Tuned Circuits Containing Negative Resistance

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Abstract
A negative resistance connected to a ``suitable'' resonant circuit (a current-controlled negative resistance connected to a series-tuned circuit, or a voltage-controlled negative conductance connected to a parallel-tuned circuit) constitutes an almost-harmonic oscillator. In this paper the ``unsuitable'' connections (a current-controlled negative resistance connected to a parallel-tuned circuit, or a voltage-controlled negative conductance connected to a series-tuned circuit) are analyzed qualitatively in terms of variables leading to a single-valued phase plane. Physical considerations, expressed in a jump condition, serve to connect different regions of analyticity of the differential equations of the circuit in this plane. The ``unsuitable'' connections cannot sustain almost-harmonic oscillations, and their theoretically possible relaxation oscillations are unstable; they yield bistable circuits.

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