The angle property of positive real functions simply derived

Helge Jørsboe

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Abstract

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
Volume20
Issue number3
Pages (from-to)327-328
ISSN0098-4094
Publication statusPublished - 1973

Bibliographical note

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