Abstract:
A waveguide bandpass filter for use in microwave and millimeter-wave satellite communications equipment is presented. The filter is based on a substrate integrated waveguide (SIW) having several cascaded oversized SIW cavities. The filter is implemented in a printed circuit board (PCB) or a ceramic substrate using arrays of standard metalized via holes to define the perimeters of the SIW cavities. Transmission lines of a microstrip line, a stripline or coplanar waveguide are used as input and output feeds. The transmission lines have coupling slots for improved stopband performance. The filter can be easily integrated with planar circuits for microwave and millimeter wave applications.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Provisional Patent Application No. 61/039,942, filed Mar. 27, 2008, and Canadian Patent Application No. 2,629,035, filed Apr. 11, 2008, which are incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    This invention relates to waveguide filters. More particularly, this invention relates to substrate integrated waveguide bandpass filters. 
       BACKGROUND OF THE INVENTION 
       [0003]    An electrical bandpass filter is a fundamental element used for selecting an electrical signal in a frequency passband while suppressing electrical signals in a frequency stopband of the filter. Microwave and millimeter-wave bandpass filters are often used in modern radio-frequency transceivers. Filters having low in-band insertion loss, high spectral selectivity, and a wide stopband are commonly required. As an example, in a typical ground terminal for communication with satellites in the K a  frequency band, a filter is required to suppress signals at transmission frequencies in a 29.5 GHz-30 GHz frequency range while conveying the signals at reception frequencies in a 19.2 GHz-21.2 GHz frequency range. An insertion loss of less than 1 dB and a stopband suppression level of at least 45 dB are desired to select the signal while avoiding self-jamming effects during simultaneous reception and transmission of electromagnetic signals by the ground terminal. 
         [0004]    Microwave bandpass filters can be implemented as bulk waveguide structures. These are relatively heavy, bulky, and expensive; due to their size and weight, integration of bulk waveguide filters with planar components and electronic circuits can be a challenging task. 
         [0005]    Substrate integrated waveguides (SIWs) are waveguide structures formed in a substrate of an electronic circuit. SIWs allow easy integration of planar circuits on a single substrate using a standard printed circuit board (PCB) or low-temperature co-fired ceramic (LTCC) process, or any other process of planar circuit fabrication. By using SIWs in an electronic circuit, the interconnection loss between components can be reduced. The size and the weight of the entire circuit can also be reduced. 
         [0006]    SIW filters are known in the art. They offer a low-cost, low mass and compact size alternative to conventional waveguide filters, while maintaining high performance. Although various techniques have been implemented to improve the stopband performance of conventional rectangular waveguide filters, these techniques often utilize E-plane discontinuities that are difficult to realize for SIW filters implemented on a single-layer substrate. The SIW filters of the prior art have often been limited to resonant structures based on physical coupling elements to achieve a pre-selected spectral shape of the filter response function and/or high levels of stopband suppression. For example, a SIW filter designed to block an electromagnetic signal at a frequency f 0  has a slit in the top or bottom conducting layer to provide an attenuation pole at the frequency f 0 . 
         [0007]    Transmission zeros (TZs) in the insertion loss response of a microwave filter can be used to improve the spectral selectivity and the stopband attenuation of the filter. To generate the TZs, an “extracted pole” technique can be implemented to construct so called “bandstop” resonators. Alternatively, electrical couplings can be introduced between non-adjacent resonators, wherein the TZs are generated due to a phenomenon of multipath interference of electromagnetic waves propagating inside the resonators. However, such filters are usually constructed using conventional waveguide technology, which tends to use bulky and complex filter structures. Furthermore, the TZs implemented using these prior-art methods cannot be far away from the desired passband due to the limitation of the physical structure of a prior-art waveguide filter. 
         [0008]    The present invention overcomes the above stated problems of the prior art. It provides a low-cost, high-performance SIW filter that is easy to integrate with planar circuits. Advantageously, the spectral shape of the SIW filter of the present invention can be adapted to provide a high level of attenuation away from a desired passband. Furthermore, SIW filters can offer a significant improvement in passive intermodulation performance over conventional filters. 
       SUMMARY OF THE INVENTION 
