Patent Publication Number: US-2005140473-A1

Title: Microstrip cross-coupled bandpass filter with asymmetric frequency characteristic

Description:
CROSS REFERENCE TO RELATED APPLICATION  
      This application claims priority to and the benefit of Korea Patent Application No. 2003-96309 filed on Dec. 24, 2003 in the Korean Intellectual Property Office, the entire content of which is incorporated herein by reference.  
     BACKGROUND OF THE INVENTION  
      (a) Field of the Invention  
      The present invention relates to a bandpass filter, and more particularly, to a microstrip bandpass filter with an asymmetric frequency characteristic, which includes cross coupling and resonators.  
      (b) Description of the Related Art  
      Recently, a component in the form of a waveguide has been generally used as a bandpass filter in a millimeter-wave home network system. Although the waveguide component has low loss and high attenuation characteristics, its cost, size, and weight cannot satisfy the millimeter-wave home network&#39;s demand.  
      A conventional microstrip cross-coupled bandpass filter that includes resonators and has an asymmetric frequency characteristic is explained with reference to  FIGS. 1, 2 ,  3 , and  4 .  FIG. 1  shows a pattern of a bandpass filter including open-loop resonators.  FIG. 1   a  shows a bandpass filter pattern having an attenuation pole on the high side of a passband, and  FIG. 1   b  shows a bandpass filter pattern having an attenuation pole on the low side of the passband.  
      The bandpass filter  100  shown in  FIG. 1  includes an input port  101 , an output port  102 , an input resonator  111 , an upper resonator  112 , and an output resonator  113 . The bandpass filter  100  includes coupling  121  between the input port  101  and the input resonator  111 , coupling  122  between the input resonator  111  and the upper resonator  112 , coupling  123  between the upper resonator  112  and the output resonator  113 , coupling  124  between the output port  102  and the output resonator  112 , and coupling  131  between the input resonator  111  and the output resonator  112 . However, the band pass filter pattern shown in  FIG. 1   a  has no coupling between the input port  101  and the input resonator  111  and no coupling between the output port  102  and the output resonator  113  because the input port  101  and the output port  102  respectively come into contact with the input resonator  111  and the output resonator  113 .  
      When a signal is input through the input terminal  101 , the input signal is electric-coupled at coupling  121  to the input port  101  and the open-loop input resonator  111 . The electric-coupled signal is electric-coupled at coupling  122  with the open-loop upper resonator  112  to be transmitted to the upper resonator  112 . The transmitted signal is electric-coupled at coupling  123  to the open-loop output resonator  113  to be transferred from the upper resonator  112  to the open-loop output resonator  113 . The signal transferred to the output resonator  113  selects a characteristic band to be output through electric coupling of the output port  102  and the open-loop output resonator  113 .  
      In  FIG. 1   a , main coupling is electric coupling, and the open-loop input resonator  111  and the open-loop output resonator  113  are electric-coupled. Accordingly, an attenuation pole is formed on the high side of the passband, and the attenuation pole characteristic and frequency are controlled by cross coupling.  
      In  FIG. 1   b , main coupling is electric coupling, and the open-loop input resonator  111  and the open-loop output resonator  113  are magnetic-coupled. Thus, an attenuation pole exists on the low side of the passband. The bandpass filter of  FIG. 1  is suitable for a mobile communication system because it has high selectivity channeling and low insertion loss. However, the bandpass filter has only a single attenuation pole and there is a restriction on its design caused by the value of the dielectric constant.  
       FIG. 2  shows a pattern of a bandpass filter including triangular patch resonators.  FIG. 2   a  shows a bandpass filter pattern having an attenuation pole on the high side of a passband, and  FIG. 2   b  shows a bandpass filter pattern having an attenuation pole on the low side of the passband.  
      The bandpass filter including the triangular patch resonators has a small size and forms an attenuation pole on each of the high and low sides of the passband.  
      In  FIG. 2 , the bandpass filter  200  includes an input port  201 , an output port  202 , an input resonator  211 , an upper resonator  212 , and an output resonator  213 . The bandpass filter  200  further includes coupling  221  between the input port  201  and the input resonator  211 , coupling  222  between the input resonator  211  and the upper resonator  212 , coupling  223  between the upper resonator  212  and the output resonator  213 , coupling  224  between the output port  202  and the output resonator  213 , and coupling  231  between the input resonator  211  and the output resonator  213 . However, the bandpass filter pattern shown in  FIG. 2   a  has no coupling between the input port  201  and the input resonator  211  and no coupling between the output port  202  and the output resonator  213  because the input port  201  and the output port  202  respectively come into contact with the input resonator  211  and the output resonator  213 .  
