Solution of TiO$_{2}$ memristor-capacitor series circuit excited by a constant voltage source and its application to calculate operation frequency of a programmable TiO$_{2}$ memristor-capacitor relaxation oscillator

The memristor is a new-found circuit element and its applications in programmable circuits are also under study. Analysis of most of its combinations with other circuit elements such as resistors, capacitors, and inductors does not exist. In this work, a TiO$_{2}$ memristor model with linear dopant drift speed is used and the solution of a TiO$_{2}$ memristor and capacitor series circuit driven by a constant voltage source is given. It is then used to analyze a novel M-C oscillator circuit. In previous programmable oscillator studies, the memristance of the oscillator was assumed to be constant. However, in this study, the analysis of the M-C oscillator is done considering time-varying memristance and using the solution of the TiO$_{2}$ memristor and capacitor series circuit supplied by a constant voltage. In this work, a formula for calculation of the exact value of the M-C oscillator frequency is given. Minimum and maximum operation frequencies of the oscillator are also calculated.