44 
                 14.52 
                 14.61 
                 14.69 
                 14.78 
                 14.87 
                 14.95 
                 15.04 
                 15.12 
                 15.21 
                 15.29 
               
               
                 — 
                 0.48 
                 0.40 
                 0.34 
                 0.29 
                 0.24 
                 0.21 
                 0.18 
                 0.16 
                 0.14 
                 0.13 
                 0.11 
                 0.11 
               
               
                 #15 
                 15.38 
                 15.46 
                 15.55 
                 15.63 
                 15.72 
                 15.81 
                 15.89 
                 15.98 
                 16.06 
                 16.15 
                 16.23 
                 16.32 
               
               
                 — 
                 0.10 
                 0.10 
                 0.10 
                 0.10 
                 0.10 
                 0.11 
                 0.12 
                 0.13 
                 0.15 
                 0.17 
                 0.19 
                 0.23 
               
               
                 #16 
                 16.41 
                 16.49 
                 16.58 
                 16.66 
                 16.75 
                 16.84 
                 16.93 
                 17.01 
                 17.10 
                 17.19 
                 17.28 
                 17.37 
               
               
                 — 
                 0.27 
                 0.32 
                 0.38 
                 0.46 
                 0.56 
                 0.67 
                 0.82 
                 0.99 
                 1.20 
                 1.44 
                 1.72 
                 2.05 
               
               
                 #17 
                 17.47 
                 17.56 
                 17.66 
                 17.76 
                 17.86 
                 17.96 
                 18.07 
                 18.17 
                 18.28 
                 18.39 
                 18.51 
                 18.62 
               
               
                 — 
                 2.42 
                 2.82 
                 3.27 
                 3.75 
                 4.26 
                 4.79 
                 5.34 
                 5.88 
                 6.42 
                 6.94 
                 7.42 
                 7.85 
               
               
                 #18 
                 18.74 
                 18.85 
                 18.97 
                 19.09 
                 19.20 
                 19.32 
                 19.44 
                 19.55 
                 19.67 
                 19.78 
                 19.89 
                 20.00 
               
               
                 — 
                 8.21 
                 8.50 
                 8.70 
                 8.80 
                 8.81 
                 8.72 
                 8.54 
                 8.27 
                 7.93 
                 7.52 
                 7.07 
                 6.58 
               
               
                 #19 
                 20.11 
                 20.21 
                 20.32 
                 20.42 
                 20.52 
                 20.62 
                 20.72 
                 20.81 
                 20.90 
                 21.00 
                 21.09 
                 21.18 
               
               
                 — 
                 6.07 
                 5.55 
                 5.04 
                 4.53 
                 4.05 
                 3.59 
                 3.16 
                 2.77 
                 2.41 
                 2.09 
                 1.80 
                 1.55 
               
               
                 #20 
                 21.27 
                 21.35 
                 21.44 
                 21.53 
                 21.62 
                 21.70 
                 21.79 
                 21.88 
                 21.96 
                 22.05 
                 22.14 
                 22.22 
               
               
                 — 
                 1.33 
                 1.14 
                 0.08 
                 0.84 
                 0.73 
                 0.63 
                 0.56 
                 0.49 
                 0.44 
                 0.39 
                 0.36 
                 0.33 
               
               
                 #21 
                 22.31 
                 22.39 
                 22.48 
                 22.57 
                 22.65 
                 22.74 
                 22.82 
                 22.91 
                 22.99 
                 23.08 
                 23.17 
                 23.25 
               
               
                 — 
                 0.30 
                 0.28 
                 0.27 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.26 
                 0.27 
                 0.29 
                 0.30 
                 0.32 
               
               
                 #22 
                 23.34 
                 23.43 
                 23.51 
                 23.60 
                 23.68 
                 23.77 
                 23.86 
                 23.95 
                 24.03 
                 24.12 
                 24.21 
                 24.30 
               
               
                 — 
                 0.35 
                 0.38 
                 0.42 
                 0.46 
                 0.52 
                 0.58 
                 0.64 
                 0.72 
                 0.81 
                 0.91 
                 1.02 
                 1.14 
               
               
                 #23 
                 24.39 
                 24.48 
                 24.57 
                 24.66 
                 24.75 
                 24.84 
                 24.93 
                 25.03 
                 25.12 
                 25.22 
                 25.31 
                 25.41 
               
               
                 — 
                 1.28 
                 1.42 
                 1.58 
                 1.74 
                 1.91 
                 2.08 
                 2.26 
                 2.43 
                 2.61 
                 2.77 
                 2.93 
                 3.07 
               
               
                 #24 
                 25.50 
                 25.60 
                 25.70 
                 25.80 
                 25.89 
                 25.99 
                 26.09 
                 26.19 
                 26.29 
                 26.38 
                 26.48 
                 26.58 
               
               
                 — 
                 3.20 
                 3.31 
                 3.40 
                 3.48 
                 3.53 
                 3.56 
                 3.56 
                 3.55 
                 3.51 
                 3.46 
                 3.39 
                 3.30 
               
               
                 #25 
                 26.67 
                 26.77 
                 26.87 
                 26.96 
                 27.06 
                 27.15 
                 27.24 
                 27.34 
                 27.43 
                 27.52 
                 27.61 
                 27.70 
               
               
                 — 
                 3.20 
                 3.09 
                 2.97 
                 2.84 
                 2.71 
                 2.58 
                 2.45 
                 2.32 
                 2.20 
                 2.08 
                 1.96 
                 1.85 
               
               
                 #26 
                 27.80 
               
               
                 — 
                 1.74 
               
               
                   
               
             
          
         
       
     
       FIG. 16  shows the shape of the coplanar strip in the reflection-type bandpass filter  1  of Embodiment 3. In the figure, the lightly shaded portion represents the center conductor  3  and the side conductors  5   a  and  5   b , and the heavily shaded portion represents the non-conducting portions  4   a  and  4   b . A non-reflecting terminator, or an R=50Ω resistance, is provided on the terminating side (the face at z=27.8 mm) of this reflection-type bandpass filter  1 . The thicknesses of the metal films of the center conductor  3  and of the side conductors  5   a ,  5   b  are to be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the center conductor  3  and of the side conductors  5   a ,  5   b  may be 2.1 μm or greater. This bandpass filter  1  is used in a system with a characteristic impedance of 50Ω. 
       FIG. 17  and  FIG. 18  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter  1  of Embodiment 3. As shown in the figures, in the range of frequencies f for which 4.1 GHz≦f≦9.5 GHz, the reflectance is −5 dB or greater, and the group delay variation is within ±0.1 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −15 dB or lower. 
     In the above, exemplary embodiments of the invention have been explained; but the invention is not limited to these embodiments. Various additions, omissions, substitutions, and other modifications to the configuration can be made, without deviating from the scope of the invention. The invention is not limited by the above explanation, but is limited only by the scope of the attached claims.