Abstract:
Provided is a reflection-type bandpass filter for ultra-wideband wireless data communication. The filter includes a substrate including a dielectric layer and a conducting layer layered on the top and bottom surfaces thereof, and a center conductor provided within the dielectric layer and serving as a strip line. A width distribution of the center conductor is non-uniform in a length direction of the center conductor.

Description:
This application claims priority from Japanese Patent Application No. 2006-274324, filed on Oct. 5, 2006, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     Apparatuses consistent with the present invention relate to a reflection-type bandpass filter for use in ultra-wideband (UWB) wireless data communication. 
     2. Description of the Related Art 
     As technology of the art related to embodiments of this invention, for example, the technology disclosed in the following references 1 through 12 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. 9-11, Marcel Dekker, 1991 
     However, the bandpass filters proposed in the related art may not satisfy the FCC specifications, due to manufacturing tolerances and other reasons. 
     Further, bandpass filters having an open construction with the microstrip line exposed are easily affected by external influences. 
     This invention was devised in light of the above circumstances, and has as an exemplary object the provision of a high-performance UWB reflection-type bandpass filter which is not easily affected by external influences, and which satisfies FCC specifications. 
     SUMMARY OF THE INVENTION 
     Exemplary embodiments of this invention provide a reflection-type bandpass filter for ultra-wideband wireless data communication, having a substrate comprising a dielectric layer and a conducting layer layered on the top and bottom surfaces thereof, and a center conductor provided within the dielectric layer and serving as the strip line, and in which the center conductor width distribution is non-uniform in the length direction thereof. 
     By using exemplary embodiments of a UWB reflection-type bandpass filter of this invention, U.S. Federal Communications Commission requirements for spectrum masks can be satisfied. 
     In a reflection-type bandpass filter of an exemplary embodiment of this invention, there may be a difference of 10 dB or higher 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 ±0.05 ns. 
     In a reflection-type bandpass filter of another exemplary embodiment of this invention, there may be a difference of 10 dB or greater 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 3.9 GHz≦f≦9.8 GHz, and in a range 3.9 GHz≦f≦9.8 GHz the group delay variation may be within ±0.07 ns. 
     In a reflection-type bandpass filter of another exemplary embodiment of this invention, there may be a difference of 10 dB or greater 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 4.4 GHz≦f≦9.2 GHz, and in a range 4.4 GHz≦f≦9.2 GHz a group delay variation may be within ±0.05 ns. 
     In a reflection-type bandpass filter of another exemplary embodiment of this invention, there may be a difference of 10 dB or greater 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 3.8 GHz≦f≦9.8 GHz, and in a range 3.8 GHz≦f≦9.8 GHz a group delay variation may be within ±0.2 ns. 
     In a reflection-type bandpass filter of another exemplary embodiment of this invention, there may be a difference of 10 dB or greater 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 an exemplary embodiment of this invention, a characteristic impedance Zc of an input terminal of the filter may be in a range 10Ω≦Zc≦300Ω. 
     Further, a resistance having the same impedance as the characteristic impedance value, or a non-reflecting terminator, may be provided on the terminating side of the filter. 
     In a reflection-type bandpass filter of an exemplary embodiment of this invention, the center conductor and the conducting layers of the substrate may comprise metal plates of thickness equal to or greater than a skin depth at f=1 GHz. 
     In a reflection-type bandpass filter of an exemplary embodiment of this invention, the dielectric layer may have a thickness h in a range 0.1 mm≦h≦10 mm, a relative permittivity ∈ r  in a range 1≦∈ r ≦100, a width W in a range 2 mm≦W≦100 mm, and a length L be in a range 2 mm≦L≦500 mm. 
     In a reflection-type bandpass filter of an exemplary embodiment of this invention, a length-direction distribution of the center conductor width 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 an exemplary embodiment of this invention, a length-direction distribution of the center conductor width may satisfy a window function method. 
     In a reflection-type bandpass filter of an exemplary embodiment of this invention, a length-direction distribution of the center conductor width may satisfy a Kaiser window function method. 
     According to exemplary embodiments, by applying a window function technique to design a reflection-type bandpass filter comprising a non-uniform microstrip line, the pass band can be made extremely broad compared with bandpass filters of the prior art, and variations in the group delay within the pass band can be made extremely small, so that a UWB reflection-type bandpass filter which satisfies FCC specifications can be realized. 
     Further, in an exemplary configuration in which the center conductor is provided in the interior of dielectric layers with conductor layers on both faces, the filter is not easily affected by external influences, and stable filter characteristics can be obtained. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings in which: 
         FIG. 1  is a perspective view showing one aspect of a reflection-type bandpass filter of an exemplary embodiment of the invention; 
         FIG. 2  is a graph showing the center conductor width dependence of the characteristic impedance in a reflection-type bandpass filter of an exemplary embodiment of this invention; 
         FIG. 3  is a graph showing the distribution of the characteristic impedance of the reflection-type bandpass filter manufactured in Embodiment 1; 
         FIG. 4  is a graph showing the center conductor width distribution in the reflection-type bandpass filter manufactured in Embodiment 1; 
         FIG. 5  is a graph showing the shape of the center conductor in the reflection-type bandpass filter manufactured in Embodiment 1; 
         FIG. 6  is a graph showing the reflected-wave amplitude characteristic in the reflection-type bandpass filter manufactured in Embodiment 1; 
         FIG. 7  is a graph showing the reflected-wave group delay characteristic in the reflection-type bandpass filter manufactured in Embodiment 1; 
         FIG. 8  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter manufactured in Embodiment 2; 
         FIG. 9  is a graph showing the center conductor width distribution in the reflection-type bandpass filter manufactured in Embodiment 2; 
         FIG. 10  is a graph showing the shape of the center conductor in the reflection-type bandpass filter manufactured in Embodiment 2; 
         FIG. 11  is a graph showing the reflected-wave amplitude characteristic in the reflection-type bandpass filter manufactured in Embodiment 2; 
         FIG. 12  is a graph showing the reflected-wave group delay characteristic in the reflection-type bandpass filter manufactured in Embodiment 2; 
         FIG. 13  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter manufactured in Embodiment 3; 
         FIG. 14  is a graph showing the center conductor width distribution in the reflection-type bandpass filter manufactured in Embodiment 3; 
         FIG. 15  is a graph showing the shape of the center conductor in the reflection-type bandpass filter manufactured in Embodiment 3; 
         FIG. 16  is a graph showing the reflected-wave amplitude characteristic in the reflection-type bandpass filter manufactured in Embodiment 3; 
         FIG. 17  is a graph showing the reflected-wave group delay characteristic in the reflection-type bandpass filter manufactured in Embodiment 3; 
         FIG. 18  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter manufactured in Embodiment 4; 
         FIG. 19  is a graph showing the center conductor width distribution in the reflection-type bandpass filter manufactured in Embodiment 4; 
         FIG. 20  is a graph showing the shape of the center conductor in the reflection-type bandpass filter manufactured in Embodiment 4; 
         FIG. 21  is a graph showing the reflected-wave amplitude characteristic in the reflection-type bandpass filter manufactured in Embodiment 4; 
         FIG. 22  is a graph showing the reflected-wave group delay characteristic in the reflection-type bandpass filter manufactured in Embodiment 4; 
         FIG. 23  is a graph showing the characteristic impedance distribution of the reflection-type bandpass filter manufactured in Embodiment 5; 
         FIG. 24  is a graph showing the center conductor width distribution in the reflection-type bandpass filter manufactured in Embodiment 5; 
         FIG. 25  is a graph showing the shape of the center conductor in the reflection-type bandpass filter manufactured in Embodiment 5; 
         FIG. 26  is a graph showing the reflected-wave amplitude characteristic in the reflection-type bandpass filter manufactured in Embodiment 5; 
         FIG. 27  is a graph showing the reflected-wave group delay characteristic in the reflection-type bandpass filter manufactured in Embodiment 5; and, 
         FIG. 28  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 embodiment of this invention. In the figure, the symbol  1  is the reflection-type bandpass filter,  2  is a substrate,  3  is a dielectric layer,  4  and  5  are conductive layers, and  6  is a center conductor. 
     The reflection-type bandpass filter  1  of this aspect has a substrate  2 , which in turn has a dielectric layer  3  and conducting layers  4  and  5  layered on the top and bottom surfaces thereof, and a center conductor  6  which serves as a strip line, provided within the dielectric layer  3 ; the center conductor  6  has a width which is distributed non-uniformly in the length direction. 
     As shown in  FIG. 1 , the z axis is taken along the length direction of the center conductor  6 , the y axis is orthogonal to the z axis and in the direction parallel to the surface of the substrate  2 , and the x axis is taken in the direction orthogonal to the y axis and z axis. Also, the length of the filter extending in the z-axis direction from the input-side face is taken to be z. 
     This reflection-type bandpass filter  1  has a structure in which the center conductor  6  is shielded by the conducting layers  4 ,  5 , so that compared with bandpass filters in which the microstrip line is exposed to the outside, the reflection-type bandpass filter  1  is not easily affected by external influences. 
     A reflection-type bandpass filter of an exemplary embodiment of this 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 an exemplary embodiment of this invention can be represented by a non-uniformly distributed constant circuit such as in  FIG. 28 . 
     From  FIG. 28 , the following equation (1) can be obtained for the line voltage v(z,t) and the line current i(z,t). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               - 
                               
                                 
                                   ∂ 
                                   
                                     v 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   z 
                                 
                               
                             
                             = 
                             
                               
                                 L 
                                 ⁡ 
                                 
                                   ( 
                                   z 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   ∂ 
                                   
                                     i 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         z 
                                         , 
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             - 
                             
                               
                                 ∂ 
                                 
                                   i 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       z 
                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                           
                           = 
                           
                             
                               C 
                               ⁡ 
                               
                                 ( 
                                 z 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   ∂ 
                                   
                                     v 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         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 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                                       t 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
                                       c 
                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     ∂ 
                                     
                                       
                                         ϕ 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           z 
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                                           t 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     ∂ 
                                     t 
                                   
                                 
                               
                               - 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       ⅆ 
                                       
                                           
                                       
                                       ⁢ 
                                       ln 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       Z 
                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                   
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                                 ⁢ 
                                 
                                   
                                     ϕ 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                           , 
                         
                       
                     
                     
                       
                         
                           
                             
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                                 ⁡ 
                                 
                                   ( 
                                   
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                           = 
                           
                             
                               
                                 1 
                                 
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                                   ⁡ 
                                   
                                     ( 
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                               ⁢ 
                               
                                 
                                   ∂ 
                                   
                                     
                                       ϕ 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
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                                       ) 
                                     
                                   
                                 
                                 
                                   ∂ 
                                   t 
                                 
                               
                             
                             - 
                             
                               
                                 1 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   
                                     ⅆ 
                                     
                                         
                                     
                                     ⁢ 
                                     ln 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     Z 
                                     ⁡ 
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                 
                                   ⅆ 
                                   z 
                                 
                               
                               ⁢ 
                               
                                 
                                   
                                     ϕ 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
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                                       , 
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                                     ) 
                                   
                                 
                                 . 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Here Z(z)=√{square root over ( )}{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). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
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                                     ϕ 
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                                   ⁡ 
                                   
                                     ( 
                                     
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                                 ∂ 
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                             = 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
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                                       ⁡ 
                                       
                                         ( 
                                         z 
                                         ) 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
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                                         ϕ 
                                         1 
                                       
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                                         ( 
                                         
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                                         ) 
                                       
                                     
                                   
                                   
                                     ∂ 
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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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                                       , 
                                       t 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 
                                   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 
                   
                   ) 
                 
               
             
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 
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                                       1 
                                     
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                                       ( 
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                                       ) 
                                     
                                   
                                 
                                 
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                                 ⁢ 
                                 
                                     
                                 
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                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                             
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                                   ⁡ 
                                   
                                     ( 
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                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                 
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                                   2 
                                 
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                               ⁢ 
                               
                                   
                               
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                                 q 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               
                                 
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                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
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                                   ) 
                                 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     e 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     q 
                     ⁢ 
                     
                         
                     
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                     u 
                     ⁢ 
                     
                         
                     
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                     t 
                     ⁢ 
                     
                         
                     
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                     o 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     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, according to related art, 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 
                           
                             
                               - 
                               j 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅆ 
                           ω 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     In exemplary embodiments of 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). 
     
       
         
           
             
               
                 
                   
                     ω 
                     ⁡ 
                     
                       [ 
                       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 the width w of the center conductor  6  (hereafter the “center conductor width w”) is changed in the strip line of an exemplary embodiment of this invention, the local characteristic impedance can be changed.  FIG. 2  shows the dependence of the local characteristic impedance of the strip line on the center conductor width w when the thickness h of the dielectric layer  3  is 2 mm and the relative permittivity ∈ r  of the dielectric layer  3  is 1. 
     In exemplary embodiments of this invention, the center conductor width w was calculated based on the local characteristic impedance obtained from equation (7), and bandpass filters  1  were fabricated so as to satisfy the calculated center conductor width w. By this means, reflection-type bandpass filter  1  having the desired pass band was obtained. 
     Below, exemplary embodiments of the invention are explained in further detail. 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 1 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 frequency f=1 GHz propagating in the microstrip as the waveguide length, and setting the system characteristic impedance to 50Ω.  FIG. 3  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. 8 ,  FIG. 13 ,  FIG. 18 , and  FIG. 23  below. “z” is the length extending in the z-axis direction from the end face on the input end. The horizontal axis indicates the value which is obtained by dividing z by one wavelength at f=1 GHz. 
       FIG. 4  shows the distribution in the z-axis of the center conductor width w, when using a dielectric layer  3  of thickness h=2 mm and with relative permittivity ∈ r =4.2. Tables 1 through 3 list the center conductor widths w. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Center conductor widths (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.15 
                 0.29 
                 0.44 
                 0.59 
                 0.73 
                 0.88 
                 1.02 
                 1.17 
                 1.32 
                 1.46 
                 1.61 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 1.76 
                 1.00 
                 2.05 
                 2.20 
                 2.34 
                 2.49 
                 2.68 
                 2.78 
                 2.99 
                 3.07 
                 3.22 
                 3.37 
               
               
                 — 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
               
               
                  #3 
                 3.51 
                 3.66 
                 3.81 
                 3.95 
                 4.10 
                 4.25 
                 4.39 
                 4.54 
                 4.68 
                 4.83 
                 4.98 
                 5.12 
               
               
                 — 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
               
               
                  #4 
                 5.27 
                 5.42 
                 5.56 
                 5.71 
                 5.56 
                 6.00 
                 6.15 
                 6.29 
                 6.44 
                 6.59 
                 6.73 
                 6.88 
               
               
                 — 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
               
               
                  #5 
                 7.03 
                 7.17 
                 7.32 
                 7.47 
                 7.61 
                 7.76 
                 7.90 
                 8.05 
                 8.20 
                 8.34 
                 8.49 
                 8.54 
               
               
                 — 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.95 
                 0.95 
               
               
                  #6 
                 8.78 
                 8.93 
                 9.08 
                 9.22 
                 9.37 
                 9.52 
                 9.66 
                 9.81 
                 9.95 
                 10.10 
                 10.25 
                 10.39 
               
               
                 — 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
               
               
                  #7 
                 10.54 
                 10.69 
                 10.83 
                 10.98 
                 11.13 
                 11.27 
                 11.42 
                 11.56 
                 11.71 
                 11.86 
                 12.00 
                 12.15 
               
               
                 — 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
               
               
                  #8 
                 12.30 
                 12.44 
                 12.59 
                 12.74 
                 12.88 
                 13.03 
                 13.17 
                 13.32 
                 13.47 
                 13.61 
                 13.76 
                 13.91 
               
               
                 — 
                 0.96 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.98 
                 0.98 
               
               
                  #9 
                 14.05 
                 14.20 
                 14.35 
                 14.49 
                 14.64 
                 14.78 
                 14.93 
                 15.08 
                 15.22 
                 15.37 
                 15.52 
                 15.66 
               
               
                 — 
                 0.98 
                 0.98 
                 0.99 
                 0.99 
                 0.99 
                 0.99 
                 1.00 
                 1.00 
                 1.00 
                 1.01 
                 1.01 
                 1.01 
               
               
                 #10 
                 15.81 
                 15.96 
                 16.10 
                 16.25 
                 16.40 
                 16.54 
                 16.69 
                 16.83 
                 16.98 
                 17.13 
                 17.27 
                 17.42 
               
               
                 — 
                 1.01 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.03 
                 1.02 
                 1.02 
               
               
                 #11 
                 17.57 
                 17.71 
                 17.86 
                 18.01 
                 18.15 
                 18.30 
                 18.44 
                 18.59 
                 18.74 
                 18.88 
                 19.03 
                 19.18 
               
               
                 — 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.01 
                 1.01 
                 1.01 
                 1.01 
                 1.00 
                 1.00 
               
               
                 #12 
                 19.32 
                 19.47 
                 19.62 
                 19.76 
                 19.91 
                 20.06 
                 20.20 
                 20.35 
                 20.49 
                 20.64 
                 20.79 
                 20.93 
               
               
                 — 
                 1.00 
                 1.00 
                 0.99 
                 0.99 
                 0.99 
                 0.99 
                 0.99 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
               
               
                 #13 
                 21.08 
                 21.23 
                 21.37 
                 21.52 
                 21.66 
                 21.81 
                 21.96 
                 22.10 
                 22.25 
                 22.40 
                 22.54 
                 22.69 
               
               
                 — 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
               
               
                 #14 
                 22.84 
                 22.98 
                 23.13 
                 23.28 
                 23.42 
                 23.57 
                 23.71 
                 23.86 
                 24.01 
                 24.15 
                 24.30 
                 24.45 
               
               
                 — 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.97 
                 0.96 
                 0.96 
                 0.96 
               
               
                 #15 
                 24.59 
                 24.74 
                 24.89 
                 25.03 
                 25.18 
                 25.32 
                 25.47 
                 25.62 
                 25.76 
                 25.91 
                 26.06 
                 26.20 
               
               
                 — 
                 0.96 
                 0.96 
                 0.95 
                 0.94 
                 0.94 
                 0.93 
                 0.93 
                 0.93 
                 0.92 
                 0.92 
                 0.91 
                 0.91 
               
               
                 #16 
                 26.35 
                 26.50 
                 26.64 
                 26.79 
                 26.93 
                 27.08 
                 27.23 
                 27.37 
                 27.52 
                 27.67 
                 27.81 
                 27.96 
               
               
                 — 
                 0.91 
                 0.90 
                 0.90 
                 0.90 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
               
               
                 #17 
                 28.11 
                 28.25 
                 28.40 
                 28.55 
                 28.69 
                 28.84 
                 28.98 
                 29.13 
                 29.28 
                 29.42 
                 29.57 
                 29.72 
               
               
                 — 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.90 
                 0.90 
                 0.90 
                 0.90 
                 0.91 
                 0.91 
                 0.91 
               
               
                 #18 
                 29.86 
                 30.01 
                 30.16 
                 30.30 
                 30.45 
                 30.59 
                 30.74 
                 30.89 
                 31.03 
                 31.18 
                 31.33 
                 31.47 
               
               
                 — 
                 0.92 
                 0.92 
                 0.92 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
               
               
                 #19 
                 31.62 
                 31.77 
                 31.91 
                 32.06 
                 32.20 
                 32.35 
                 32.50 
                 32.64 
                 32.79 
                 32.94 
                 33.08 
                 33.23 
               
               
                 — 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
               
               
                 #20 
                 33.36 
                 33.52 
                 33.67 
                 33.81 
                 33.96 
                 34.11 
                 34.25 
                 34.40 
                 34.55 
                 34.69 
                 34.84 
                 34.99 
               
               
                 — 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.97 
               
               
                 #21 
                 35.19 
                 35.28 
                 35.43 
                 35.57 
                 35.72 
                 35.86 
                 36.01 
                 36.16 
                 36.30 
                 36.46 
                 36.60 
                 36.74 
               
               
                 — 
                 0.97 
                 0.98 
                 0.98 
                 0.99 
                 1.00 
                 1.00 
                 1.01 
                 1.02 
                 1.03 
                 1.03 
                 1.04 
                 1.05 
               
               
                 #22 
                 36.89 
                 37.04 
                 37.18 
                 37.33 
                 37.47 
                 37.62 
                 37.77 
                 37.91 
                 38.06 
                 38.21 
                 38.35 
                 38.50 
               
               
                 — 
                 1.00 
                 1.06 
                 1.06 
                 1.07 
                 1.08 
                 1.08 
                 1.08 
                 1.09 
                 1.09 
                 1.09 
                 1.09 
                 1.09 
               
               
                 #23 
                 38.65 
                 38.79 
                 38.94 
                 39.08 
                 39.23 
                 39.38 
                 39.52 
                 39.67 
                 39.82 
                 39.96 
                 40.11 
                 40.26 
               
               
                 — 
                 1.09 
                 1.09 
                 1.09 
                 1.09 
                 1.08 
                 1.08 
                 1.08 
                 1.07 
                 1.07 
                 1.06 
                 1.06 
                 1.05 
               
               
                 #24 
                 40.40 
                 40.55 
                 40.70 
                 40.84 
                 40.99 
                 41.13 
                 41.28 
                 41.43 
                 41.57 
                 41.72 
                 41.87 
                 42.01 
               
               
                 — 
                 1.05 
                 1.05 
                 1.04 
                 1.04 
                 1.03 
                 1.03 
                 1.03 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
               
               
                 #25 
                 42.16 
                 42.31 
                 42.45 
                 42.60 
                 42.74 
                 42.89 
                 43.04 
                 43.18 
                 43.33 
                 43.48 
                 43.52 
                 43.77 
               
               
                 — 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
               
               
                 #26 
                 43.92 
                 44.06 
                 44.21 
                 44.35 
                 44.56 
                 44.65 
                 44.79 
                 44.94 
                 45.09 
                 45.23 
                 45.38 
                 45.53 
               
               
                 — 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.02 
                 1.01 
                 1.01 
                 1.00 
                 1.00 
                 0.99 
                 0.98 
               
               
                 #27 
                 45.67 
                 45.82 
                 45.96 
                 46.11 
                 46.25 
                 46.48 
                 46.55 
                 46.70 
                 46.84 
                 46.99 
                 47.14 
                 47.28 
               
               
                 — 
                 0.98 
                 0.97 
                 0.96 
                 0.95 
                 0.94 
                 0.93 
                 0.92 
                 0.91 
                 0.90 
                 0.88 
                 0.87 
                 0.86 
               
               
                 #28 
                 47.43 
                 47.58 
                 47.72 
                 47.87 
                 48.01 
                 48.16 
                 48.31 
                 48.45 
                 48.60 
                 48.75 
                 45.89 
                 49.04 
               
