Minimal Realizations of the Biquadratic Minimum Function
- 1 December 1959
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 6 (4), 345-350
- https://doi.org/10.1109/tct.1959.1086572
Abstract
The purpose of this paper is to obtain rigorously minimal realizations of the biquadratic minimum positive real function without the use of transformers. For this purpose a few theorems are proved about the structure of the network realizing a minimum pr function. This is followed by an exhaustive search of networks in increasing order of number of elements. It is proved that the modified Bott-Duffin (or the Reza-Pantell-Fialkow-Gerst) realization using seven elements is rigorously minimal in number of elements, except for the special casesZ(0) = 4 Z(\infty)andZ(\infty) = 4 Z(0). These two special cases have five element realizations.Keywords
This publication has 8 references indexed in Scilit:
- Author's Reply to comments on 'The Degrees of Freedom in RLC Networks'IRE Transactions on Circuit Theory, 1960
- General Topological Formulas for Linear Network FunctionsIRE Transactions on Circuit Theory, 1958
- On the Solution of the Equations Obtained from the Investigation of the Linear Distribution of Galvanic CurrentsIRE Transactions on Circuit Theory, 1958
- Reliable circuits using less reliable relaysJournal of the Franklin Institute, 1956
- A supplement to the Brune synthesisTransactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, 1955
- Impedance synthesis without mutual couplingQuarterly of Applied Mathematics, 1955
- Impedance Synthesis without Use of TransformersJournal of Applied Physics, 1949
- Synthesis of Reactance 4‐Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter DesignJournal of Mathematics and Physics, 1939