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Sum rules and constraints on passive systems

Författare:
Publiceringsår: 2010
Språk: Engelska
Sidor: 31
Publikation/Tidskrift/Serie: Technical Report LUTEDX/(TEAT-7193)/1-31/(2010)
Dokumenttyp: Rapport
Ytterligare information: Published version: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 14, pp. 145205, 2011.

Sammanfattning

A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic functions mapping the open upper half plane to the closed upper half plane, is closely related to the transfer functions of passive systems. Following a well-known representation theorem, Herglotz functions can be represented by means of positive measures on the real line. This fact is exploited in this paper in order to rigorously prove a set of integral identities for Herglotz functions that relate weighted integrals of the function to its asymptotic expansions at the origin and infinity.

The integral identities are the core of a general approach introduced here to derive sum rules and physical limitations on various passive physical systems. Although similar approaches have previously been applied to a wide range of specific applications, this paper is the first to deliver a general procedure together with the necessary proofs. This procedure is described thoroughly, and exemplified with examples from electromagnetic theory.

Disputation

Nyckelord

  • Technology and Engineering

Övriga

  • Swedish Foundation for Strategic Research (SSF)
Published
  • EIT_HSWC:Antenna MIMO antennas and channels
TEAT-7193
  • Electromagnetic theory

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