Matrices for dual representation of four-terminal non-uniform transmission lines

The matrix characterization of general fourterminal non-uniform transmission lines is derived by current and voltage gradient considerations and appropriate application of boundary conditions. The parameters allow ready simplification to any particular component cascade for any class of non-uniformities with solutions expressible in separable variables. By invoking the Principle of Duality, the corresponding immittance and transmission matrices of the dual structures can be simply written by inspection. Previous solutions are treated as special cases arid, in particular, a useful property of three-terminal autonomic lines is deduced.