      When a signal is input through the input port  201 , the input signal is electric-coupled at coupling  221  with the input port  201  and the triangular patch input resonator  211 . The electric-coupled signal is transmitted to the triangular patch upper resonator  212  through the electric coupling  222 . This signal is transmitted to the triangular patch output resonator  213  through the electric coupling  223 . The signal transferred to the output resonator  213  selects a characteristic band to be transmitted as an output signal through the electric coupling of the output port  202  and the triangular patch output resonator  213 .  
      In  FIG. 2   a , main coupling is electric coupling, and the triangular patch input resonator  211  and the triangular patch output resonator  213  are electric-coupled. Accordingly, an attenuation pole is formed on the high side of the passband, and the attenuation pole characteristic and frequency are controlled by cross coupling.  
      In  FIG. 2   b , main coupling is electric coupling, and the input resonator  211  and the output resonator  213  are magnetic-coupled. Thus, an attenuation pole is formed on the low side of the passband. The bandpass filter of  FIG. 2  is suitable for a mobile communication system because it has high selectivity channeling and low insertion loss.  
       FIG. 3  shows a pattern of a bandpass filter including multilayer resonators, disclosed in U.S. Pat. No. 6,608,538. The bandpass filter  300  shown in  FIG. 3  includes an input port  301 , an output port  302 , an input resonator L 11 , L 12 , and C 2 , an upper resonator L 21 , L 22 , and C 2 , and an output resonator L 31 , L 32 , and C 3 . Each of the three resonators is composed of an inductive portion and a capacitive portion. The inductive portion of the second resonator is folded such that the inductive portion of the first resonator is coupled to the inductive portion of the third resonator forming a trisection filtering structure. An attenuation pole is formed on the low side of the passband by cross coupling between the first and third resonators.  
      When a signal is input through the input port  301 , the input signal is resonated through the input resonator L 11 , L 12 , and C 1 . The resonated signal is transmitted to the upper resonator L 21 , L 22 , and C 2  through electric coupling and resonated. Then, the resonated signal is transferred to the output resonator L 31 , L 32 , and C 3  through electric coupling and resonated. This resonated signal is output through the output port  302 .  
      The main coupling of the bandpass filter is electric coupling, and the input resonator L 11 , L 12 , and C 2  and the output resonator L 31 , L 32 , and C 3  are magnetic-coupled. Accordingly, the attenuation pole exists on the low side of the passband, and the attenuation pole characteristic and frequency are controlled by cross coupling. The bandpass filter shown in  FIG. 3  is suitable for microwave devices, and its size and weight can be reduced because it uses LC-coupled resonators formed on multiple layers.  
       FIG. 4  shows a pattern of a bandpass filter including LC-coupled resonators. The bandpass filter of  FIG. 4  includes three LC-coupled resonators, a cross coupling gap, a cross coupling line or a mixed structure of the cross coupling gap and cross coupling line.  
      Specifically, the bandpass filter  400  of  FIG. 4  includes an input port  401 , an output port  402 , an input resonator  411 , an upper resonator  412 , and an output resonator  413 . The bandpass filter  400  further includes coupling  422  between the input resonator  411  and the upper resonator  412 . A cross coupling gap  423  exists between the upper resonator  411  and the output resonator  413 , and a cross coupling line  431  exists between the input resonator  411  and the output resonator  413 . In addition, a cross coupling line  432  exists between the input resonator  411  and the output resonator  413 , and a cross coupling gap and a cross coupling line  433  exist between the input resonator  411  and the output resonator  413 .  
      When a microwave signal is input to the LC-coupled input resonator  401  through the input port  201 , the input signal is transmitted to the LC-coupled upper resonator  412  according to electric coupling and is then output to the output port  402  through the LC-coupled output resonator  413 . An attenuation pole is formed on each of high and low sides of a passband according to the cross coupling gap, cross coupling line, or mixture of cross coupling gap and line existing between the input resonator and the output resonator.  
      The main coupling of the bandpass filter of  FIG. 4  is electric coupling, and cross coupling is magnetic coupling or electric coupling. This bandpass filter is suitable for microwave devices and its size and weight can be reduced because it uses the LC-coupled resonators.  
      However, as a millimeter-wave home network system is miniaturized, the size, weight, and cost of a passive element such as the bandpass filter are required to be reduced. In addition, low loss and high attenuation characteristics of the bandpass filter are increasingly needed.  
