Patent Publication Number: US-9893400-B2

Title: Method for performing frequency band splitting

Description:
PRIORITY CLAIM 
     This application is a continuation of U.S. patent application Ser. No. 14/523,685 entitled “METHOD FOR PERFORMING FREQUENCY BAND SPLITTING,” filed on Oct. 24, 2014 and has been issued as U.S. Pat. No. 9,368,852, on Jun. 14, 2016, the disclosure of which is incorporated herein by reference in its entirety for all purposes. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention relates to frequency band splitting in general, and, in particular, to a method for performing passive frequency band splitting. 
     2. Description of Related Art 
     High-speed signaling systems typically employ multiple single carrier frequency channels to transfer data present within a frequency band from a transmitter (or driver) to a receiver on a printed circuit board. Those single carrier frequency channels are physical channels that are required to maintain wiring rules, such as spacing and density requirements, in order to be able to transmit signals with integrity within a high-speed signaling system. 
     Instead of using separate physical channels for each carrier frequency signal, a single guiding structure can be utilized to transfer multiple carrier frequency signals. This would require combining and splitting individual carrier frequency signals at the inset and outset of the wave-guiding structure. This approach can be achieved by using frequency division multiplexing methods. To separate signals at the receiving end, a power divider and band pass filters are utilized. Power divided signals are sent to band pass filters, each designed for a specific carrier frequency and associated with a certain receiver. Due to the power division, signals sent to band-pass filters have less amplitude. This approach makes the data signals at each individual receiver more prone to noise. To alleviate the lower signal amplitude characteristic, various amplifiers may be employed; however, this would result in increased costs and resource utilization. 
     Consequently it would be desirable to provide an improved method to perform frequency band splitting in high-speed signaling systems. 
     SUMMARY OF THE INVENTION 
     In accordance with a preferred embodiment of the present invention, a frequency band splitter includes a first, a second, and a third waveguides. A first narrow rectangular waveguide is utilized to connect the first waveguide to second waveguide. The first narrow rectangular waveguide has a first width to allow signals of a frequency band centered around a first frequency to be transmitted from the first waveguide to the second waveguide. A second narrow rectangular waveguide is utilized to connect the first waveguide to the third waveguide. The second narrow rectangular waveguide has a second width, which is different from the first width, to allow signals of a frequency band centered around a second frequency to be transmitted from the first waveguide to the third waveguide. 
     All features and advantages of the present invention will become apparent in the following detailed written description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention itself, as well as a preferred mode of use, further objects, and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is a diagram of a wave-guiding structure in which a preferred embodiment of the present invention can be incorporated; 
         FIG. 2  is an equivalent circuit representation of the wave-guiding structure from  FIG. 1 ; 
         FIG. 3  is a diagram of a two-branch frequency band splitter, in accordance with a preferred embodiment of the present invention; and 
         FIGS. 4-5  are graphs showing transmission coefficient magnitudes for the frequency band splitter from  FIG. 3 . 
     
    
    
     DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
     I. Theory and Method 
     Referring now to the drawings and in particular to  FIG. 1 , there is illustrated a diagram of a wave-guiding structure in which a preferred embodiment of the present invention can be incorporated. As shown, a wave-guiding structure  10  includes two rectangular metallic waveguides  11  and  12 , each having a cross-sectional width w 1  and a cross-sectional height h 1 . Waveguide  11  is connected to waveguide  12  via a narrow rectangular waveguide  15  having a cross-sectional width w 2  and a cross-sectional height h 2 . 
     Wave-guiding structure  10  can be represented as a transmission line equivalent circuit as shown in  FIG. 2 . In  FIG. 2 , β 1  and Z 1  respectively represent the propagation constant and the characteristic impedance within waveguides  11  and  12 , while β 2  and Z 2  respectively represent the propagation constant and the characteristic impedance within narrow rectangular waveguide  15 . In addition, jB is an admittance factor to account for the change in widths and heights at the inset and outset of narrow rectangular waveguide  15 . 
     Consider dominant mode (TE01) wave propagation in waveguides  11  and  12 , propagation constant β 1  can be described as 
                     β   ⁢           ⁢   1     =         k   ⁢           ⁢     1   2       -       (     Π     w   ⁢           ⁢   1       )     2                 (   1   )               
where k 1  represents the wave number within waveguides  11 ,  12  and is described as k 1 =2π/λ 1 , where λ 1  is the wavelength of the dielectric material filling waveguides  11 ,  12 , which can be expressed as
 
               λ   ⁢           ⁢   1     =     c     f   ⁢       ɛ   ⁢           ⁢     1   r                   
where c is the speed of light in free space, f is frequency, and ∈ 1   r  is the dielectric constant of the material filling waveguides  11 ,  12 . Similarly, the propagation constant β 2  can be described as
 
                     β   ⁢           ⁢   2     =         k   ⁢           ⁢     2   2       -       (     Π     w   ⁢           ⁢   2       )     2                 (   2   )               
where k 2  represents the wave number within the waveguide and is described as k 2 =2π/λ 2 , where λ 2  is the wavelength of the dielectric material filling narrow rectangular waveguide  15 , which can be expressed as
 
               λ   ⁢           ⁢   2     =     c     f   ⁢       ɛ   ⁢           ⁢     2   r                   
where c is the speed of light in free space, f is frequency, and ∈ 2   r  is the dielectric constant of the material filling narrow rectangular waveguide  15 .
 
