Driving-point-function synthesis using nonuniform lines

Necessary and sufficient conditions for the synthesis of a driving-point function using any two kinds of one-port impedances are presented, and the result is used to develop a procedure for synthetising a driving-point function using tapered lines. The result also provides a short proof for O´Shea´s necessary and sufficient conditions for the realisation of a driving-point function using symmetric structures. It is shown that any impedance which can be realised using symmetric lines may always be realised using the one-port impedances of the nonuniform transmission lines used in the construction of the symmetric lines. It is shown that all the existing synthesis procedures for the realisation of a driving-point function using any two one-port impedances are special cases of the general procedure advanced in this paper. Necessary and sufficient conditions for realising a driving-point function as a cascade of symmetric structures have been advanced. These are shown to be equivalent to those for realising the same driving-point function using the open- and short-circuit impedances of a symmetric structure. A procedure for such a cascade synthesis is advanced. If the structure is a uniform line, it provides a simple alternative to Wyndrum´s cascade-synthesis procedure. An illustrative example is also included. By using known transformations, all the results may be applied to other types of lines such as lossless lines.