Physical realizable circuit structure for adaptive frequency Hopf oscillator

This paper presents a novel structure for the adaptive frequency Hopf oscillator where the nonlinear function is modified to make the system realizable using analog circuit components. A mathematical model is derived and it is shown using VHDL-AMS model that despite using a new nonlinear function, the oscillator exhibits the same characteristics as the original. Our simulation results show the same learning behavior with improved learning time. Subsequently, an equivalent circuit model and transistor level implementation for the oscillator is suggested and the mathematical model is confirmed with system and circuit level simulations.