Coupled Wave Theory and Waveguide Applications

This paper describes some theoretical relations in coupled transmission lines, and the use of coupled lines as circuit elements. In order to illustrate the points of interest in the theoretical material, several applications 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 transmission lines which in the perfect waveguide are completely independent. Geometric imperfections in the waveguide, if distributed over many wavelengths, cause a transfer of power between modes which in general 661 668 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 195-4 form is predicted by coupled transmission line theory. As a consequence, analysis of the mode-conversion effects associated with circular-electricwave transmission in commercial round pipe has been aided materially by applying the coupled-transmission-line concept.1 In another problem, the transmission of the circular-electric waves through bends,2 the coupled-wave theory of subsequent sections has also provided valuable insight. Coupled transmission lines can be employed as circuit elements to exchange power between one mode of a multi-mode line and a designated mode of another transmission line. Consider Fig. 1, which shows a rectangular waveguide having entries 1 and 2 coupled through a series of apertures to a parallel round waveguide having entries 3 and 4.