Patent Publication Number: US-8970322-B2

Title: Waveguide based five or six port circuit

Description:
CROSS REFERENCE TO RELATED APPLICATION(S) 
     This application is a 35 U.S.C. §371 National Phase Entry Application from PCT/EP2010/070870, filed Dec. 29, 2010, designating the United States, the disclosure of which is incorporated herein in its entirety by reference. 
     TECHNICAL FIELD 
     The present invention discloses a novel five or six port circuit. 
     BACKGROUND 
     Five and six-port circuits are often applied in microwave systems and in wireless communications systems, in particular for use in homodyne receivers. In a five/six-port circuit, there are two input ports and three/four output ports. The input ports of a five/six port circuit are connected to an RF signal and an LO signal, respectively, while the signals at the output ports of the five/six-port circuit are used as input to power detectors, with one power detector for each output port each. 
     Using the power measured by the power detectors, the in-phase and quadrature components of the base-band signal can be determined. As compared with a receiver which utilizes mixers, a receiver with a five/six port circuit has advantages regarding low DC power consumption, low circuit complexity, low cost, as well as wide bandwidth and re-configurability. 
     A conventional five/six-port circuit for receivers is often built on a substrate, and is usually a planar circuit which consists of Wilkinson power splitters and 90 degree hybrid couplers, usually designed as microstrip lines on a microwave motherboard. At very high frequencies, for instance, at 60 GHz, such a five/six-port circuit can be integrated with transistors and diodes on MMIC or RFIC chips. 
     In many microwave applications, existing waveguides are used to connect between a five/six-port circuit designed as a planar circuit and, for example, an antenna or a waveguide duplexer. A waveguide transition, e.g. a microstrip-to-waveguide transition is required for such a connection, which adds to the costs when using a planar five/six port circuit, and which also causes losses at the transition. 
     SUMMARY 
     It is an object of the present invention to obviate at least some of the above mentioned drawbacks of a conventional five/six-port circuit and to provide an improved five/six-port circuit. 
     This object is met by the present invention in that it discloses a five-port circuit which comprises a hollow waveguide mounted with a contacting surface on a first main surface of a non-conducting substrate. 
     The hollow waveguide comprises an input port at its one end and a matched load at its other end, and the five-port circuit additionally comprises three probes which are arranged along the longitudinal extension of the hollow waveguide. The five-port circuit also comprises three power detectors, with each probe being arranged to contact the input port of one of the power detectors. The output ports of the power detectors are arranged to contact the conductor of an open waveguide which is also comprised in the five-port circuit and which extends in parallel to the hollow waveguide, with an input port at its one end and a matched load at its other end, i.e. a load which is equal to the characteristic impedance of the hollow waveguide. 
     In the five-port circuit, the probes are equidistantly spaced with a distance L between neighbouring probes which corresponds to an electrical length θ, defined as θ=2πL/λ, where λ is the wavelength which corresponds to the operational frequency of the five-port circuit, and the five-port circuit also comprises three low pass filters, each of which is connected with its input port to the conductor of the open waveguide at a position which corresponds to the position of one of the power detectors, so that each probe is arranged in a straight line with one of the power detectors and one of the low pass filters. 
     The output ports of the low pass filters are arranged to be used as the output ports of the five-port circuit, and the input ports of the hollow waveguide and the open waveguide are arranged at distal ends from each other. 