     SUMMARY OF THE INVENTION  
      It is an advantage of the present invention to provide a microstrip cross-coupled bandpass filter with an asymmetric frequency characteristic, which can be miniaturized and fabricated by an optimized fabrication process at a low manufacturing cost, and provide low loss and high attenuation pole characteristics.  
      It is another advantage of the present invention to provide a bandpass filter that is designed unrestrictedly, has a simplified pattern such that it can be fabricated by an optimized process at a low manufacturing cost, and is suitable for an system on package (SOP) of a millimeter-wave home network system and module.  
      In one aspect of the present invention, a microstrip cross-coupled bandpass filter comprises: an input port through which a signal is input; an output port through which a select signal of a characteristic band is output; and a plurality of resonators including at least a first resonator that is electric-coupled with at least a part of the input port and a second resonator that is electric-coupled with at least a part of the output port. Magnetic coupling is formed according to a cross coupling gap corresponding to the distance between the first and second resonators.  
      The bandpass filter can further comprise a third resonator that is electric-coupled with at least a part of the first resonator and at least a part of the second resonator.  
      The cross coupling gap forming the magnetic coupling generates an attenuation pole on the high side of a passband.  
      The attenuation frequency of the attenuation pole can be varied with a variation in the distance of the cross coupling gap.  
      The plurality of resonators can be λ/2 transmission line resonators.  
      The bandpass filter can further includes a cross coupling line that is coupled to at least a part of the input port and at least a part of the output port in a mixed form of capacitive coupling and transmission line inductive coupling.  
      The cross coupling line can generate an attenuation pole on each of the high and low sides of the passband.  
      The attenuation frequency of the attenuation pole can be varied with the distance between the cross coupling line and the input port and the distance between the cross coupling line and the output port, the length of the cross coupling line, and the width of the cross coupling line.  
      In another aspect of the present invention, a microstrip cross coupling bandpass filter comprises: an input port through which a signal is input; an output port through which a select signal of a characteristic band is output; a plurality of resonators including at least a first resonator that is electric-coupled with at least a part of the input port and a second resonator that is electric-coupled with at least a part of the output port; and a cross coupling line that is coupled to at least a part of the input port and at least a part of the output port in a mixed form of capacitive coupling and transmission line inductive coupling, and that generates an attenuation pole on each of the high and low sides of a passband.  
      The attenuation frequency of the attenuation pole can be varied with the distance between the cross coupling line and the input port and the distance between the cross coupling line and the output port, and the length and width of the cross coupling line.  
      The bandpass filter can further include a third resonator that is electric-coupled with at least a part of the first resonator and at least a part of the second resonator.  
      Magnetic coupling is formed according to a cross coupling gap corresponding to the distance between the first and second resonators to generate an attenuation pole on the high side of the passband. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention, and, together with the description, serve to explain the principles of the invention:  
       FIG. 1  shows patterns of a conventional microstrip cross-coupled bandpass filter that includes open-loop resonators, and has an asymmetric frequency characteristic;  
       FIG. 2  shows patterns of a conventional microstrip cross-coupled bandpass filter that includes triangular patch resonators, and has an asymmetric frequency characteristic;  
       FIG. 3  shows a pattern of a conventional microstrip cross-coupled bandpass filter that includes multi-layer resonators, and has an asymmetric frequency characteristic;  
       FIG. 4  shows a pattern of a conventional microstrip cross-coupled bandpass filter that includes LC resonators, and has an asymmetric frequency characteristic;  
       FIG. 5  shows a pattern of a microstrip cross-coupled bandpass filter that includes λ/2 transmission line resonators, and has an asymmetric frequency characteristic according to a first embodiment of the present invention;  
       FIG. 6  shows a pattern of a microstrip cross-coupled bandpass filter that includes λ/2 transmission line resonators, and has an asymmetric frequency characteristic according to a second embodiment of the present invention;  
       FIG. 7   a  is a Pi-type equivalent circuit diagram of a cross coupling gap;  
       FIG. 7   b  is a circuit diagram of an ideal J-inverter;  
       FIG. 7   c  is an equivalent circuit diagram of an ideal J-converter and transmission line;  
       FIG. 8   a  shows a converted circuit of the equivalent circuit of the cross coupling gap of  FIG. 7   c;    
       FIG. 8   b  is an equivalent circuit diagram of a cross coupling line;  
       FIG. 8   c  shows a converted circuit of the equivalent circuit of the cross coupling of  FIG. 8   b;    
       FIG. 8   d  is an equivalent circuit diagram of a microstrip cross coupling gap and line;  
       FIG. 9   a  is an equivalent circuit diagram of the bandpass filter according to the first embodiment of the present invention;  
       FIG. 9   b  is an equivalent circuit diagram of the bandpass filter according to the second embodiment of the present invention; and  
       FIGS. 10   a  through  10   e  are graphs showing response characteristics of the bandpass filters according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
      In the following detailed description, only the preferred embodiment of the invention has been shown and described, simply by way of illustration of the best mode contemplated by the inventor(s) of carrying out the invention. As will be realized, the invention is capable of modification in various obvious respects, all without departing from the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not restrictive. To clarify the present invention, parts which are not described in the specification are omitted, and parts for which similar descriptions are provided have the same reference numerals.  