               
                 — 
                 0.86 
                 0.85 
                 0.84 
                 0.83 
                 0.82 
                 0.82 
                 0.81 
                 0.81 
                 0.80 
                 0.80 
                 0.80 
                 0.80 
               
               
                 #29 
                 49.19 
                 49.33 
                 49.48 
                 49.62 
                 49.77 
                 49.92 
                 50.06 
                 50.21 
                 50.36 
                 50.50 
                 50.65 
                 50.80 
               
               
                 — 
                 0.80 
                 0.80 
                 0.80 
                 0.80 
                 0.80 
                 0.81 
                 0.81 
                 0.81 
                 0.82 
                 0.82 
                 0.83 
                 0.83 
               
               
                 #30 
                 50.94 
                 51.00 
                 51.23 
                 51.38 
                 51.53 
                 51.67 
                 51.82 
                 51.97 
                 52.11 
                 52.26 
                 52.41 
                 52.55 
               
               
                 — 
                 0.84 
                 0.84 
                 0.85 
                 0.85 
                 0.86 
                 0.86 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Center conductor widths (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 52.76 
                 52.84 
                 52.99 
                 53.14 
                 53.28 
                 53.43 
                 53.58 
                 53.72 
                 53.87 
                 54.02 
                 54.16 
                 54.31 
               
               
                 — 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.87 
                 0.86 
                 0.86 
                 0.86 
                 0.86 
                 0.85 
                 0.85 
               
               
                 #32 
                 54.46 
                 54.60 
                 54.75 
                 54.89 
                 55.04 
                 55.19 
                 55.33 
                 55.48 
                 55.63 
                 55.77 
                 55.92 
                 56.07 
               
               
                 — 
                 0.85 
                 0.85 
                 0.86 
                 0.86 
                 0.86 
                 0.86 
                 0.87 
                 0.88 
                 0.88 
                 0.89 
                 0.90 
                 0.92 
               
               
                 #33 
                 56.21 
                 56.36 
                 56.50 
                 56.65 
                 56.80 
                 56.94 
                 57.09 
                 57.24 
                 57.38 
                 57.53 
                 57.68 
                 57.82 
               
               
                 — 
                 0.93 
                 0.94 
                 0.96 
                 0.98 
                 1.00 
                 1.02 
                 1.04 
                 1.06 
                 1.08 
                 1.10 
                 1.12 
                 1.14 
               
               
                 #34 
                 57.97 
                 58.11 
                 58.20 
                 58.41 
                 58.55 
                 58.70 
                 58.85 
                 58.99 
                 59.14 
                 59.29 
                 59.43 
                 59.58 
               
               
                 — 
                 1.17 
                 1.19 
                 1.21 
                 1.23 
                 1.25 
                 1.26 
                 1.28 
                 1.29 
                 1.30 
                 1.31 
                 1.32 
                 1.32 
               
               
                 #35 
                 59.73 
                 59.87 
                 60.02 
                 60.16 
                 60.31 
                 60.46 
                 60.60 
                 60.75 
                 60.90 
                 61.04 
                 61.19 
                 61.34 
               
               
                 — 
                 1.33 
                 1.33 
                 1.33 
                 1.32 
                 1.32 
                 1.31 
                 1.30 
                 1.29 
                 1.28 
                 1.27 
                 1.25 
                 1.25 
               
               
                 #36 
                 61.48 
                 61.63 
                 61.77 
                 61.92 
                 62.07 
                 62.21 
                 62.36 
                 62.51 
                 62.65 
                 62.80 
                 62.95 
                 63.09 
               
               
                 — 
                 1.24 
                 1.23 
                 1.22 
                 1.21 
                 1.20 
                 1.19 
                 1.18 
                 1.18 
                 1.18 
                 1.17 
                 1.17 
                 1.18 
               
               
                 #37 
                 63.24 
                 63.38 
                 63.63 
                 63.68 
                 63.82 
                 63.97 
                 64.12 
                 64.26 
                 64.41 
                 64.56 
                 64.70 
                 64.85 
               
               
                 — 
                 1.18 
                 1.18 
                 1.19 
                 1.20 
                 1.20 
                 1.21 
                 1.22 
                 1.23 
                 1.24 
                 1.25 
                 1.26 
                 1.26 
               
               
                 #38 
                 64.99 
                 65.14 
                 65.29 
                 65.43 
                 65.58 
                 65.73 
                 65.87 
                 65.02 
                 66.17 
                 66.31 
                 66.46 
                 66.61 
               
               
                 — 
                 1.27 
                 1.27 
                 1.27 
                 1.26 
                 1.26 
                 1.25 
                 1.23 
                 1.21 
                 1.19 
                 1.16 
                 1.13 
                 1.10 
               
               
                 #39 
                 66.75 
                 66.90 
                 67.04 
                 67.19 
                 67.34 
                 67.48 
                 67.63 
                 67.78 
                 67.92 
                 68.07 
                 68.22 
                 68.36 
               
               
                 — 
                 1.06 
                 1.01 
                 0.97 
                 0.92 
                 0.87 
                 0.82 
                 0.77 
                 0.72 
                 0.66 
                 0.61 
                 0.56 
                 0.52 
               
               
                 #40 
                 68.51 
                 68.65 
                 68.80 
                 68.95 
                 69.09 
                 69.24 
                 69.39 
                 69.53 
                 69.68 
                 69.83 
                 69.97 
                 70.12 
               
               
                 — 
                 0.47 
                 0.43 
                 0.39 
                 0.35 
                 0.32 
                 0.29 
                 0.27 
                 0.24 
                 0.22 
                 0.21 
                 0.20 
                 0.19 
               
               
                 #41 
                 70.26 
                 70.41 
                 70.56 
                 70.70 
                 70.85 
                 71.00 
                 71.14 
                 71.29 
                 71.44 
                 71.58 
                 71.73 
                 71.88 
               
               
                 — 
                 0.18 
                 0.17 
                 0.17 
                 0.17 
                 0.18 
                 0.18 
                 0.19 
                 0.21 
                 0.22 
                 0.24 
                 0.27 
                 0.30 
               
               
                 #42 
                 72.02 
                 72.17 
                 72.31 
                 72.46 
                 72.61 
                 72.75 
                 72.90 
                 73.05 
                 73.19 
                 73.34 
                 73.49 
                 73.63 
               
               
                 — 
                 0.34 
                 0.30 
                 0.45 
                 0.51 
                 0.58 
                 0.66 
                 0.76 
                 0.86 
                 0.97 
                 1.10 
                 1.23 
                 1.38 
               
               
                 #43 
                 73.78 
                 73.92 
                 74.07 
                 74.22 
                 74.36 
                 74.51 
                 74.66 
                 74.80 
                 74.95 
                 75.10 
                 75.24 
                 75.39 
               
               
                 — 
                 1.64 
                 1.70 
                 1.88 
                 2.05 
                 2.24 
                 2.43 
                 2.52 
                 2.81 
                 2.99 
                 3.17 
                 3.33 
                 3.48 
               
               
                 #44 
                 75.53 
                 75.68 
                 75.83 
                 75.97 
                 76.13 
                 76.27 
                 76.41 
                 76.56 
                 76.71 
                 76.35 
                 77.00 
                 77.14 
               
               
                 — 
                 3.61 
                 3.71 
                 3.79 
                 3.85 
                 3.87 
                 3.86 
                 3.83 
                 3.76 
                 3.67 
                 3.55 
                 3.41 
                 3.25 
               
               
                 #45 
                 77.29 
                 77.44 
                 77.58 
                 77.78 
                 77.83 
                 78.02 
                 78.17 
                 78.32 
                 78.46 
                 78.61 
                 78.76 
                 78.90 
               
               
                 — 
                 3.07 
                 2.89 
                 2.69 
                 2.49 
                 2.29 
                 2.09 
                 1.90 
                 1.71 
                 1.53 
                 1.36 
                 1.20 
                 1.05 
               
               
                 #46 
                 79.05 
                 79.19 
                 79.34 
                 79.49 
                 79.63 
                 79.78 
                 79.93 
                 80.07 
                 80.22 
                 80.37 
                 80.51 
                 80.66 
               
               
                 — 
                 0.91 
                 0.79 
                 0.68 
                 0.58 
                 0.49 
                 0.41 
                 0.34 
                 0.29 
                 0.24 
                 0.20 
                 0.17 
                 0.14 
               
               
                 #47 
                 80.80 
                 80.95 
                 81.10 
                 81.24 
                 81.39 
                 81.54 
                 81.68 
                 81.83 
                 81.98 
                 82.12 
                 82.27 
                 82.41 
               
               
                 — 
                 0.12 
                 0.11 
                 0.09 
                 0.05 
                 0.08 
                 0.07 
                 0.07 
                 0.07 
                 0.07 
                 0.08 
                 0.08 
                 0.09 
               
               
                 #48 
                 82.56 
                 82.71 
                 82.85 
                 83.00 
                 83.15 
                 83.29 
                 83.44 
                 83.59 
                 83.73 
                 83.88 
                 84.02 
                 84.17 
               
               
                 — 
                 0.10 
                 0.11 
                 0.13 
                 0.15 
                 0.18 
                 0.21 
                 0.25 
                 0.30 
                 0.35 
                 0.41 
                 0.43 
                 0.55 
               
               
                 #49 
                 84.32 
                 84.46 
                 84.61 
                 84.76 
                 84.90 
                 85.05 
                 85.20 
                 85.34 
                 85.49 
                 85.64 
                 85.78 
                 85.93 
               
               
                 — 
                 0.64 
                 0.73 
                 0.83 
                 0.93 
                 1.04 
                 1.15 
                 1.27 
                 1.39 
                 1.51 
                 1.62 
                 1.74 
                 1.85 
               
               
                 #50 
                 86.07 
                 86.22 
                 86.37 
                 86.51 
                 86.66 
                 86.81 
                 86.95 
                 87.10 
                 87.25 
                 87.39 
                 87.54 
                 87.68 
               
               
                 — 
                 1.95 
                 2.04 
                 2.13 
                 2.20 
                 2.27 
                 2.32 
                 2.35 
                 2.38 
                 2.39 
                 2.38 
                 2.37 
                 2.34 
               
               
                 #51 
                 87.83 
                 87.95 
                 88.12 
                 88.27 
                 88.42 
                 88.56 
                 88.71 
                 88.86 
                 89.00 
                 89.15 
                 89.29 
                 89.44 
               
               
                 — 
                 2.30 
                 2.25 
                 2.20 
                 2.13 
                 2.07 
                 2.00 
                 1.93 
                 1.85 
                 1.78 
                 1.71 
                 1.64 
                 1.57 
               
               
                 #52 
                 89.59 
                 89.73 
                 89.88 
                 90.03 
                 90.17 
                 90.32 
                 90.47 
                 90.61 
                 90.76 
                 90.91 
                 91.05 
                 91.20 
               
               
                 — 
                 1.50 
                 1.44 
                 1.39 
                 1.33 
                 1.23 
                 1.24 
                 1.20 
                 1.17 
                 1.14 
                 1.11 
                 1.09 
                 1.07 
               
               
                 #53 
                 91.34 
                 91.49 
                 91.64 
                 91.78 
                 91.93 
                 92.08 
                 92.22 
                 92.37 
                 92.52 
                 92.65 
                 92.81 
                 92.95 
               
               
                 — 
                 1.00 
                 1.04 
                 1.04 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.04 
                 1.04 
               
               
                 #54 
                 93.10 
                 93.25 
                 93.39 
                 93.54 
                 93.69 
                 93.83 
                 93.98 
                 94.13 
                 94.27 
                 94.42 
                 94.56 
                 94.71 
               
               
                 — 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.03 
                 1.03 
                 1.02 
                 1.01 
                 0.99 
                 0.98 
                 0.96 
                 0.94 
               
               
                 #55 
                 94.86 
                 95.00 
                 95.15 
                 95.30 
                 95.44 
                 95.59 
                 95.74 
                 95.88 
                 96.03 
                 96.17 
                 96.32 
                 96.47 
               
               
                 — 
                 0.91 
                 0.89 
                 0.86 
                 0.83 
                 0.80 
                 0.78 
                 0.75 
                 0.72 
                 0.69 
                 0.66 
                 0.64 
                 0.61 
               
               
                 #56 
                 96.61 
                 96.76 
                 96.91 
                 97.05 
                 97.20 
                 97.35 
                 97.49 
                 97.64 
                 97.79 
                 97.93 
                 98.06 
                 98.22 
               
               
                 — 
                 0.59 
                 0.57 
                 0.55 
                 0.53 
                 0.51 
                 0.50 
                 0.49 
                 0.48 
                 0.47 
                 0.47 
                 0.47 
                 0.47 
               
               
                 #57 
                 98.37 
                 98.52 
                 98.66 
                 98.81 
                 98.96 
                 99.10 
                 99.25 
                 99.40 
                 99.54 
                 99.69 
                 99.83 
                 99.98 
               
               
                 — 
                 0.47 
                 0.48 
                 0.49 
                 0.50 
                 0.51 
                 0.53 
                 0.55 
                 0.57 
                 0.59 
                 0.61 
                 0.64 
                 0.67 
               
               
                 #58 
                 100.13 
                 100.27 
                 100.42 
                 100.57 
                 100.71 
                 100.86 
                 101.01 
                 101.15 
                 101.30 
                 101.44 
                 101.59 
                 101.74 
               
               
                 — 
                 0.70 
                 0.73 
                 0.75 
                 0.79 
                 0.83 
                 0.86 
                 0.89 
                 0.92 
                 0.95 
                 0.98 
                 1.01 
                 1.04 
               
               
                 #59 
                 101.88 
                 102.03 
                 102.18 
                 102.32 
                 102.47 
                 102.62 
                 102.76 
                 102.91 
                 103.06 
                 103.20 
                 103.35 
                 103.49 
               
               
                 — 
                 1.06 
                 1.08 
                 1.10 
                 1.12 
                 1.13 
                 1.14 
                 1.15 
                 1.15 
                 1.16 
                 1.16 
                 1.16 
                 1.16 
               
               
                 #60 
                 103.64 
                 103.79 
                 103.93 
                 104.08 
                 104.23 
                 104.37 
                 104.52 
                 104.67 
                 104.81 
                 104.95 
                 105.10 
                 105.25 
               
               
                 — 
                 1.15 
                 1.15 
                 1.14 
                 1.14 
                 1.13 
                 1.13 
                 1.12 
                 1.11 
                 1.11 
                 1.11 
                 1.10 
                 1.10 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Center conductor widths (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 105.40 
                 105.54 
                 105.63 
                 105.84 
                 105.98 
                 106.13 
                 106.28 
                 106.42 
                 106.57 
                 106.71 
                 106.86 
                 107.01 
               
               
                 — 
                 1.10 
                 1.11 
                 1.11 
                 1.12 
                 1.12 
                 1.13 
                 1.14 
                 1.15 
                 1.16 
                 1.18 
                 1.18 
                 1.21 
               
               
                 #62 
                 107.15 
                 107.30 
                 107.45 
                 107.59 
                 107.74 
                 107.89 
                 108.03 
                 108.18 
                 108.32 
                 108.47 
                 108.62 
                 108.76 
               
               
                 — 
                 1.22 
                 1.24 
                 1.26 
                 1.27 
                 1.29 
                 1.30 
                 1.31 
                 1.33 
                 1.34 
                 1.34 
                 1.35 
                 1.35 
               
               
                 #63 
                 108.93 
                 109.09 
                 109.29 
                 109.35 
                 109.50 
                 109.64 
                 109.79 
                 109.94 
                 110.08 
                 110.23 
                 110.37 
                 110.52 
               
               
                 — 
                 1.35 
                 1.35 
                 1.35 
                 1.34 
                 1.33 
                 1.31 
                 1.30 
                 1.26 
                 1.26 
                 1.24 
                 1.21 
                 1.19 
               
               
                 #64 
                 110.67 
                 110.81 
                 110.96 
                 111.11 
                 111.25 
                 111.40 
                 111.55 
                 111.60 
                 111.84 
                 111.98 
                 112.13 
                 112.28 
               
               
                 — 
                 1.16 
                 1.13 
                 1.10 
                 1.08 
                 1.05 
                 1.02 
                 0.99 
                 0.96 
                 0.94 
                 0.91 
                 0.89 
                 0.87 
               
               
                 #65 
                 112.42 
                 112.57 
                 112.72 
                 112.86 
                 113.01 
                 113.16 
                 113.30 
                 113.46 
                 113.59 
                 113.74 
                 113.89 
                 114.03 
               
               
                 — 
                 0.83 
                 0.83 
                 0.81 
                 0.80 
                 0.79 
                 0.77 
                 0.76 
                 0.76 
                 0.75 
                 0.75 
                 0.75 
                 0.74 
               
               
                 #66 
                 114.18 
                 114.33 
                 114.47 
                 114.62 
                 114.77 
                 114.91 
                 115.06 
                 115.21 
                 115.36 
                 115.50 
                 115.64 
                 115.79 
               
               
                 — 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.76 
                 0.77 
                 0.77 
                 0.78 
                 0.79 
                 0.80 
                 0.80 
                 0.81 
               
               
                 #67 
                 115.84 
                 116.08 
                 116.23 
                 116.38 
                 116.52 
                 116.67 
                 116.82 
                 116.96 
                 117.11 
                 117.25 
                 117.40 
                 117.55 
               
               
                 — 
                 0.82 
                 0.82 
                 0.83 
                 0.83 
                 0.84 
                 0.84 
                 0.85 
                 0.85 
                 0.85 
                 0.85 
                 0.85 
                 0.85 
               
               
                 #68 
                 117.69 
                 117.84 
                 117.99 
                 118.13 
                 118.23 
                 118.43 
                 118.57 
                 118.72 
                 118.86 
                 119.01 
                 119.16 
                 119.30 
               
               
                 — 
                 0.84 
                 0.84 
                 0.83 
                 0.82 
                 0.82 
                 0.82 
                 0.81 
                 0.81 
                 0.80 
                 0.80 
                 0.80 
                 0.79 
               
               
                 #69 
                 119.45 
                 119.60 
                 119.74 
                 119.89 
                 120.04 
                 120.18 
                 120.33 
                 120.47 
                 120.62 
                 120.77 
                 120.91 
                 121.06 
               
               
                 — 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.80 
                 0.80 
                 0.81 
                 0.82 
                 0.82 
                 0.84 
                 0.85 
               
               
                 #70 
                 121.21 
                 121.35 
                 121.50 
                 121.65 
                 121.79 
                 121.94 
                 122.09 
                 122.23 
                 122.38 
                 122.52 
                 122.67 
                 122.82 
               
               
                 — 
                 0.86 
                 0.87 
                 0.89 
                 0.91 
                 0.92 
                 0.94 
                 0.96 
                 0.98 
                 1.00 
                 1.02 
                 1.04 
                 1.06 
               
               
                 #71 
                 122.98 
                 123.11 
                 123.28 
                 123.40 
                 123.56 
                 123.70 
                 123.84 
                 123.99 
                 124.13 
                 124.28 
                 124.43 
                 124.57 
               
               
                 — 
                 1.08 
                 1.10 
                 1.12 
                 1.13 
                 1.15 
                 1.16 
                 1.18 
                 1.19 
                 1.20 
                 1.20 
                 1.21 
                 1.21 
               
               
                 #72 
                 124.72 
                 124.87 
                 125.01 
                 125.16 
                 125.31 
                 125.46 
                 125.60 
                 125.74 
                 125.80 
                 126.04 
                 126.18 
                 126.33 
               
               
                 — 
                 1.21 
                 1.21 
                 1.21 
                 1.21 
                 1.20 
                 1.20 
                 1.18 
                 1.18 
                 1.17 
                 1.16 
                 1.15 
                 1.14 
               
               
                 #73 
                 126.48 
                 126.62 
                 126.77 
                 126.92 
                 127.06 
                 127.21 
                 127.38 
                 127.50 
                 127.65 
                 127.79 
                 127.94 
                 128.09 
               
               
                 — 
                 1.13 
                 1.12 
                 1.11 
                 1.10 
                 1.00 
                 1.08 
                 1.07 
                 1.06 
                 1.05 
                 1.05 
                 1.04 
                 1.03 
               
               
                 #74 
                 128.23 
                 128.38 
                 128.53 
                 128.67 
                 128.82 
                 128.97 
                 129.11 
                 129.26 
                 129.40 
                 129.55 
                 129.70 
                 129.84 
               
               
                 — 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.03 
                 1.04 
                 1.04 
               
               
                 #75 
                 129.99 
                 130.14 
                 130.28 
                 130.43 
                 130.58 
                 130.72 
                 130.87 
                 131.01 
                 131.16 
                 131.31 
                 131.45 
                 131.60 
               
               
                   
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.03 
                 1.03 
                 1.02 
               
               
                 #76 
                 131.75 
                 131.89 
                 132.04 
                 132.19 
                 132.33 
                 132.48 
                 132.52 
                 132.77 
                 132.92 
                 133.06 
                 133.21 
                 133.36 
               
               
                 — 
                 1.02 
                 1.01 
                 1.00 
                 0.99 
                 0.98 
                 0.97 
                 0.95 
                 0.94 
                 0.93 
                 0.92 
                 0.90 
                 0.89 
               
               
                 #77 
                 133.50 
                 133.65 
                 133.80 
                 133.94 
                 134.09 
                 134.24 
                 134.38 
                 134.53 
                 134.67 
                 134.82 
                 134.87 
                 135.11 
               
               
                 — 
                 0.88 
                 0.86 
                 0.85 
                 0.84 
                 0.83 
                 0.82 
                 0.81 
                 0.80 
                 0.79 
                 0.79 
                 0.78 
                 0.78 
               
               
                 #78 
                 135.26 
                 135.41 
                 135.55 
                 135.76 
                 135.85 
                 135.99 
                 136.14 
                 136.28 
                 136.43 
                 136.58 
                 136.72 
                 136.87 
               
               
                 — 
                 0.77 
                 0.77 
                 0.77 
                 0.77 
                 0.78 
                 0.78 
                 0.78 
                 0.79 
                 0.79 
                 0.80 
                 0.81 
                 0.81 
               
               
                 #79 
                 137.02 
                 137.16 
                 137.31 
                 137.46 
                 137.66 
                 137.75 
                 137.89 
                 138.04 
                 138.19 
                 138.33 
                 138.48 
                 138.63 
               
               
                 — 
                 0.82 
                 0.83 
                 0.84 
                 0.85 
                 0.86 
                 0.87 
                 0.88 
                 0.89 
                 0.90 
                 0.91 
                 0.92 
                 0.93 
               
               
                 #80 
                 138.77 
                 138.92 
                 139.07 
                 139.21 
                 139.36 
                 139.50 
                 139.65 
                 139.80 
                 139.94 
                 140.09 
                 140.24 
                 140.38 
               
               
                 — 
                 0.93 
                 0.94 
                 0.94 
                 0.95 
                 0.95 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
               
