Quantized amplitudes in a nonlinear resonant electrical circuit

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. The excitation voltage, synchronously switched at the current frequency, enables electrical supply while keeping the oscillation of the system. The excitation frequency is 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: measured stable amplitudes depend on initial conditions and excitation frequency, for the same amplitude of the excitation. Moreover, a variation of the dumping does not affect significantly the amplitudes as long as the oscillation is observed. 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), in energy conversion and in time and frequency domains.