# A reactance theorem

@article{FosterART, title={A reactance theorem}, author={Ronald M. Foster}, journal={Bell System Technical Journal}, volume={3}, pages={259-267} }

The theorem gives the most general form of the driving-point impedance of any network composed of a finite number of self-inductances, mutual inductances, and capacities. This impedance is a pure reactance with a number of resonant and anti-resonant frequencies which alternate with each other. Any such impedance may be physically realized (provided resistances can be made negligibly small) by a network consisting of a number of simple resonant circuits (inductance and capacity in series) in…

## 304 Citations

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- Mathematics
- 1952

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- MathematicsProceedings of the IRE
- 1944

The conventional extension of Foster's reactance theorem to electric circuits with an infinite number of degrees of freedom (sections of transmission lines and cavity resonators) leads to series…

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A method is presented for finding the zeros of the impedance or admittance function of a Foster reactance network. More generally, the method is one of finding the zeros of a rational function having…

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- 1945

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- Geology
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Elementary methods, avoiding the manipulation of determinants, are used to prove theorems, not previously enunciated, on the voltage and current gains obtainable from a resistance network, and to…

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- Engineering, MathematicsProceedings of the IRE
- 1943

Foster's reactance theorem for the driving-point impedance of a two-terminal electric network is extended to more general cases comprising mechanical and acoustical as well as electrical systems. The…

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- 2014

A (one-port) RLC circuit is an interconnection of resistors and reactive elements (inductors and capacitors) with a pair of driving-point terminals. The circuit may be characterised by its impedance,…