Synthesis of Optimal Ladder Networks.
Rept. for Jun 73-May 77,
NAVAL ACADEMY ANNAPOLIS MD DIV OF ENGINEERING AND WEAPONS
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This project treats synthesis procedures for optimal ladder networks. The first part of the project deals with a chain-matrix decomposition technique for realizing two-port LC ladder networks. Two chain-matrix decomposition theorems are proved. These theorems state the necessary and sufficient conditions that must be satisfied by a 2x2 matrix S sub ns that is to be decomposed into a product of simple matrices, i.e., S sub ns K sub 1 K sub 2...K sub n. It is found that the zeroes of the adjacent elements of S sub ns alternate pairwise along the jomega axis in the s-plane. It is also found that if the matrix S sub ns is the overall chain matrix of an LC ladder network, then each of the simple matrices K sub is for i 1,2,...n represents a simple LC ladder section. These decomposition techniques are then applied to the design of filters. Of particular interest are Butterworth, Chebyshev, and Bessel filters with single and double terminations. These filters are designed by the decomposition of chain matrices whose elements are predetermined by the orthogonal polynomials that approximate the ideal filter characteristics.
- Theoretical Mathematics
- Operations Research