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POYNTING's THEOREM                                                      151

                                               18
            structures as close to each other as possible . Then the only difference between the incident,
            reflected, and aperture field vectors are their intensities (amplitude and phase). If so, we can
            omit the vector symbols and write

                                              =    
                                          
                                                  �    (3.83)
                                             =   
                                               
            Here   and   are called the electric and magnetic reflection coefficient, respectively. Since
                 
                       
            the incident and reflected  waves  move  in opposite  directions,  their Poynting’s  vectors are
            adverse as it is illustrated in Figure 3.4.1b and 3.4.1c. According to the last expression in (3.49),
            such change in Poynting’s vector occurs if, for example, the tangential component of reflected
            magnetic vector reverses as shown in Figure 3.4.1c while the tangential component of electric
            vector keeps its direction or vice versa. If so, one of reflection coefficients in (3.83) must be
            negative.  Which  is  one?  The traditional  concession  is to change the sign  of  the magnetic
            reflection coefficient as  = − . Why is it  not the electric coefficient? The electric field
                                   
            and  , respectively, are easier measurable as compared to the magnetic field. Finally, putting
                
            (3.83) into (3.82) we obtain

                                           =    (1 +  )
                                        
                                                  �       (3.84)
                                          =    (1 −  )
                                             
            It follows from (3.84) that the volume

                                      
                                           1+ 
                                    
                                = � � = �  �     [(V/m)/(A/m) = V/A = Ω]                  (3.85)
                                            1− 
                                      
            as measured in Ohms and can be interpreted as the input impedance of the cavity shown in
            Figure 3.4.1a. Then the ratio in the parenthesis in the right-hand side of (3.85) is customarily
            called the wave or characteristic impedance
                                                   
                                                                     (3.86)
                                               =
                                                
                                                   
            Representing the reflection coefficient in phasor form we have

                                                      1+ 
                                         =  +  =  
                                                      1− �                  (3.87)
                                             = | |  
                                                 
                                            
            Separating the real and imaginary part in (3.87), we have
                                                 1−|  | 2
                                        = 
                                            
                                             1+|  | 2 −2|  |cos �         (3.88)
                                                 2|  |sin
                                         = 
                                            
                                              1+|  | 2 −2|  |cos
            18  It is customary to call such regime as “dominant or single mode”.
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