NDLI: The Driving-Point Immittances of Infinite Cascades of Nonlinear Resistive Two Ports

Content Provider	IEEE Xplore Digital Library
Author	Zemanian, A.
Copyright Year	1974
Description	Infinite cascades of nonlinear resistive two ports can have characteristic immittances in the uniform-cascade case and driving-point immittances in the nonuniform-cascade case at each of their ports. By definition any such immittance is a curve specifying the voltage-current pairs at a given port corresponding to a polarity convention for power flowing to the right (or left) under the condition that the power injected into the cascade from infinity at the right (respectively, left) is zero. Our result is shown by imposing certain monotonicity, continuity, Lipschitz, and boundedness conditions on the lattice parameters of the two ports. They ensure that the equivalent lattice networks of the two ports do not balance as wheatstone bridges. In this case, the forms of the their trajectories of consecutive port voltage-current pairs can be quite completely described. However, when balancing does occur, those trajectories can behave in peculiar ways. For example, an infinite uniform cascade can be totally unenergized in a section extending infinitely to the left and totally energized in its other part. Also, trajectories can intersect; in fact, an infinity of different trajectories can meet at a nonequilibrium point. Furthermore, there can be certain portions of the voltage-current plane that cannot be penetrated by any trajectory.
Starting Page	960
Ending Page	968
Page Count	9
File Size	1104942
File Format	PDF
ISSN	00984094
Volume Number	31
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1984-11-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Voltage Lattices H infinity control Bridge circuits Terminology
Content Type	Text
Resource Type	Article
Subject	Engineering

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