               
                 #81 
                 140.53 
                 140.68 
                 140.82 
                 140.97 
                 141.12 
                 141.26 
                 141.41 
                 141.55 
                 141.70 
                 141.85 
                 141.90 
                 142.14 
               
               
                 — 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
               
               
                 #82 
                 142.20 
                 142.43 
                 142.58 
                 142.73 
                 142.87 
                 143.02 
                 143.16 
                 143.31 
                 143.46 
                 143.60 
                 143.75 
                 143.90 
               
               
                 — 
                 0.95 
                 0.96 
                 0.96 
                 0.96 
                 0.97 
                 0.98 
                 0.98 
                 0.99 
                 1.00 
                 1.00 
                 1.01 
                 1.02 
               
               
                 #83 
                 144.04 
                 144.19 
                 144.34 
                 144.48 
                 144.63 
                 144.77 
                 144.92 
                 145.07 
                 145.21 
                 145.36 
                 145.51 
                 145.65 
               
               
                 — 
                 1.03 
                 1.04 
                 1.05 
                 1.06 
                 1.07 
                 1.08 
                 1.08 
                 1.09 
                 1.10 
                 1.11 
                 1.11 
                 1.12 
               
               
                 #84 
                 145.80 
                 145.95 
                 146.09 
                 146.24 
                 146.39 
               
               
                 — 
                 1.12 
                 1.13 
                 1.13 
                 1.13 
                 1.13 
               
               
                   
               
             
          
         
       
     
       FIG. 5  shows the shape of the center conductor  6  in the reflection-type bandpass filter  1  of Embodiment 1. In the figure, the dark portion represents the center conductor  6 . A non-reflecting terminator, or an R=50Ω resistance, is provided on the terminating side (the face at z=146.39 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 conducting layers  4 ,  5  and of the center conductor  6  may 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 vacuum, and the conductivity of the metal. For example, when using copper, the thickness of the conducting layers  4 ,  5  and of the center conductor  6  may be 2.1 μm or greater. This bandpass filter is used in a system with a characteristic impedance of 50Ω. 
       FIG. 6  and  FIG. 7  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 3.7 GHz≦f≦10.0 GHz, the reflectance is −1 dB or greater, and the group delay variation is within ±0.05 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −17 dB or lower. 
     Embodiment 2 
     A Kaiser window was used for which the reflectance is 1 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-half the wavelength of signals at frequency f=1 GHz propagating in the microstrip as the waveguide length, and setting the system characteristic impedance to 50Ω.  FIG. 8  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 9  shows the z-axis distribution of the center conductor width w, when using a dielectric layer  3  of thickness h=3 mm and with relative permittivity ∈ r =2. Tables 4 through 6 list the center conductor widths w. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Center conductor widths (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.11 
                 0.21 
                 0.32 
                 0.42 
                 0.53 
                 0.64 
                 0.74 
                 0.85 
                 0.95 
                 1.06 
                 1.17 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.69 
                 2.69 
                 2.69 
                 2.70 
                 2.70 
                 2.70 
                 2.71 
                 2.71 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 1.27 
                 1.58 
                 1.48 
                 1.50 
                 1.70 
                 1.80 
                 1.91 
                 2.02 
                 2.12 
                 2.23 
                 2.33 
                 2.44 
               
               
                 — 
                 2.71 
                 2.71 
                 2.71 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.73 
               
               
                  #3 
                 2.55 
                 2.65 
                 2.70 
                 2.80 
                 2.97 
                 3.08 
                 3.18 
                 3.29 
                 3.39 
                 3.50 
                 3.61 
                 3.71 
               
               
                 — 
                 2.73 
                 2.73 
                 2.73 
                 2.73 
                 2.73 
                 2.73 
                 2.72 
                 2.72 
                 2.72 
                 2.73 
                 2.72 
                 2.72 
               
               
                  #4 
                 3.82 
                 3.92 
                 4.03 
                 4.14 
                 4.24 
                 4.35 
                 4.45 
                 4.56 
                 4.67 
                 4.77 
                 4.88 
                 4.99 
               
               
                 — 
                 2.72 
                 2.72 
                 2.72 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.70 
                 2.70 
                 2.70 
               
               
                  #5 
                 5.09 
                 5.20 
                 5.30 
                 5.41 
                 5.52 
                 5.62 
                 5.73 
                 5.83 
                 5.94 
                 6.05 
                 6.15 
                 6.26 
               
               
                 — 
                 2.70 
                 2.70 
                 2.70 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.68 
               
               
                  #6 
                 6.36 
                 6.47 
                 6.68 
                 6.68 
                 6.79 
                 6.89 
                 7.00 
                 7.11 
                 7.21 
                 7.32 
                 7.42 
                 7.53 
               
               
                 — 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
                 2.68 
               
               
                  #7 
                 7.64 
                 7.74 
                 7.85 
                 7.95 
                 8.06 
                 8.17 
                 8.27 
                 8.38 
                 8.40 
                 8.50 
                 8.70 
                 8.80 
               
               
                 — 
                 2.68 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.69 
                 2.70 
                 2.70 
                 2.70 
               
               
                  #8 
                 8.91 
                 9.02 
                 9.12 
                 9.23 
                 9.33 
                 9.44 
                 9.55 
                 9.65 
                 9.76 
                 9.80 
                 9.97 
                 10.08 
               
               
                 — 
                 2.70 
                 2.70 
                 2.70 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
               
               
                  #9 
                 10.18 
                 10.29 
                 10.30 
                 10.50 
                 10.61 
                 10.71 
                 10.82 
                 10.92 
                 11.03 
                 11.14 
                 11.24 
                 11.36 
               
               
                 — 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.72 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
                 2.71 
               
               
                 #10 
                 11.46 
                 11.56 
                 11.67 
                 11.77 
                 11.88 
                 11.98 
                 12.09 
                 12.20 
                 12.30 
                 12.41 
                 12.52 
                 12.62 
               
               
                 — 
                 2.71 
                 2.70 
                 2.70 
                 2.70 
                 2.69 
                 2.69 
                 2.69 
                 2.68 
                 2.68 
                 2.67 
                 2.67 
                 2.66 
               
               
                 #11 
                 12.73 
                 12.83 
                 12.94 
                 13.06 
                 13.16 
                 13.26 
                 13.36 
                 13.47 
                 13.58 
                 13.68 
                 13.79 
                 13.89 
               
               
                 — 
                 2.65 
                 2.65 
                 2.64 
                 2.63 
                 2.63 
                 2.62 
                 2.61 
                 2.61 
                 2.60 
                 2.59 
                 2.58 
                 2.57 
               
               
                 #12 
                 14.00 
                 14.31 
                 14.21 
                 14.32 
                 14.42 
                 14.53 
                 14.64 
                 14.74 
                 14.85 
                 14.90 
                 15.00 
                 15.17 
               
               
                 — 
                 2.57 
                 2.55 
                 2.55 
                 2.54 
                 2.53 
                 2.52 
                 2.51 
                 2.50 
                 2.50 
                 2.49 
                 2.48 
                 2.47 
               
               
                 #13 
                 15.27 
                 15.38 
                 15.49 
                 15.59 
                 15.70 
                 15.80 
                 15.91 
                 16.02 
                 16.12 
                 16.23 
                 16.33 
                 16.44 
               
               
                 — 
                 2.46 
                 2.45 
                 2.45 
                 2.44 
                 2.43 
                 2.42 
                 2.42 
                 2.41 
                 2.40 
                 2.40 
                 2.39 
                 2.38 
               
               
                 #14 
                 16.55 
                 16.65 
                 16.76 
                 16.86 
                 16.97 
                 17.06 
                 17.18 
                 17.29 
                 17.39 
                 17.50 
                 17.61 
                 17.71 
               
               
                 — 
                 2.38 
                 2.37 
                 2.37 
                 2.36 
                 2.36 
                 2.36 
                 2.35 
                 2.35 
                 2.35 
                 2.34 
                 2.34 
                 2.34 
               
               
                 #15 
                 17.82 
                 17.93 
                 18.03 
                 18.14 
                 18.24 
                 18.35 
                 18.46 
                 18.56 
                 18.67 
                 18.77 
                 18.88 
                 18.99 
               
               
                 — 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
               
               
                 #16 
                 19.00 
                 19.20 
                 19.30 
                 19.41 
                 19.52 
                 19.62 
                 19.73 
                 19.83 
                 19.94 
                 20.05 
                 20.15 
                 20.26 
               
               
                 — 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.36 
                 2.36 
                 2.36 
                 2.37 
                 2.37 
                 2.37 
                 2.38 
                 2.38 
               
               
                 #17 
                 20.36 
                 20.47 
                 20.58 
                 20.68 
                 20.79 
                 20.90 
                 21.00 
                 21.11 
                 21.21 
                 21.32 
                 21.43 
                 21.53 
               
               
                 — 
                 2.38 
                 2.39 
                 2.39 
                 2.39 
                 2.40 
                 2.40 
                 2.40 
                 2.40 
                 2.41 
                 2.41 
                 2.41 
                 2.41 
               
               
                 #18 
                 21.64 
                 21.74 
                 21.85 
                 21.96 
                 22.06 
                 22.17 
                 22.27 
                 22.38 
                 22.49 
                 22.59 
                 22.70 
                 22.80 
               
               
                 — 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
                 2.42 
               
               
                 #19 
                 22.91 
                 23.02 
                 23.12 
                 23.23 
                 23.33 
                 23.44 
                 23.55 
                 23.65 
                 23.76 
                 23.86 
                 23.97 
                 24.08 
               
               
                 — 
                 2.42 
                 2.41 
                 2.41 
                 2.41 
                 2.41 
                 2.41 
                 2.40 
                 2.40 
                 2.40 
                 2.39 
                 2.39 
                 2.39 
               
               
                 #20 
                 24.18 
                 24.29 
                 24.40 
                 24.50 
                 24.61 
                 24.71 
                 24.82 
                 24.93 
                 25.03 
                 25.14 
                 25.24 
                 25.35 
               
               
                 — 
                 2.38 
                 2.38 
                 2.38 
                 2.37 
                 2.37 
                 2.37 
                 2.36 
                 2.36 
                 2.36 
                 2.36 
                 2.35 
                 2.35 
               
               
                 #21 
                 25.46 
                 25.56 
                 25.67 
                 25.77 
                 25.88 
                 25.99 
                 26.09 
                 26.20 
                 26.30 
                 26.41 
                 26.52 
                 26.62 
               
               
                 — 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.35 
                 2.36 
               
               
                 #22 
                 26.73 
                 26.83 
                 26.94 
                 27.05 
                 27.15 
                 27.26 
                 27.37 
                 27.47 
                 27.58 
                 27.68 
                 27.79 
                 27.90 
               
               
                 — 
                 2.36 
                 2.36 
                 2.37 
                 2.37 
                 2.38 
                 2.39 
                 2.39 
                 2.40 
                 2.41 
                 2.42 
                 2.43 
                 2.44 
               
               
                 #23 
                 28.00 
                 28.11 
                 28.21 
                 28.32 
                 28.43 
                 28.53 
                 28.64 
                 28.74 
                 28.85 
                 28.98 
                 29.00 
                 29.17 
               
               
                 — 
                 2.45 
                 2.46 
                 2.48 
                 2.49 
                 2.50 
                 2.52 
                 2.53 
                 2.55 
                 2.56 
                 2.58 
                 2.60 
                 2.62 
               
               
                 #24 
                 29.27 
                 29.38 
                 29.49 
                 29.59 
                 29.70 
                 29.80 
                 29.91 
                 30.02 
                 30.12 
                 30.23 
                 30.33 
                 30.44 
               
               
                 — 
                 2.63 
                 2.65 
                 2.67 
                 2.69 
                 2.71 
                 2.73 
                 2.75 
                 2.77 
                 2.79 
                 2.82 
                 2.84 
                 2.86 
               
               
                 #25 
                 30.55 
                 30.55 
                 30.76 
                 30.87 
                 30.97 
                 31.08 
                 31.18 
                 31.29 
                 31.40 
                 31.50 
                 31.61 
                 31.71 
               
               
                 — 
                 2.88 
                 2.90 
                 2.92 
                 2.94 
                 2.96 
                 2.98 
                 3.00 
                 3.02 
                 3.04 
                 3.06 
                 3.07 
                 3.09 
               
               
                 #26 
                 31.82 
                 31.93 
                 32.03 
                 32.14 
                 32.24 
                 32.35 
                 32.46 
                 32.56 
                 32.67 
                 32.77 
                 32.88 
                 32.99 
               
               
                 — 
                 3.11 
                 3.12 
                 3.14 
                 3.15 
                 3.16 
                 3.18 
                 3.19 
                 3.20 
                 3.21 
                 3.22 
                 3.23 
                 3.23 
               
               
                 #27 
                 33.09 
                 33.20 
                 33.30 
                 33.41 
                 33.52 
                 33.62 
                 33.73 
                 33.84 
                 33.94 
                 34.05 
                 34.15 
                 34.26 
               
               
                 — 
                 3.24 
                 3.24 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.25 
                 3.24 
               
               
                 #28 
                 34.37 
                 34.47 
                 34.58 
                 34.68 
                 34.79 
                 34.90 
                 35.00 
                 35.11 
                 35.21 
                 35.32 
                 35.43 
                 35.53 
               
               
                 — 
                 3.24 
                 3.23 
                 3.23 
                 3.22 
                 3.21 
                 3.20 
                 3.20 
                 3.19 
                 3.18 
                 3.17 
                 3.16 
                 3.15 
               
               
                 #29 
                 35.64 
                 35.74 
                 35.85 
                 35.96 
                 36.06 
                 36.17 
                 36.27 
                 36.38 
                 36.49 
                 36.50 
                 36.70 
                 36.80 
               
               
                 — 
                 3.14 
                 3.13 
                 3.12 
                 3.12 
                 3.11 
                 3.10 
                 3.09 
                 3.08 
                 3.07 
                 3.07 
                 3.06 
                 3.05 
               
               
                 #30 
                 36.91 
                 37.02 
                 37.12 
                 37.23 
                 37.34 
                 37.44 
                 37.55 
                 37.65 
                 37.76 
                 37.87 
                 37.97 
                 38.08 
               
               
                 — 
                 3.05 
                 3.04 
                 3.04 
                 3.04 
                 3.03 
                 3.03 
                 3.03 
                 3.03 
                 3.03 
                 3.03 
                 3.03 
                 3.04 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 Center conductor widths (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 38.18 
                 38.29 
                 38.40 
                 38.50 
                 38.61 
                 38.71 
                 38.82 
                 38.93 
                 39.03 
                 39.14 
                 39.24 
                 39.35 
               
               
                 — 
                 3.04 
                 3.04 
                 3.05 
                 3.05 
                 3.06 
                 3.07 
                 3.08 
                 3.08 
                 3.09 
                 3.10 
                 3.11 
                 3.12 
               
               
                 #32 
                 39.46 
                 39.56 
                 39.67 
                 39.77 
                 39.88 
                 39.90 
                 40.09 
                 40.20 
                 40.31 
                 40.41 
                 40.52 
                 40.62 
               
               
                 — 
                 3.13 
                 3.14 
                 3.15 
                 3.17 
                 3.18 
                 3.19 
                 3.20 
                 3.21 
                 3.22 
                 3.23 
                 3.24 
                 3.25 
               
               
                 #33 
                 40.73 
                 40.84 
                 40.94 
                 41.05 
                 41.15 
                 41.26 
                 41.37 
                 41.47 
                 41.58 
                 41.68 
                 41.79 
                 41.90 
               
               
                 — 
                 3.26 
                 3.27 
                 3.27 
                 3.28 
                 3.28 
                 3.29 
                 3.29 
                 3.29 
                 3.29 
                 3.28 
                 3.28 
                 3.27 
               
               
                 #34 
                 42.00 
                 42.11 
                 42.21 
                 42.32 
                 42.43 
                 42.53 
                 42.64 
                 42.74 
                 42.85 
                 42.96 
                 43.06 
                 43.17 
               
               
                 — 
                 3.26 
                 3.25 
                 3.24 
                 3.22 
                 3.21 
                 3.19 
                 3.17 
                 3.14 
                 3.12 
                 3.09 
                 3.06 
                 3.02 
               
               
                 #35 
                 43.27 
                 43.38 
                 43.49 
                 43.59 
                 43.70 
                 43.81 
                 43.91 
                 44.02 
                 44.12 
                 44.23 
                 44.34 
                 44.44 
               
               
                 — 
                 2.99 
                 2.95 
                 2.91 
                 2.87 
                 2.83 
                 2.78 
                 2.73 
                 2.69 
                 2.64 
                 2.58 
                 2.53 
                 2.48 
               
               
                 #36 
                 44.55 
                 44.65 
                 44.76 
                 44.87 
                 44.97 
                 45.08 
                 45.18 
                 45.29 
                 45.40 
                 45.50 
                 45.61 
                 45.71 
               
               
                 — 
                 2.42 
                 2.37 
                 2.31 
                 2.25 
                 2.19 
                 2.14 
                 2.08 
                 2.02 
                 1.96 
                 1.99 
                 1.85 
                 1.79 
               
               
                 #37 
                 45.82 
                 45.93 
                 46.03 
                 46.14 
                 46.24 
                 46.35 
                 46.46 
                 46.56 
                 46.67 
                 46.78 
                 46.88 
                 46.99 
               
               
                 — 
                 1.73 
                 1.68 
                 1.63 
                 1.57 
                 1.52 
                 1.47 
                 1.42 
                 1.37 
                 1.33 
                 1.28 
                 1.24 
                 1.20 
               
               
                 #38 
                 47.09 
                 47.20 
                 47.31 
                 47.41 
                 47.52 
                 47.62 
                 47.73 
                 47.84 
                 47.94 
                 48.05 
                 48.15 
                 48.26 
               
               
                 — 
                 1.16 
                 1.12 
                 1.08 
                 1.05 
                 1.01 
                 0.98 
                 0.95 
                 0.93 
                 0.90 
                 0.88 
                 0.86 
                 0.84 
               
               
                 #39 
                 48.37 
                 48.47 
                 48.58 
                 48.68 
                 48.79 
                 48.90 
                 49.00 
                 49.11 
                 49.21 
                 49.32 
                 49.43 
                 49.53 
               
               
                 — 
                 0.82 
                 0.80 
                 0.79 
                 0.78 
                 0.77 
                 0.76 
                 0.76 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.76 
               
               
                 #40 
                 49.64 
                 49.74 
                 49.65 
                 49.96 
                 50.06 
                 50.17 
                 50.28 
                 50.38 
                 50.49 
                 50.59 
                 50.70 
                 50.81 
               
               
                 — 
                 0.76 
                 0.77 
                 0.78 
                 0.80 
                 0.81 
                 0.83 
                 0.85 
                 0.87 
                 0.90 
                 0.93 
                 0.96 
                 1.00 
               
               
                 #41 
                 50.01 
                 51.02 
                 51.12 
                 51.23 
                 51.34 
                 51.44 
                 51.55 
                 51.65 
                 51.76 
                 51.87 
                 51.97 
                 52.08 
               
               
                 — 
                 1.03 
                 1.07 
                 1.12 
                 1.17 
                 1.22 
                 1.27 
                 1.33 
                 1.40 
                 1.47 
                 1.54 
                 1.61 
                 1.69 
               
               
                 #42 
                 52.18 
                 52.29 
                 52.40 
                 52.50 
                 52.61 
                 52.71 
                 52.82 
                 52.93 
                 53.03 
                 53.14 
                 53.25 
                 53.35 
               
               
                 — 
                 1.78 
                 1.87 
                 1.96 
                 2.06 
                 2.17 
                 2.28 
                 2.39 
                 2.51 
                 2.63 
                 2.76 
                 2.90 
                 3.04 
               
               
                 #43 
                 53.46 
                 53.56 
                 53.67 
                 53.78 
                 53.88 
                 53.99 
                 54.09 
                 54.20 
                 54.31 
                 54.41 
                 54.52 
                 54.62 
               
               
                 — 
                 3.18 
                 3.33 
                 3.49 
                 3.65 
                 3.81 
                 3.98 
                 4.15 
                 4.33 
                 4.51 
                 4.69 
                 4.88 
                 5.07 
               
               
                 #44 
                 54.73 
                 54.84 
                 54.94 
                 55.05 
                 55.15 
                 55.26 
                 55.37 
                 55.47 
                 55.58 
                 55.68 
                 55.79 
                 55.80 
               
               
                 — 
                 5.26 
                 5.45 
                 5.64 
                 5.83 
                 6.03 
                 6.22 
                 6.41 
                 6.59 
                 6.77 
                 6.95 
                 7.12 
                 7.29 
               
               
                 #45 
                 56.00 
                 56.11 
                 56.21 
                 56.32 
                 56.43 
                 56.53 
                 56.64 
                 56.75 
                 56.85 
                 56.96 
                 57.06 
                 57.17 
               
               
                 — 
                 7.45 
                 7.60 
                 7.74 
                 7.87 
                 7.99 
                 8.10 
                 8.20 
                 8.28 
                 8.35 
                 8.41 
                 8.45 
                 8.48 
               
               
                 #46 
                 57.28 
                 57.38 
                 57.49 
                 57.59 
                 57.70 
                 57.81 
                 57.91 
                 58.02 
                 58.12 
                 58.23 
                 58.34 
                 58.44 
               
               
                 — 
                 8.49 
                 8.48 
                 8.47 
                 8.43 
                 8.38 
                 8.32 
                 8.24 
                 8.15 
                 8.05 
                 7.93 
                 7.80 
                 7.66 
               
               
                 #47 
                 58.55 
                 58.65 
                 58.76 
                 58.87 
                 58.97 
                 59.08 
                 59.18 
                 59.29 
                 59.40 
                 59.50 
                 59.61 
                 59.72 
               
               
                 — 
                 7.51 
                 7.35 
                 7.18 
                 7.01 
                 6.82 
                 6.64 
                 6.44 
                 6.29 
                 6.05 
                 5.84 
                 5.64 
                 5.44 
               
               
                 #48 
                 59.82 
                 59.93 
                 60.03 
                 60.14 
                 60.25 
                 60.35 
                 60.46 
                 60.56 
                 60.67 
                 60.78 
                 60.88 
                 60.99 
               
               
                 — 
                 5.23 
                 5.03 
                 4.83 
                 4.63 
                 4.43 
                 4.24 
                 4.05 
                 3.87 
                 3.68 
                 3.51 
                 3.33 
                 3.17 
               
               
                 #49 
                 61.09 
                 61.20 
                 61.31 
                 61.41 
                 61.52 
                 61.62 
                 61.73 
                 61.84 
                 61.94 
                 62.05 
                 62.15 
                 62.25 
               
               
                 — 
                 3.00 
                 2.85 
                 2.70 
                 2.55 
                 2.41 
                 2.27 
                 2.15 
                 2.02 
                 1.90 
                 1.79 
                 1.68 
                 1.58 
               
