Harmonic Balance Design of Oscillatory Circuits Based on Stanford Memristor Model

Abstract

Oscillatory circuits with real memristors have attracted a lot of interest in recent years. The vast majority of circuits involve volatile memristors, while less explored is the use of non-volatile ones. This paper considers a circuit composed by the interconnection of a two-terminal (one port) element, based on the linear part of Chua's circuit, and a non-volatile memristor obeying the Stanford model. A peculiar feature of such a memristor is that its state displays negligible time-variations under some voltage threshold. Exploiting this feature, the memristor is modeled below threshold as a programmable nonlinear resistor whose resistance depends on the gap distance. Then, the first-order Harmonic Balance (HB) method is employed to derive a procedure for selecting the parameters of the two-terminal element in order to generate programmable subthreshold oscillatory behaviors, within a given range of the gap, via a supercritical Hopf bifurcation. Finally, the dynamic behaviors of the designed circuits as well as the sensitivity of the procedure with respect to the location of the bifurcating equilibrium point and the range of the gap are discussed and illustrated via some application examples.