Quantized amplitudes in a nonlinear resonant electrical circuit

Abstract

We present a simple nonlinear resonant analog circuit which demonstrates quantization of resonating amplitudes, for a given excitation level. The system is a simple RLC resonator where C is an active capacitor whose value is related to the current in the circuit. This variation is energetically equivalent to a variation of the potential energy and the circuit acts as a pendulum in the gravitational field. The excitation voltage, synchronously switched at the current frequency, enables electrical supply and keeping the oscillation of the system. The excitation frequency has been set to high harmonic of the fundamental oscillation so that anisochronicity can keep constant the amplitude of the circuit voltage and current. The behavior of the circuit is unusual: different stable amplitudes have been measured depending on initial conditions and excitation frequency, for the same amplitude of the excitation. The excitation frequency is naturally divided by the circuit and the ratio is kept constant without external disturbance. Moreover, a variation of the dumping does not affect significantly the amplitudes as long as the oscillation is observed. And lastly, electrical pulses can change, as in quantum systems, the operating amplitude which is auto-stable without disturbances. Many applications of this circuit can be imagined in microelectronics (including computing), energy conversion and time and frequency domains.