               
                 #50 
                 62.37 
                 62.47 
                 62.58 
                 62.69 
                 62.79 
                 62.90 
                 63.00 
                 63.11 
                 63.22 
                 63.32 
                 63.43 
                 63.53 
               
               
                 — 
                 1.48 
                 1.39 
                 1.30 
                 1.22 
                 1.15 
                 1.07 
                 1.01 
                 0.94 
                 0.88 
                 0.83 
                 0.78 
                 0.73 
               
               
                 #51 
                 63.64 
                 63.76 
                 63.85 
                 63.96 
                 64.06 
                 64.17 
                 64.28 
                 64.38 
                 64.49 
                 64.59 
                 64.70 
                 64.81 
               
               
                 — 
                 0.69 
                 0.65 
                 0.61 
                 0.58 
                 0.55 
                 0.52 
                 0.50 
                 0.48 
                 0.46 
                 0.44 
                 0.43 
                 0.41 
               
               
                 #52 
                 64.91 
                 65.02 
                 65.12 
                 65.23 
                 65.34 
                 65.44 
                 65.55 
                 65.65 
                 65.76 
                 65.87 
                 65.97 
                 66.08 
               
               
                 — 
                 0.40 
                 0.39 
                 0.39 
                 0.38 
                 0.38 
                 0.38 
                 0.38 
                 0.38 
                 0.39 
                 0.39 
                 0.40 
                 0.41 
               
               
                 #53 
                 66.19 
                 66.29 
                 66.40 
                 66.50 
                 66.61 
                 66.72 
                 66.82 
                 66.93 
                 67.03 
                 67.14 
                 67.25 
                 67.35 
               
               
                 — 
                 0.42 
                 0.44 
                 0.46 
                 0.47 
                 0.50 
                 0.52 
                 0.55 
                 0.57 
                 0.61 
                 0.64 
                 0.68 
                 0.72 
               
               
                 #54 
                 67.46 
                 67.56 
                 67.67 
                 67.78 
                 67.88 
                 67.99 
                 68.09 
                 68.20 
                 68.31 
                 68.41 
                 68.52 
                 68.62 
               
               
                 — 
                 0.76 
                 0.81 
                 0.86 
                 0.92 
                 0.96 
                 1.04 
                 1.11 
                 1.18 
                 1.26 
                 1.33 
                 1.42 
                 1.51 
               
               
                 #55 
                 68.73 
                 68.84 
                 68.94 
                 69.05 
                 69.16 
                 69.25 
                 69.37 
                 69.47 
                 69.58 
                 69.69 
                 69.79 
                 69.90 
               
               
                 — 
                 1.60 
                 1.70 
                 1.80 
                 1.90 
                 2.01 
                 2.13 
                 2.24 
                 2.37 
                 2.49 
                 2.52 
                 2.76 
                 2.89 
               
               
                 #56 
                 70.00 
                 70.11 
                 70.22 
                 70.32 
                 70.43 
                 70.53 
                 70.64 
                 70.75 
                 70.86 
                 70.96 
                 71.00 
                 71.17 
               
               
                 — 
                 3.03 
                 3.18 
                 3.32 
                 3.47 
                 3.62 
                 3.77 
                 3.93 
                 4.08 
                 4.24 
                 4.40 
                 4.55 
                 4.71 
               
               
                 #57 
                 71.28 
                 71.38 
                 71.49 
                 71.59 
                 71.70 
                 71.81 
                 71.91 
                 72.02 
                 72.12 
                 72.23 
                 72.34 
                 72.44 
               
               
                 — 
                 4.86 
                 5.01 
                 5.16 
                 5.31 
                 5.45 
                 5.59 
                 5.72 
                 5.85 
                 5.97 
                 6.08 
                 6.19 
                 6.28 
               
               
                 #58 
                 72.55 
                 72.66 
                 72.76 
                 72.87 
                 72.97 
                 73.08 
                 73.19 
                 73.29 
                 73.40 
                 73.50 
                 73.61 
                 73.72 
               
               
                 — 
                 6.38 
                 6.46 
                 6.54 
                 6.60 
                 6.65 
                 6.70 
                 6.73 
                 6.76 
                 6.77 
                 6.77 
                 6.77 
                 6.75 
               
               
                 #59 
                 73.82 
                 73.93 
                 74.03 
                 74.14 
                 74.25 
                 74.35 
                 74.46 
                 74.56 
                 74.67 
                 74.78 
                 74.88 
                 74.90 
               
               
                 — 
                 6.72 
                 6.69 
                 6.64 
                 6.59 
                 6.52 
                 6.45 
                 6.37 
                 6.29 
                 6.19 
                 6.09 
                 5.99 
                 5.88 
               
               
                 #60 
                 75.09 
                 75.20 
                 75.31 
                 75.41 
                 75.52 
                 75.63 
                 75.73 
                 75.84 
                 75.94 
                 76.05 
                 76.16 
                 76.25 
               
               
                 — 
                 5.77 
                 5.65 
                 5.53 
                 5.41 
                 5.28 
                 5.15 
                 5.02 
                 4.90 
                 4.77 
                 4.64 
                 4.51 
                 4.38 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Center conductor widths (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 76.37 
                 76.47 
                 76.58 
                 76.69 
                 76.79 
                 76.90 
                 77.00 
                 77.11 
                 77.22 
                 77.32 
                 77.43 
                 77.53 
               
               
                 — 
                 4.25 
                 4.13 
                 4.01 
                 3.88 
                 3.77 
                 3.65 
                 3.53 
                 3.42 
                 3.32 
                 3.21 
                 3.11 
                 3.01 
               
               
                 #62 
                 77.64 
                 77.75 
                 77.85 
                 77.96 
                 78.06 
                 78.17 
                 78.28 
                 78.38 
                 78.49 
                 78.59 
                 78.70 
                 78.81 
               
               
                 — 
                 2.92 
                 2.82 
                 2.74 
                 2.65 
                 2.57 
                 2.49 
                 2.41 
                 2.34 
                 2.28 
                 2.21 
                 2.15 
                 2.09 
               
               
                 #63 
                 78.91 
                 79.02 
                 79.13 
                 79.23 
                 79.34 
                 79.44 
                 79.55 
                 79.66 
                 79.76 
                 79.87 
                 79.97 
                 80.08 
               
               
                 — 
                 2.03 
                 1.98 
                 1.93 
                 1.89 
                 1.84 
                 1.80 
                 1.77 
                 1.73 
                 1.70 
                 1.67 
                 1.64 
                 1.62 
               
               
                 #64 
                 80.19 
                 80.29 
                 80.40 
                 80.50 
                 80.61 
                 80.72 
                 80.82 
                 80.93 
                 81.03 
                 81.14 
                 81.25 
                 81.35 
               
               
                 — 
                 1.59 
                 1.57 
                 1.56 
                 1.54 
                 1.53 
                 1.52 
                 1.51 
                 1.50 
                 1.50 
                 1.49 
                 1.49 
                 1.49 
               
               
                 #65 
                 81.46 
                 51.56 
                 81.67 
                 81.78 
                 81.88 
                 81.99 
                 82.10 
                 82.20 
                 82.31 
                 82.41 
                 82.52 
                 82.03 
               
               
                 — 
                 1.49 
                 1.50 
                 1.50 
                 1.51 
                 1.52 
                 1.53 
                 1.54 
                 1.55 
                 1.56 
                 1.58 
                 1.59 
                 1.61 
               
               
                 #66 
                 82.73 
                 82.84 
                 82.94 
                 83.05 
                 83.16 
                 83.26 
                 83.37 
                 83.47 
                 83.58 
                 83.69 
                 83.79 
                 83.90 
               
               
                 — 
                 1.63 
                 1.65 
                 1.67 
                 1.69 
                 1.71 
                 1.73 
                 1.75 
                 1.77 
                 1.80 
                 1.82 
                 1.84 
                 1.86 
               
               
                 #67 
                 84.00 
                 84.11 
                 84.22 
                 84.32 
                 84.43 
                 84.53 
                 84.64 
                 84.75 
                 84.85 
                 84.96 
                 85.06 
                 85.17 
               
               
                 — 
                 1.89 
                 1.91 
                 1.93 
                 1.96 
                 1.98 
                 2.00 
                 2.02 
                 2.04 
                 2.07 
                 2.09 
                 2.10 
                 2.12 
               
               
                 #68 
                 85.28 
                 85.38 
                 85.49 
                 85.60 
                 85.70 
                 85.81 
                 85.91 
                 86.02 
                 86.13 
                 86.23 
                 86.34 
                 86.44 
               
               
                 — 
                 2.14 
                 2.16 
                 2.17 
                 2.19 
                 2.20 
                 2.22 
                 2.23 
                 2.24 
                 2.25 
                 2.26 
                 2.27 
                 2.28 
               
               
                 #69 
                 86.55 
                 86.66 
                 86.76 
                 86.87 
                 86.97 
                 87.86 
                 87.19 
                 87.29 
                 87.40 
                 87.59 
                 87.61 
                 87.72 
               
               
                 — 
                 2.28 
                 2.29 
                 2.29 
                 2.30 
                 2.30 
                 2.30 
                 2.30 
                 2.30 
                 2.30 
                 2.30 
                 2.30 
                 2.29 
               
               
                 #70 
                 87.82 
                 87.93 
                 88.03 
                 88.14 
                 88.25 
                 88.35 
                 88.46 
                 88.57 
                 88.67 
                 88.78 
                 88.88 
                 88.99 
               
               
                 — 
                 2.29 
                 2.29 
                 2.29 
                 2.28 
                 2.28 
                 2.27 
                 2.27 
                 2.27 
                 2.26 
                 2.26 
                 2.26 
                 2.25 
               
               
                 #71 
                 89.10 
                 89.20 
                 89.31 
                 89.41 
                 89.52 
                 89.63 
                 89.73 
                 89.84 
                 89.94 
                 90.05 
                 90.16 
                 90.26 
               
               
                 — 
                 2.25 
                 2.25 
                 2.25 
                 2.25 
                 2.24 
                 2.24 
                 2.25 
                 2.25 
                 2.25 
                 2.25 
                 2.26 
                 2.26 
               
               
                 #72 
                 90.37 
                 90.47 
                 90.58 
                 90.69 
                 90.79 
                 90.90 
                 91.00 
                 91.11 
                 91.22 
                 91.32 
                 91.43 
                 91.53 
               
               
                 — 
                 2.27 
                 2.27 
                 2.28 
                 2.29 
                 2.30 
                 2.31 
                 2.33 
                 2.34 
                 2.35 
                 2.37 
                 2.39 
                 2.41 
               
               
                 #73 
                 91.64 
                 91.75 
                 91.85 
                 91.06 
                 92.07 
                 92.17 
                 92.28 
                 92.38 
                 92.49 
                 92.60 
                 92.70 
                 92.81 
               
               
                 — 
                 2.43 
                 2.45 
                 2.47 
                 2.49 
                 2.52 
                 2.54 
                 2.57 
                 2.60 
                 2.63 
                 2.66 
                 2.69 
                 2.72 
               
               
                 #74 
                 92.91 
                 93.02 
                 93.13 
                 93.23 
                 93.34 
                 93.44 
                 93.55 
                 93.65 
                 93.76 
                 93.87 
                 93.97 
                 94.08 
               
               
                 — 
                 2.75 
                 2.78 
                 2.82 
                 2.85 
                 2.89 
                 2.93 
                 2.96 
                 3.00 
                 3.04 
                 3.08 
                 3.11 
                 3.15 
               
               
                 #75 
                 94.19 
                 94.29 
                 94.40 
                 94.50 
                 94.61 
                 94.72 
                 94.82 
                 94.93 
                 95.04 
                 95.14 
                 95.25 
                 95.35 
               
               
                 — 
                 3.19 
                 3.23 
                 3.27 
                 3.30 
                 3.34 
                 3.38 
                 3.41 
                 3.45 
                 3.48 
                 3.52 
                 3.55 
                 3.58 
               
               
                 #76 
                 95.46 
                 95.57 
                 95.67 
                 95.78 
                 95.88 
                 95.99 
                 96.10 
                 96.20 
                 96.31 
                 96.41 
                 96.52 
                 96.63 
               
               
                 — 
                 3.61 
                 3.64 
                 3.66 
                 3.69 
                 3.71 
                 3.73 
                 3.75 
                 3.77 
                 3.78 
                 3.79 
                 3.81 
                 3.81 
               
               
                 #77 
                 98.73 
                 96.84 
                 96.94 
                 97.05 
                 97.16 
                 97.26 
                 97.37 
                 97.47 
                 97.58 
                 97.69 
                 97.79 
                 97.90 
               
               
                 — 
                 3.82 
                 3.82 
                 3.83 
                 3.82 
                 3.82 
                 3.82 
                 3.81 
                 3.80 
                 3.79 
                 3.77 
                 3.76 
                 3.74 
               
               
                 #78 
                 98.00 
                 98.11 
                 98.22 
                 98.32 
                 98.43 
                 98.54 
                 98.64 
                 98.75 
                 98.85 
                 98.96 
                 99.07 
                 99.17 
               
               
                 — 
                 3.72 
                 3.69 
                 3.67 
                 3.64 
                 3.62 
                 3.59 
                 3.56 
                 3.52 
                 3.49 
                 3.46 
                 3.42 
                 3.38 
               
               
                 #79 
                 99.28 
                 99.38 
                 99.49 
                 99.60 
                 99.70 
                 99.81 
                 99.91 
                 100.02 
                 100.13 
                 100.23 
                 100.34 
                 100.44 
               
               
                 — 
                 3.35 
                 3.31 
                 3.27 
                 3.23 
                 3.19 
                 3.15 
                 3.12 
                 3.08 
                 3.04 
                 3.00 
                 2.96 
                 2.92 
               
               
                 #80 
                 100.55 
                 100.66 
                 100.76 
                 100.87 
                 100.97 
                 101.08 
                 101.19 
                 101.29 
                 101.40 
                 101.51 
                 101.61 
                 101.72 
               
               
                 — 
                 2.88 
                 2.85 
                 2.81 
                 2.77 
                 2.74 
                 2.70 
                 2.67 
                 2.64 
                 2.60 
                 2.57 
                 2.54 
                 2.51 
               
               
                 #81 
                 101.82 
                 101.93 
                 102.04 
                 102.14 
                 102.25 
                 102.35 
                 102.46 
                 102.57 
                 102.67 
                 102.78 
                 102.88 
                 102.99 
               
               
                 — 
                 2.49 
                 2.46 
                 2.43 
                 2.41 
                 2.39 
                 2.36 
                 2.34 
                 2.32 
                 2.31 
                 2.29 
                 2.27 
                 2.26 
               
               
                 #82 
                 103.10 
                 103.20 
                 103.31 
                 103.41 
                 103.52 
                 103.63 
                 103.73 
                 103.84 
                 103.94 
                 104.05 
                 104.16 
                 104.26 
               
               
                 — 
                 2.24 
                 2.23 
                 2.22 
                 2.21 
                 2.20 
                 2.19 
                 2.19 
                 2.18 
                 2.18 
                 2.17 
                 2.17 
                 2.17 
               
               
                 #83 
                 104.37 
                 104.48 
                 104.58 
                 104.69 
                 104.79 
                 104.90 
                 105.01 
                 105.11 
                 105.22 
                 105.32 
                 105.43 
                 105.54 
               
               
                 — 
                 2.17 
                 2.16 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.18 
                 2.18 
                 2.19 
                 2.19 
                 2.20 
               
               
                 #84 
                 105.64 
                 105.75 
                 105.85 
                 105.96 
                 106.07 
               
               
                 — 
                 2.20 
                 2.21 
                 2.21 
                 2.22 
                 2.22 
               
               
                   
               
             
          
         
       
     
       FIG. 10  shows the shape of the center conductor  6  in the reflection-type bandpass filter  1  of Embodiment 2. In the figure, the dark portion represents the center conductor  6 . A non-reflecting terminator, or an R=50Ω resistance, is provided on the terminating side (the face at z=106.07 mm) of this reflection-type bandpass filter  1 . The thicknesses of the conducting layers  4 ,  5  and of the center conductor  6  may be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the conducting layers  4 ,  5  and of the center conductor  6  may be 2.1 μm or greater. This bandpass filter is used in a system with a characteristic impedance of 50Ω. 
       FIG. 11  and  FIG. 12  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter of Embodiment 2. As shown in the figures, in the range of frequencies f for which 3.9 GHz≦f≦9.8 GHz, the reflectance is −1 dB or greater, and the group delay variation is within ±0.07 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −15 dB or lower. 
     Embodiment 3 
     A Kaiser window was used for which the reflectance is 0.9 at frequencies f in the range 4.0 GHz≦f≦9.6 GHz, and is 0 elsewhere, and for which A=30. Design was performed using the wavelength of signals at frequency f=0.3 GHz propagating in the microstrip as the waveguide length, and setting the system characteristic impedance to 50Ω.  FIG. 13  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 14  shows the z-axis distribution of the center conductor width w, when using a dielectric layer  3  of thickness h=2 mm and with relative permittivity ∈ r =4.2. Tables 7 and 8 list the center conductor widths. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Center conductor widths (1/2) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.07 
                 0.15 
                 0.22 
                 0.29 
                 0.37 
                 0.44 
                 0.51 
                 0.59 
                 0.66 
                 0.73 
                 0.81 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.96 
                 0.95 
                 0.95 
                 0.95 
                 0.95 
                 0.94 
                 0.94 
                 0.94 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 0.88 
                 0.95 
                 1.02 
                 1.10 
                 1.17 
                 1.24 
                 1.32 
                 1.39 
                 1.46 
                 1.54 
                 1.61 
                 1.68 
               
               
                 — 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.92 
                 0.92 
                 0.92 
                 0.92 
                 0.91 
                 0.91 
                 0.91 
                 0.90 
               
               
                  #3 
                 1.76 
                 1.83 
                 1.90 
                 1.98 
                 2.05 
                 2.12 
                 2.20 
                 2.27 
                 2.34 
                 2.42 
                 2.49 
                 2.56 
               
               
                 — 
                 0.90 
                 0.90 
                 0.90 
                 0.90 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.88 
                 0.88 
                 0.88 
               
               
                  #4 
                 2.63 
                 2.71 
                 2.78 
                 2.86 
                 2.93 
                 3.00 
                 3.07 
                 3.15 
                 3.22 
                 3.29 
                 3.37 
                 3.44 
               
               
                 — 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
               
               
                  #5 
                 3.51 
                 3.59 
                 3.68 
                 3.73 
                 3.81 
                 3.88 
                 3.95 
                 4.03 
                 4.10 
                 4.17 
                 4.25 
                 4.32 
               
               
                 — 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
                 0.90 
                 0.90 
               
               
                  #6 
                 4.39 
                 4.46 
                 4.54 
                 4.61 
                 4.68 
                 4.76 
                 4.83 
                 4.90 
                 4.98 
                 5.05 
                 5.12 
                 5.20 
               
               
                 — 
                 0.90 
                 0.91 
                 0.91 
                 0.91 
                 0.91 
                 0.92 
                 0.92 
                 0.93 
                 0.93 
                 0.93 
                 0.94 
                 0.94 
               
               
                  #7 
                 5.27 
                 5.34 
                 5.42 
                 5.49 
                 5.56 
                 5.64 
                 5.71 
                 5.78 
                 5.86 
                 5.93 
                 6.00 
                 6.07 
               
               
                 — 
                 0.94 
                 0.95 
                 0.95 
                 0.96 
                 0.96 
                 0.96 
                 0.97 
                 0.97 
                 0.98 
                 0.98 
                 0.98 
                 0.99 
               
               
                  #8 
                 6.15 
                 6.22 
                 6.29 
                 6.37 
                 6.44 
                 6.51 
                 6.59 
                 6.66 
                 6.73 
                 6.81 
                 6.88 
                 6.95 
               
               
                 — 
                 0.99 
                 1.00 
                 1.00 
                 1.00 
                 1.01 
                 1.01 
                 1.01 
                 1.02 
                 1.02 
                 1.02 
                 1.03 
                 1.03 
               
               
                  #9 
                 7.03 
                 7.10 
                 7.17 
                 7.25 
                 7.32 
                 7.39 
                 7.47 
                 7.54 
                 7.61 
                 7.69 
                 7.76 
                 7.83 
               
               
                 — 
                 1.03 
                 1.03 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.04 
                 1.05 
                 1.05 
                 1.05 
               
               
                 #10 
                 7.90 
                 7.98 
                 8.05 
                 8.12 
                 8.20 
                 8.27 
                 8.34 
                 8.42 
                 8.49 
                 8.56 
                 8.64 
                 8.71 
               
               
                 — 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
               
               
                 #11 
                 8.78 
                 8.86 
                 8.93 
                 9.00 
                 9.08 
                 9.15 
                 9.22 
                 9.30 
                 9.37 
                 9.44 
                 9.52 
                 9.59 
               
               
                 — 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
                 1.05 
               
               
                 #12 
                 9.66 
                 9.73 
                 9.81 
                 9.88 
                 9.95 
                 10.03 
                 10.10 
                 10.17 
                 10.25 
                 10.32 
                 10.39 
                 10.47 
               
               
                 — 
                 1.06 
                 1.06 
                 1.06 
                 1.06 
                 1.06 
                 1.06 
                 1.07 
                 1.07 
                 1.07 
                 1.07 
                 1.08 
                 1.08 
               
               
                 #13 
                 10.54 
                 10.61 
                 10.69 
                 10.76 
                 10.83 
                 10.91 
                 10.98 
                 11.05 
                 11.13 
                 11.20 
                 11.27 
                 11.34 
               
               
                 — 
                 1.09 
                 1.09 
                 1.09 
                 1.10 
                 1.10 
                 1.11 
                 1.12 
                 1.12 
                 1.13 
                 1.13 
                 1.14 
                 1.15 
               
               
                 #14 
                 11.42 
                 11.40 
                 11.56 
                 11.64 
                 11.71 
                 11.78 
                 11.86 
                 11.93 
                 12.00 
                 12.05 
                 12.15 
                 12.22 
               
               
                 — 
                 1.16 
                 1.16 
                 1.17 
                 1.18 
                 1.19 
                 1.20 
                 1.21 
                 1.21 
                 1.22 
                 1.23 
                 1.24 
                 1.25 
               
               
                 #15 
                 12.30 
                 12.37 
                 12.44 
                 12.52 
                 12.59 
                 12.66 
                 12.74 
                 12.81 
                 12.88 
                 12.96 
                 13.03 
                 13.10 
               
               
                 — 
                 1.26 
                 1.27 
                 1.28 
                 1.29 
                 1.30 
                 1.31 
                 1.31 
                 1.32 
                 1.33 
                 1.34 
                 1.35 
                 1.35 
               