       [0009]    According to the present invention, a substrate integrated waveguide (SIW) filter includes a chain of sequentially coupled conterminous multimode SIW cavities, of which the first and the last multimode SIW cavities can be directly excited by a transmission line. The entire filter is implemented using arrays of metalized via holes on a dielectric substrate. The via holes are produced by using a standard printed circuit board (PCB) or other planar circuit manufacturing process. The diameter of the via holes and the pitch between neighboring via holes are selected so as to suppress radiation losses in the SIW cavities. A desired passband is generated by the fundamental mode of propagation in the SIW cavities. The finite transmission zeros (TZs) are generated by destructive interference between the fundamental and a higher-order electromagnetic mode of the SIW cavities. The size and the shape of the SIW cavities are selected so that the TZs are far away from the passband, for high out-of-band rejection. The position of every finite TZ is independently controllable. The freedom of positioning the TZs is achieved by changing the inter-cavity coupling ratios and the size of corresponding multimode SIW cavities. According to the present invention, no other mode discriminating physical structures within the SIW cavities, such as openings in a conductive layer of the PCB, are required to control the position of the TZs. 
         [0010]    In accordance with the invention there is provided a filter having a passband and a stopband, for conveying passband frequency components of an electromagnetic signal, while suppressing stopband frequency components of the electromagnetic signal, the filter comprising:
       an SIW formed in a planar dielectric layer sandwiched between first and second opposing planar conductive layers, the SIW having a chain of sequentially coupled conterminous multimode SIW cavities defined on their perimeters by an array of conductive vias connecting the first and the second conductive layers through the dielectric layer, the chain having first and second ends;   an input transmission line coupled to the first end of the chain, for coupling the electromagnetic signal to the first end of the chain; and   an output transmission line coupled to the second end of the chain, for outputting the passband frequency components of the electromagnetic signal from the second end of the chain;   wherein a distance between neighboring vias of the array of conductive vias is small enough to suppress radiation losses of the SIW, for example less than half of a shortest wavelength of the electromagnetic signal in the SIW cavities.       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    Exemplary embodiments will now be described in conjunction with the drawings in which: 
           [0016]      FIG. 1  is a three-dimensional view of a single-cavity substrate integrated waveguide (SIW) filter having opposing input and output microstrip transmission lines; 
           [0017]      FIG. 2  is a three-dimensional view of a single-cavity SIW filter having input and output microstrip transmission lines disposed at 90° with respect to each other; 
           [0018]      FIG. 3  is an equivalent circuit model for the mode coupling in the SIW cavities of  FIGS. 1 and 2 ; 
           [0019]      FIGS. 4A and 4B  are magnetic field distributions of the fundamental mode and a higher-order mode, respectively, of the SIW filter of  FIG. 1 ; 
           [0020]      FIG. 5  is an insertion loss spectral plot for the SIW filter of  FIG. 1 , superimposed with electric field distribution patterns in the SIW cavity corresponding to a first transmission maximum, a first transmission zero (TZ), and a second transmission maximum; 
           [0021]      FIGS. 6 ,  7 , and  8  are three-dimensional views of SIW filters of the present invention, having four sequentially coupled conterminous multimode SIW cavities; 
           [0022]      FIGS. 9A and 9B  are electric field distribution patterns in a four-cavity SIW filter at a fundamental passband and a spurious passband frequency of a signal, respectively; 
           [0023]      FIGS. 10 to 12  are spectral plots of transmission and reflection of the SIW filters of  FIGS. 6 to 8 , respectively; 
           [0024]      FIGS. 13 to 15  are plan views of SIW filters of  FIGS. 6 to 8 , respectively, showing dimension notations of the filters; 
           [0025]      FIG. 16  is a comparative spectral plot of simulated and measured insertion loss of a SIW filter of  FIG. 7 ; and 
           [0026]      FIG. 17  is a comparative spectral plot of simulated and measured insertion loss of a SIW filter of  FIG. 8 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0027]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. In  FIGS. 6 ,  7 ,  8 ,  9 A, and  9 B, like numerals refer to like elements. 
         [0028]    A waveguide filter of the present invention uses at least two electromagnetic modes, propagating or evanescent. A passband of the filter is defined by a frequency range at which only the fundamental mode appears at an output port of the filter. A stopband of the filter is defined by all frequencies outside of the passband. Within the stopband, higher-order modes may create spurious passbands. By carefully selecting the dimensions of the substrate integrated waveguide (SIW) cavity, one transmission zero (TZ) or multiple TZs can be generated at specific locations in the stopband to suppress these spurious passbands. 
         [0029]    In general, the insertion loss of a filter is proportional to the number of resonators n, inversely proportional to the unloaded quality factor Qu of the resonator, and also the relative bandwidth FBW of the filter. For a small-ripple, less than 0.1 dB, Chebyshev filter, the increase in insertion loss ΔS 21  at a center frequency ω 0  is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         
                           S 
                           21 
                         
