A Mathematical Theory of Directional Couplers

Directional couplers are becoming an increasingly important component in microwave radio-frequency circuits. By the suitable generalization of concepts used in discussing the lumped loading of a single transmission line, it is possible to discuss the interaction of the coupling elements of these more complicated circuits in a reasonably complete and elementary manner. Input impedances are analyzed in terms of equivalent tee and pi sections. The transformation of line impedances is shown to commute with similarity transformations, so that the circuit problem is equivalent to one involving independent but properly loaded transmission lines. The behavior of many aperture-coupled directional couplers may be analyzed by the use of a single conventional impedance diagram. A small-hole theory is given which predicts previously unexplained results.