Complexity analysis of general realization procedures for passive networks

This paper is concerned with the complexity of general realization procedures for passive network synthesis. The concept of the complexity of a realization procedure is first defined. As a consequence, the expressions of the complexity of Bott-Duffin procedure, that of modified Bott-Duffin procedure, and that of Miyata procedure (n + 1 ladder breakdown) are derived. In addition, we obtain an upper bound of the complexity of modified Miyata procedure (tree breakdown), which is shown to be less than the complexities of the previous three procedures, and has a well approximation at low degrees. Furthermore, two kinds of procedures that combine modified Miyata procedure and modified Bott-Duffin procedure are investigated in terms of their complexities. The comparison between the complexities of these two procedures is made, and sufficient conditions for them to be less complex than the modified Bott-Duffin procedure are presented. Besides, some results of this paper are illustrated by a table and several figures.