     The characteristic impedances of waveguides  11 ,  12  and narrow rectangular waveguide  15  can be described as 
     
       
         
           
             
               
                 
                   
                     
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     Assuming h 2 &lt;&lt;h 1 , w 2 &lt;w 1 , and ∈ 1   r =∈ 2   r , it can be thought, at a first glance, that the impedance mismatch between waveguides  11 ,  12  and narrow rectangular waveguide  15  will lead to almost complete reflection at the interface, resulting in very minute transmission between waveguides  11  and  12 . However, the reality is different and may be understood upon examining the global reflection coefficient R due to narrow rectangular waveguide  15 . 
     The global reflection coefficient R can be described as 
                   R   =       Γ   ⁡     [     1   -     e         -   j     ·   2   ·           ⁢   β     ⁢           ⁢     2   ·   d     ⁢           ⁢   2         ]         1   -       Γ   2     ⁢     e         -   j     ·   2   ·   β     ⁢           ⁢     2   ·   d     ⁢           ⁢   2                     (   5   )               
where e −j·2·β2·d2  represents the phase shift factor due to wave propagation twice the length of narrow rectangular waveguide  15  in which d 2  represents the length of narrow rectangular waveguide  15  along the propagation direction, and Γ is the interfacial reflection coefficient between waveguides  11 ,  12  and narrow rectangular waveguide  15 , which is a function of Z 1 , Z 2  and jB.
 
     The main idea behind super tunneling is that a wave can be transmitted (or tunneled) within a narrow frequency band between two transmission lines that are mismatched to a large extent. This may be reached when R=0 by making
 
1− e   −·2·β2·d2 =0  (6)
 
Equation (6) can be achieved when β 2  tends to 0. This property takes place at the dominant mode cut-off frequency within narrow rectangular waveguide  15 , which is when
 
     
       
         
           
             
               
                 
                   
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     The super tunneling effect resulting from satisfying equation (7) is not dependent on the length of narrow rectangular waveguide  15  or its intermediary shape as long as the width and narrow height relative to the large waveguides are preserved. However, there might exist within a certain frequency band higher frequency tunneling effects due to the Fabry Perot resonance. Unlike the super tunneling effect resulting from satisfying equation (7), such tunneling will depend on, inter alia, the length of narrow rectangular waveguide  15 . 
     II. Frequency Band Splitter Design 
     Based on the theoretical description in the previous section, a frequency band splitter can be built by connecting a large rectangular waveguide section characterized by a wide frequency band to similar large rectangular waveguide sections using narrow rectangular waveguides each having a different width w. In this case, each narrow rectangular waveguide passes only a narrow frequency band centered around the cutoff frequency f, which results in a β tending to 0. Due to reciprocity, this same frequency band splitter can also be utilized as a frequency band combiner (coupler). 
     Referring now to  FIG. 3 , there is illustrated an exemplary design of a two-branch frequency band splitter, in accordance with a preferred embodiment of the present invention. As shown, a frequency band splitter  30  includes a waveguide  31  connected to two waveguides  32  and  33  via two narrow rectangular waveguides  34  and  35 . The height, width and length of waveguide  31  are 2.39 mm, 4.78 mm and 5.00 mm, respectively. The height, width and length of waveguide  32  are 2.39 mm, 4.78 mm and 5.00 mm, respectively. The height, width and length of waveguide  33  are 2.39 mm, 4.78 mm and 5.00 mm, respectively. The height, width and length of narrow rectangular waveguide  34  are 0.05 mm, 2.70 mm and 1.00 mm, respectively. The height, width and length of narrow rectangular waveguide  35  are 0.05 mm, 3.30 mm and 1.00 mm, respectively. 
     Waveguide  31  is a U-band (40-60 GHz) waveguide that is the main trunk of the frequency band splitter. Waveguides  34  and  32  compose one branch from waveguide  31  while waveguides  35  and  33  compose a second branch. Like waveguide  31 , waveguides  32  and  33  are U-band waveguides. The frequency bands allowed to pass through waveguides  32  and  33  are determined by the width of waveguides  34  and  35  calculated using equation (7) respectively. The amplitudes of the transmission coefficients between waveguide  31  and each of waveguides  32 - 33  are shown in  FIG. 4 . The frequency splitting operation of frequency band splitter  30  can be clearly observed in which each branch mainly transmits a specific band with high amplitude. 
       FIG. 5  shows the magnitudes of the transmission coefficient between waveguide  31  and each of waveguides  32 - 33  with the lengths L of narrow rectangular waveguides  34 - 35  extended from 1.00 mm to 3.00 mm. The increase in lengths of narrow rectangular waveguides  34 - 35  did not change the location of the peaks of the frequency split bands corresponding to the widths used to get β tending to 0, as shown in  FIG. 4 . This is expected because under ideal conditions, the lengths of narrow rectangular waveguides  34 - 35  do not affect the super tunneling frequency achieved with equation (7) (or when β tends to 0). Comparing with  FIG. 4 , the increased lengths of narrow rectangular waveguides  34 - 35  in  FIG. 5  result in less high amplitude frequency band around the super tunneling frequency. In addition, the higher frequency peaks appearing in  FIG. 5  in the frequency split band curves are attributed to Fabry Perot resonance effects. These resonance effects are dependent on the lengths of narrow rectangular waveguides  34 - 35 . 
     As has been described, the present invention provides an improved method for performing passive frequency band splitting in high-speed signaling systems. 
     While the invention has been particularly shown and described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.