               
                 #16 
                 13.17 
                 13.25 
                 13.32 
                 13.39 
                 13.47 
                 13.54 
                 13.61 
                 13.69 
                 13.76 
                 13.83 
                 13.91 
                 13.98 
               
               
                 — 
                 1.36 
                 1.37 
                 1.37 
                 1.38 
                 1.38 
                 1.39 
                 1.39 
                 1.39 
                 1.39 
                 1.40 
                 1.40 
                 1.40 
               
               
                 #17 
                 14.05 
                 14.13 
                 14.20 
                 14.27 
                 14.35 
                 14.42 
                 14.49 
                 14.57 
                 14.64 
                 14.71 
                 17.78 
                 14.86 
               
               
                 — 
                 1.39 
                 1.39 
                 1.39 
                 1.38 
                 1.38 
                 1.37 
                 1.37 
                 1.36 
                 1.35 
                 1.34 
                 1.33 
                 1.31 
               
               
                 #18 
                 14.93 
                 15.00 
                 15.08 
                 15.15 
                 15.22 
                 15.30 
                 15.37 
                 15.44 
                 15.52 
                 15.59 
                 15.66 
                 15.74 
               
               
                 — 
                 1.30 
                 1.29 
                 1.27 
                 1.26 
                 1.24 
                 1.22 
                 1.20 
                 1.18 
                 1.17 
                 1.14 
                 1.12 
                 1.10 
               
               
                 #19 
                 15.81 
                 15.88 
                 15.96 
                 16.03 
                 16.10 
                 16.18 
                 16.25 
                 16.32 
                 16.40 
                 16.47 
                 16.54 
                 16.61 
               
               
                 — 
                 1.08 
                 1.06 
                 1.03 
                 1.01 
                 0.99 
                 0.96 
                 0.94 
                 0.92 
                 0.89 
                 0.87 
                 0.84 
                 0.82 
               
               
                 #20 
                 16.69 
                 16.76 
                 16.83 
                 16.91 
                 16.98 
                 17.05 
                 17.13 
                 17.20 
                 17.27 
                 17.35 
                 17.42 
                 17.49 
               
               
                 — 
                 0.80 
                 0.77 
                 0.75 
                 0.73 
                 0.71 
                 0.68 
                 0.66 
                 0.64 
                 0.62 
                 0.60 
                 0.58 
                 0.56 
               
               
                 #21 
                 17.57 
                 17.64 
                 17.71 
                 17.79 
                 17.86 
                 17.93 
                 18.01 
                 18.08 
                 18.15 
                 18.22 
                 18.30 
                 18.37 
               
               
                 — 
                 0.55 
                 0.53 
                 0.51 
                 0.50 
                 0.48 
                 0.47 
                 0.45 
                 0.44 
                 0.43 
                 0.42 
                 0.40 
                 0.39 
               
               
                 #22 
                 18.44 
                 18.52 
                 18.59 
                 18.66 
                 18.74 
                 18.81 
                 18.88 
                 18.96 
                 19.03 
                 19.10 
                 19.18 
                 19.25 
               
               
                 — 
                 0.39 
                 0.38 
                 0.37 
                 0.36 
                 0.36 
                 0.35 
                 0.35 
                 0.34 
                 0.34 
                 0.34 
                 0.33 
                 0.33 
               
               
                 #23 
                 19.32 
                 19.40 
                 19.47 
                 19.54 
                 19.62 
                 19.69 
                 19.76 
                 19.84 
                 19.91 
                 19.98 
                 20.05 
                 20.13 
               
               
                 — 
                 0.33 
                 0.33 
                 0.33 
                 0.34 
                 0.34 
                 0.34 
                 0.35 
                 0.35 
                 0.36 
                 0.37 
                 0.37 
                 0.38 
               
               
                 #24 
                 20.20 
                 20.27 
                 20.35 
                 20.42 
                 20.49 
                 20.57 
                 20.64 
                 20.71 
                 20.79 
                 20.86 
                 20.93 
                 21.01 
               
               
                 — 
                 0.39 
                 0.40 
                 0.42 
                 0.43 
                 0.44 
                 0.46 
                 0.48 
                 0.49 
                 0.51 
                 0.53 
                 0.55 
                 0.58 
               
               
                 #25 
                 21.08 
                 21.15 
                 21.23 
                 21.30 
                 21.37 
                 21.45 
                 21.52 
                 21.59 
                 21.66 
                 21.74 
                 21.81 
                 21.88 
               
               
                 — 
                 0.60 
                 0.63 
                 0.65 
                 0.68 
                 0.71 
                 0.74 
                 0.78 
                 0.81 
                 0.84 
                 0.88 
                 0.92 
                 0.96 
               
               
                 #26 
                 21.90 
                 22.03 
                 22.10 
                 22.18 
                 22.25 
                 22.32 
                 32.40 
                 22.47 
                 22.54 
                 22.62 
                 22.69 
                 22.76 
               
               
                 — 
                 1.00 
                 1.04 
                 1.08 
                 1.13 
                 1.17 
                 1.22 
                 1.27 
                 1.31 
                 1.36 
                 1.41 
                 1.46 
                 1.51 
               
               
                 #27 
                 22.84 
                 22.91 
                 22.98 
                 23.06 
                 23.13 
                 23.20 
                 23.28 
                 23.35 
                 23.42 
                 23.49 
                 23.57 
                 23.64 
               
               
                 — 
                 1.56 
                 1.61 
                 1.66 
                 1.71 
                 1.76 
                 1.81 
                 1.86 
                 1.91 
                 1.96 
                 2.01 
                 2.05 
                 2.09 
               
               
                 #28 
                 23.71 
                 23.79 
                 23.86 
                 23.93 
                 24.01 
                 24.08 
                 24.15 
                 24.23 
                 24.30 
                 24.37 
                 24.45 
                 24.52 
               
               
                 — 
                 2.14 
                 2.18 
                 2.22 
                 2.25 
                 2.29 
                 2.32 
                 2.35 
                 2.37 
                 2.39 
                 2.41 
                 2.43 
                 2.45 
               
               
                 #29 
                 24.59 
                 24.67 
                 24.74 
                 24.81 
                 24.89 
                 24.96 
                 25.03 
                 25.11 
                 25.18 
                 25.25 
                 25.32 
                 25.40 
               
               
                 — 
                 2.46 
                 2.46 
                 2.47 
                 2.47 
                 2.47 
                 2.46 
                 2.45 
                 2.44 
                 2.42 
                 2.40 
                 2.38 
                 2.36 
               
               
                 #30 
                 25.47 
                 25.54 
                 25.62 
                 25.69 
                 25.76 
                 25.84 
                 25.91 
                 25.98 
                 26.06 
                 26.13 
                 26.20 
                 26.28 
               
               
                 — 
                 2.33 
                 2.30 
                 2.27 
                 2.23 
                 2.19 
                 2.15 
                 2.11 
                 2.07 
                 2.03 
                 1.98 
                 1.93 
                 1.88 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Center conductor widths (2/2) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 25.35 
                 26.42 
                 26.50 
                 26.57 
                 26.64 
                 26.72 
                 26.79 
                 26.86 
                 26.93 
                 27.01 
                 27.08 
                 27.15 
               
               
                 — 
                 1.84 
                 1.79 
                 1.74 
                 1.69 
                 1.64 
                 1.59 
                 1.54 
                 1.49 
                 1.44 
                 1.39 
                 1.34 
                 1.29 
               
               
                 #32 
                 27.23 
                 27.30 
                 27.37 
                 27.45 
                 27.52 
                 27.59 
                 27.67 
                 27.74 
                 27.81 
                 27.80 
                 27.96 
                 28.03 
               
               
                 — 
                 1.24 
                 1.20 
                 1.15 
                 1.11 
                 1.07 
                 1.02 
                 0.98 
                 0.94 
                 0.91 
                 0.87 
                 0.83 
                 0.80 
               
               
                 #33 
                 28.11 
                 28.18 
                 28.26 
                 28.33 
                 28.40 
                 28.47 
                 28.55 
                 28.62 
                 28.69 
                 28.76 
                 28.84 
                 28.91 
               
               
                 — 
                 0.77 
                 0.73 
                 0.70 
                 0.68 
                 0.65 
                 0.62 
                 0.60 
                 0.58 
                 0.55 
                 0.53 
                 0.51 
                 0.40 
               
               
                 #34 
                 28.99 
                 29.06 
                 29.13 
                 29.20 
                 29.28 
                 29.35 
                 29.42 
                 29.50 
                 29.57 
                 29.64 
                 29.72 
                 29.79 
               
               
                 — 
                 0.48 
                 0.46 
                 0.45 
                 0.43 
                 0.42 
                 0.41 
                 0.40 
                 0.39 
                 0.38 
                 0.37 
                 0.37 
                 0.36 
               
               
                 #35 
                 29.86 
                 29.94 
                 30.01 
                 30.08 
                 30.16 
                 30.23 
                 30.30 
                 30.37 
                 30.45 
                 30.52 
                 30.59 
                 30.67 
               
               
                 — 
                 0.36 
                 0.35 
                 0.35 
                 0.35 
                 0.35 
                 0.34 
                 0.34 
                 0.35 
                 0.35 
                 0.35 
                 0.35 
                 0.36 
               
               
                 #36 
                 30.74 
                 30.81 
                 30.89 
                 30.96 
                 31.03 
                 31.11 
                 31.18 
                 31.25 
                 31.33 
                 31.40 
                 31.47 
                 31.56 
               
               
                 — 
                 0.36 
                 0.37 
                 0.37 
                 0.38 
                 0.39 
                 0.40 
                 0.40 
                 0.41 
                 0.43 
                 0.44 
                 0.45 
                 0.46 
               
               
                 #37 
                 31.62 
                 31.69 
                 31.77 
                 31.84 
                 31.91 
                 31.99 
                 32.06 
                 32.13 
                 32.20 
                 32.28 
                 32.35 
                 32.42 
               
               
                 — 
                 0.48 
                 0.49 
                 0.51 
                 0.52 
                 0.54 
                 0.56 
                 0.57 
                 0.59 
                 0.61 
                 0.63 
                 0.65 
                 0.68 
               
               
                 #38 
                 32.50 
                 32.57 
                 32.64 
                 32.72 
                 32.79 
                 32.86 
                 32.94 
                 33.01 
                 33.08 
                 33.16 
                 33.23 
                 33.30 
               
               
                 — 
                 0.70 
                 0.72 
                 0.74 
                 0.77 
                 0.79 
                 0.82 
                 0.84 
                 0.87 
                 0.89 
                 0.92 
                 0.94 
                 0.97 
               
               
                 #39 
                 33.38 
                 33.45 
                 33.52 
                 33.60 
                 33.67 
                 33.74 
                 33.81 
                 33.89 
                 33.96 
                 34.03 
                 34.11 
                 34.18 
               
               
                 — 
                 1.00 
                 1.02 
                 1.05 
                 1.07 
                 1.10 
                 1.12 
                 1.15 
                 1.17 
                 1.19 
                 1.22 
                 1.24 
                 1.26 
               
               
                 #40 
                 34.25 
                 34.33 
                 34.40 
                 34.47 
                 34.55 
                 34.62 
                 34.69 
                 34.77 
                 34.84 
                 34.91 
                 34.99 
                 35.06 
               
               
                 — 
                 1.28 
                 1.30 
                 1.32 
                 1.34 
                 1.36 
                 1.37 
                 1.39 
                 1.40 
                 1.42 
                 1.43 
                 1.44 
                 1.45 
               
               
                 #41 
                 35.13 
                 35.21 
                 35.28 
                 35.35 
                 35.43 
                 35.50 
                 35.57 
                 35.64 
                 35.72 
                 35.79 
                 35.86 
                 35.94 
               
               
                 — 
                 1.46 
                 1.47 
                 1.47 
                 1.48 
                 1.48 
                 1.49 
                 1.49 
                 1.49 
                 1.49 
                 1.49 
                 1.49 
                 1.49 
               
               
                 #42 
                 36.01 
                 36.08 
                 36.16 
                 36.23 
                 36.30 
                 36.38 
                 36.45 
                 36.52 
                 36.60 
                 36.67 
                 36.74 
                 36.82 
               
               
                 — 
                 1.48 
                 1.48 
                 1.47 
                 1.46 
                 1.46 
                 1.46 
                 1.44 
                 1.43 
                 1.42 
                 1.41 
                 1.40 
                 1.39 
               
               
                 #43 
                 36.89 
                 36.96 
                 37.04 
                 37.11 
                 37.18 
                 37.25 
                 37.33 
                 37.40 
                 37.47 
                 37.55 
                 37.62 
                 37.69 
               
               
                 — 
                 1.37 
                 1.36 
                 1.35 
                 1.34 
                 1.32 
                 1.31 
                 1.30 
                 1.28 
                 1.27 
                 1.25 
                 1.24 
                 1.22 
               
               
                 #44 
                 37.77 
                 37.84 
                 37.91 
                 37.99 
                 38.06 
                 38.13 
                 38.21 
                 38.28 
                 38.35 
                 38.43 
                 38.50 
                 38.57 
               
               
                 — 
                 1.21 
                 1.20 
                 1.18 
                 1.17 
                 1.16 
                 1.14 
                 1.13 
                 1.12 
                 1.10 
                 1.00 
                 1.08 
                 1.07 
               
               
                 #45 
                 38.65 
                 38.72 
                 38.79 
                 38.87 
                 38.94 
                 39.01 
                 39.08 
                 39.16 
                 39.23 
                 39.30 
                 39.38 
                 39.45 
               
               
                 — 
                 1.06 
                 1.04 
                 1.03 
                 1.02 
                 1.01 
                 1.00 
                 0.99 
                 0.99 
                 0.98 
                 0.97 
                 0.96 
                 0.95 
               
               
                 #46 
                 39.52 
                 39.60 
                 39.67 
                 39.74 
                 39.82 
                 39.89 
                 39.96 
                 40.04 
                 40.11 
                 40.18 
                 40.26 
                 40.33 
               
               
                 — 
                 0.95 
                 0.94 
                 0.93 
                 0.93 
                 0.92 
                 0.92 
                 0.91 
                 0.91 
                 0.90 
                 0.90 
                 0.90 
                 0.89 
               
               
                 #47 
                 40.40 
                 40.48 
                 40.55 
                 40.62 
                 40.70 
                 40.77 
                 40.84 
                 40.91 
                 40.99 
                 41.06 
                 41.13 
                 41.21 
               
               
                 — 
                 0.89 
                 0.89 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
               
               
                 #48 
                 41.28 
                 41.35 
                 41.43 
                 41.50 
                 41.57 
                 41.65 
                 41.72 
                 41.79 
                 41.87 
                 41.94 
                 42.01 
                 42.09 
               
               
                 — 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.88 
                 0.89 
                 0.89 
                 0.89 
                 0.89 
               
               
                 #49 
                 42.16 
                 42.23 
                 42.31 
                 42.38 
                 42.45 
                 42.52 
                 42.60 
                 42.67 
                 42.74 
                 42.82 
                 42.89 
                 42.96 
               
               
                 — 
                 0.89 
                 0.90 
                 0.90 
                 0.90 
                 0.90 
                 0.90 
                 0.91 
                 0.91 
                 0.91 
                 0.91 
                 0.92 
                 0.92 
               
               
                 #50 
                 43.04 
                 43.11 
                 43.18 
                 43.26 
                 43.33 
                 43.40 
                 43.48 
                 43.55 
                 43.62 
                 43.70 
                 43.77 
                 43.84 
               
               
                 — 
                 0.92 
                 0.92 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.93 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
                 0.94 
               
               
                 #51 
                 43.92 
               
               
                 — 
                 0.95 
               
               
                   
               
             
          
         
       
     
       FIG. 15  shows the shape of the center conductor  6  in the reflection-type bandpass filter  1  of Embodiment 3. In the figure, the dark portion represents the center conductor  6 . A non-reflecting terminator, or an R=50Ω resistance, is provided on the terminating side (the face at z=43.92 mm) of this reflection-type bandpass filter  1 . The thicknesses of the conducting layers  4 ,  5  and of the center conductor  6  may be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the conducting layers  4 ,  5  and of the center conductor  6  may be 2.1 μm or greater. This bandpass filter is used in a system with a characteristic impedance of 50Ω. 
       FIG. 16  and  FIG. 17  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter of Embodiment 3. As shown in the figures, in the range of frequencies f for which 4.4 GHz≦f≦9.2 GHz, the reflectance is −5 dB or greater, and the group delay variation is within ±0.05 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −20 dB or lower. 
     Embodiment 4 
     A Kaiser window was used for which the reflectance is 1 at frequencies f in the range 3.6 GHz≦f≦10.0 GHz, and is 0 elsewhere, and for which A=35. Design was performed using 0.8 times the wavelength of signals at frequency f=1 GHz propagating in the microstrip as the waveguide length, and setting the system characteristic impedance to 25Ω.  FIG. 18  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 19  shows the z-axis distribution of the center conductor width w, when using a dielectric layer  3  of thickness h=2 mm and with relative permittivity ∈ r =6.35. Tables 9 through 11 list the center conductor widths w. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 Center conductor widths (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.10 
                 0.19 
                 0.29 
                 0.38 
                 0.48 
                 0.57 
                 0.67 
                 0.76 
                 0.86 
                 0.95 
                 1.05 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 1.14 
                 1.24 
                 1.33 
                 1.43 
                 1.52 
                 1.62 
                 1.71 
                 1.81 
                 1.90 
                 2.00 
                 2.10 
                 2.19 
               
               
                 — 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
               
               
                  #3 
                 2.29 
                 2.38 
                 2.48 
                 2.57 
                 2.67 
                 2.76 
                 2.86 
                 2.95 
                 3.05 
                 3.14 
                 3.24 
                 3.33 
               
               
                 — 
                 2.11 
                 2.11 
                 2.11 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
               
               
                  #4 
                 3.43 
                 3.52 
                 3.62 
                 3.71 
                 3.81 
                 3.90 
                 4.00 
                 4.10 
                 4.19 
                 4.29 
                 4.38 
                 4.48 
               
               
                 — 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.14 
                 2.14 
                 2.14 
                 2.14 
                 2.15 
                 2.15 
                 2.15 
               
               
                  #5 
                 4.57 
                 4.67 
                 4.76 
                 4.86 
                 4.95 
                 5.05 
                 5.14 
                 5.24 
                 5.33 
                 5.43 
                 5.52 
                 5.62 
               
               
                 — 
                 2.15 
                 2.15 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
               
               
                  #6 
                 5.71 
                 5.81 
                 5.90 
                 6.00 
                 6.10 
                 6.19 
                 6.29 
                 6.38 
                 6.48 
                 6.57 
                 6.67 
                 6.76 
               
               
                 — 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
                 2.17 
               
               
                  #7 
                 6.86 
                 6.96 
                 7.05 
                 7.14 
                 7.24 
                 7.33 
                 7.43 
                 7.52 
                 7.62 
                 7.71 
                 7.81 
                 7.91 
               
               
                 — 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.15 
                 2.15 
                 2.15 
                 2.15 
                 2.14 
                 2.14 
                 2.14 
               
               
                  #8 
                 8.00 
                 8.10 
                 8.19 
                 8.29 
                 8.38 
                 8.48 
                 8.57 
                 8.67 
                 8.76 
                 8.86 
                 8.95 
                 9.05 
               
               
                 — 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.11 
                 2.11 
                 2.11 
               
               
                  #9 
                 9.14 
                 9.24 
                 9.33 
                 9.43 
                 9.52 
                 9.62 
                 9.71 
                 9.81 
                 9.91 
                 10.00 
                 10.10 
                 10.19 
               
               
                 — 
                 2.11 
                 2.11 
                 2.11 
                 2.11 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
               
               
                 #10 
                 10.29 
                 10.38 
                 10.48 
                 10.57 
                 10.67 
                 10.76 
                 10.85 
                 10.95 
                 11.05 
                 11.14 
                 11.24 
                 11.33 
               
               
                 — 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
                 2.10 
               
               
                 #11 
                 11.43 
                 11.52 
                 11.62 
                 11.71 
                 11.81 
                 11.91 
                 12.00 
                 12.10 
                 12.19 
                 12.29 
                 12.38 
                 12.48 
               
               
                 — 
                 2.10 
                 2.10 
                 2.10 
                 2.09 
                 2.09 
                 2.09 
                 2.09 
                 2.09 
                 2.08 
                 2.08 
                 2.08 
                 2.07 
               
               
                 #12 
                 12.57 
                 12.67 
                 12.76 
                 12.85 
                 12.95 
                 13.05 
                 13.14 
                 13.24 
                 13.33 
                 13.43 
                 13.52 
                 13.62 
               
               
                 — 
                 2.07 
                 2.07 
                 2.06 
                 2.06 
                 2.06 
                 2.05 
                 2.05 
                 2.04 
                 2.04 
                 2.04 
                 2.03 
                 2.03 
               
               
                 #13 
                 13.71 
                 13.81 
                 13.91 
                 14.00 
                 14.10 
                 14.19 
                 14.29 
                 14.38 
                 14.48 
                 14.57 
                 14.67 
                 14.76 
               
               
                 — 
                 2.02 
                 2.02 
                 2.02 
                 2.02 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
               
               
                 #14 
                 14.86 
                 14.95 
                 15.05 
                 15.14 
                 15.24 
                 15.33 
                 15.43 
                 15.52 
                 15.62 
                 15.71 
                 15.81 
                 15.91 
               
               
                 — 
                 2.00 
                 2.00 
                 2.00 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
                 2.02 
                 2.02 
                 2.02 
                 2.03 
                 2.03 
               
               
                 #15 
                 16.00 
                 16.10 
                 16.19 
                 16.29 
                 16.38 
                 16.48 
                 16.57 
                 16.67 
                 16.76 
                 16.86 
                 16.95 
                 17.05 
               
               
                 — 
                 2.04 
                 2.04 
                 2.05 
                 2.05 
                 2.06 
                 2.06 
                 2.07 
                 2.07 
                 2.08 
                 2.09 
                 2.09 
                 2.10 
               
               
                 #16 
                 17.14 
                 17.24 
                 17.33 
                 17.43 
                 17.52 
                 17.62 
                 17.71 
                 17.81 
                 17.91 
                 18.00 
                 18.10 
                 18.19 
               
               
                 — 
                 2.10 
                 2.11 
                 2.11 
                 2.12 
                 2.12 
                 2.13 
                 2.13 
                 2.14 
                 2.14 
                 2.14 
                 2.15 
                 2.15 
               
               
                 #17 
                 18.29 
                 18.38 
                 18.48 
                 18.57 
                 18.67 
                 18.76 
                 18.86 
                 18.95 
                 19.05 
                 19.14 
                 19.24 
                 19.33 
               
               
                 — 
                 2.15 
                 2.15 
                 2.15 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
               