                          
                         
                           ( 
                           dB 
                           ) 
                         
                       
                     
                      
                     
                       | 
                       
                         ω 
                         - 
                         
                           ω 
                           0 
                         
                       
                     
                   
                   = 
                   
                     
                       4.343 
                       
                         F 
                          
                         
                             
                         
                          
                         B 
                          
                         
                             
                         
                          
                         W 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         n 
                       
                        
                       
                         
                           g 
                           i 
                         
                         
                           Qu 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0030]    wherein g i  is a generalized low-pass prototype element (inductor or capacitor) value for an i th  resonator. 
         [0031]    The Qu of an SIW cavity is determined by three Q-factors, namely, the Q-factor related to lossy conducting walls Qc, the Q-factor related to dielectric loss D: Qd=1/tan(D), and the Q-factor related to energy leakage via gaps in the SIW cavity Qr. The unloaded quality factor is then expressed as 
         [0000]      1 /Qu =1 /Qc +1 /Qd +1 /Qr    (2) 
         [0032]    As is known in the art, by properly selecting the SIW substrate materials and the shape of the filter, the radiation loss represented by 1/Qr can be made much smaller than the dielectric and conductive losses represented respectively by 1/Qd or 1/Qc. At K a -band, the SIW cavity based on a conventional microwave dielectric substrate with a height of 20 mil and a dielectric loss tangent tan(D) of 0.0012 has a Qu of about 350, which is a typical quality factor of finline waveguide resonators. Therefore, a small number of SIW cavities, preferably four cavities, are used in a filter of the present invention to minimize insertion loss. The spectral selectivity of a filter of the present invention is improved by selecting SIW cavities of certain size and shape as will now be described. 
         [0033]    Referring to  FIG. 1 , a single-cavity SIW filter  10  is presented having a dielectric layer  11  sandwiched between a top planar conductive layer  12  and a bottom planar conductive layer  13 . A SIW cavity  19  of the filter  10  is defined on the perimeter of the cavity  19  by an array of conductive vias  14  connecting the top and the bottom conductive layers  12  and  13  through the dielectric layer  11 . The SIW cavity  19  is directly excited by one of symmetrical 50Ω microstrip lines  15  or  16 . Due to the symmetry of the SIW cavity  19 , it supports only TE n0m  modes of propagation, wherein m is a positive number and n is an odd positive number. Preferably, the SIW cavity  19  is shaped and sized so as to support only two modes of propagation of the intended signal, the TE 101  mode and the TE 301  mode. The SIW filter  10  can be manufactured at a low cost using a standard printed circuit board (PCB) manufacturing process, or a low-temperature co-fired ceramic (LTCC) manufacturing process. 
         [0034]    Throughout the specification, multimode SIW cavities are called, interchangeably, “oversized” cavities. This means that the size of the cavities can support more than one mode of propagation of an incoming signal. The SIW cavity  19  is termed herein as “oversized TE 101 /TE 301  SIW cavity”. 
         [0035]    The distance b between neighboring vias  14  is small enough to suppress radiation losses of the SIW cavity  19 . As a rule, the distance b should be less than one half of the shortest wavelength of the electromagnetic signal in the SIW cavity  19 . The distance b for the cavity  19  of  FIG. 1  is 1 mm, and the diameter d of the vias  14  is 0.5 mm. The overall size of the SIW cavity  19  is approximately 4.5 mm×10.5 mm for the given passband frequency range and the selected dielectric layer material Rogers RT/Duroid™ 6002. A central frequency f 0  of the passband is related to effective width a eff  and length l eff  of the SIW cavity  19  as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     0 
                   
