DocumentCode :
1177668
Title :
Graph-theoretic properties of dynamic nonlinear networks
Author :
Chua, Leon O. ; Green, Douglas N.
Volume :
23
Issue :
5
fYear :
1976
fDate :
5/1/1976 12:00:00 AM
Firstpage :
292
Lastpage :
312
Abstract :
Graph-theoretic concepts are used to deduce properties of nonlinear networks and properties of nonlinear resistive n -ports. The basic result is that if the ports of an n -port form no cutsets (resp., loops), then each port voltage (resp., port current) is a linear function of the internal element voltages (resp., currents) only; i.e., no other external port voltage (resp., port current) is involved. This result is very general in the sense that it is independent of the constitutive relations of the internal n -port elements. It is also a rather subtle result because it forms the basis of a large number of new network and n -port theorems. For example, in examining the closure properties of n -ports, this result is used to show, among other things, that if the ports of an n -port form neither loops nor cutsets, and if the internal resistors are strictly passive, or strictly increasing, then the n -port is also strictly passive, or strictly increasing. Moreover, many of these conclusions remain valid when the n -port contains independent voltage and current sources. The main result is extended to a network containing capacitors, inductors, resistors, and sources. Here, graph-theoretic conditions are given such that the voltage and current waveforms of the capacitors and inductors are functions of the resistor and source voltage and current waveforms. Dynamic nonlinear networks containing capacitors, inductors, resistors, and sources such that there are loops of capacitors, or cutsets of inductors are shown to be equivalent to networks without such loops or cutsets. Explicit analytical expressions are given for specifying the constitutive relations of the elements of the equivalent circuit. This result allows the generalization of many previous results in nonlinear networks which exclude capacitor loops and inductor cutsets.
Keywords :
Graph theory; Multiport networks; Nonlinear circuits and systems; Nonlinear networks; Capacitors; Circuit stability; Equivalent circuits; Graph theory; Inductors; Nonlinear equations; Resistors; Stability analysis; Steady-state; Voltage;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1976.1084220
Filename :
1084220
Link To Document :
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