               
                 #18 
                 19.43 
                 19.52 
                 19.62 
                 19.71 
                 19.81 
                 19.91 
                 20.00 
                 20.10 
                 20.19 
                 20.29 
                 20.38 
                 20.48 
               
               
                 — 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.16 
                 2.17 
               
               
                 #19 
                 20.57 
                 20.67 
                 20.76 
                 20.86 
                 20.95 
                 21.05 
                 21.14 
                 21.24 
                 21.33 
                 21.43 
                 21.52 
                 21.62 
               
               
                 — 
                 2.17 
                 2.17 
                 2.17 
                 2.18 
                 2.18 
                 2.18 
                 2.19 
                 2.19 
                 2.20 
                 2.20 
                 2.21 
                 2.21 
               
               
                 #20 
                 21.71 
                 21.81 
                 21.91 
                 22.00 
                 22.10 
                 22.19 
                 22.29 
                 22.38 
                 22.48 
                 22.57 
                 22.67 
                 22.76 
               
               
                 — 
                 2.22 
                 2.23 
                 2.23 
                 2.24 
                 2.25 
                 2.25 
                 2.26 
                 2.27 
                 2.27 
                 2.28 
                 2.28 
                 2.29 
               
               
                 #21 
                 22.86 
                 22.95 
                 23.05 
                 23.14 
                 23.24 
                 23.33 
                 23.43 
                 23.52 
                 23.62 
                 23.72 
                 23.81 
                 23.91 
               
               
                 — 
                 2.29 
                 2.30 
                 2.30 
                 2.30 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
               
               
                 #22 
                 24.00 
                 24.10 
                 24.19 
                 24.29 
                 24.38 
                 24.48 
                 24.57 
                 24.67 
                 24.76 
                 24.86 
                 24.96 
                 25.05 
               
               
                 — 
                 2.30 
                 2.30 
                 2.29 
                 2.29 
                 2.28 
                 2.27 
                 2.26 
                 2.25 
                 2.24 
                 2.23 
                 2.22 
                 2.21 
               
               
                 #23 
                 25.14 
                 25.24 
                 25.33 
                 25.43 
                 25.52 
                 25.62 
                 25.72 
                 25.81 
                 25.91 
                 26.00 
                 26.10 
                 26.19 
               
               
                 — 
                 2.20 
                 2.19 
                 2.18 
                 2.17 
                 2.16 
                 2.14 
                 2.13 
                 2.12 
                 2.11 
                 2.10 
                 2.09 
                 2.08 
               
               
                 #24 
                 26.29 
                 26.38 
                 26.48 
                 26.57 
                 26.67 
                 26.76 
                 26.86 
                 26.95 
                 27.05 
                 27.14 
                 27.24 
                 27.33 
               
               
                 — 
                 2.07 
                 2.06 
                 2.05 
                 2.04 
                 2.03 
                 2.02 
                 2.02 
                 2.01 
                 2.01 
                 2.00 
                 2.00 
                 1.99 
               
               
                 #25 
                 27.43 
                 27.52 
                 27.62 
                 27.72 
                 27.81 
                 27.91 
                 28.00 
                 28.10 
                 28.19 
                 28.29 
                 28.38 
                 28.48 
               
               
                 — 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
               
               
                 #26 
                 28.57 
                 28.67 
                 28.76 
                 28.86 
                 28.95 
                 29.05 
                 29.14 
                 29.24 
                 29.33 
                 29.43 
                 29.52 
                 29.62 
               
               
                 — 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.99 
                 1.98 
               
               
                 #27 
                 29.72 
                 29.81 
                 29.91 
                 30.00 
                 30.10 
                 30.19 
                 30.29 
                 30.38 
                 30.49 
                 30.57 
                 30.67 
                 30.76 
               
               
                 — 
                 1.98 
                 1.98 
                 1.97 
                 1.97 
                 1.96 
                 1.96 
                 1.95 
                 1.94 
                 1.93 
                 1.93 
                 1.92 
                 1.91 
               
               
                 #28 
                 30.86 
                 30.95 
                 31.05 
                 31.14 
                 31.24 
                 31.33 
                 31.43 
                 31.52 
                 31.62 
                 31.72 
                 31.81 
                 31.91 
               
               
                 — 
                 1.90 
                 1.89 
                 1.88 
                 1.87 
                 1.87 
                 1.86 
                 1.85 
                 1.84 
                 1.84 
                 1.83 
                 1.82 
                 1.82 
               
               
                 #29 
                 32.00 
                 32.10 
                 32.19 
                 32.29 
                 32.38 
                 32.48 
                 32.57 
                 32.67 
                 32.76 
                 32.86 
                 32.95 
                 33.05 
               
               
                 — 
                 1.82 
                 1.81 
                 1.81 
                 1.81 
                 1.81 
                 1.81 
                 1.82 
                 1.82 
                 1.83 
                 1.83 
                 1.84 
                 1.85 
               
               
                 #30 
                 33.14 
                 33.24 
                 33.33 
                 33.43 
                 33.52 
                 33.62 
                 33.72 
                 33.81 
                 33.91 
                 34.00 
                 34.10 
                 34.10 
               
               
                 — 
                 1.86 
                 1.87 
                 1.89 
                 1.90 
                 1.92 
                 1.94 
                 1.95 
                 1.97 
                 1.98 
                 2.02 
                 2.04 
                 2.06 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Center conductor widths (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 34.29 
                 34.38 
                 34.45 
                 34.57 
                 34.67 
                 34.76 
                 34.86 
                 34.95 
                 35.05 
                 35.14 
                 35.24 
                 35.33 
               
               
                 — 
                 2.09 
                 2.11 
                 2.14 
                 2.16 
                 2.18 
                 2.21 
                 2.23 
                 2.26 
                 2.28 
                 2.30 
                 2.33 
                 2.35 
               
               
                 #32 
                 35.43 
                 35.52 
                 35.62 
                 35.72 
                 35.81 
                 35.91 
                 36.00 
                 36.10 
                 36.19 
                 36.29 
                 36.38 
                 36.48 
               
               
                 — 
                 2.37 
                 2.39 
                 2.40 
                 2.42 
                 2.44 
                 2.45 
                 2.46 
                 2.47 
                 2.48 
                 2.49 
                 2.49 
                 2.49 
               
               
                 #33 
                 36.57 
                 36.67 
                 36.76 
                 36.86 
                 36.95 
                 37.05 
                 37.14 
                 37.24 
                 37.33 
                 37.43 
                 37.52 
                 37.62 
               
               
                 — 
                 2.50 
                 2.50 
                 2.50 
                 2.50 
                 2.49 
                 2.49 
                 2.49 
                 2.48 
                 2.47 
                 2.47 
                 2.46 
                 2.46 
               
               
                 #34 
                 37.72 
                 37.81 
                 37.91 
                 38.00 
                 38.10 
                 38.19 
                 38.29 
                 38.38 
                 38.48 
                 38.57 
                 38.67 
                 38.76 
               
               
                 — 
                 2.45 
                 2.45 
                 2.44 
                 2.44 
                 2.43 
                 2.43 
                 2.43 
                 2.43 
                 2.43 
                 2.44 
                 2.44 
                 2.45 
               
               
                 #35 
                 38.86 
                 38.95 
                 39.05 
                 39.14 
                 39.24 
                 39.33 
                 39.43 
                 39.53 
                 39.62 
                 39.72 
                 39.91 
                 39.91 
               
               
                 — 
                 2.45 
                 2.45 
                 2.47 
                 2.48 
                 2.50 
                 2.51 
                 2.53 
                 2.55 
                 2.56 
                 2.58 
                 2.60 
                 2.62 
               
               
                 #36 
                 40.00 
                 40.10 
                 40.19 
                 40.29 
                 40.38 
                 40.48 
                 40.57 
                 40.67 
                 40.76 
                 40.86 
                 40.95 
                 41.05 
               
               
                 — 
                 2.64 
                 2.66 
                 2.68 
                 2.70 
                 2.72 
                 2.74 
                 2.75 
                 2.77 
                 2.78 
                 2.79 
                 2.79 
                 2.79 
               
               
                 #37 
                 41.14 
                 41.24 
                 41.33 
                 41.43 
                 41.53 
                 41.62 
                 41.72 
                 41.81 
                 41.91 
                 42.00 
                 42.10 
                 42.19 
               
               
                 — 
                 2.79 
                 2.79 
                 2.78 
                 2.76 
                 2.74 
                 2.72 
                 2.69 
                 2.66 
                 2.62 
                 2.58 
                 2.53 
                 2.48 
               
               
                 #38 
                 42.29 
                 42.38 
                 42.48 
                 42.57 
                 42.67 
                 42.76 
                 42.86 
                 42.95 
                 43.05 
                 43.14 
                 43.24 
                 43.33 
               
               
                 — 
                 2.43 
                 2.37 
                 2.31 
                 2.24 
                 2.18 
                 2.11 
                 2.04 
                 1.96 
                 1.89 
                 1.82 
                 1.74 
                 1.67 
               
               
                 #39 
                 43.43 
                 43.53 
                 43.62 
                 43.72 
                 43.81 
                 43.91 
                 44.00 
                 44.10 
                 44.19 
                 44.29 
                 44.38 
                 44.48 
               
               
                 — 
                 1.60 
                 1.53 
                 1.40 
                 1.39 
                 1.33 
                 1.26 
                 1.21 
                 1.16 
                 1.10 
                 1.05 
                 1.00 
                 0.96 
               
               
                 #40 
                 44.57 
                 44.67 
                 44.76 
                 44.86 
                 44.95 
                 45.05 
                 45.14 
                 45.24 
                 45.33 
                 45.43 
                 45.53 
                 45.62 
               
               
                 — 
                 0.92 
                 0.88 
                 0.85 
                 0.82 
                 0.80 
                 0.78 
                 0.76 
                 0.75 
                 0.74 
                 0.74 
                 0.74 
                 0.74 
               
               
                 #41 
                 45.72 
                 45.81 
                 45.91 
                 46.00 
                 46.10 
                 46.19 
                 46.29 
                 46.38 
                 46.48 
                 46.57 
                 46.67 
                 46.76 
               
               
                 — 
                 0.75 
                 0.75 
                 0.78 
                 0.80 
                 0.83 
                 0.86 
                 0.89 
                 0.94 
                 0.99 
                 1.04 
                 1.10 
                 1.17 
               
               
                 #42 
                 46.86 
                 46.95 
                 47.05 
                 47.14 
                 47.24 
                 47.33 
                 47.43 
                 47.53 
                 47.62 
                 47.72 
                 47.81 
                 47.91 
               
               
                 — 
                 1.26 
                 1.33 
                 1.42 
                 1.52 
                 1.62 
                 1.74 
                 1.86 
                 1.99 
                 2.13 
                 2.28 
                 2.43 
                 2.60 
               
               
                 #43 
                 48.00 
                 48.10 
                 48.19 
                 48.29 
                 48.38 
                 48.48 
                 48.57 
                 48.67 
                 48.76 
                 48.86 
                 48.95 
                 49.05 
               
               
                 — 
                 2.77 
                 2.95 
                 3.14 
                 3.33 
                 3.53 
                 3.73 
                 3.94 
                 4.41 
                 4.35 
                 4.55 
                 4.75 
                 4.94 
               
               
                 #44 
                 49.14 
                 49.24 
                 49.33 
                 49.43 
                 49.53 
                 49.62 
                 49.72 
                 49.81 
                 49.91 
                 50.00 
                 50.10 
                 50.19 
               
               
                 — 
                 5.13 
                 5.30 
                 5.46 
                 5.61 
                 5.74 
                 5.84 
                 5.93 
                 6.00 
                 6.04 
                 6.05 
                 6.04 
                 6.01 
               
               
                 #45 
                 50.29 
                 50.38 
                 50.48 
                 50.57 
                 50.67 
                 50.76 
                 50.86 
                 50.95 
                 51.05 
                 51.14 
                 51.24 
                 51.33 
               
               
                 — 
                 5.95 
                 5.87 
                 5.76 
                 5.64 
                 5.49 
                 5.33 
                 5.15 
                 4.95 
                 4.76 
                 4.55 
                 4.34 
                 4.12 
               
               
                 #46 
                 51.43 
                 51.53 
                 51.62 
                 51.72 
                 51.81 
                 51.91 
                 52.00 
                 52.10 
                 52.19 
                 52.29 
                 52.38 
                 52.48 
               
               
                 — 
                 3.90 
                 3.69 
                 3.47 
                 3.26 
                 3.05 
                 2.85 
                 2.66 
                 2.47 
                 2.29 
                 2.13 
                 1.97 
                 1.81 
               
               
                 #47 
                 52.57 
                 52.67 
                 52.76 
                 52.86 
                 52.95 
                 53.05 
                 53.14 
                 53.24 
                 53.34 
                 53.43 
                 53.53 
                 53.62 
               
               
                 — 
                 1.67 
                 1.54 
                 1.42 
                 1.30 
                 1.20 
                 1.10 
                 1.01 
                 0.93 
                 0.85 
                 0.79 
                 0.73 
                 0.68 
               
               
                 #48 
                 53.72 
                 53.81 
                 53.91 
                 54.00 
                 54.10 
                 54.19 
                 54.29 
                 54.38 
                 54.48 
                 54.57 
                 54.67 
                 54.76 
               
               
                 — 
                 0.63 
                 0.59 
                 0.55 
                 0.52 
                 0.50 
                 0.48 
                 0.46 
                 0.45 
                 0.45 
                 0.44 
                 0.45 
                 0.45 
               
               
                 #49 
                 54.86 
                 54.95 
                 55.05 
                 55.14 
                 55.24 
                 55.34 
                 55.43 
                 55.53 
                 55.62 
                 55.72 
                 55.83 
                 55.91 
               
               
                 — 
                 0.46 
                 0.48 
                 0.49 
                 0.52 
                 0.54 
                 0.58 
                 0.62 
                 0.66 
                 0.71 
                 0.76 
                 0.83 
                 0.89 
               
               
                 #50 
                 56.00 
                 56.10 
                 56.19 
                 56.29 
                 56.38 
                 56.48 
                 56.57 
                 56.67 
                 56.76 
                 56.86 
                 56.95 
                 57.05 
               
               
                 — 
                 0.97 
                 1.05 
                 1.14 
                 1.24 
                 1.34 
                 1.45 
                 1.57 
                 1.69 
                 1.83 
                 1.96 
                 2.11 
                 2.26 
               
               
                 #51 
                 57.14 
                 57.24 
                 57.34 
                 57.43 
                 57.53 
                 57.62 
                 57.72 
                 57.81 
                 57.91 
                 58.00 
                 58.10 
                 58.19 
               
               
                 — 
                 2.42 
                 2.58 
                 2.75 
                 2.92 
                 3.09 
                 3.26 
                 3.43 
                 3.60 
                 3.77 
                 3.93 
                 4.09 
                 4.24 
               
               
                 #52 
                 58.29 
                 58.38 
                 58.48 
                 58.57 
                 58.67 
                 58.76 
                 58.86 
                 58.95 
                 59.05 
                 59.14 
                 59.24 
                 59.34 
               
               
                 — 
                 4.38 
                 4.51 
                 4.62 
                 4.73 
                 4.81 
                 4.89 
                 4.94 
                 4.98 
                 5.00 
                 5.00 
                 4.98 
                 4.95 
               
               
                 #53 
                 59.43 
                 59.53 
                 59.62 
                 59.72 
                 59.81 
                 59.91 
                 60.00 
                 60.10 
                 60.19 
                 60.29 
                 60.38 
                 60.48 
               
               
                 — 
                 4.90 
                 4.84 
                 4.76 
                 4.67 
                 4.57 
                 4.46 
                 4.34 
                 4.21 
                 4.08 
                 3.95 
                 3.81 
                 3.67 
               
               
                 #54 
                 60.57 
                 60.67 
                 60.76 
                 60.86 
                 60.95 
                 61.05 
                 61.14 
                 61.24 
                 61.34 
                 61.43 
                 61.53 
                 61.62 
               
               
                 — 
                 3.52 
                 3.38 
                 3.25 
                 3.11 
                 2.98 
                 2.85 
                 2.72 
                 2.60 
                 2.49 
                 2.38 
                 2.28 
                 2.18 
               
               
                 #55 
                 61.72 
                 61.81 
                 61.91 
                 62.00 
                 62.10 
                 62.19 
                 62.29 
                 62.38 
                 62.48 
                 62.57 
                 62.67 
                 62.76 
               
               
                 — 
                 2.09 
                 2.01 
                 1.93 
                 1.85 
                 1.76 
                 1.72 
                 1.66 
                 1.61 
                 1.57 
                 1.53 
                 1.49 
                 1.46 
               
               
                 #56 
                 62.86 
                 62.95 
                 63.05 
                 63.14 
                 63.24 
                 63.34 
                 63.43 
                 63.53 
                 63.62 
                 63.72 
                 63.81 
                 63.91 
               
               
                 — 
                 1.43 
                 1.41 
                 1.39 
                 1.37 
                 1.36 
                 1.35 
                 1.35 
                 1.35 
                 1.35 
                 1.36 
                 1.36 
                 1.37 
               
               
                 #57 
                 64.00 
                 64.10 
                 64.19 
                 64.29 
                 64.38 
                 64.48 
                 64.57 
                 64.67 
                 64.76 
                 64.86 
                 64.95 
                 65.05 
               
               
                 — 
                 1.39 
                 1.40 
                 1.42 
                 1.44 
                 1.46 
                 1.48 
                 1.50 
                 1.52 
                 1.55 
                 1.57 
                 1.59 
                 1.62 
               
               
                 #58 
                 65.14 
                 65.24 
                 65.34 
                 65.43 
                 65.53 
                 65.62 
                 65.72 
                 65.81 
                 65.91 
                 66.00 
                 66.10 
                 66.19 
               
               
                 — 
                 1.64 
                 1.67 
                 1.69 
                 1.71 
                 1.73 
                 1.75 
                 1.76 
                 1.78 
                 1.79 
                 1.81 
                 1.82 
                 1.83 
               
               
                 #59 
                 66.20 
                 66.38 
                 66.48 
                 66.57 
                 66.67 
                 66.76 
                 66.86 
                 66.95 
                 67.05 
                 67.14 
                 67.24 
                 67.34 
               
               
                 — 
                 1.83 
                 1.84 
                 1.84 
                 1.84 
                 1.85 
                 1.84 
                 1.84 
                 1.84 
                 1.84 
                 1.83 
                 1.83 
                 1.82 
               
               
                 #60 
                 67.43 
                 67.53 
                 67.62 
                 67.72 
                 67.81 
                 67.91 
                 68.00 
                 68.10 
                 68.19 
                 68.29 
                 68.38 
                 68.48 
               
               
                 — 
                 1.81 
                 1.81 
                 1.80 
                 1.80 
                 1.79 
                 1.79 
                 1.79 
                 1.79 
                 1.79 
                 1.79 
                 1.79 
                 1.80 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 Center conductor widths (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 68.57 
                 68.67 
                 68.76 
                 68.86 
                 68.95 
                 69.05 
                 69.15 
                 69.24 
                 69.34 
                 69.43 
                 69.53 
                 69.62 
               
               
                 — 
                 1.80 
                 1.81 
                 1.82 
                 1.84 
                 1.85 
                 1.87 
                 1.89 
                 1.91 
                 1.93 
                 1.96 
                 1.99 
                 2.02 
               
               
                 #62 
                 69.72 
                 69.81 
                 69.91 
                 70.00 
                 70.10 
                 70.19 
                 70.29 
                 70.38 
                 70.48 
                 70.57 
                 70.67 
                 70.76 
               
               
                 — 
                 2.05 
                 2.09 
                 2.12 
                 2.16 
                 2.20 
                 2.24 
                 2.28 
                 2.33 
                 2.37 
                 2.41 
                 2.46 
                 2.50 
               
               
                 #63 
                 70.86 
                 70.95 
                 71.05 
                 71.15 
                 71.24 
                 71.34 
                 71.43 
                 71.53 
                 71.62 
                 71.72 
                 71.81 
                 71.91 
               
               
                 — 
                 2.55 
                 2.59 
                 2.64 
                 2.68 
                 2.72 
                 2.76 
                 2.79 
                 2.83 
                 2.86 
                 2.89 
                 2.91 
                 2.93 
               
               
                 #64 
                 72.00 
                 72.10 
                 72.19 
                 72.29 
                 72.38 
                 72.48 
                 72.57 
                 72.67 
                 72.76 
                 72.86 
                 72.95 
                 73.05 
               
               
                 — 
                 2.95 
                 2.96 
                 2.97 
                 2.98 
                 2.98 
                 2.97 
                 2.97 
                 2.96 
                 2.94 
                 2.92 
                 2.90 
                 2.88 
               
               
                 #65 
                 73.15 
                 73.24 
                 73.34 
                 73.43 
                 73.53 
                 73.62 
                 73.72 
                 73.81 
                 73.91 
                 74.00 
                 74.10 
                 74.19 
               
               
                 — 
                 2.85 
                 2.81 
                 2.78 
                 2.74 
                 2.71 
                 2.67 
                 2.62 
                 2.58 
                 2.54 
                 2.49 
                 2.45 
                 2.41 
               
               
                 #66 
                 74.29 
                 74.38 
                 74.48 
                 74.57 
                 74.67 
                 74.76 
                 74.86 
                 74.96 
                 75.05 
                 75.15 
                 75.24 
                 75.34 
               
               
                 — 
                 2.36 
                 2.32 
                 2.28 
                 2.24 
                 2.20 
                 2.16 
                 2.12 
                 2.09 
                 2.06 
                 2.03 
                 2.00 
                 1.97 
               
               
                 #67 
                 75.43 
                 75.53 
                 75.62 
                 75.72 
                 75.81 
                 75.91 
                 76.00 
                 76.10 
                 76.19 
                 76.29 
                 76.38 
                 76.48 
               
               
                 — 
                 1.94 
                 1.92 
                 1.90 
                 1.88 
                 1.86 
                 1.85 
                 1.84 
                 1.82 
                 1.82 
                 1.81 
                 1.80 
                 1.80 
               
               
                 #68 
                 76.57 
                 76.67 
                 76.76 
                 76.86 
                 76.95 
                 77.05 
                 77.15 
                 77.24 
                 77.34 
                 77.43 
                 77.53 
                 77.62 
               
               
                 — 
                 1.80 
                 1.80 
                 1.80 
                 1.80 
                 1.80 
                 1.81 
                 1.82 
                 1.82 
                 1.83 
                 1.84 
                 1.85 
                 1.86 
               
               
                 #69 
                 77.72 
                 77.81 
                 77.91 
                 78.00 
                 78.10 
                 78.19 
                 78.29 
                 78.38 
                 78.48 
                 78.57 
                 78.67 
                 78.76 
               
