page_title: Foster's reactance theorem
section_title: Examples
hierarchical_section_title: Foster's reactance theorem / Examples
context_page_description: 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 network always strictly monotonically increases with frequency. It is easily seen that the reactances of inductors and capacitors individually increase with frequency and from that basis a proof for passive lossless networks generally can be constructed. The proof of the theorem was presented by Ronald Martin Foster in 1924, although the principle had been published earlier by Foster's colleagues at American Telephone & Telegraph.
  The theorem can be extended to admittances and the encompassing concept of immittances. A consequence of Foster's theorem is that zeros and poles 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.
context_section_description: The following examples illustrate this theorem in a number of simple circuits.
caption: Plot of the reactance of a capacitor against frequency