     Thus, by means of probes arranged inside the hollow waveguide, a transition between waveguide and the open waveguide is not needed, and accordingly, the problems with such transitions are obviated by means of the invention. In addition, since the input ports of the hollow waveguide and the open waveguide are arranged at distal ends from each other, signals which are connected to those input ports will propagate in opposite directions to each other, which is also useful, as will be realized from the detailed description given in this text. 
     The invention also discloses a six-port circuit, which comprises the five-port circuit described above, but which is also equipped with one additional probe, power detector and low pass filter. The additional probe is arranged to contact the input port of the additional power detector and the output port of the additional power detector is arranged to contact the conductor of the open waveguide. All four probes are equidistantly arranged at a distance L which corresponds to the electrical length θ, and the additional probe is arranged in a straight line with the additional power detector and the additional low pass filter. 
     The input ports of the hollow waveguide and the open waveguide are arranged at distal ends from each other, which means that input signals to the hollow waveguide and to the open waveguide will propagate in opposing directions. 
     In embodiments of the five/six-port circuit described above, the probes are through-going from the contacting surface of the hollow waveguide to a second main surface of the substrate. 
     In embodiments of the five/six-port circuit described above, the probes are arranged to contact the power detectors inside or on the surface of the non-conducting substrate. 
     In some embodiments of the five/six-port circuit, the hollow waveguide and the open waveguides are straight. 
     In some embodiments of the five/six-port circuit, the hollow waveguide is a surface mounted waveguide, i.e. the contacting surface comprises a separate part of the hollow waveguide which has been fixed to the rest of the hollow waveguide. 
     In some embodiments of the five/six-port circuit, the power detectors, the open waveguide and the low pass filters are arranged on the second main surface of the substrate. 
     In some embodiments of the five/six-port circuit, the power detectors, the open waveguide and the low pass filters are arranged on the first main surface of the substrate, and the probes are connect to the power detectors via a connecting open waveguide on the second main surface of the substrate which connects to the power detectors by means of via holes in the substrate. In such embodiments, the connecting open waveguide can be arranged either on the second main surface of the substrate or inside the substrate. 
     In some embodiments of the five/six-port circuit, the open waveguide is a microstrip line. 
     In some embodiments of the five/six-port circuit, the open waveguide is a coplanar waveguide line. 
     According to a method of the invention for using the five- or six-port circuit described above, an LO signal is input to one of the input ports and an RF signal is input to the other input port, and the LO frequency is chosen to be half of RF frequency. Such a choice of LO frequency solves the problem of leakage of the LO signal into the RF input port, since a frequency which is half of the RF frequency will be below the cutoff frequency of the hollow waveguide. Suitably, the RF signal is used as input signal to the hollow waveguide and the LO signal is used as input signal to the open waveguide, although the opposite is also useful, i.e. that the LO signal is used as input signal to the hollow waveguide and the RF signal is used as input signal to the open waveguide. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described in more detail in the following, with reference to the appended drawings, in which 
         FIG. 1  shows an open top view of a first embodiment of the invention, and 
         FIG. 2  shows an open top view of a second embodiment of the invention, and 
         FIG. 3  shows a top view of the embodiment of  FIG. 1 , and 
         FIG. 4  shows a cross section of the embodiment of  FIG. 1  and  FIG. 3 , and 
         FIG. 5  shows a bottom view of the embodiment of  FIG. 1 , and 
         FIG. 6  shows a top view of a probe used in the invention, and 
         FIG. 7  shows a top view of a third embodiment of the invention, and 
         FIG. 8  shows a more detailed top view of the embodiment of  FIG. 6 , and 
         FIG. 9  shows a cross section of the embodiment of  FIG. 6  and  FIG. 7 , and 