               
                 — 
                 1.86 
                 1.87 
                 1.88 
                 1.89 
                 1.90 
                 1.91 
                 1.92 
                 1.92 
                 1.93 
                 1.93 
                 1.94 
                 1.94 
               
               
                 #70 
                 78.86 
                 78.95 
                 79.05 
                 79.15 
                 79.24 
                 79.34 
                 79.43 
                 79.53 
                 79.62 
                 79.72 
                 79.81 
                 79.91 
               
               
                 — 
                 1.95 
                 1.95 
                 1.95 
                 1.95 
                 1.95 
                 1.95 
                 1.95 
                 1.94 
                 1.94 
                 1.93 
                 1.93 
                 1.92 
               
               
                 #71 
                 80.00 
                 80.10 
                 80.19 
                 80.29 
                 80.38 
                 80.48 
                 80.57 
                 80.67 
                 80.76 
                 80.86 
                 80.95 
                 81.05 
               
               
                 — 
                 1.92 
                 1.91 
                 1.90 
                 1.90 
                 1.89 
                 1.89 
                 1.88 
                 1.87 
                 1.87 
                 1.86 
                 1.86 
                 1.86 
               
               
                 #72 
                 81.15 
                 81.24 
                 81.34 
                 81.43 
                 81.53 
                 81.62 
                 81.72 
                 81.81 
                 81.91 
                 82.00 
                 82.10 
                 82.19 
               
               
                 — 
                 1.86 
                 1.85 
                 1.85 
                 1.86 
                 1.86 
                 1.86 
                 1.87 
                 1.87 
                 1.88 
                 1.89 
                 1.90 
                 1.91 
               
               
                 #73 
                 82.29 
                 82.38 
                 82.48 
                 82.57 
                 82.67 
                 82.76 
                 82.86 
                 82.95 
                 83.05 
                 83.15 
                 83.24 
                 83.34 
               
               
                 — 
                 1.93 
                 1.94 
                 1.96 
                 1.98 
                 1.99 
                 2.01 
                 2.04 
                 2.06 
                 2.08 
                 2.11 
                 2.13 
                 2.16 
               
               
                 #74 
                 83.43 
                 83.53 
                 83.62 
                 83.72 
                 83.81 
                 83.91 
                 84.00 
                 84.10 
                 84.19 
                 84.29 
                 84.38 
                 84.48 
               
               
                 — 
                 2.18 
                 2.21 
                 2.24 
                 2.26 
                 2.29 
                 2.32 
                 2.34 
                 2.37 
                 2.39 
                 2.42 
                 2.44 
                 2.46 
               
               
                 #75 
                 84.57 
                 84.67 
                 84.76 
                 84.86 
                 84.96 
                 85.05 
                 85.15 
                 85.24 
                 85.34 
                 85.43 
                 85.53 
                 85.62 
               
               
                 — 
                 2.48 
                 2.50 
                 2.52 
                 2.52 
                 2.53 
                 2.56 
                 2.57 
                 2.58 
                 2.58 
                 2.58 
                 2.59 
                 2.58 
               
               
                 #76 
                 89.72 
                 85.81 
                 85.91 
                 86.00 
                 86.10 
                 86.19 
                 86.29 
                 86.38 
                 86.48 
                 86.57 
                 86.67 
                 86.76 
               
               
                 — 
                 2.58 
                 2.57 
                 2.57 
                 2.56 
                 2.55 
                 2.53 
                 2.52 
                 2.50 
                 2.49 
                 2.47 
                 2.45 
                 2.43 
               
               
                 #77 
                 86.86 
                 86.96 
                 87.05 
                 87.15 
                 87.24 
                 87.34 
                 87.43 
                 87.53 
                 87.62 
                 87.72 
                 87.81 
                 87.91 
               
               
                 — 
                 2.41 
                 2.38 
                 2.36 
                 2.34 
                 2.32 
                 2.30 
                 2.27 
                 2.25 
                 2.23 
                 2.21 
                 2.19 
                 2.17 
               
               
                 #78 
                 88.00 
                 88.10 
                 88.19 
                 88.29 
                 88.38 
                 88.48 
                 88.57 
                 88.67 
                 88.76 
                 88.86 
                 88.96 
                 89.05 
               
               
                 — 
                 2.15 
                 2.13 
                 2.12 
                 2.10 
                 2.09 
                 2.07 
                 2.06 
                 2.05 
                 2.04 
                 2.03 
                 2.02 
                 2.02 
               
               
                 #79 
                 89.15 
                 89.24 
                 89.34 
                 89.43 
                 89.53 
                 89.62 
                 89.72 
                 89.81 
                 89.91 
                 90.00 
                 90.10 
                 90.19 
               
               
                 — 
                 2.01 
                 2.01 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
                 2.00 
                 2.01 
                 2.01 
               
               
                 #80 
                 90.29 
                 90.38 
                 90.48 
                 90.57 
                 90.67 
                 90.76 
                 90.86 
                 90.96 
                 91.05 
                 91.15 
                 91.24 
                 91.34 
               
               
                 — 
                 2.01 
                 2.01 
                 2.02 
                 2.02 
                 2.02 
                 2.03 
                 2.03 
                 2.03 
                 2.03 
                 2.03 
                 2.04 
                 2.04 
               
               
                 #81 
                 91.43 
                 91.53 
                 91.62 
                 91.72 
                 91.81 
                 91.91 
                 92.00 
                 92.10 
                 92.19 
                 92.29 
                 92.38 
                 92.48 
               
               
                 — 
                 2.04 
                 2.03 
                 2.03 
                 2.03 
                 2.03 
                 2.03 
                 2.02 
                 2.02 
                 2.01 
                 2.01 
                 2.00 
                 1.99 
               
               
                 #82 
                 92.57 
                 92.67 
                 92.76 
                 92.86 
                 92.96 
                 93.05 
                 93.15 
                 93.24 
                 93.34 
                 93.43 
                 93.53 
                 99.62 
               
               
                 — 
                 1.99 
                 1.98 
                 1.97 
                 1.96 
                 1.95 
                 1.95 
                 1.94 
                 1.93 
                 1.92 
                 1.92 
                 1.91 
                 1.90 
               
               
                 #83 
                 93.72 
                 93.81 
                 93.91 
                 94.00 
                 94.10 
                 94.19 
                 94.29 
                 94.38 
                 94.48 
                 94.57 
                 94.67 
                 94.76 
               
               
                 — 
                 1.90 
                 1.89 
                 1.89 
                 1.88 
                 1.88 
                 1.88 
                 1.87 
                 1.87 
                 1.87 
                 1.88 
                 1.88 
                 1.88 
               
               
                 #84 
                 94.86 
                 94.96 
                 95.05 
                 95.15 
                 95.24 
               
               
                 — 
                 1.89 
                 1.89 
                 1.90 
                 1.91 
                 1.91 
               
               
                   
               
             
          
         
       
     
       FIG. 20  shows the shape of the center conductor  6  in the reflection-type bandpass filter  1  of Embodiment 4. In the figure, the dark portion represents the center conductor  6 . A non-reflecting terminator, or an R=25Ω resistance, is provided on the terminating side (the face at z=95.24 mm) of this reflection-type bandpass filter  1 . The thicknesses of the conducting layers  4 ,  5  and of the center conductor  6  may be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the conducting layers  4 ,  5  and of the center conductor  6  may be 2.1 μm or greater. This bandpass filter is used in a system with a characteristic impedance of 50Ω. 
       FIG. 21  and  FIG. 22  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter of Embodiment 4. As shown in the figures, in the range of frequencies f for which 3.8 GHz≦f≦9.8 GHz, the reflectance is −3 dB or greater, and the group delay variation is within ±0.2 ns. In the region f&lt;3.1 GHz or f&gt;10.6 GHz, the reflectance is −17 dB or lower. 
     Embodiment 5 
     A Kaiser window was used for which the reflectance is 1 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 0.7 times the wavelength of signals at frequency f=1 GHz propagating in the microstrip as the waveguide length, and setting the system characteristic impedance to 75Ω.  FIG. 23  shows the distribution in the z-axis direction of the local characteristic impedance obtained in the inverse problem. 
       FIG. 24  shows the z-axis distribution of the center conductor width w, when using a dielectric layer  3  of thickness h=3 mm and with relative permittivity ∈ r =1. Tables 12 through 14 list the center conductor widths w. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 Center conductor widths (1/3) 
               
             
          
           
               
                   
                 z[mm] 
               
             
          
           
               
                   
                 0.00 
                 0.21 
                 0.42 
                 0.63 
                 0.84 
                 1.05 
                 1.26 
                 1.47 
                 1.68 
                 1.89 
                 2.10 
                 2.31 
               
             
          
           
               
                   
                 w[mm] 
               
             
          
           
               
                   
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
                 2.45 
               
               
                   
                   
               
             
          
           
               
                  #2 
                 2.52 
                 2.73 
                 2.94 
                 3.15 
                 3.36 
                 3.57 
                 3.78 
                 3.99 
                 4.20 
                 4.41 
                 4.62 
                 4.83 
               
               
                 — 
                 2.44 
                 2.44 
                 2.44 
                 2.44 
                 2.44 
                 2.43 
                 2.43 
                 2.43 
                 2.43 
                 2.42 
                 2.42 
                 2.42 
               
               
                  #3 
                 5.04 
                 5.25 
                 5.46 
                 5.67 
                 5.88 
                 6.09 
                 6.30 
                 6.61 
                 6.72 
                 6.93 
                 7.14 
                 7.35 
               
               
                 — 
                 2.41 
                 2.41 
                 2.40 
                 2.40 
                 2.40 
                 2.39 
                 2.39 
                 2.38 
                 2.38 
                 2.37 
                 2.37 
                 2.36 
               
               
                  #4 
                 7.56 
                 7.77 
                 7.98 
                 8.19 
                 8.40 
                 8.61 
                 8.82 
                 9.03 
                 9.24 
                 9.45 
                 9.66 
                 9.87 
               
               
                 — 
                 2.36 
                 2.35 
                 2.35 
                 2.35 
                 2.34 
                 2.34 
                 2.33 
                 2.33 
                 2.33 
                 2.32 
                 2.32 
                 2.32 
               
               
                  #5 
                 10.08 
                 10.29 
                 10.50 
                 10.71 
                 10.92 
                 11.13 
                 11.34 
                 11.55 
                 11.76 
                 11.97 
                 12.18 
                 12.39 
               
               
                 — 
                 2.32 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
               
               
                  #6 
                 12.60 
                 12.81 
                 13.02 
                 13.23 
                 13.44 
                 13.65 
                 13.86 
                 14.07 
                 14.28 
                 14.49 
                 14.70 
                 14.91 
               
               
                 — 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.31 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
               
               
                  #7 
                 15.12 
                 15.33 
                 15.54 
                 15.75 
                 15.96 
                 16.17 
                 16.38 
                 16.59 
                 16.80 
                 17.01 
                 17.22 
                 17.43 
               
               
                 — 
                 2.32 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
               
               
                  #8 
                 17.64 
                 17.85 
                 18.06 
                 18.27 
                 18.48 
                 18.69 
                 18.90 
                 19.11 
                 19.32 
                 19.53 
                 19.74 
                 19.95 
               
               
                 — 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.34 
                 2.33 
               
               
                  #9 
                 20.16 
                 20.37 
                 20.58 
                 20.79 
                 21.00 
                 21.21 
                 21.42 
                 21.63 
                 21.84 
                 22.05 
                 22.26 
                 22.47 
               
               
                 — 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
               
               
                 #10 
                 22.68 
                 22.89 
                 23.10 
                 23.31 
                 23.52 
                 23.73 
                 23.94 
                 24.15 
                 24.86 
                 24.57 
                 24.78 
                 24.99 
               
               
                 — 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.32 
                 2.33 
                 2.33 
                 2.33 
                 2.33 
               
               
                 #11 
                 25.20 
                 25.41 
                 25.62 
                 25.83 
                 26.04 
                 26.25 
                 26.46 
                 26.67 
                 26.88 
                 27.09 
                 27.30 
                 27.51 
               
               
                 — 
                 2.34 
                 2.34 
                 2.35 
                 2.35 
                 2.36 
                 2.36 
                 2.37 
                 2.38 
                 2.38 
                 2.39 
                 2.40 
                 2.41 
               
               
                 #12 
                 27.72 
                 27.93 
                 28.14 
                 28.35 
                 28.56 
                 28.77 
                 28.98 
                 29.19 
                 29.40 
                 29.61 
                 29.82 
                 30.03 
               
               
                 — 
                 2.41 
                 2.42 
                 2.43 
                 2.44 
                 2.45 
                 2.45 
                 2.46 
                 2.47 
                 2.48 
                 2.49 
                 2.50 
                 2.50 
               
               
                 #13 
                 30.24 
                 30.45 
                 30.86 
                 30.87 
                 31.08 
                 31.29 
                 31.50 
                 31.71 
                 31.92 
                 32.13 
                 32.34 
                 32.55 
               
               
                 — 
                 2.51 
                 2.52 
                 2.53 
                 2.53 
                 2.54 
                 2.55 
                 2.55 
                 2.56 
                 2.56 
                 2.57 
                 2.57 
                 2.57 
               
               
                 #14 
                 32.76 
                 32.97 
                 33.18 
                 33.39 
                 33.60 
                 33.81 
                 34.02 
                 34.23 
                 34.44 
                 34.65 
                 34.86 
                 35.07 
               
               
                 — 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
                 2.58 
               
               
                 #15 
                 35.28 
                 35.49 
                 35.70 
                 35.91 
                 36.12 
                 36.33 
                 36.54 
                 36.75 
                 36.96 
                 37.17 
                 37.38 
                 37.59 
               
               
                 — 
                 2.57 
                 2.57 
                 2.57 
                 2.57 
                 2.56 
                 2.56 
                 2.56 
                 2.55 
                 2.55 
                 2.55 
                 2.54 
                 2.54 
               
               
                 #16 
                 37.80 
                 38.01 
                 38.22 
                 38.43 
                 38.64 
                 38.85 
                 39.06 
                 39.27 
                 39.48 
                 39.69 
                 39.90 
                 40.11 
               
               
                 — 
                 2.54 
                 2.53 
                 2.53 
                 2.53 
                 2.53 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
               
               
                 #17 
                 40.32 
                 40.53 
                 40.74 
                 40.95 
                 41.16 
                 41.37 
                 41.58 
                 41.79 
                 42.00 
                 42.21 
                 42.42 
                 42.63 
               
               
                 — 
                 2.52 
                 2.52 
                 2.52 
                 2.53 
                 2.53 
                 2.53 
                 2.53 
                 2.53 
                 2.54 
                 2.54 
                 2.54 
                 2.55 
               
               
                 #18 
                 42.84 
                 43.05 
                 43.26 
                 43.47 
                 43.68 
                 43.89 
                 44.10 
                 44.31 
                 44.52 
                 44.73 
                 44.94 
                 45.15 
               
               
                 — 
                 2.55 
                 2.55 
                 2.55 
                 2.56 
                 2.56 
                 2.56 
                 2.56 
                 2.56 
                 2.57 
                 2.57 
                 2.57 
                 2.56 
               
               
                 #19 
                 45.36 
                 45.57 
                 45.78 
                 45.99 
                 46.20 
                 46.41 
                 46.62 
                 46.83 
                 47.04 
                 47.25 
                 47.46 
                 47.67 
               
               
                 — 
                 2.56 
                 2.56 
                 2.56 
                 2.56 
                 2.55 
                 2.55 
                 2.54 
                 2.54 
                 2.53 
                 2.52 
                 2.51 
                 2.50 
               
               
                 #20 
                 47.88 
                 48.09 
                 48.30 
                 48.51 
                 48.72 
                 48.93 
                 49.14 
                 49.35 
                 49.56 
                 49.77 
                 49.98 
                 50.19 
               
               
                 — 
                 2.49 
                 2.48 
                 2.47 
                 2.46 
                 2.45 
                 2.44 
                 2.42 
                 2.41 
                 2.40 
                 2.38 
                 2.37 
                 2.35 
               
               
                 #21 
                 50.40 
                 50.61 
                 50.82 
                 51.03 
                 51.24 
                 51.45 
                 51.66 
                 51.87 
                 52.08 
                 52.29 
                 52.50 
                 52.71 
               
               
                 — 
                 2.34 
                 2.33 
                 2.33 
                 2.30 
                 2.38 
                 2.27 
                 2.26 
                 2.24 
                 2.23 
                 2.22 
                 2.21 
                 2.19 
               
               
                 #22 
                 52.92 
                 53.13 
                 53.34 
                 53.55 
                 53.76 
                 53.97 
                 54.18 
                 54.39 
                 54.60 
                 54.81 
                 55.02 
                 55.23 
               
               
                 — 
                 2.18 
                 2.17 
                 2.17 
                 2.16 
                 2.15 
                 2.14 
                 2.14 
                 2.13 
                 2.13 
                 2.12 
                 2.12 
                 2.12 
               
               
                 #23 
                 55.44 
                 55.65 
                 55.86 
                 56.07 
                 56.28 
                 56.49 
                 56.70 
                 56.91 
                 57.12 
                 57.33 
                 57.54 
                 57.75 
               
               
                 — 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.12 
                 2.13 
                 2.13 
                 2.14 
                 2.14 
               
               
                 #24 
                 57.96 
                 58.17 
                 58.38 
                 58.59 
                 58.80 
                 59.01 
                 59.22 
                 59.43 
                 59.64 
                 59.85 
                 60.06 
                 60.27 
               
               
                 — 
                 2.15 
                 2.15 
                 2.16 
                 2.16 
                 2.17 
                 2.17 
                 2.18 
                 2.18 
                 2.19 
                 2.19 
                 2.19 
                 2.20 
               
               
                 #25 
                 60.48 
                 60.69 
                 60.90 
                 61.11 
                 61.32 
                 61.53 
                 61.74 
                 61.95 
                 62.16 
                 62.37 
                 62.58 
                 62.79 
               
               
                 — 
                 2.20 
                 2.20 
                 2.20 
                 2.21 
                 2.21 
                 2.21 
                 2.21 
                 2.21 
                 2.20 
                 2.20 
                 2.20 
                 2.20 
               
               
                 #26 
                 63.00 
                 63.21 
                 63.42 
                 63.63 
                 63.84 
                 64.05 
                 64.26 
                 64.47 
                 64.68 
                 64.89 
                 65.10 
                 65.31 
               
               
                 — 
                 2.19 
                 2.19 
                 2.19 
                 2.18 
                 2.18 
                 2.17 
                 2.17 
                 2.16 
                 2.16 
                 2.15 
                 2.15 
                 2.14 
               
               
                 #27 
                 65.52 
                 65.73 
                 65.94 
                 66.15 
                 66.36 
                 66.57 
                 66.78 
                 66.99 
                 67.20 
                 67.41 
                 67.62 
                 67.83 
               
               
                 — 
                 2.14 
                 2.14 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.13 
                 2.14 
                 2.14 
               
               
                 #28 
                 68.04 
                 68.25 
                 68.46 
                 68.67 
                 68.88 
                 69.09 
                 69.30 
                 69.51 
                 69.72 
                 69.93 
                 70.14 
                 70.35 
               
               
                 — 
                 2.15 
                 2.18 
                 2.16 
                 2.17 
                 2.19 
                 2.20 
                 2.21 
                 2.23 
                 2.25 
                 2.26 
                 2.28 
                 2.30 
               
               
                 #29 
                 70.56 
                 70.77 
                 70.98 
                 71.19 
                 71.40 
                 71.61 
                 71.82 
                 72.03 
                 72.24 
                 72.45 
                 72.66 
                 72.87 
               
               
                 — 
                 2.33 
                 2.33 
                 2.37 
                 2.40 
                 2.42 
                 2.45 
                 2.48 
                 2.51 
                 2.54 
                 2.57 
                 2.60 
                 2.63 
               
               
                 #30 
                 73.08 
                 73.29 
                 73.50 
                 73.71 
                 73.92 
                 74.13 
                 74.34 
                 74.55 
                 74.76 
                 74.97 
                 75.18 
                 75.39 
               
               
                 — 
                 2.68 
                 2.69 
                 2.72 
                 2.75 
                 2.77 
                 2.80 
                 2.83 
                 2.86 
                 2.88 
                 2.90 
                 2.93 
                 2.95 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 Center conductor widths (2/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #31 
                 75.60 
                 75.81 
                 76.02 
                 76.23 
                 76.44 
                 76.65 
                 76.86 
                 77.07 
                 77.28 
                 77.49 
                 77.70 
                 77.91 
               
               
                 — 
                 2.97 
                 2.98 
                 3.00 
                 3.01 
                 3.03 
                 3.04 
                 3.04 
                 3.05 
                 3.05 
                 3.06 
                 3.06 
                 3.06 
               
               
                 #32 
                 78.12 
                 78.33 
                 78.54 
                 78.75 
                 78.96 
                 79.17 
                 70.38 
                 79.58 
                 79.80 
                 80.01 
                 80.22 
                 80.43 
               
               
                 — 
                 3.05 
                 3.05 
                 3.04 
                 3.03 
                 3.03 
                 3.02 
                 3.01 
                 2.99 
                 2.98 
                 2.97 
                 2.96 
                 2.94 
               
               
                 #33 
                 80.64 
                 80.85 
                 81.06 
                 81.27 
                 81.48 
                 81.69 
                 81.90 
                 82.11 
                 82.32 
                 82.53 
                 82.74 
                 82.95 
               
               
                 — 
                 2.93 
                 2.92 
                 2.91 
                 2.90 
                 2.88 
                 2.87 
                 2.86 
                 2.86 
                 2.85 
                 2.84 
                 2.84 
                 2.84 
               
               
                 #34 
                 83.16 
                 83.37 
                 83.58 
                 83.79 
                 84.00 
                 84.21 
                 84.42 
                 84.63 
                 84.84 
                 85.05 
                 85.26 
                 85.47 
               
               
                 — 
                 2.83 
                 2.83 
                 2.84 
                 2.84 
                 2.84 
                 2.85 
                 2.86 
                 2.86 
                 2.87 
                 2.89 
                 2.90 
                 2.91 
               
               
                 #35 
                 85.68 
                 85.89 
                 86.10 
                 86.31 
                 86.52 
                 86.73 
                 86.94 
                 87.15 
                 87.36 
                 87.57 
                 87.78 
                 87.99 
               
               
                 — 
                 2.93 
                 2.94 
                 2.96 
                 2.97 
                 2.98 
                 3.00 
                 3.02 
                 3.03 
                 3.05 
                 3.06 
                 3.07 
                 3.08 
               
               
                 #36 
                 88.20 
                 88.41 
                 88.62 
                 88.83 
                 89.04 
                 89.25 
                 89.46 
                 89.67 
                 89.88 
                 90.09 
                 90.39 
                 90.51 
               
