6.1 Introduction

When two (or more) unshielded transmission lines are located in close proximity to one another, they become electromagnetically coupled via their associated electric and magnetic fields; particularly if the line axes are parallel. In many situations, such coupling is highly undesirable since it gives rise to "cross-talk," background noise, distortion, loss of energy, and other detrimental effects. These can usually be avoided, or at least reduced to an acceptable level, by the provision of shielding conductors: either separately, or as an integral part of the transmission line structure, e.g. the outer conductor of the coaxial line (Chapter 2) which, if sufficiently thick, provides a highly efficient electromagnetic screen.

However, the present text is rather more concerned with those cases in which coupling between adjacent lines is desired, as in the practical realization of microwave devices such as frequency filters (for the selection and/or suppression of specified bands of frequencies), directional couplers (for power-dividing or power-sampling applications), phase changers, group delay equalizers, etc.

In designing such devices, the desired degree of coupling is usually known or specified, and it is required to determine the line dimensions and spacing necessary to achieve this degree of coupling. This can be effected via a knowledge of the even-mode and odd-mode characteristic impedances, Z _0e and Z _0o, of a pair of coupled lines, which were defined in Section 1.5.2.

It has been shown, for instance ^{[1] , [2]}, that when two (matched) transmission lines are electromagnetically coupled by following...