         FIG. 10  shows an embodiment of a power detector for use in the invention, and 
         FIG. 11  shows a schematic flow chart of a method of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. The invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Like numbers in the drawings refer to like elements throughout. 
     The terminology used herein is for the purpose of describing particular embodiments only, and is not intended to limit the invention. 
       FIG. 1  shows an open top view of a first embodiment  100  of a five-port circuit of the invention. The embodiment  100  comprises a hollow waveguide  105  which has a lateral extension, and which is arranged on a first main surface  113  of a non-conducting substrate  112 . In this particular embodiment, the hollow waveguide  105  extends in a straight line, which is suitable but not necessary, the hollow waveguide  105  can “meander” or have other varying bent forms along the first main surface  113  of the substrate  112 . At its one end  110 , the hollow waveguide has an input port for, for example, RF-signals, and at its other end  118 , it has a matched load  115 , i.e. a load which has an impedance equal to characteristic impedance of the hollow waveguide. 
     The term “hollow waveguide” is used here in order to distinguish the waveguide  105  from such technologies as microstrip or strip line. 
     The hollow waveguide  105  is mounted on the first main surface  113  of the non-conducting substrate  112  in such a way that a contacting surface of the hollow waveguide contacts the first main surface  113 . The five-port circuit  100  also comprises three probes  106 ,  107  and  108 , which are suitably through-going from the contacting surface of the hollow waveguide  105  to a second main surface of the substrate  112 , i.e. to the “bottom surface” of the substrate  112 , if the side on which the hollow waveguide is located is seen as the top surface of the substrate  112 . Naturally, in other embodiments, the probes can be made to extend to “side surfaces” such as edges of the substrate  112 , if desired. 
     Each probe  106 ,  107 ,  108  is, in a manner which will be described in more detail later, connected to the input port of a power detector  120 ,  125 ,  130 , with one power detector for each probe. 
     The five-port circuit  100  also comprises a microstrip line  135 , of which the conductor is seen in  FIG. 1 . Alternatively, instead of a microstrip line, the five-port circuit can instead use a co-planar waveguide; these two technologies are here referred to as “open waveguides”. In addition, the term “microstrip line” may also be used in this text to refer to what is actually the conductor of the microstrip line—the ground plane of the microstrip line is suitably arranged on the opposite surface of the substrate  112  or inside the substrate  112 . 
     The microstrip line  135  extends in parallel to the hollow waveguide  105 , and the output ports of the power detectors  120 ,  125  and  130  are connected to the microstrip line  135 . 
     As shown in  FIG. 1 , the microstrip line  135  has a matched load  145  at its one end and an input port  140  for signals such as, for example, LO-signals at its other end. As shown in  FIG. 1 , the input ports  110  and  140  of the hollow waveguide and the microstrip line are placed at opposing ends, as are their matched loads  115  and  145 , so that signals which are connected to the hollow waveguide will propagate in a direction opposite to the propagation direction of signals which are connected to the microstrip line. In the example shown in  FIG. 1 , RF-signals are connected to the hollow waveguide and LO-signals to the microstrip line, although the opposite is also perfectly feasible, i.e. LO-signals to the hollow waveguide and RF-signals to the microstrip line. 
     Thus, input signals are input to the input ports at opposing ends of the hollow waveguide  105  and the microstrip line  135 . The input signals to the hollow waveguide are accessed by means of the probes  106 ,  107  and  108 , and are connected to the microstrip line  135  via the power detectors  120 ,  125  and  130 . In order to access the output signals of the five-port circuit  100 , there are also arranged three low pass filters  150 ,  155  and  160 , one for each power detector  120 ,  125  and  130 . The bandwidth and the low pass characteristics of the low pass filters is determined by the bandwidth of the baseband signal which it is desired to receive by means of the five port circuit  100 . Suitably, all of the three low pass filters  150 ,  155 ,  160  have identical filter characteristics. 
