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New general approach to commensurate tem transmission line networks using state space techniques
Author(s) -
Kittel Ludwig
Publication year - 1973
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.4490010404
Subject(s) - emphasis (telecommunications) , frequency domain , transmission line , computer science , line (geometry) , state space , transmission (telecommunications) , state (computer science) , matrix (chemical analysis) , domain (mathematical analysis) , fourier transform , network element , algorithm , state variable , topology (electrical circuits) , mathematics , telecommunications , mathematical analysis , physics , statistics , materials science , geometry , combinatorics , composite material , thermodynamics
The paper begins with an investigation of the scattering properties of commensurate TEM transmission line networks, and emphasis is placed upon the distinction between normal networks and general (including non‐normal) networks. It is then shown that the state space concept of linear discrete systems is applicable to these networks. This provides a general and powerful systemtheoretical method for determining the network behaviour in the time and frequency domains. The waves on the transmission line elements are chosen as state variables; and for the important technical case of normal networks it is shown that each transmission line element contributes one state variable only. The entries in the state space matrices are formed by the scattering parameters of the connections and endings of the line elements; and the general method of obtaining these matrices is explained by detailed examples. An automatic network analysis program based on the state space approach needs only matrix multiplications. The program works primarily in the time domain, and the frequency behaviour is then computed by Fast Fourier Transform. The advantages of the program are demonstrated by a typical example. Finally an application to digital filters imitating TEM transmission line networks is presented.