Realization
A one-port passive immittance consisting of discrete elements (that is, not a distributed element circuit) is described as rational in that in can be represented as a rational function of s,
- where,
- is immittance
- are polynomials with real, positive coefficiencts
- is the Laplace operator, which can be replaced with when dealing with steady-state AC signals.
This is sometimes referred to as the driving point impedance because it is the impedance at the place in the network at which the external circuit is connected and "drives" it with a signal. Foster in his paper describes how such a lossless rational function may be realised in two ways. Foster's first form consists of a number of series connected parallel LC circuits. Foster's second form of driving point impedance consists of a number of parallel connected series LC circuits. The realisation of the driving point impedance is by no means unique. Foster's realisation has the advantage that the poles and/or zeroes are directly associated with a particular resonant circuit, but there are many other realisations. Perhaps the most well known is Cauer's ladder realisation from filter design.
Read more about this topic: Foster's Reactance Theorem
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