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.
Source: A.Prabhakar & S.C. Dutta Roy, “Application of Topological Formulas to Distributed Parameter Networks,” JITE, vol 18, pp 197–199, May 1972.
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Abbreviations
- \(T_{{2_{{i_{1} i_{2} \ldots j_{1} j_{2} }} }}\) :
-
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
S. Seshu, M.B. Reed, Linear Graphs and Electrical Networks (Addison-Wesley)
M.T. Jong, G.W. Zobrist, IEEE Trans. CT-15 251 (1968)
A. Prabhakar, Generalized topological formulas for linear network functions. Ph.D. thesis, Indian Institute of Science, Bangalore, 1967
E.N. Protonotarios, O. Wing, IEEE Int. Conv. Rec. Part 7 1 (1965)
F. Walker, Proc. IEEE 52, 860 (1964)
S.C. Dutta Roy, Proc. IEEE 52, 738 (1964)
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Dutta Roy, S. (2020). Application of Topological Formulas to Distributed Parameter Networks. In: Topics in Signal Processing. Springer, Singapore. https://doi.org/10.1007/978-981-13-9532-1_5
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DOI: https://doi.org/10.1007/978-981-13-9532-1_5
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