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Exact analysis of inhomogeneous ladder networks having a tridiagonal interaction matrix
Author(s) -
Haley Stephen B.
Publication year - 1981
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490090104
Subject(s) - tridiagonal matrix , diagrammatic reasoning , representation (politics) , factorization , mathematics , matrix (chemical analysis) , chain (unit) , node (physics) , projection (relational algebra) , topology (electrical circuits) , matrix representation , algebra over a field , algorithm , pure mathematics , computer science , physics , combinatorics , group (periodic table) , quantum mechanics , eigenvalues and eigenvectors , materials science , politics , political science , law , composite material , programming language
A projection‐recurrence method is applied to active and passive ladder networks with a tridiagonal interaction matrix to obtain a factorization of the response functions. The factors are partial chain parameters, determined by third order recurrences. For a ladder with N nodes, the number of arithmetic operations to calculate response functions ranges from 4 N to 6 N . A diagrammatic representation is developed for passive ladders which makes it possible to obtain the partial chain parameters by inspection, and a compact formula for the node‐voltage response is presented for active doubly‐terminated ladders.