     As shown in  FIG. 1 , each probe and its corresponding power detector and low pass filter are arranged in a straight line which is perpendicular to the direction of extension of the microstrip line  135  and the hollow waveguide  105 . As is also shown in  FIG. 1 , the probes  106 ,  107  and  108  are equidistantly spaced along the direction of extension of the hollow waveguide  105 , with a distance L between neighbouring probes, which corresponds to an electrical length of θ=2πL/λ, where λ is the wavelength which corresponds to the operational frequency of the five-port circuit  100 . 
     Thus, if the input port of each low pass filter is connected to the microstrip line, the three output signals of the five port circuit  100  can be accessed at the respective output ports of the low pass filters, shown as  171 ,  172 , and  173  in  FIG. 1 . The phase differences between the signals at the output ports and how those phase differences are obtained will be explained later in this text. 
     In  FIG. 1 , RF signals are shown as the input signals to the hollow waveguide  105 , and LO signals as the input signals to the open waveguide  135 . This is an example only, other signals can of course also be used, and if RF and LO signals, are used, they can also be input in “the other way”, i.e. LO signals to the hollow waveguide  105  and RF signals to the open waveguide  135 . 
       FIG. 2  shows an embodiment  200  of the invention, which follows the same principles as those described above in connection with the embodiment  100  of  FIG. 1 , with reference numbers being retained from  FIG. 1 . However, as opposed to the embodiment  100 , the embodiment  200  is a six-port circuit, as opposed to the five-port circuit of  FIG. 1 . Since the principles used by the embodiment  200  are the same as those of the embodiment  100 , the basic function of the embodiment  200  will not be repeated here, but as shown in  FIG. 2 , the embodiment  200  comprises a fourth “set” of probe  161 , power detector  162  and low pass filter  163 , where the output port  164  of the fourth low pass filter  263  is used as the fourth output port of the six-port circuit  200 . As also shown in  FIG. 2 , the equidistant spacing L between the probes is used here as well, as is the principle of arranging the fourth probe  261  and its accompanying power detector  262  and low pass filter  263  in a straight line, perpendicular to the microstrip line  140 . The invention will be described below as being a five-port circuit, but it should be made clear that the principles disclosed herein can equally well be applied to embodiments such as the one in  FIG. 2 , i.e. to six-port circuits. In the following text, the invention will be described with reference to a five-port circuit such as the one on  FIG. 1 . However, it should be understood that the same principles can equally well be applied to a six-port circuit such as the one in  FIG. 3 , or in fact to an N-port circuit, where N is an integer larger than or equal to four. 
       FIG. 3  shows an open top view of part of the embodiment  100  of the invention, in which the hollow waveguide  105  is shown, along with the three probes  106 ,  107  and  108 . The equidistant spacing L between the probes can also be seen clearly. The first main surface  113  of the substrate  112  is shown with dashed lines in order to indicate that what is seen in  FIG. 3  may be only a part of the first main surface  113 , i.e. a “cut-out”. 
       FIG. 4  shows a cross-section of the embodiment  300  along the line A-A indicated in  FIG. 3 . The hollow waveguide  105  is seen clearly, as is the cavity  403  inside of it. The substrate  112  is also shown here, as is the first main surface  113  on which the hollow waveguide is arranged. In this embodiment, the hollow waveguide is a so called surface mounted waveguide, in which the hollow waveguide  105  comprises a first part  105 ′ which is mounted on the first main surface  113  and which here becomes the contacting surface of the hollow waveguide  105 , and a second part  105 ″ which is attached to the first part  105 ′, suitably by means of solder  409 . The probe  107  is also shown, and in  FIG. 4  the probe  107  (as well as the other probes) is shown as extending through a via hole from the cavity  403  of the hollow waveguide through the contacting surface  105 ′, and contacts the power detector  125  by means of metallic material from the via hole to the power detector  125  on the second main surface  183  of the substrate  112 . Thus, in this embodiment, the probe  107  contacts the power detector inside the via hole, although the probe  107  can of course also be made through going to the second main surface  183 , where it then contacts the power detector directly or by means of conducting material. 
