Beyond Impedance Additivity: A Systematic Nonlinear Perspective on Memristor Associations

Abstract

We investigate the validity of the superposition principle and impedance additivity in AC circuits containing a memristive device connected in series with a resistor, capacitor, or inductor. While the series association of impedances is a cornerstone of linear circuit theory, its applicability to memory-bearing nonlinear systems remains largely unexplored. Using a state-dependent memristive model, we numerically analyze the stationary current response under sinusoidal excitation and characterize the resulting harmonic spectra, Bode diagrams, and Nyquist plots. To assess whether the fundamental response can still be interpreted through an equivalent-circuit framework, we introduce the concept of an apparent memristor, whose effective parameters are extracted directly from the composite impedance. We show that, although the fundamental harmonic can be accurately reproduced by an apparent equivalent circuit over selected parameter ranges, the effective parameters differ substantially from those of the isolated memristor, revealing a renormalization induced by the coupling to the passive element. More importantly, we identify parameter regimes in which the apparent-circuit description breaks down altogether, particularly for capacitor and inductor-coupled systems, demonstrating that the composite impedance cannot generally be expressed as the sum of independent impedances. These results establish boundaries for the use of equivalent-circuit models in memory-enabled electronic systems and provide practical guidelines for the interpretation of impedance spectroscopy in nonlinear devices exhibiting memory.