       FIG. 5  shows a pattern of a microstrip cross-coupled bandpass filter that includes λ/2 transmission line resonators and has an asymmetric frequency characteristic according to a first embodiment of the present invention. The bandpass filter  500  according to the first embodiment of the present invention includes a cross coupling gap  531 .  
      Specifically, the bandpass filter  500  is a parallel coupled filter and includes a λ/2 transmission line input resonator  511 , a λ/2 transmission line upper resonator  512 , a λ/2 transmission line output resonator  513 , an input port  501 , and an output port  502 . In addition, the bandpass filter  500  further includes electric coupling  522  between the λ/2 transmission line input resonator  511  and the λ/2 transmission line upper resonator  512 , electric coupling  523  between the λ/2 transmission line upper resonator  512  and the λ/2 transmission line output resonator  513 , electric coupling  521  between the input port  501  and the λ/2 transmission line input resonator  511 , and electric coupling  524  between the λ/2 transmission line output resonator  513  and the output port  502 , and the cross coupling gap  531  has an attenuation pole characteristic.  
      When a microwave/millimeter-wave signal is input through the input port  501 , the input signal is electric-coupled with the input port  501 . Here, impedance is easily controlled irrespective of the degree of the dielectric constant because image impedance is used as the impedance.  
      The input electric coupling  521  is formed so that the microwave/millimeter-wave signal is transmitted to the λ/2 transmission line input resonator  511 . Then, the microwave/millimeter-wave signal is transferred to the λ/2 transmission line upper resonator  512  by the electric coupling  522  between the λ/2 transmission line input resonator  511  and the λ/2 transmission line upper resonator  512 .  
      Subsequently, the microwave/millimeter-wave signal is transferred to the λ/2 transmission line output resonator  513  through the electric coupling  523  between the λ/2 transmission line upper resonator  512  and the λ/2 transmission line output resonator  513 . The microwave/millimeter-wave signal is filtered by the output electric coupling  524 , and the filtered signal is output.  
      In the bandpass filter according to the first embodiment of the present invention, the ports and the resonators are mainly electric-coupled, and the λ/2 transmission line input resonator  511  and the λ/2 transmission line output resonator  513  are magnetic-coupled. Accordingly, an attenuation pole is formed on the high side of a passband, and an attenuation pole characteristic and frequency are controlled by the cross coupling gap  531 .  
       FIG. 6  shows a pattern of a microstrip cross-coupled bandpass filter that includes λ/2 transmission line resonators and has asymmetric frequency characteristic according to a second embodiment of the present invention.  
      The bandpass filter  600  according to the second embodiment of the present invention is distinguished from the bandpass filter according to the first embodiment of the present invention in that the bandpass filter  600  has a cross coupling line  641  and coupling  642  of input/output ports and the cross coupling line  641 . That is, the bandpass filter  600  includes the cross coupling gap and cross coupling line.  
      Specifically, the bandpass filter  600  includes λ/2 transmission line resonators that are parallel coupled filters  611 ,  612 , and  613 , an input port  601 , an output port  602 , electric coupling  621  between the input port  601  and the λ/2 transmission line input resonator  611 , electric coupling  622  between the λ/2 transmission line input resonator  611  and the λ/2 transmission line upper resonator  612 , electric coupling between the λ/2 transmission line upper resonator  612  and the λ/2 transmission line output resonator  613 , electric coupling  624  between the λ/2 transmission line output resonator  613  and the output port  602 , and a cross coupling gap  631  with an attenuation pole, and the cross coupling line  641  has another attenuation pole.  
      When a microwave/millimeter-wave signal is input through the input port  601 , the input signal is electric-coupled with the input port  601 . Here, impedance is easily controlled irrespective of the degree of dielectric constant because image impedance is used as the impedance.  
