Topics in Signal Processing pp 39-44 | Cite as

# Application of Topological Formulas to Distributed Parameter Networks

## 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 {

*i*_{1},*i*_{2}, …} and {*j*_{1},*j*_{2}, …} 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 {

*j*_{1},*j*_{2}, …}, {*j*_{1},*j*_{2}, …} and {*k*_{1},*k*_{2}, …} 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

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