Coupled Wave Theory and Waveguide 

 Applications 



By S. E. MILLER 



(Manuscript received February 2, 1954) 



Some theory describing the behavior of two coupled waves is presented, 

 and it is shown that this theory applies to coupled transmission lines. A 

 loose-coupling theory, applicable when very lilile power is transferred be- 

 tween the coupled waves, shows how to taper the coupling distribution to 

 minimize the length of the coupling region. A tight-coupling theory, appli- 

 cable when the coupling is uniform along the direction of wave propagation, 

 shows that a periodic exchange of energy between coupled waves takes place 

 provided that the attenuation and phase constants (a and /3 respectively) 

 are both equal, or provided that the phase constants are equal and the dif- 

 ference between the attenuation constants (on — 0:2) is small compared to the 

 coefficient of coupling c. Either {a-i — a^j/c or (^i — /32)/c being large 

 compared to unity is sufficient to prevent appreciable energy exchange be- 

 tween the coupled waves. Experimental work has confirmed the theory. Appli- 

 cations include highly efficient pure-mode transducers in multi-mode sys- 

 tems, and frequency-selective filters. 



INTRODUCTION 



This paper describes some theoretical relations in coupled transmission 

 lines, and the use of coupled lines as circuit elements. In order to illus- 

 trate the points of interest in the theoretical material, several applica- 

 tions will be stated first. Detailed discussion of experimental models 

 will be given after the theoretical sections. 



The theory of coupled transmission lines may be used to determine 

 many properties of a multi-mode transmission system in which there is 

 distributed coupling between modes. In round pipe, for example, the 

 individual modes of propagation can be considered as separate trans- 

 mission lines which in the perfect waveguide are completely independent. 

 Geometric imperfections in the waveguide, if distributed ()\'er many 

 wavelengths, cause a transfer of power between modes which in general 



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