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Application of Topological Formulas to Distributed Parameter Networks

  • Suhash Chandra Dutta RoyEmail author
Chapter

Abstract

Topological formulas for lumped electrical networks are extended to distributed parameter networks, and explicit expressions are obtained for the two-port parameters of a non-uniform transmission line. The results agree with those derived earlier by Protonotarios and Wing, following a different procedure.

Keywords

Topological formulas Distributed network Non-uniform transmission line 

Nomenclature

\(T_{{2_{{i_{1} i_{2} \ldots j_{1} j_{2} }} }}\)

a two-tree in which the sets of vertices {i1, i2, …} and {j1, j2, …} are in different connected parts.

\(U_{{i_{1} i_{2} \ldots ,j_{1} j_{2} \ldots ,k_{1} k_{2} \ldots }}\)

sum of admittance products of three-trees in each of which the sets of vertices {j1, j2, …}, {j1, j2, …} and {k1, k2, …} are in different connected parts.

V(Y)

sum of admittance products of trees.

\(W_{{i_{1} i_{2} \ldots j_{1} j_{2} \ldots }} (Y)\)

sum of admittance products of two-trees \(T_{{2_{{i_{1} i_{1}\ldots ,j_{1} j_{2} \ldots }} }} .\)

[z]

matrix of open-circuit impedance parameters of a two-port network.

References

  1. 1.
    S. Seshu, M.B. Reed, Linear Graphs and Electrical Networks (Addison-Wesley)Google Scholar
  2. 2.
    M.T. Jong, G.W. Zobrist, IEEE Trans. CT-15 251 (1968)Google Scholar
  3. 3.
    A. Prabhakar, Generalized topological formulas for linear network functions. Ph.D. thesis, Indian Institute of Science, Bangalore, 1967Google Scholar
  4. 4.
    E.N. Protonotarios, O. Wing, IEEE Int. Conv. Rec. Part 7 1 (1965)Google Scholar
  5. 5.
    F. Walker, Proc. IEEE 52, 860 (1964)CrossRefGoogle Scholar
  6. 6.
    S.C. Dutta Roy, Proc. IEEE 52, 738 (1964)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology DelhiNew DelhiIndia

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