General microwave circuit theorems

A waveguide junction in the generalized sense that is to be used here is defined as a region of space completely enclosed by a perfectly conducting metal surface except for one or more transmission lines that perforate the surface. Nothing will be assumed about the interior of the junction except that the dielectric constant, permeability, and conductivity are everywhere within it independent of time and of the field quantities. It will be assumed for the present that there is only one propagating mode for each of the transmission lines. This definition will be extended later to include cases in which several modes are present. It has been pointed out that a complete solution of an electromagnetic problem is not always desired. Often a description of conditions at the terminals of a junction is sufficient. It is a purpose of the remainder of the chapter to make use of Maxwell's equations to obtain conditions that hold at the terminals of a general waveguide junction. In so doing, it will be found that the stored electric and magnetic energy and the dissipated power are the three most important field parameters for the description of conditions at the terminals of a junction.