                   = 
                   
                     
                       
                         c 
                         0 
                       
                       
                         2 
                          
                         
                           
                             ɛ 
                             r 
                           
                         
                       
                     
                      
                     
                       
                         
                           
                             ( 
                             
                               1 
                               
                                 a 
                                 eff 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               1 
                               
                                 l 
                                 eff 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0036]    where c 0  is the speed of light in air, a eff =a−d 2 /0.95b, l eff =l−d 2 /0.95b, and where a and l are the geometrical width and length of the SIW cavity  19 , respectively. 
         [0037]    Referring to  FIG. 2 , a single-cavity SIW filter  20  has the same elements as the filter  10  of  FIG. 1 , but the microstrip line  16  is at 90° w.r.t. the microstrip line  15 . An oversized cavity  29  of the filter  20  supports two modes of propagation of an electromagnetic signal, the TE 101  mode and the TE 201  mode. The SIW cavity  29  is termed herein as “oversized TE 101 /TE 201  SIW cavity”. The coupling between the input and the output microstrip lines  15  or  16  and the higher-order TE 201  mode can reverse when the relative position of the lines  15  and  16  changes from the same half of the SIW cavity  29  to the opposite half of the cavity  29 . This coupling, which reaches a maximum when the input and the output are at an angle of 90°, can be adjusted by changing the relative position of the input and the output microstrip lines  15  and  16  and the size of the SIW cavity  29 . Therefore, a finite TZ can be on the lower-frequency side or the higher-frequency side of the resonance of the higher-order TE 201  mode, and can be positioned slightly closer to the resonance of the fundamental TE 101  mode, to further improve the stopband performance of the filter  20 . 
         [0038]    Turning now to  FIG. 3 , an equivalent circuit model  30  for the mode coupling in the SIW cavities  19  and  29  of  FIGS. 1 and 2  is illustrated. The model  30  shows, in a symbolic form, signal paths between a source port S and a load port L. The fundamental resonant mode TE 101  generates a transmission pole in the desired passband. A second-order resonant mode TE 301  provides a different path for the signal flow between the two ports S and L corresponding to microstrip lines  15  and  16  of the SIW filter  10  from a path corresponding to the fundamental resonant mode TE 101 . Similarly, a second-order resonant mode TE 201  provides a different path for the signal flow between the two ports S and L corresponding to microstrip lines  15  and  16  of the SIW filter  20  as compared to a path provided by the fundamental resonant mode TE 101 . Because all the couplings J 1 ′, J 2 ′, J 3 ′, and J 4 ′ in an oversized SIW cavity of the present invention have the same sign, and J 1 ′ and J 2 ′ are much larger than J 3 ′ and J 4 ′ close to the resonant frequency of the second-order mode TE 201 , or TE 301 , a TZ between the resonant frequency of the TE 101  mode and the resonant frequency of the TE 201  or TE 301  mode is generated. The location of the TZ can be approximately determined by using the following relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     ω 
                     z 
                     ′ 
                   
                   ≈ 
                   
                     
                       - 
                       
                         
                           
                             J 
                             3 
                             ′ 
                           
                            
                           
                             J 
                             4 
                             ′ 
                           
                         
                         
                           
                             J 
                             1 
                             ′ 
                           
                            
                           
                             J 
                             2 
                             ′ 
                           
                         
                       
                     
                      
