Network Synthesis Using Tchebycheff Polynomial Series
01 July 1952
Network synthesis is the opposite of network analysis--namely, the design of a network to have assigned characteristics, as opposed to the evaluation of the characteristics of an assigned network. In general, there are specifications on the internal constitution of the network, as well as requirements relating to its external performance. A common form of the general problem is the design of a finite network of linear lumped elements, to produce an assigned gain or phase characteristic over a prescribed interval of useful frequencies. The present paper relates to this particular form. In general, the restrictions on the network are such that the assigned performance cannot be matched exactly. This gives rise to an approximation or interpolation problem. For present purposes, the problem is: to choose a function of frequency which matches the assigned gain or phase to a satisfactory accuracy, from that special class of functions which can be realized exactly with physical finite networks of linear lumped elements. The function of frequency may be defined in terms of network singularities (natural modes and infinite loss points). The t P r e s e n t e d o r a l l y , in b r i e f e r f o r m , at t h e 1951 W e s t e r n C o n v e n t i o n of t h e I n s t i t u t e of R a d i o E n g i n e e r s , a n d at t h e S y m p o s i u m on Modern Network Synthesis s p o n s o r e d by (lie P o l y t e c h n i c I n s t i t u t e of B r o o k l y n a n d T h e Ollice of N a v a l R e s e a r c h , N e w Y o r k C i t y , April, 1952.