     The embodiment  300  comprises the low pass filters  171 ,  172 ,  173 , the open waveguide  135  and the power detectors  120 ,  125 ,  130  shown in  FIG. 1 , all of which are arranged on the second main surface  183  of the substrate. In the cross section of  FIG. 4 , the open waveguide  135 , the power detector  125  and the low pass filter  172  can be seen, since they “belong to” the probe  107 . As can also be seen in  FIG. 4 , the probe  107  is surrounded by a groove, suitably annular, in the conducting material of the contacting surface  105 ′, so as to protect the probe from short-circuiting the hollow waveguide. Since  FIG. 4  is a cross sectional view, two parts  401 ,  402  of the groove around the probe  107  are seen in  FIG. 4 , but the groove is in a contiguous suitably annular shape. Such grooves are also arranged around the other probes, i.e. the probes  106  and  108 . 
     In  FIG. 5 , the embodiment  100  is shown in a “bottom view”, i.e. the second main surface  183  of the substrate  112  is shown. Since the microstrip line  135  in this embodiment is arranged on the second main surface  183  of the substrate  112 , the conductor of the microstrip line is seen in its entirety in  FIG. 5 , with the ground plane suitably being arranged on the first main surface of the substrate  112 . Also shown in  FIG. 5  are the probes  106 ,  107 ,  108 , which reach the second main surface  183  from the inside of the hollow waveguide through via-holes  503 ,  502 ,  501 . 
     Also shown in  FIG. 5  are the power detectors  130 ,  125 ,  120 , which are arranged to connect with their input ports to respective probes  108 ,  107  and  106 , and with their output ports to the microstrip line  135 . On the other side of the microstrip line  135 , as seen from the side of the probes and the power detector, are the low pass filters  160 ,  155 ,  150  which are arranged to connect with their input ports to the microstrip line  135  at the positions of respective power detectors  130 ,  125 ,  120 , and are also arranged to have their output ports  173 ,  172 ,  171  as the output ports of the embodiment  100 .  FIG. 5  also shows, by means of an arrow, one end of the microstrip line  140  being arranged for used as input port to the embodiment  100 , with the other end of the microstrip line having a matched load  145  arranged at it. 
       FIG. 6  illustrates a probe&#39;s position in the contacting surface  105 ′ of the hollow waveguide in more detail, with the probe  106  being used as an example: the probe  106  is made of a conducting material and is arranged in a part of the contacting surface  105 ′ with an annular groove  600  around it, which is a groove in the contacting surface  105 ′ of the hollow wave guide  105 , down to the non-conducting material in the substrate  112 . Naturally, the groove  600  can be given other shapes than annular. 
       FIG. 7  shows an example of a further embodiment  700  of the invention. As opposed to the embodiments previously shown and described, in the embodiment  700  the power detectors  120 ,  125 ,  130 , the microstrip line  135  (or rather, its conductor) and the low pass filters  150 ,  155 ,  160  are arranged on the same main surface of the substrate as the hollow waveguide  105 , said main surface in this case being the main surface  113 . Since the components involved are the same as those in the previous embodiments, all reference numbers have been retained from the previous embodiments. In addition, although the power detectors, the microstrip line and the low pass filters are arranged on the opposite main surface of the substrate  112  as opposed to previous embodiments, the same principles are used, i.e. for each probe  106 ,  107 ,  108  there is one power detector  120 ,  125 ,  130  which contacts the microstrip line, and one low pass filter  150 ,  155 ,  160  which contacts the microstrip line  135  with its input port, and whose output port is used as an output port for the entire embodiment  700 . 