                     
                       B 
                       
                         
                           TE 
                           201 
                         
                         / 
                         
                           TE 
                           301 
                         
                       
                       ′ 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0039]    wherein ω′ z  is the generalized angular frequency of the TZ, J 1 ′ and J 2 ′ are the generalized coupling admittances between the source port S and the load port L and TE 101  mode, and J 3   40  and J 4 ′ are the generalized coupling admittances between the source port S and the load port L and one of TE 201  or TE 301  modes, as is denoted in  FIG. 3 . B′ TE201/TE301  is the generalized constant susceptance of one of the TE 201  or TE 301  modes. In general, the TZ is shifted in frequency relative to the transmission pole of the fundamental mode TE 101  because the product of J 1 ′ and J 2 ′ is much larger than the product of J 3 ′ and J 4 ′ close to the resonance frequency of the TE 201  or TE 301  mode. For the oversized SIW cavity  19 , the location of the TZ can be slightly tuned by changing the width of the SIW cavity  19  with little effect on the desired passband response generated by the TE 101  mode. The location of the TZ in the oversized SIW cavity  29  can be tuned by changing the relative position of the microstrip lines  15  and  16 , as noted above. 
         [0040]    Turning now to  FIGS. 4A and 4B , magnetic field distributions  40 A and  40 B of the fundamental mode TE 101  and the higher-order mode TE 301  are illustrated. The modes TE 101  and TE 301  are symmetrically excited in the SIW cavity  19  by the 50Ω microstrip line  15 . The mode couplings between the microstrip line  15  and the modes TE 101  and TE 301  are both positive, the coupling between the microstrip line  15  and the TE 101  mode being significantly stronger than the coupling between the microstrip line  15  and the TE 301  mode. Thus, a TZ above the resonance of the TE 101  mode is generated; this TZ is shifted far away from the resonance of the TE 101  mode because the coupling between the microstrip line  15  and the TE 101  mode is much stronger than the coupling between the microstrip line  15  and the TE 301  mode. 
         [0041]    Referring to  FIG. 5 , a simulated spectral plot  50  of the insertion loss of the single-cavity SIW filter  10  is shown, having superimposed thereupon electric field distributions in the SIW cavity  19  of the filter  10  corresponding to a first transmission maximum  54 , a first TZ  55 , and a second transmission maximum  56 . A pattern  51  denotes the electric field distribution at the resonance point  54  in the SIW cavity  19  of the filter  10  excited by the input microstrip line  15 . The pattern  51  corresponds to an electric field distribution of a transmission pole, when the TE 101  mode is in resonance. Similarly, patterns  52  and  53  denote the electric field distribution at the TZ  55  and at the transmission pole  56 , respectively. At the point  55 , the TE 301  mode is close to being in resonance, at which point it is of a sufficient strength to cancel the off-resonance mode TE 101  at the output microstrip line  16 . One can see that the TZ  55  is generated at about 30 GHz, while the point of maximum transmission  54  is at 20 GHz. Advantageously, such a large distance between the TZ  55  and the transmission pole  54  is generated without resorting to placing any discriminating physical structures inside the cavity  10 , such as openings in the top conductive layer  12  or the bottom conductive layer  13  of the SIW cavity  10 . 
         [0042]    Referring now to  FIG. 6 , a three-dimensional view of an SIW filter  60  of the present invention is shown. Similar to the single-cavity SIW filter  10  of  FIG. 1 , the SIW filter  60  of  FIG. 6  has a dielectric layer  61  sandwiched between top and bottom opposing planar conductive layers  62  and  63 , respectively. An array of the conductive vias  14  connects the conductive layers  62  and  63  through the dielectric layer  61  thereby forming a chain of four sequentially coupled conterminous multimode SIW cavities  69   1  to  69   4  defined on their perimeters by an array of the vias  14  as shown. The neighboring cavities  69   1  and  69   2 ;  69   2  and  69   3 ; and  69   3  and  69   4  are coupled to each other by a via-free opening  101  in a common wall therebetween. The SIW cavity  69   1  is directly excited by an input signal coupled to a transmission line  65 , and a transmission line  66  is used to output the signal. The lines  65  and  66  are preferably microstrips, however striplines or coplanar waveguides can also be used. Inside the outer SIW cavities  69   1  and  69   4 , the lines  65  and  66  are defined by non-conductive slots  67  and  68 , respectively. The slots  67  and  68  have ends perpendicular to the lines  65  and  66 , which facilitates improvement of the stopband performance without deteriorating the passband performance of the filter  60 . Preferably, the slots  67  and  68  and the microstrips  65  and  66  are formed by patterning the top conductive layer  62 . The electromagnetic signal is coupled into the first SIW cavity  69   1  by the line  65  having slots  67 , and then is coupled into the next cavities  69   2 ;  69   3 ; and  69   4  by the via-free openings, or “post-wall irises”  101  as shown in  FIG. 6 . The via-free openings are defined by eight conductive vias  14  common to perimeters of neighboring SIW cavities. At least two vias can be used for this purpose. The line  66  is used to output the electromagnetic signal from the last cavity  69   4  of the filter  60 . 
