Non-linear op-amp circuits: Existence and uniqueness of solution by inspection

Authors

  • Tetsuo Nishi,

    1. Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, Berkeley, California 94720, U.S.A.
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  • Leon O. Chua

    1. Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, Berkeley, California 94720, U.S.A.
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Abstract

Even simple circuits containing only one op amp and linear resistors can have multiple d.c. operating points. Using a realistic non-linear d.c. op-amp model which includes the saturation characteristics, this paper gives the necessary and sufficient conditions for an arbitrary op-amp circuit (containing op amps, linear resistors, strictly-increasing non-linear resistors and independent sources) to have a unique solution for all values of circuit parameters. These conditions are remarkable because they are couched strictly in topological terms. For many op-amp circuits (e.g. those containing only one op amp), the necessary and sufficient conditions can be checked by inspection.

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