## 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 language | English |
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Journal | IEEE Transactions on Circuits and Systems |

Volume | 20 |

Issue number | 3 |

Pages (from-to) | 327-328 |

ISSN | 0098-4094 |

Publication status | Published - 1973 |