               
                 — 
                 3.08 
                 3.09 
                 3.09 
                 3.09 
                 3.08 
                 3.07 
                 3.06 
                 3.04 
                 3.02 
                 3.00 
                 2.97 
                 2.94 
               
               
                 #37 
                 90.72 
                 90.93 
                 91.14 
                 91.36 
                 91.56 
                 91.77 
                 91.98 
                 92.19 
                 92.40 
                 92.61 
                 92.82 
                 93.03 
               
               
                 — 
                 2.90 
                 2.86 
                 2.81 
                 2.76 
                 2.71 
                 2.65 
                 2.59 
                 2.52 
                 2.45 
                 2.38 
                 2.31 
                 2.24 
               
               
                 #38 
                 93.24 
                 93.45 
                 93.66 
                 93.87 
                 94.08 
                 94.29 
                 94.50 
                 94.71 
                 94.92 
                 95.13 
                 95.34 
                 95.55 
               
               
                 — 
                 2.16 
                 2.08 
                 2.01 
                 1.93 
                 1.85 
                 1.77 
                 1.70 
                 1.62 
                 1.55 
                 1.47 
                 1.40 
                 1.33 
               
               
                 #39 
                 95.76 
                 95.97 
                 96.18 
                 96.39 
                 96.60 
                 96.81 
                 97.02 
                 97.23 
                 97.44 
                 97.65 
                 97.85 
                 98.07 
               
               
                 — 
                 1.27 
                 1.21 
                 1.15 
                 1.09 
                 1.04 
                 0.99 
                 0.94 
                 0.90 
                 0.86 
                 0.82 
                 0.79 
                 0.76 
               
               
                 #40 
                 98.28 
                 98.49 
                 98.70 
                 98.91 
                 99.12 
                 99.33 
                 99.54 
                 99.75 
                 99.96 
                 100.17 
                 100.38 
                 100.59 
               
               
                 — 
                 0.73 
                 0.71 
                 0.69 
                 0.68 
                 0.67 
                 0.66 
                 0.66 
                 0.66 
                 0.65 
                 0.67 
                 0.68 
                 0.69 
               
               
                 #41 
                 100.80 
                 101.01 
                 101.22 
                 101.43 
                 101.64 
                 101.85 
                 102.06 
                 102.27 
                 102.48 
                 102.69 
                 102.90 
                 103.11 
               
               
                 — 
                 0.71 
                 0.74 
                 0.76 
                 0.80 
                 0.84 
                 0.88 
                 0.93 
                 0.99 
                 1.05 
                 1.12 
                 1.20 
                 1.28 
               
               
                 #42 
                 103.32 
                 103.53 
                 103.74 
                 103.95 
                 104.16 
                 104.37 
                 104.58 
                 104.79 
                 105.00 
                 105.21 
                 105.42 
                 105.63 
               
               
                 — 
                 1.38 
                 1.48 
                 1.58 
                 1.70 
                 1.83 
                 1.96 
                 2.11 
                 2.26 
                 2.43 
                 2.60 
                 2.79 
                 2.98 
               
               
                 #43 
                 105.84 
                 106.06 
                 106.26 
                 106.47 
                 106.68 
                 106.89 
                 107.10 
                 107.31 
                 107.52 
                 107.73 
                 107.94 
                 108.15 
               
               
                 — 
                 3.18 
                 3.39 
                 3.61 
                 3.84 
                 4.07 
                 4.32 
                 4.50 
                 4.82 
                 5.07 
                 5.33 
                 5.58 
                 5.84 
               
               
                 #44 
                 108.36 
                 108.57 
                 108.78 
                 108.99 
                 109.20 
                 109.41 
                 109.62 
                 109.83 
                 110.04 
                 110.25 
                 110.46 
                 110.67 
               
               
                 — 
                 6.09 
                 6.34 
                 6.57 
                 6.80 
                 7.02 
                 7.32 
                 7.40 
                 7.56 
                 7.70 
                 7.82 
                 7.91 
                 7.97 
               
               
                 #45 
                 110.88 
                 111.00 
                 111.30 
                 111.51 
                 111.72 
                 111.93 
                 112.14 
                 112.35 
                 112.56 
                 112.77 
                 112.98 
                 113.19 
               
               
                 — 
                 8.01 
                 8.02 
                 8.00 
                 7.95 
                 7.88 
                 7.77 
                 7.65 
                 7.49 
                 7.32 
                 7.12 
                 6.91 
                 6.68 
               
               
                 #46 
                 113.40 
                 113.61 
                 113.82 
                 114.03 
                 114.24 
                 114.45 
                 114.66 
                 114.87 
                 115.08 
                 115.29 
                 115.50 
                 116.71 
               
               
                 — 
                 6.44 
                 6.19 
                 5.93 
                 5.65 
                 5.39 
                 5.12 
                 4.85 
                 4.58 
                 4.31 
                 4.05 
                 3.80 
                 3.55 
               
               
                 #47 
                 115.92 
                 116.13 
                 116.34 
                 116.55 
                 116.76 
                 116.97 
                 117.18 
                 117.39 
                 117.60 
                 117.81 
                 118.02 
                 118.23 
               
               
                 — 
                 3.31 
                 3.08 
                 2.86 
                 2.65 
                 2.45 
                 2.26 
                 2.08 
                 1.91 
                 1.75 
                 1.60 
                 1.46 
                 1.33 
               
               
                 #48 
                 118.44 
                 118.65 
                 118.85 
                 119.07 
                 119.28 
                 119.49 
                 119.70 
                 119.91 
                 120.12 
                 120.33 
                 120.54 
                 120.75 
               
               
                 — 
                 1.21 
                 1.10 
                 1.00 
                 0.91 
                 0.83 
                 0.75 
                 0.69 
                 0.63 
                 0.57 
                 0.53 
                 0.49 
                 0.46 
               
               
                 #49 
                 120.96 
                 121.17 
                 121.38 
                 121.59 
                 121.80 
                 122.01 
                 122.22 
                 122.43 
                 122.64 
                 122.85 
                 123.06 
                 123.27 
               
               
                 — 
                 0.42 
                 0.40 
                 0.37 
                 0.35 
                 0.34 
                 0.33 
                 0.33 
                 0.32 
                 0.32 
                 0.32 
                 0.33 
                 0.34 
               
               
                 #50 
                 123.48 
                 123.69 
                 123.90 
                 124.11 
                 124.32 
                 124.53 
                 124.74 
                 124.95 
                 125.16 
                 125.37 
                 125.58 
                 125.79 
               
               
                 — 
                 0.35 
                 0.37 
                 0.39 
                 0.41 
                 0.44 
                 0.47 
                 0.51 
                 0.55 
                 0.60 
                 0.66 
                 0.72 
                 0.79 
               
               
                 #51 
                 126.00 
                 126.21 
                 126.42 
                 126.63 
                 126.84 
                 127.05 
                 127.26 
                 127.47 
                 127.68 
                 127.89 
                 128.19 
                 128.31 
               
               
                 — 
                 0.86 
                 0.94 
                 1.03 
                 1.13 
                 1.24 
                 1.35 
                 1.47 
                 1.60 
                 1.73 
                 1.88 
                 2.03 
                 2.10 
               
               
                 #52 
                 128.52 
                 125.73 
                 126.94 
                 129.15 
                 129.36 
                 129.57 
                 129.78 
                 129.99 
                 130.20 
                 130.41 
                 130.02 
                 130.83 
               
               
                 — 
                 2.35 
                 2.52 
                 2.70 
                 2.88 
                 3.07 
                 3.26 
                 3.45 
                 3.65 
                 3.84 
                 4.04 
                 4.23 
                 4.42 
               
               
                 #53 
                 131.04 
                 131.25 
                 131.46 
                 131.67 
                 131.88 
                 132.09 
                 132.30 
                 132.51 
                 132.72 
                 132.93 
                 133.14 
                 133.35 
               
               
                 — 
                 4.61 
                 4.79 
                 4.97 
                 5.13 
                 5.29 
                 5.43 
                 5.56 
                 5.68 
                 5.78 
                 5.87 
                 5.94 
                 5.99 
               
               
                 #54 
                 133.56 
                 133.77 
                 133.98 
                 134.13 
                 134.40 
                 134.61 
                 134.82 
                 135.03 
                 135.24 
                 135.45 
                 135.65 
                 135.87 
               
               
                 — 
                 6.03 
                 6.05 
                 6.05 
                 6.04 
                 6.01 
                 5.96 
                 5.90 
                 5.82 
                 5.73 
                 5.63 
                 5.52 
                 5.40 
               
               
                 #55 
                 136.08 
                 136.29 
                 136.50 
                 136.71 
                 136.92 
                 137.13 
                 137.34 
                 137.55 
                 137.76 
                 137.97 
                 138.18 
                 138.39 
               
               
                 — 
                 5.27 
                 5.13 
                 4.99 
                 4.85 
                 4.70 
                 4.55 
                 4.40 
                 4.25 
                 4.11 
                 3.96 
                 3.82 
                 3.68 
               
               
                 #56 
                 138.60 
                 138.81 
                 139.02 
                 139.23 
                 139.44 
                 139.65 
                 139.86 
                 140.07 
                 140.28 
                 140.49 
                 140.70 
                 140.91 
               
               
                 — 
                 3.54 
                 3.41 
                 3.28 
                 3.16 
                 3.04 
                 2.93 
                 2.82 
                 2.72 
                 2.63 
                 2.54 
                 2.45 
                 2.38 
               
               
                 #57 
                 141.12 
                 141.33 
                 141.54 
                 141.75 
                 141.96 
                 142.17 
                 142.38 
                 142.59 
                 142.80 
                 143.01 
                 143.22 
                 143.43 
               
               
                 — 
                 2.30 
                 2.24 
                 2.18 
                 2.12 
                 2.07 
                 2.02 
                 1.98 
                 1.94 
                 1.91 
                 1.88 
                 1.86 
                 1.83 
               
               
                 #58 
                 143.64 
                 143.65 
                 144.05 
                 144.27 
                 144.48 
                 144.69 
                 144.90 
                 145.11 
                 145.32 
                 145.53 
                 145.74 
                 145.95 
               
               
                 — 
                 1.82 
                 1.80 
                 1.79 
                 1.79 
                 1.78 
                 1.78 
                 1.78 
                 1.78 
                 1.79 
                 1.80 
                 1.80 
                 1.81 
               
               
                 #59 
                 146.16 
                 146.37 
                 146.58 
                 146.79 
                 147.00 
                 147.21 
                 147.42 
                 147.63 
                 147.84 
                 148.05 
                 148.25 
                 148.47 
               
               
                 — 
                 1.83 
                 1.84 
                 1.85 
                 1.86 
                 1.88 
                 1.89 
                 1.90 
                 1.92 
                 1.93 
                 1.94 
                 1.95 
                 1.96 
               
               
                 #60 
                 146.68 
                 148.89 
                 149.10 
                 149.31 
                 149.52 
                 149.73 
                 149.94 
                 150.15 
                 150.36 
                 150.57 
                 150.78 
                 150.99 
               
               
                 — 
                 1.97 
                 1.98 
                 1.98 
                 1.98 
                 1.98 
                 1.98 
                 1.98 
                 1.98 
                 1.97 
                 1.97 
                 1.96 
                 1.95 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 Center conductor widths (3/3) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 #61 
                 151.20 
                 151.41 
                 151.62 
                 151.83 
                 152.04 
                 152.25 
                 152.46 
                 152.67 
                 152.88 
                 153.09 
                 153.30 
                 153.51 
               
               
                 — 
                 1.94 
                 1.92 
                 1.91 
                 1.89 
                 1.87 
                 1.86 
                 1.84 
                 1.82 
                 1.80 
                 1.78 
                 1.76 
                 1.74 
               
               
                 #62 
                 153.72 
                 153.93 
                 154.14 
                 154.35 
                 154.56 
                 154.77 
                 154.98 
                 155.19 
                 155.40 
                 155.61 
                 155.82 
                 156.03 
               
               
                 — 
                 1.72 
                 1.71 
                 1.69 
                 1.67 
                 1.66 
                 1.65 
                 1.63 
                 1.62 
                 1.61 
                 1.61 
                 1.60 
                 1.60 
               
               
                 #63 
                 156.24 
                 156.45 
                 156.66 
                 156.87 
                 157.08 
                 157.29 
                 157.50 
                 157.71 
                 157.92 
                 158.13 
                 158.34 
                 158.55 
               
               
                 — 
                 1.60 
                 1.60 
                 1.60 
                 1.61 
                 1.62 
                 1.63 
                 1.64 
                 1.66 
                 1.68 
                 1.70 
                 1.73 
                 1.75 
               
               
                 #64 
                 158.76 
                 158.97 
                 159.18 
                 159.39 
                 159.60 
                 159.81 
                 160.02 
                 160.23 
                 160.44 
                 160.65 
                 160.85 
                 161.07 
               
               
                 — 
                 1.78 
                 1.81 
                 1.85 
                 1.89 
                 1.93 
                 1.97 
                 2.01 
                 2.06 
                 2.11 
                 2.16 
                 2.21 
                 2.27 
               
               
                 #65 
                 161.28 
                 161.49 
                 161.70 
                 161.91 
                 162.12 
                 162.33 
                 162.54 
                 162.75 
                 162.96 
                 163.17 
                 163.38 
                 163.59 
               
               
                 — 
                 2.32 
                 2.38 
                 2.44 
                 2.50 
                 2.56 
                 2.62 
                 2.68 
                 2.74 
                 2.80 
                 2.85 
                 2.91 
                 2.97 
               
               
                 #66 
                 163.80 
                 164.01 
                 164.22 
                 164.43 
                 164.64 
                 164.85 
                 165.06 
                 165.27 
                 165.48 
                 165.69 
                 165.90 
                 166.11 
               
               
                 — 
                 3.02 
                 3.07 
                 3.12 
                 3.17 
                 3.21 
                 3.25 
                 3.29 
                 3.33 
                 3.36 
                 3.38 
                 3.40 
                 3.42 
               
               
                 #67 
                 166.32 
                 166.53 
                 166.74 
                 166.95 
                 167.16 
                 167.37 
                 167.58 
                 167.79 
                 168.00 
                 168.21 
                 168.42 
                 168.63 
               
               
                 — 
                 3.44 
                 3.45 
                 3.45 
                 3.45 
                 3.45 
                 3.44 
                 3.43 
                 3.42 
                 3.40 
                 3.38 
                 3.36 
                 3.34 
               
               
                 #68 
                 168.84 
                 169.05 
                 169.26 
                 169.47 
                 169.68 
                 169.89 
                 170.10 
                 170.31 
                 170.52 
                 170.73 
                 170.94 
                 171.15 
               
               
                 — 
                 3.31 
                 3.28 
                 3.25 
                 3.21 
                 3.18 
                 3.14 
                 3.11 
                 3.07 
                 3.03 
                 3.00 
                 2.96 
                 2.92 
               
               
                 #69 
                 171.36 
                 171.57 
                 171.78 
                 171.99 
                 172.20 
                 172.41 
                 172.62 
                 172.83 
                 173.04 
                 173.25 
                 173.46 
                 173.67 
               
               
                 — 
                 2.89 
                 2.85 
                 2.82 
                 2.79 
                 2.76 
                 2.72 
                 2.70 
                 2.67 
                 2.64 
                 2.62 
                 2.60 
                 2.58 
               
               
                 #70 
                 173.88 
                 174.08 
                 174.30 
                 174.51 
                 174.72 
                 174.93 
                 175.14 
                 175.35 
                 175.56 
                 175.77 
                 175.98 
                 176.19 
               
               
                 — 
                 2.56 
                 2.54 
                 2.53 
                 2.51 
                 2.50 
                 2.49 
                 2.48 
                 2.48 
                 2.47 
                 2.47 
                 2.47 
                 2.46 
               
               
                 #71 
                 176.40 
                 176.61 
                 176.82 
                 177.03 
                 177.24 
                 177.45 
                 177.66 
                 177.87 
                 178.08 
                 178.29 
                 178.50 
                 178.71 
               
               
                 — 
                 2.46 
                 2.46 
                 2.46 
                 2.47 
                 2.47 
                 2.47 
                 2.47 
                 2.48 
                 2.48 
                 2.48 
                 2.49 
                 2.49 
               
               
                 #72 
                 178.92 
                 179.13 
                 179.34 
                 179.55 
                 179.76 
                 179.97 
                 180.18 
                 180.39 
                 180.60 
                 180.81 
                 181.02 
                 181.23 
               
               
                 — 
                 2.49 
                 2.49 
                 2.49 
                 2.49 
                 2.49 
                 2.49 
                 2.48 
                 2.48 
                 2.47 
                 2.46 
                 2.45 
                 2.44 
               
               
                 #73 
                 181.44 
                 181.65 
                 181.86 
                 182.07 
                 182.28 
                 182.49 
                 182.70 
                 182.91 
                 183.12 
                 183.33 
                 183.54 
                 183.75 
               
               
                 — 
                 2.43 
                 2.41 
                 2.40 
                 2.38 
                 2.37 
                 2.35 
                 2.33 
                 2.31 
                 2.28 
                 2.26 
                 2.24 
                 2.21 
               
               
                 #74 
                 183.96 
                 184.17 
                 184.38 
                 184.59 
                 184.80 
                 185.01 
                 185.22 
                 185.43 
                 185.64 
                 185.85 
                 186.06 
                 186.27 
               
               
                 — 
                 2.19 
                 2.16 
                 2.14 
                 2.11 
                 2.09 
                 2.07 
                 2.04 
                 2.02 
                 1.99 
                 1.97 
                 1.95 
                 1.93 
               
               
                 #75 
                 185.48 
                 185.69 
                 186.90 
                 187.11 
                 187.32 
                 187.53 
                 187.74 
                 187.95 
                 188.16 
                 188.37 
                 188.58 
                 188.79 
               
               
                 — 
                 1.91 
                 1.89 
                 1.87 
                 1.86 
                 1.84 
                 1.83 
                 1.82 
                 1.81 
                 1.80 
                 1.79 
                 1.79 
                 1.79 
               
               
                 #76 
                 189.00 
                 189.21 
                 189.42 
                 189.60 
                 189.84 
                 190.05 
                 190.26 
                 190.47 
                 190.68 
                 190.89 
                 191.10 
                 191.31 
               
               
                 — 
                 1.79 
                 1.79 
                 1.79 
                 1.79 
                 1.80 
                 1.81 
                 1.82 
                 1.83 
                 1.84 
                 1.86 
                 1.87 
                 1.89 
               
               
                 #77 
                 191.52 
                 191.73 
                 191.94 
                 192.15 
                 192.36 
                 192.57 
                 192.78 
                 192.99 
                 193.20 
                 193.41 
                 193.62 
                 193.83 
               
               
                 — 
                 1.91 
                 1.93 
                 1.95 
                 1.98 
                 2.00 
                 3.03 
                 2.06 
                 2.08 
                 2.11 
                 2.14 
                 2.17 
                 2.20 
               
               
                 #78 
                 194.04 
                 194.25 
                 194.46 
                 194.67 
                 194.88 
                 195.09 
                 195.30 
                 195.51 
                 195.72 
                 195.93 
                 196.14 
                 196.35 
               
               
                 — 
                 2.23 
                 2.27 
                 2.30 
                 2.33 
                 2.36 
                 2.39 
                 2.42 
                 2.45 
                 2.47 
                 2.50 
                 2.53 
                 2.55 
               
               
                 #79 
                 196.56 
                 196.77 
                 196.99 
                 197.19 
                 197.40 
                 197.61 
                 197.82 
                 198.03 
                 198.24 
                 198.45 
                 198.66 
                 198.87 
               
               
                 — 
                 2.57 
                 2.60 
                 2.62 
                 2.64 
                 2.65 
                 2.67 
                 2.68 
                 2.69 
                 2.71 
                 2.71 
                 2.72 
                 2.73 
               
               
                 #80 
                 199.08 
                 199.29 
                 199.50 
                 199.71 
                 199.92 
                 200.13 
                 200.34 
                 200.55 
                 200.76 
                 200.97 
                 201.18 
                 201.39 
               
               
                 — 
                 2.73 
                 2.73 
                 2.74 
                 2.74 
                 2.73 
                 2.73 
                 2.73 
                 2.72 
                 2.72 
                 2.71 
                 2.70 
                 2.70 
               
               
                 #81 
                 201.60 
                 201.81 
                 202.02 
                 202.23 
                 202.44 
                 202.65 
                 202.86 
                 203.07 
                 203.28 
                 203.49 
                 203.70 
                 203.91 
               
               
                 — 
                 2.69 
                 2.68 
                 2.67 
                 2.67 
                 2.66 
                 2.65 
                 2.64 
                 2.64 
                 2.63 
                 2.62 
                 2.62 
                 2.61 
               
               
                 #82 
                 204.12 
                 204.33 
                 204.54 
                 204.75 
                 204.96 
                 205.17 
                 205.38 
                 205.59 
                 205.80 
                 206.01 
                 206.22 
                 206.43 
               
               
                 — 
                 2.61 
                 2.61 
                 2.60 
                 2.60 
                 2.60 
                 2.60 
                 2.60 
                 2.61 
                 2.61 
                 2.61 
                 2.62 
                 2.62 
               
               
                 #83 
                 206.64 
                 206.85 
                 207.06 
                 207.27 
                 207.48 
                 207.69 
                 207.90 
                 208.11 
                 208.32 
                 208.53 
                 208.74 
                 208.95 
               
               
                 — 
                 2.63 
                 2.64 
                 2.64 
                 2.65 
                 2.66 
                 2.67 
                 2.68 
                 2.69 
                 2.70 
                 2.71 
                 2.71 
                 2.72 
               
               
                 #84 
                 209.18 
                 209.37 
                 209.58 
                 209.79 
                 210.00 
               
               
                 — 
                 2.73 
                 2.74 
                 2.75 
                 2.75 
                 2.76 
               
               
                   
               
             
          
         
       
     
       FIG. 25  shows the shape of the center conductor  6  in the reflection-type bandpass filter  1  of Embodiment 5. In the figure, the dark portion represents the center conductor  6 . A non-reflecting terminator, or an R=75Ω resistance, is provided on the terminating side (the face at z=210 mm) of this reflection-type bandpass filter  1 . The thicknesses of the conducting layers  4 ,  5  and of the center conductor  6  may be thick compared with the skin depth at f=1 GHz. For example, when using copper, the thickness of the conducting layers  4 ,  5  and of the center conductor  6  may be 2.1 μm or greater. This bandpass filter is used in a system with a characteristic impedance of 75Ω. 
       FIG. 26  and  FIG. 27  show the amplitude characteristic and group delay characteristic respectively of reflected waves (S 11 ) in the bandpass filter of Embodiment 5. As shown in the figures, in the range of frequencies f for which 3.7 GHz≦f≦10.0 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. 
     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 gist of the invention. The invention is not limited by the above explanation, but is limited only by the scope of the attached claims.