Abstract :
A variational method is described for the analysis of electromagnetic-energy transfer through the common broad wall between two rectangular waveguides. The method is of general application, providing quantitative theoretical results for the coupling and directivity of a large variety of waveguide coupling mechanisms. The problem considered is that of two adjacent rectangular waveguides having an arbitrary nonzero tangential electric field in the plane of the infinitesimally thin common wall. In terms of this arbitrary electric field, variational expressions for the forward and backward coupling coefficients to the dominant wave in the auxiliary guide are deduced. It is subsequently shown that these expressions may be used to evaluate the coupling produced by any desired aperture distribution in the common wall between the guides, if a reasonable approximation to the functional form of the tangential electric field in the plane of the apertures can be made. Numerical results have been calculated for the simple problem of two waveguides coupled by means of a single transverse rectangular aperture of any length. Where possible, comparison is made with the results of other theories. Experimental results are also presented, and using these, the relative merits of the alternative theoretical treatments are discussed. With some reservations, waveguide coupling by means of a multiple array of slots and also by means of a long axial slot may be analysed using this variational method, and some consideration is given to the additional requirement of such an analysis.
