A general theory of decoupling a system of lossless coupled lines using linear transformations

This paper presents a general theory of decoupling a system of nonuniform lossless coupled lines with the aid of linear transformations. The lines have a common return and support only TEM waves. It is shown that the solution of the decoupling problem is equivalent to that of the simultaneous diagonalization of a set of real constant matrices through specially related pairs of congruent and similarity transformations. The solution of the equivalent problem yields the necessary and sufficient conditions for decoupling the system of coupled lines. A systematic procedure for decoupling is then presented. A special case is studied for which the decoupling problem becomes simpler. Finally, we have derived a set of equivalent but considerably simpler necessary and sufficient conditions for decoupling the frequently used system of a pair of lossless coupled lines.