         [0043]    According to the present invention, the size and the shape of the SIW cavities  69   1  to  69   4  of the filter  60  are selected to support at least two modes of propagation for passband frequency components and for stopband frequency components of the electromagnetic signal. At least two modes of each stopband frequency component cancel each other at TZs upon propagating through the chain of the SIW cavities  69   1  to  69   4 , thereby suppressing the stopband frequency components. Preferably, the output transmission line  66  is positioned at one of these TZs, so that the two modes of each stopband frequency component cancel each other upon propagating through the filter  60 . The output transmission line  66  may be disposed co-planar with the top conductive layer  62 , as is shown in  FIG. 6 , or, alternatively, it may be co-planar with the bottom conductive layer  63 . 
         [0044]    The position of the TZs is dependent on the position of the input transmission line  65  and the shape of the SIW cavities  69   1  to  69   4 . A specific example of dimensions of the filter  60  suitable for K a -band performance will be given below. Spatial distributions of the electric field in a filter having similar geometry as the filter  60  are shown in  FIGS. 9A and 9B , to be discussed later. 
         [0045]    The stopband frequency components are suppressed at the prescribed finite TZs produced by corresponding oversized SIW cavities. Preferably, each SIW cavity  69   1  to  69   4  is of such shape and size that the two modes of at least a fraction of the stopband frequency components cancel each other upon propagating through a corresponding SIW cavity. Shifting the frequencies of TZs of the SIW cavities  69   1  to  69   4  relative to each other results in broadening of the stopband of the filter  60 , while still attaining high levels of attenuation in the stopband. 
         [0046]    Turning to  FIGS. 7 and 8 , three-dimensional views of SIW filter  70  and  80  of the present invention are shown, respectively. The SIW filter  70  has SIW cavities  79   1  to  79   4 , and the SIW filter  80  has SIW cavities  89   1  to  89   4 . What is different between the SIW filters  60 ,  70 , and  80  of  FIGS. 6 ,  7 , and  8 , is the position of the input microstrip lines  65  and the output microstrip lines  66  relative to a longitudinal axis  102 . Specifically, in the SIW filter  60 , the microstrip lines  65  and  66  are parallel to the axis  102 ; in the SIW filter  70 , the microstrip line  65  is parallel to the axis  102  while the microstrip line  66  is perpendicular to the axis  102 ; and in the SIW filter  80 , both microstrip lines  65  and  66  are perpendicular to the axis  102 . Accordingly, the SIW cavities  69   1  to  69   4 ;  79   1 to  79   3 ; and  89   2  and  89   3  are oversized TE 101 /TE 301  SIW cavities; and the SIW cavities  79   4 ,  89   1 , and  89   4  are oversized TE 101 /TE 201  SIW cavities. Varying orientations of the microstrip lines  65  and  66  allow fine tuning of the TZ frequencies of a first and a last SIW cavity in a chain of consecutively coupled SIW cavities, in a similar manner to tuning the TZ frequencies of the SIW cavity  29  of  FIG. 2 . 
         [0047]    Referring now to  FIGS. 9A and 9B , simulated electric field distribution patterns  91 A and  91 B in the SIW cavities  99   1  to  69   4  of the filter  90  are shown. The filter  90  has the same general geometry as the filter  60  of  FIG. 6 , having input and output microstrip lines  95  and  96 , respectively, and TE 101 /TE 301  SIW cavities  99   1  to  99   4 . The patterns  91 A and  91 B correspond to electromagnetic signals at a fundamental passband frequency and a spurious passband frequency, respectively. The resonant mode of the fundamental passband is the TE 101  mode, while the resonant mode of the spurious passband is the TE 301  mode. 
         [0048]    Turning now to  FIGS. 10 to 12 , simulated transmission and reflection response characteristics of the SIW filters  60 ,  70 , and  80  of  FIGS. 6 ,  7 , and  8  are shown, respectively. The filters  60 ,  70 , and  80  are exemplary embodiments of a K a -band filter. In a K a -band satellite communications ground terminal, the transmission occurs at 29.5 to 30 GHz, while the reception occurs within 19.2-21.2 GHz. A receiving filter is normally used for suppressing a 29.5-30 GHz transmission signal to prevent self-jamming, while conveying a 19.2-21.2 GHz signal to be received by a receiver. One can see that the stopband rejection over the satellite transmit frequency band of 29.5-30 GHz, seen in  FIG. 10 , is close to 45 dB. Furthermore, in  FIGS. 11 and 12 , the stopband rejection of the filters  70  and  80  over the satellite transmit frequency band of 29.5-30 GHz is better than 50 dB, although only four multimode SIW cavities are used to arrive at a low insertion loss of 0.5-0.7 dB. An alternative way of defining the performance of the filters  60 ,  70 , and  80  as seen from  FIGS. 10 to 12 , is to define a 3 dB passband and a 35 dB stopband. The 3 dB bandwidth of the passband in  FIGS. 10 to 12  is at least 10% of a center frequency f P =20.2 GHz of the passband, that is, a middle frequency of the 3-dB points defining the passband. The 35 dB bandwidth of the stopband is at least 2% of a center frequency f S =29.75 GHz of the stopband, that is, a middle frequency of the 35-dB points defining the stopband. This performance is achieved at the stopband located away from the passband, so that f S -f P &gt;0.3* f P . 
         [0049]    Referring to  FIGS. 13 to 15 , plan views of SIW filters of the present invention are presented. The views of  FIGS. 13 ,  14 , and  15  show notations of the main dimensions of the filters  60 ,  70 , and  80 , respectively. Tables 1 to 3 below show example dimensions of the corresponding K a -band filters, in accordance with the notations of  FIGS. 13 to 15 . 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 for FILTER 60 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 w io   
                 3.22 mm 
                 l 1   
                 4.46 mm 
               
