Analytical Solution of Circuits Employing Voltage- and Current-Excited Memristors

The analysis of complicated circuits containing nonlinear electrical elements is commonly performed via numerical algorithms of simulation programs. However, an analytical solution can be preferable to the numerical approach, particularly for the needs of basic research. This paper introduces a methodology of the analytical solution of voltage/current response of the memristor to its excitation from ideal current/voltage source, with the memristor being characterized by the memristance-charge or memductance-flux relationships. The procedure is explained on examples of a TiO₂ memristor with linear dopant drift and of a hydraulic memristor.