The angle property of positive real functions simply derived

Helge Jørsboe

    Research output: Contribution to journalLetterpeer-review

    457 Downloads (Pure)


    The angle property of positive real (rational) functionsZ(s), namely, that|arg s | geqq |arg Z(s)|in the right half of thes-plane, can be demonstrated very simply by an examination of the imaginary parts of the functionsln(s/Z(s))andln (sZ(s)), i.e.,arg s mp arg Z(s). In particular, on a contour enclosing the entire first quadrant,arg s mp arg Z(s)can rather easily be shown to be nonnegative. The extremum theorem of analytic functions then assures thatarg s mp arg Z(s)cannot be negative inside the first quadrant; thus the angle property is demonstrated in the first quadrant. The same result is obtained immediately in the fourth quadrant.
    Original languageEnglish
    JournalIEEE Transactions on Circuits and Systems
    Issue number3
    Pages (from-to)327-328
    Publication statusPublished - 1973

    Bibliographical note

    Copyright: 1973 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE


    Dive into the research topics of 'The angle property of positive real functions simply derived'. Together they form a unique fingerprint.

    Cite this