               
                   
                 w 12   
                 3.19 mm 
                 l 2   
                 4.54 mm 
               
               
                   
                 w 23   
                 2.99 mm 
                 a SIW   
                 10.5 mm 
               
               
                   
                 w ms   
                 1.28 mm 
                 w SLO   
                 2.56 mm 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 for FILTER 70 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 w ms   
                 1.28 mm 
                 w 12   
                 3.19 mm 
               
               
                   
                 w io   
                 3.22 mm 
                 w 23   
                 2.99 mm 
               
               
                   
                 w i   
                 2.56 mm 
                 w 34   
                 3.24 mm 
               
               
                   
                 l i   
                 1.48 mm 
                 a 1   
                 10.66 mm  
               
               
                   
                 l 1   
                 4.46 mm 
                 a 2   
                 6.60 mm 
               
               
                   
                 l 2   
                 4.54 mm 
                 w o   
                 3.14 mm 
               
               
                   
                 l 3   
                 4.53 mm 
                 l o   
                  1.6 mm 
               
               
                   
                 l 4   
                 5.35 mm 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 for FILTER 80 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 w ms   
                 1.28 mm 
                 w 23   
                 2.99 mm 
               
               
                   
                 w io   
                 3.08 mm 
                 w 34   
                 3.24 mm 
               
               
                   
                 w i   
                 2.88 mm 
                 a 1   
                  6.6 mm 
               
               
                   
                 l i   
                 1.50 mm 
                 a 2   
                 10.75 mm  
               
               
                   
                 l 1   
                 5.43 mm 
                 a 4   
                  6.6 mm 
               
               
                   
                 l 2   
                 4.47 mm 
                 w o   
                 3.14 mm 
               
               
                   
                 l 3   
                 4.52 mm 
                 l o   
                  1.6 mm 
               
               
                   
                 l 4   
                 5.35 mm 
                 o 1   
                 3.14 mm 
               
               
                   
                 w 12   
                 3.46 mm 
                 o 4   
                 2.11 mm 
               
               
                   
                   
               
             
          
         
       
