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The example used for the Cauer I form and the Foster forms when expanded as a Cauer II form results in some elements having negative values. [64] This particular PRF, therefore, cannot be realised in passive components as a Cauer II form without the inclusion of transformers or mutual inductances .
Foster's work was an important starting point for the development of network synthesis. It is possible to construct non-Foster networks using active components such as amplifiers. These can generate an impedance equivalent to a negative inductance or capacitance. The negative impedance converter is an example of such a circuit.
Wilhelm Cauer found a transformation that could generate all possible equivalents of a given rational, [note 9] passive, linear one-port, [note 8] or in other words, any given two-terminal impedance. Transformations of 4-terminal, especially 2-port, networks are also commonly found and transformations of yet more complex networks are possible.
However, it was with Ronald M. Foster that Cauer had much correspondence and it was his work that Cauer recognised as being of such importance. His paper, A reactance theorem, [9] is a milestone in filter theory and inspired Cauer to generalise this approach into what has now become the field of network synthesis. [5]
Examples of canonical forms are the realisation of a driving-point impedance by Cauer's canonical ladder network or Foster's canonical form or Brune's realisation of an immittance from his positive-real functions. Topological methods, on the other hand, do not start from a given canonical form.
The impact of this transformation goes beyond Joy’s personal development. The video has struck a chord with audiences, with comments pouring in expressing gratitude for the fosters’ dedication ...
Wilhelm Cauer expanded on the work of Foster (1926) [47] and was the first to talk of realisation of a one-port impedance with a prescribed frequency function. Foster's work considered only reactances (i.e., only LC-kind circuits). Cauer generalised this to any 2-element kind one-port network, finding there was an isomorphism between them.
Campbell published in 1922 but had clearly been using the topology for some time before this. Cauer first picked up on ladders (published 1926) inspired by the work of Foster (1924). There are two forms of basic ladder topologies: unbalanced and balanced. Cauer topology is usually thought of as an unbalanced ladder topology.