     In addition, the matching loads at opposite ends of the hollow waveguide and the microstrip line are also used in the embodiment  700 , as is the principle of using opposite ends of the hollow waveguide and the microstrip line as input ports, in order to make input signals propagate in opposing directions in the hollow waveguide and the microstrip line. Also, the equidistant spacing L is used here as well, as is the principle of arranging each “set” of probe-power detector-low pass filter in a straight line perpendicular to the extension of the hollow waveguide and the microstrip line, which extend in parallel to each other. 
       FIG. 8  shows a view of the embodiment  700  which is similar to the view given in  FIG. 5  of the embodiment  100 . Again, here we see the hollow waveguide  105  extend in parallel to the microstrip line  135 , although on the same side of the substrate  112 , in this case on the first main surface  113 . Between the microstrip line  135  and the hollow wave guide  105 , connections from the probes  106 ,  107  and  108  “surface” through via-holes  503 ,  502  and  501 , and contact the input ports of the power detectors  130 ,  125 ,  120 , which in turn contact the microstrip line  135  with their output ports. On the other side of the microstrip line, as related to the position of the power detectors, the low pass filters  160 ,  155 ,  150  are arranged with their input ports to contact the microstrip line, and their output ports  171 ,  172  and  173  are arranged for use as output ports of the embodiment  700 . As can be seen, each “set” of probe-power detector and low pass filter is arranged in a straight line, perpendicular to the hollow waveguide  105  and the microstrip line  135 , which extend in parallel to each other. 
     Regarding the microstrip line  135 , what is shown in  FIGS. 7 and 8  is the conductor of the microstrip line. Suitably, a ground plane is arranged on the opposite main surface of the substrate  112 , a principle which is adhered to for all embodiments in which a microstrip line is used. 
       FIG. 9  shows a cross section of the embodiment  700  along the line B-B indicated in  FIG. 8 . In this figure, it is shown how the probes contact the power detectors, here shown with reference to the probe  107  and the power detector  125 : as shown in  FIG. 9 , the probe  107  is through-going, and contacts a conducting line  901  on the second main surface  183  of the substrate  112 , which extends in the direction of the power detector  125 . At a point where the power detector  125  has its input port, there is arranged a via hole  902 , through which the conducting line  901  contacts the input port of the power detector  125 . The power detector  125  in turn contacts the microstrip line  135 , and on the opposite side of the microstrip line  135 , the low pass filter  160  is arranged to have its input port contact the microstrip line  135 , and its output port is arranged to be one of the output ports of the embodiment  700 . 
       FIG. 10  shows an example of an embodiment of a surface mounted power detector  95  for use as the power detector  120 ,  125 ,  130  shown in the drawings. The power detector  95  utilizes a diode pair coupled in “anti-parallel”, i.e. in parallel but with the directions of the two diodes opposing each other. 
     The surface mounted power detector  95  is thus an anti-parallel diode pair, as shown in  FIG. 10 . It can suitably be applied in cases where the LO frequency is half of the RF frequency, and the nonlinear relationship between the voltage and the current of the APDP are used for power detection. 
     The current of an APDP is given by the expression below, which will also be used to explain how the signals at the output ports of the five/six circuit are made to have different phases: 
                     i   ⁡     (   t   )       =       ∑     k   =   0     ∞     ⁢           ⁢       a       2   ⁢   k     +   1       ⁢       v   ⁡     (   t   )           2   ⁢   k     +   1                   (   1   )               
where v(t) is the voltage across the APDP. In a five or six-port circuit, the voltage v(t), is the difference between the LO and the RF signal, which can be expressed as:
 
