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Foster's reactance theorem is an important theorem in the fields of electrical network analysis and synthesis. The theorem states that the reactance of a passive, lossless two-terminal (one-port) network always strictly monotonically increases with frequency. It is easily seen that the reactances of inductor The theorem can be extended to admittances and the encompassing concept of immittances. A consequence of Foster's theorem is that poles and zeroes of the reactance must alternate with frequency. Foster used this property to develop two canonical forms for realising these networks. 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. ==Explanation== Reactance is the imaginary part of the complex electrical impedance. Both capacitors and inductors possess reactance (but of opposite sign) and are frequency dependent. The specification that the network must be passive and lossless implies that there are no resistors (lossless), or amplifiers or energy sources (passive) in the network. The network consequently must consist entirely of inductors and capacitors and the impedance will be purely an imaginary number with zero real part. 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. This result may seem counterintuitive since admittance is the reciprocal of impedance, but is easily proved. If the impedance is : where is reactance and is the imaginary unit, then the admittance is given by : where is susceptance. If ''X'' is monotonically increasing with frequency then 1/''X'' must be monotonically decreasing. −1/''X'' must consequently be monotonically increasing and hence it is proved that ''B'' is increasing also. It is often the case in network theory that a principle or procedure applies equally well to impedance or admittance—reflecting the principle of duality for electric networks. It is convenient in these circumstances to use the concept of immittance, which can mean either impedance or admittance. The mathematics is carried out without specifying units until it is desired to calculate a specific example. Foster's theorem can thus be stated in a more general form as, :;Foster's theorem (immittance form) :''The imaginary immittance of a passive, lossless one-port strictly monotonically increases with frequency.'' Foster's theorem is quite general. In particular, it applies to distributed element networks, although Foster formulated it in terms of discrete inductors and capacitors. It is therefore applicable at microwave frequencies just as much as it is at lower frequencies.〔Aberle and Loepsinger-Romak, pp.8-9.〕〔Radmanesh, p.459.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Foster's reactance theorem」の詳細全文を読む スポンサード リンク
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