You will need only basic matrix operations to construct the Cauer-type RC ladder equivalent to the Foster-type RC chain. The algorithm is often being embedded. networks. Cauer synthesis procedure “Passive and active network analysis and synthesis”, Houghton Mifflin,. .. Foster synthesis. are the first and second Foster forms and the first and second Cauer forms. These .. One ladder network due to Cauer is obtained by a repeated removal.

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At low frequencies the reactance is dominated by the capacitor and so is large and negative. For example, the usual passive Foster impedance matching networks netwrok only match the impedance of an antenna with a transmission line at discrete frequencies, which limits the bandwidth of the antenna.

Foster’s reactance theorem

The network consequently must consist entirely of inductors and capacitors and the impedance will be purely an imaginary number with zero real part. These are called non-Foster networks. A parallel LC circuit is the dual of the series circuit and hence its admittance function is the same form as the impedance netwrok of the series circuit.

Requires Control System Toolbox. Foster used this property to develop two canonical forms for realising these networks. It is therefore applicable at microwave frequencies just as much as it is at lower frequencies.

Foster and Cauer equivalent networks – File Exchange – MATLAB Central

You are now following this Submission You will see updates in your activity feed You may receive emails, depending on your notification preferences. The algorithm is often being embedded into thermal modelling tools; therefore, usually you don’t have to perform this transformation externally. Foster’s theorem applies equally to the admittance of a network, that is the susceptance imaginary part of admittance of a passive, lossless one-port monotonically increases with frequency.


In his paper, Foster describes how such a lossless rational function may be realised if it can be realised in two ways. My submission is then purely for educational purposes.

If the impedance is. The impedance function of the capacitor is identical to the admittance function of the inductor and vice csuer. Plot of the reactance of an inductor against frequency.

Foster’s theorem can thus be stated coster a more general form as. The theorem can be extended to admittances and the encompassing concept of immittances. The specification that the network must be passive and lossless implies that there are no resistors losslessor amplifiers or energy sources passive in the network.

Retrieved from ” https: Both capacitors and inductors possess reactance but of opposite sign and are frequency dependent. For example, it is possible to create negative capacitance and inductance with negative impedance converter circuits.

A consequence of Foster’s theorem is that zeros and poles of the reactance must alternate with frequency. A one-port passive immittance consisting of discrete elements that netwoork, not a distributed element circuit can be represented as a rational function of s. Both of these were important problems in network theory and filter design.

It is possible to construct non-Foster networks using active components such as amplifiers. From Wikipedia, the free encyclopedia. You will need only basic matrix operations to construct the Cauer-type RC ladder equivalent to the Foster-type RC chain.


Cauer was interested in finding the necessary and sufficient condition for realisability of a rational one-port network from its polynomial function, a condition now known to be a positive-real functionand the reverse problem of which networks were equivalent, that is, had the same polynomial function.

This page was last edited on 19 Octoberat Foster and Cauer equivalent networks version 1. This follows from the fact the impedance of L and C elements are themselves simple rational functions and any algebraic combination of rational functions results in another rational function. It is a general result that the dual of any immittance function that obeys Foster’s theorem will fosrer follow Foster’s theorem.

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Cauer in Germany grasped the importance of Foster’s work and roster it as the foundation of network synthesis. You will also need Control System Toolbox xor Symbolic Math Toolbox to perform some initial transfer function manipulations. At low frequencies the reactance is dominated by the inductor and is small and positive. Two Foster networks that have identical poles and zeroes will be equivalent circuits in the sense that their immittance functions will be identical.

This monotonically increases towards a pole at the anti-resonant frequency where the susceptance of the inductor and capacitor are equal and opposite and fostsr. Select the China site in Chinese or English for best site performance.