Application of Topological Formulas to Distributed Parameter Networks

  • Suhash Chandra Dutta RoyEmail author


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.


Topological formulas Distributed network Non-uniform transmission line 


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

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.


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


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


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology DelhiNew DelhiIndia

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