     
       
         
           
             
               
                 
                   
                     v 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         V 
                         R 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ω 
                                 R 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               RF 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         V 
                         L 
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 
                                   ω 
                                   L 
                                 
                                 2 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               LO 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In (2) above, V R  and V L  are the amplitudes of RF and LO signals, respectively; φ RF  and φ LO  are the phases of the RF and the LO signal, respectively. Inserting (2) into (1), it can be found that, the baseband signal obtained after the low-pass filters is contributed to mainly by the term, a 3 v(t) 3 , and is given by the expression: 
     
       
         
           
             
               
                 
                   
                     
                       i 
                       b 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         3 
                         ⁢ 
                         
                           a 
                           3 
                         
                       
                       2 
                     
                     ⁢ 
                     
                       V 
                       R 
                     
                     ⁢ 
                     
                       V 
                       L 
                       2 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             ϕ 
                             RF 
                           
                           - 
                           
                             2 
                             ⁢ 
                             
                               ϕ 
                               LO 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     At ports  171 ,  172  and  173 , the phases of the RF signal are φ R , φ R +θ, and φ R +2θ, where φ R  is the phase of the baseband signal. The phases of the LO signal are θ, θ/2 and 0, where θ is the same θ as used in the expression which defines the distance L between the probes, i.e. θ=2πL/λ. 
     It should be pointed out that for the same physical lengths of transmission line or waveguide, the electrical length for the LO signal is a half that for RF frequency if an LO frequency is used which is half of the RF frequency. Inserting the RF and LO phases at ports  171 ,  172 , and  173  into expression (3) above yields following equations, in which i bn (t) represents the output of a power detector after the low pass filter at the three ports, i.e. n=1-3 i bn (t): 
     
       
         
           
             
               
                 
                   
                     
                       i 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         3 
                         ⁢ 
                         
                           a 
                           3 
                         
                       
                       2 
                     
                     ⁢ 
                     
                       V 
                       L 
                       2 
                     
                     ⁢ 
                     
                       V 
                       R 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             ϕ 
                             R 
                           
                           - 
                           
                             2 
                             ⁢ 
                             θ 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       i 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         3 
                         ⁢ 
                         
                           a 
                           3 
                         
                       
                       2 
                     
                     ⁢ 
                     
                       V 
                       L 
                       2 
                     
                     ⁢ 
                     
                       V 
                       R 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           R 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       i 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         3 
                         ⁢ 
                         
                           a 
                           3 
                         
                       
                       2 
                     
                     ⁢ 
                     
                       V 
                       L 
                       2 
                     
                     ⁢ 
                     
                       V 
                       R 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             ϕ 
                             R 
                           
                           + 
                           
                             2 
                             ⁢ 
                             θ 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     c 
                   
                   ) 
                 
               
             
           
         
       
     
     The in-phase and quadrature components of the baseband signal, i.e. I=V R  cos(φ R ) and Q=V R  sin(φ R ) are obtained from i b2 (t) and i b1 (t)-i b3 (t), respectively, which are given by: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       2 
                       
                         3 
                         ⁢ 
                         
                           a 
                           3 
                         
                         ⁢ 
                         
                           V 
                           L 
                           2 
                         
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           i 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
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       FIG. 11  shows a schematic flow chart of a method  11  for use of a five- or six-port circuit as described above. As shown in step  12 , the method comprises inputting an LO signal to one of the input ports, “Input  1 ”, of the five- or six-port circuit, and inputting, step  13 , an RF signal to the other input port. As shown in step  14 , the LO frequency is chosen to be half of RF frequency. 
     In some embodiments, as shown step  15 , the RF signal is used as input signal to the hollow waveguide  105 , and the LO signal is used as input signal to the open waveguide  135 . 
     In other embodiments, as shown in step  16 , the LO signal is used as input signal to the hollow waveguide  105 , and the RF signal is used as input signal to the open waveguide  135 . 
     In conclusion, some unique features of the proposed five- and six-port port circuit are as follows:
         A hollow waveguide based five-port circuit for a receiver is obtained, where the hollow waveguide is a part of the circuit.   The RF signal is coupled out by probes, instead of by means of a waveguide-to-microstrip transition.   The hollow waveguide can be mounted on top of a substrate such as a microwave motherboard, while the open waveguide which transmits an input signal, as well as the low-pass filters which can be designed in microstrip technology are arranged either on the other side or on the same side of the substrate as the hollow waveguide.   The power detectors are arranged on the same side of the substrate as the open waveguide   The low pass filters are arranged on the same side of the substrate as the open waveguide.       

     Embodiments of the invention are described with reference to the drawings, such as block diagrams. 
     In the drawings and specification, there have been disclosed exemplary embodiments of the invention. However, many variations and modifications can be made to these embodiments without substantially departing from the principles of the present invention. Accordingly, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation. 
     The invention is not limited to the examples of embodiments described above and shown in the drawings, but may be freely varied within the scope of the appended claims.