      The input electric coupling  621  is formed so that the microwave/millimeter-wave signal is transmitted to the λ/2 transmission line input resonator  611 . Then, the microwave/millimeter-wave signal is transferred to the λ/2 transmission line upper resonator  612  by the electric coupling  622  between the λ/2 transmission line input resonator  611  and the λ/2 transmission line upper resonator  612 .  
      Subsequently, the microwave/millimeter-wave signal is transferred to the λ/2 transmission line output resonator  613  through the electric coupling  623  between the λ/2 transmission line upper resonator  612  and the λ/2 transmission line output resonator  613 . The transferred microwave/millimeter-wave signal is filtered by the output electric coupling  624  and the filtered signal is output.  
      In the bandpass filter  600  according to the second embodiment of the present invention, the ports and the resonators are mainly electric-coupled and the λ/2 transmission line input resonator  611  and the λ/2 transmission line output resonator  613  are magnetic-coupled. In addition, the input port  601  and the cross coupling line  641  are cross-coupled and the output port  602  and the cross coupling line  641  are also cross-coupled. The cross coupling  642  between the input port  601  and the cross coupling line  641  and between the output port  602  and the cross coupling line  641  has a mixed form of serial Pi-type capacitive coupling and transmission line inductive coupling.  
      Accordingly, an attenuation pole according to the cross coupling gap is formed on the high side of the passband, and an attenuation pole according to the cross coupling line is formed on each of the high and low sides of the passband. Therefore, an attenuation pole characteristic and frequency can be controlled by the cross coupling gap and cross coupling line.  
      Equivalent circuits of the bandpass filters according to the first and second embodiments of the present invention will now be explained with reference to  FIGS. 7, 8 , and  9 .  
       FIG. 7   a  is a Pi-type equivalent circuit diagram of the microstrip cross coupling gap  531  or  631  having an asymmetrical frequency characteristic,  FIG. 7   b  is an equivalent circuit diagram of an ideal J-inverter changed from the cross coupling gaps  531  or  631  of  FIG. 7   a , and  FIG. 7   c  is an equivalent circuit diagram of an ideal J-converter and transmission line changed from the J-converter of  FIG. 7   b.    
      In  FIGS. 7   a ,  7   b , and  7   c , reference numeral  701  denotes the capacitance Cg of the cross coupling gap  531  or  631 ,  702  represents the capacitance Cp between the transmission line and ground,  703  denotes the sum of Cg+Cp,  704  indicates the J-inverter J=ωCg, and  705  represents the transmission line. Here, the J-inverter and susceptance are obtained by the following equations.  
             J   =       Y   0     ⁢   tan   ⁢          ϕ   2                    [     Equation   ⁢           ⁢   1     ]               ϕ   =       -     tan     -   1         ⁢       2   ⁢   B       Y   0                 [     Equation   ⁢           ⁢   2     ]                      B     Y   0            =       J     Y   0         1   -       (     J     Y   0       )     2                 [     Equation   ⁢           ⁢   3     ]             
  B=ωC   g   [Equation 4] 
       FIGS. 8   a ,  8   b ,  8   c , and  8   d  are equivalent circuit diagrams of the microstrip cross coupling having an asymmetric frequency characteristic according to the present invention.  FIG. 8   a  shows a converted circuit of the equivalent circuit of the cross coupling gap of  FIG. 7   c , and  FIG. 8   b  is an equivalent circuit diagram of the microstrip cross coupling line  641  (shown in  FIG. 6 ).  FIG. 8   c  is an equivalent circuit diagram of the input coupling  521  or  621  and the output coupling  524  or  624 , and  FIG. 8   d  is an equivalent circuit diagram of the microstrip cross coupling.  
       FIG. 8   a  is obtained by Equations 1, 2, 3, and 4. Each of  FIGS. 8   a ,  8   b , and  8   c  can be converted to  FIG. 8   d . The J-inverter and susceptance are obtained by Equations 5 and 6 when  FIG. 8   a  is converted to  FIG. 8   d , by Equations 7, 8, and 9 when  FIG. 8   b  is converted to  FIG. 8   d , and by Equations 10, 11, and 12 when  FIG. 8   c  is converted to  FIG. 8   d .  
