Question

Explain how does Foster's Reactance Theorem relate to electrical circuits. Use diagrams and graphs for the explanation.

Answer 1

Foster's reactance theorem is import ant theorem the fields of electrical network. analysis & synthesis. The theorem states that the reactance of a passive, lossless two terminal Cone-port) network always strictly monotonically increases with the frequency. It easily seen that the reactances inducto es Individually increase frequency & from basis for proot lossless networks generally can be construc -ted. The of proof the theorem woy presented by Ronald martin foster in 1924 & Capacitors with the passive The theorem can be extended to admitt -ances E the encompassing concept of immitt consequence of foster's theorem -ances. А is that Zerous & poles OF the reactonce must this to develop forms alternate with frequences foster cused propesty to two canonical for realising these networks, an important Starting for the development of network synthesis, work was Foster's point

95 Tt possible to construct 'non-Foster networks asing dative components such as amplifiegs. These con generate an impedende equivalent negative inductance capacitance. The negative impedance Converter ebrample not circulito such to a OO Vous of plot of the reactance an inductor against frequency. X the Prebe reactance Lib 09). plots or of capacitoy S3 against frequency, os

(2) hostag) > pe Nonnes bifon w > اور اراد (۱( ۱۱ / ۲۱/د hu reno, al Plot of the reactance of · 102 a series lo circuit Argo plot of the reactance of paralien Le circwit against frequency against frequency. Strut ohd Plot Of the react ance ot foster's figst form ot Canonical driving point of alternating showing the pottern artic resonators are impedance poles & zeroes. Three required to realise this impedance function.

А as consequence of foster's theorem that the žeros & poles of any passive immittance function must alternate frequency increases. After possing through pole the function will be negative & obliged to pass through before the reaching if it next pole monotonically increasing is Zero be lo is

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