Self-sustained oscillation in an<tex>R_H</tex>- C or<tex>R_H</tex>- L circuit containing a hysteresis resistor<tex>R_H</tex>

Abstract

When the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i - v</tex> curve of a resistor exhibits hysteresis jumps along <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</tex> axis, this resistor can be connected to an energy storage element <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> to form a relaxation oscillator. The criteria of oscillation are derived from a point of view somewhat different from those reported in the literature. It is found that only four different combinations of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{H} - C</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{H}- L</tex> will support sustained oscillations. Theoretical waveforms and frequencies of oscillations are predicted. Experiments employing an op amp realized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_H</tex> are conducted and agreement between theoretical predictions and experiments is good. A possible application of the theory to the explanation of biological oscillation across an active membrane is proposed.