               J   eff     =     1     (           -   J     ⁢           ⁢     sin   2     ⁢     θ   2         Y   0   2       +         cos   2     ⁢     θ   2       J       )               [     Equation   ⁢           ⁢   5     ]                 B   ⁡     (   ω   )       =       sin   ⁢     θ   2     ⁢   cos   ⁢           ⁢     θ   2     ⁢     (       J     Y   0       +       Y   0     J       )         (           -   J     ⁢           ⁢     sin   2     ⁢     θ   2         Y   0   2       +         cos   2     ⁢     θ   2       J       )               [     Equation   ⁢           ⁢   6     ]                       ⁢     =       J   eff     ⁡     (     sin   ⁢           ⁢     θ   2     ⁢   cos   ⁢           ⁢     θ   2     ⁢     (       J     Y   0       +       Y   0     J       )       )                                   J   eff     =         J   a     ⁢     J   b           Y   0     ⁢   sin   ⁢           ⁢   θ               [     Equation   ⁢           ⁢   7     ]                   B   1     ⁡     (   ω   )       =         -       J   eff     ⁡     (       J   a       J   b       )         ⁢   cos   ⁢           ⁢   θ     =       -       J   a   2       Y   0         ⁢   cos   ⁢           ⁢   θ               [     Equation   ⁢           ⁢   8     ]                   B   2     ⁡     (   ω   )       =         -       J   eff     ⁡     (       J   n       J   a       )         ⁢   cos   ⁢           ⁢   θ     =       -       J   b   2       Y   0         ⁢   cos   ⁢           ⁢   θ               [     Equation   ⁢           ⁢   9     ]                 J   eff     =     J     cos   ⁢           ⁢   θ               [     Equation   ⁢           ⁢   10     ]                   B   1     ⁡     (   ω   )       =       -       J   2       Y   0         ⁢   tan   ⁢           ⁢   θ             [     Equation   ⁢           ⁢   11     ]             
  B   2  (ω)=− Y   o  tan θ  [Equation 12] 
       FIG. 9   a  is an equivalent circuit diagram of the bandpass filter  500  having the microstrip cross coupling gap, shown in  FIG. 5 , and  FIG. 9   b  is an equivalent circuit diagram of the bandpass filter  600  having the microstrip cross coupling gap and microstrip cross coupling line, shown in  FIG. 6 .  
      In  FIGS. 9   a  and  9   b , reference numerals  901  through  906  denote inverters,  911  and  912  represent susceptance,  913  and  914  denote cross coupling gap susceptance, and  915  and  916  represent cross coupling line susceptance. In  FIGS. 9   a  and  9   b , the input admittance is represented by the following equation.  
                 Y   ln     =         Y   1     ⁢         Y   0     +       jY   1     ⁢   tan   ⁢           ⁢   β   ⁢           ⁢   l           Y   1     +       JY   0     ⁢   tan   ⁢           ⁢   β   ⁢           ⁢   l           =         Y   1     ⁢         Y   1     -       jY   0     ⁢   cot   ⁢           ⁢   β   ⁢           ⁢   l           Y   0     -       jY   1     ⁢   cot   ⁢           ⁢   β   ⁢           ⁢   l           ⁢     
     ⁢           =         Y   1     ⁢         Y   1     -       jY   0     ⁢     cot   ⁡     (       π   2     ⁢     ω     ω   0         )               Y   0     -       jY   1     ⁢     cot   ⁡     (       π   2     ⁢     ω     ω   0         )               ⁢     
     ⁢           =         Y   1     ⁢         Y   1     +       jY   0     ⁢     tan   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )               Y   0     +       jY   1     ⁢     tan   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )               ⁢     
     ⁢           =         Y   1     ⁢         Y   1     +       jY   0     ⁢     tan   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )               Y   0     +       jY   1     ⁢     tan   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )               ⁢     
     ⁢           =           Y   1     ⁢           Y   1       Y   0       +     j   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )           1   +     j   ⁢       Y   1       Y   0       ⁢     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )             ⁢     |     ω   =     ω   0           ⁢     
     ⁢           =         Y   1   2       Y   0       +       jY   1     ⁢     X   ⁡     (     1   -     A   2       )                         ⁢     
     ⁢     In  Equation  13,     ⁢     
     ⁢         1     j   ⁢           ⁢   tan   ⁢           ⁢   β   ⁢           ⁢   l       =     j   ⁢           ⁢   cot   ⁢           ⁢   β   ⁢           ⁢   l       ,       β   ⁢           ⁢   l     =           2   ⁢           ⁢   π       λ   0       ⁢   θ     =     π   2         ,     
     ⁢       X   ⁡     (   ω   )       =       π   2     ⁢     (       ω   -     ω   0         ω   0       )         ,   and     ⁢     
     ⁢       cot   ⁡     (       π   2     ⁢     ω     ω   0         )       =       -     tan   ⁡     (         π   2     ⁢     ω     ω   0         -     π   2       )         ⁢     
     ⁢           =     -       tan   ⁡     (       π   2     ⁢     (       ω   -     ω   0         ω   0       )       )       .                   [     Equation   ⁢           ⁢   13     ]             
 
      In the meantime, the admittance Ya at the J 01  inverter  901  is obtained by the following equation.  
