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Sum rules and constraints on passive systems

Publiceringsår: 2011
Språk: Engelska
Publikation/Tidskrift/Serie: Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00
Volym: 44
Nummer: 14
Dokumenttyp: Artikel i tidskrift
Förlag: IOP Publishing


A passive system is one that cannot produce energy, a property that

naturally poses constraints on the system. A system in 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.


  • Electrical Engineering, Electronic Engineering, Information Engineering


  • EIT_HSWC:Antenna MIMO antennas and channels
  • Electromagnetic theory-lup-obsolete
  • ISSN: 1751-8113

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