Dominant Pole Synthesis of Transmission Line Networks

This paper describes a procedure for synthesizing transmission networks which are interconnections of uniform line elements. An iterative, digital computer algorithm is developed which achieves a dominant pole synthesis. The line lengths and the characteristic impedances are controlled individually, which gives design flexibility not found in synthesis procedures based on Richards' transformation. Thus, the characteristic impedances may be restricted by upper and lower bounds when there is no restriction on the line lengths. The procedure is detailed for a TEM mode structure of alternating open stubs and connecting lines. The method uses a Newton-Raphson iterative scheme to adjust the characteristic impedances and lengths of the transmission lines for a prescribed set of dominant transmission poles. By controlling the stub line lengths and the dominant pole positions, the principal transmission zeros and bounded characteristic impedances can be achieved simultaneously.