               Y   A     =         J   01   2       Y   in       =         J   01   2           Y   1   2       Y   0       +       jY   1     ⁢     X   ⁡     (     1   -     A   2       )             ⁢     
     ⁢           =         J   01   2           Y   1     ⁢   A     +       jY   1     ⁢     X   ⁡     (     1   -     A   2       )             ⁢     
     ⁢           =           J   01   2         Y   1     ⁢   A       ⁡     [     1   +     jX   ⁡     (     A   -     1   A       )         ]       ⁢     
     ⁢           =         J   01   2         Y   1     ⁢   A       +       jB   A     ⁡     (   ω   )                         [     Equation   ⁢           ⁢   14     ]             
 
      In Equation 14, a λ/2 transmission line resonator jB A (ω) can be represented by the following equation.  
                 B   A     ⁡     (   ω   )       =           J   01   2         Y   1     ⁢   A       ⁢     X   ⁡     (   ω   )       ⁢     (     A   -     1   A       )       =         J   01   2       Y   1       ⁢     X   ⁡     (   ω   )       ⁢     (     1   -     1     A   2         )                 [     Equation   ⁢           ⁢   15     ]             
 
      In  FIG. 9   a , the susceptance of the first λ/2 transmission line resonator  511  can be obtained by the following equation. 
 
 B   1 (ω)= B   A (ω)+ B (ω)+ω 0   C   g   [Equation 16]
 
      In  FIG. 9   b , the susceptance of the first λ/2 transmission line resonator  611  can be obtained by the following equation. 
 
 B   1 (ω)= B   A (ω)+ B (ω)+ω C   g   +B   A (ω)  [Equation 17]
 
      The input electric coupling  521  and  621  is formed through the aforementioned equations such that the microwave/millimeter-wave signal is transmitted to the λ/2 transmission line resonators  511  and  611 .  
      The microwave/millimeter-wave signal is transmitted to the λ/2 transmission line upper resonator  512  or  612  through the electric coupling  522   622  between the λ/2 transmission line input resonator and the λ/2 transmission line upper resonator.  
      The λ/2 transmission line upper resonators  512  and  612  are formed by the following equation when the length of the transmission line is 20=π/2.  
               Z   in     =         Z   1     ⁢         Z   1     +       jZ   1     ⁢   tan   ⁢           ⁢   β   ⁢           ⁢   l           Z   1     +       jZ   L     ⁢   tan   ⁢           ⁢   β   ⁢           ⁢   l           ⁢     
     ⁢           =           Z   1     ⁢         Z   L     +       jZ   1     ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )               Z   1     +       jZ   L     ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )               ⁢     |     ω   =     ω   0           ⁢     
     ⁢           =           Z   1     ⁢       1   +     j   ⁢           ⁢       Z   1       Z   L       ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )                 Z   1       Z   L       +     j   ⁢           ⁢   π   ⁢           ⁢     (       ω   -     ω   0         ω   0       )             ⁢     |     ω   =     ω   0           ⁢     
     ⁢           =           Z   1       j   ⁢           ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )           ⁢     |     ω   -     ω   0           ⁢     
     ⁢           =       1       jY   1     ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )           ⁢     |             ω   =     ω   0       ,     Z   L       〉     〉     ⁢   Z                         [     Equation   ⁢           ⁢   18     ]             
 
      The susceptance of the λ/2 transmission line resonators  512  and  612  can be obtained by the following equation.  
               B   ⁡     (   ω   )       =         Y   1     ⁢     π   ⁡     (       ω   -     ω   0         ω   0       )         =       Y   1     ⁢   2   ⁢     X   ⁡     (   ω   )                   [     Equation   ⁢           ⁢   19     ]             
 
      The microwave/millimeter-wave signal is transmitted to the λ/2 transmission line output resonator  513  through the electric coupling  523  between the λ/2 transmission line upper resonator  512  and the λ/2 transmission line output resonator  513 . The transmitted microwave/millimeter-wave signal is filtered by the output electric coupling  524  and output.  