     
         [0050]    A skilled artisan will realize that the filter shapes and sizes, defined by the sets of dimensions tabulated in Tables 1 to 3, are not the only possible shapes and sizes of a K a -band filter of the present invention. Furthermore, for another passband and stopband frequency and attenuation level specification, as well as for another dielectric layer material, the dimensions can be different. It is to be understood, however, that the invention encompasses various sizes and shapes of SIW cavities that support two modes, so that the two modes cancel each other upon propagating through the sequential chain of the SIW cavities, thereby suppressing the stopband frequency components at defined TZ locations. As is appreciated by one skilled in the art, the above described “mode cancelling” function will determine the shape and size of SIW cavities. In particular, one can observe from the Tables 1 to 3 that individual SIW TE 101 /TE 301  cavities are more than twice as wide as they are long. One can also observe that the individual SIW cavities are more than three times as wide as the width of the corresponding via-free openings. As for the size of the SIW cavities, for a K a -band application, the TE 101 /TE 301  cavities are preferably 8 mm to 14 mm wide, the TE 101 /TE 201  cavities are between 5 mm to 8 mm wide, with the total length of the entire chain of four cavities being in the range of 16 mm to 22 mm. The size of the cavities may vary and depends on the dielectric constant of the substrate material used. 
         [0051]    The filters  60 ,  70 , and  80  are preferably manufactured in a PCB having linear arrays of metalized via holes with a diameter of 0.5 mm and a center-to-center pitch of 1 mm, although other pitch dimensions that are fine enough to prevent radiation losses may be used. For the PCB, a 20 mil thick RT/Duroid™ 6002 or 20 mil thick RT/Duroid 5880 PCB material may be used. Both materials are supplied by Rogers Corp., having headquarters in Rogers, Conn., USA. In theory, the unloaded quality factor Qu of an SIW resonator based on 20 mil thick Rogers RT/Duroid 5880 is about 500, while the Qu of an SIW resonator based on 20 mil thick Rogers RT/Duroid 6002 is only about 350. Hence, the RT/Duroid 5880 substrate is expected to be beneficial from the insertion loss standpoint. In reference to Eq. (2) above, both Qd and Qc of an SIW cavity made of RT/Duroid 5880 are higher than Qd and Qc of an SIW cavity made of RT/Duroid 6002. The Qd is higher because of a lower loss tangent tan(D). The Qc is higher for the RT/Duroid 5880 because of larger cavity dimensions, due to a lower dielectric constant as compared to Rogers RT/Duroid 6002. 
         [0052]    Both abovementioned Rogers substrates use a similar fabrication process and have a similar fabrication cost. However, RT/Duroid 6002 has better mechanical properties than RT/Duroid 5880. The RT/Duroid 6002 material is suitable for laser drilling, and via holes of a wide range of diameters can be drilled by this method. The RT/Duroid 5880 material must be mechanically drilled, and mechanical drilling generally has a lower degree of precision than laser drilling. The better suitability for machining of the RT/Duroid 6002 material makes it preferable over the RT/Duroid 5880 material, even though the 5880 material has a better electrical performance as explained above. The filters  60 ,  70 , and  80  were designed and fabricated using 20 mil thick Rogers RT/Duroid 6002 material. 
         [0053]    Turning now to  FIG. 16 , spectral plots of simulated and measured insertion loss of the SIW filter  70  of  FIG. 7  are presented. A variation of the dielectric constant of the substrate and a fabrication error led to a slight frequency shift of about 1.5% between the simulated and the measured responses. The measured minimum in-band insertion loss is approximately 0.9 dB, which is slightly higher than the simulated loss of 0.75 dB due to the additional loss of a 90° microstrip bend, not shown, and an additional section of microstrip line, not shown. There is a maximum variation of about 0.6 dB in the insertion loss across the passband. The attenuation in the frequency band of 25.3 GHz -31.7 GHz is better than 40 dB, while in the transmission (Tx) band of 29.5 GHz-30 GHz it is better than 58 dB. There is a spike around 31.7 GHz due to higher-order resonances of the TE 201  mode and TE 301  mode. 
         [0054]    Referring now to  FIG. 17 , spectral plots of simulated and measured insertion loss of the SIW filter  80  of  FIG. 8  are presented. Similar to the spectral plot of  FIG. 16 , a slight frequency shift of about 1.3% between the simulated and measured responses occurs due to the variation of the dielectric constant of the substrate, as well as due to fabrication tolerances. The measured minimum in-band insertion loss is around 0.8 dB, which is very close to the simulated loss of 0.77 dB. The attenuation in the frequency band of 23.94 GHz-31.48 GHz is better than 40 dB, while in the Tx band of 29.5 GHz-30 GHz it is better than 52 dB. There is a spike around 31.6 GHz due to the higher-order resonances of the TE 201  mode and TE 301  mode.