      The mixed coupling  632  between the input port  601  and the cross coupling line  641  and between the output port  602  and the cross coupling line  641  can be obtained by Equations 5 and 6. Equations 5 and 6 can be attained from Equations 7, 8, and 9.  
      The response characteristic of the bandpass filter according to the present invention will now be explained with reference to  FIGS. 10   a  through  10   e .  FIG. 10   a  shows the response characteristic of the bandpass filter  500  shown in  FIG. 5  with respect to a variation in the microstrip cross coupling gap. That is,  FIG. 10   a  is a graph showing the response characteristic of the bandpass filter having the cross coupling gap with a size of 0.1 through 0.2 mm.  
      Referring to  FIG. 10   a , there is no variation in a passband  1001  even when the distance of the gap is varied, and the attenuation frequency of an attenuation pole  1003  according to the cross coupling gap is increased as the distance of the gap is increased. Accordingly, the attenuation frequency can be controlled by the distance of the gap.  
       FIG. 10   b  shows the relationship between the bandwidth of the bandpass filter  500  having the microstrip cross coupling gap and the attenuation pole and attenuation frequency.  FIG. 10   c  is a graph of the response characteristic of the bandpass filter  600  having the microstrip cross coupling gap and microstrip cross coupling line, which shows the relationship between the distance of the cross coupling gap and attenuation poles. Specifically,  FIG. 10   c  shows the response characteristics when the distance of the cross coupling gap is 0.095 mm, 1.27 mm, and 1.59 mm. From  FIG. 10   c , it can be known that the attenuation pole  1003  is formed according to the cross coupling gap, and the upper and lower attenuation poles  1004  are formed according to the cross coupling line. Furthermore, as the distance of the cross coupling gap is increased, the attenuation frequency of the upper attenuation pole (right attenuation pole)  1004  is increased while the attenuation frequency of the lower attenuation pole (left attenuation pole)  1004  is decreased. Here, the attenuation pole  1003  according to the cross coupling gap is barely changed.  
       FIG. 10   d  is a graph of the response characteristic of the bandpass filter  600  having the microstrip cross coupling gap and microstrip cross coupling line, which shows the relationship between the width of the cross coupling line and attenuation poles. Specifically,  FIG. 10   d  shows the response characteristics when the width of the cross coupling line is 0.059 mm, 1.29 mm, and 1.89 mm.  
      Referring to  FIG. 10   d , there is a small variation in the attenuation pole  1003  according to the cross coupling gap. Furthermore, the attenuation frequency of the lower attenuation pole  1002  is decreased as the width of the cross coupling line is increased. The attenuation frequency of the upper attenuation pole  1004  barely depends on a variation in the width of the cross coupling line. Accordingly, the lower attenuation pole can be changed by varying the width of the cross coupling line.  
       FIG. 10   e  is a graph of the response characteristic of the bandpass filter  600  having the microstrip cross coupling gap and cross coupling line, which shows the relationship between the length of the cross coupling line and attenuation poles. Specifically,  FIG. 10   e  shows the response characteristics when the length of the cross coupling line is 0.217 mm, 0.207 mm and 0.107 mm.  
      Referring to  FIG. 10   e , the attenuation frequency of the upper attenuation pole is decreased as the length of the cross coupling line is increased. The attenuation frequency of the lower attenuation pole hardly depends on a variation in the length of the cross coupling line. Accordingly, the upper attenuation pole can be varied by changing the line of the cross coupling line.  
      As described above, the present invention can change the cross coupling gap and cross coupling line to vary the attenuation frequencies of the attenuation poles without changing the passband.  
      While this invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.  
      The bandpass filters according to the present invention use resonators including a cross coupling gap or a cross coupling line. Thus, the size and weight of the microstrip cross coupling bandpass filter having an asymmetric frequency characteristic can be reduced. Furthermore, the pattern of the bandpass filter according to the present invention can be simplified so that the filter can be designed unrestrictedly. In addition, the filter fabrication process can be optimized to reduce the manufacturing cost.  
      Moreover, the present invention can change the attenuation frequency of an attenuation pole without changing a passband by varying the cross coupling gap and cross coupling line of the resonators. This provides low loss and a high attenuation pole.  
      Therefore, the bandpass filters according to the present invention are suitable for an SOP of a millimeter-wave home network system and module. Furthermore, the bandpass filters of the present invention can be easily used as RF filters for microwave mobile communication, personal communication, CT and satellite communication systems, and an image removal filter.