Analysis and application for the source-free RMLC circuits - Gao, Xiang; Qian, Yuhan; Li, Shengpeng; Li, Wenjuan; Su, Yao; Liu, Yue (Frontiers in Physics, 2025)
IntroductionMemristor systems and their application circuits have attracted growing research interest. When a memristor circuit/network is designed, both memristors and conventional electronic components are inevitably required, particularly energy storage elements (e.g., capacitors and inductors). It has found that most existing studies focus on oscillatory phenomena generated by memristive systems, such as chaotic attractors, period-doubling oscillations, spiking and bursting oscillations. However, there is a notable lack of literature exploring and analyzing the energy exchange between these components, as well as the resulting oscillatory behaviors and outcomes arising from such interactions. It is well known that the unit of a memristor, like that of a resistor, is the ohm (Ω). In general circuits, the energy exchange between resistors and energy storage elements can induce nonlinear behaviors such as step functions, damping phenomena, both of which stem from the energy exchange between resistors and capacitors/inductors. So, when a memristor (though physical implementations are rare, several classic mathematical models exist) exchanges energy with energy storage elements, will similar behaviors emerge?MethodsIn this paper, to advance the theoretical completeness of memristive systems and take the classical HP memristor model as an example, four source-free circuit topologies integrating memristors with energy-storage elements are investigated deeply. They are categorized into two types: RMC/RML circuits and series/parallel RMLC circuits. Firstly, through mathematical modeling, the four circuits are all found to be governed by transcendental equations. Secondly, two types of four-component source-free circuits are configured and analysis. Finally, the application circuits comprising four fundamental components was configured and explored.Results and DiscussionSimulation results for the mathematical models of the four circuits demonstrate memristor states (R0, kRd) and energy-storage elements collectively regulate response characteristics, damped oscillatory and decay behavior. The active power and apparent power curves reveal distinct energy exchange behaviors between components, differing fundamentally from conventional RL, RC, and RLC circuits. These findings demonstrate that due to the presence of memristors, such circuits cannot be employed for step response generation, but are exclusively applicable for energy memorization and dissipation. Then, the following conclusion on two types of source-free circuits are demonstrated: (1) capacitor and inductor provide energy (i.e., ϕ and q) to the system, while memristors exhibit hysteretic behavior, collectively and fundamentally co-modulating oscillation modes and attractor phenomenon; (2) The dual characteristics of memristors—memory capability and energy dissipation—endow them with the potential to break the von Neumann bottleneck, making them essential candidates for implementing next-generation neural networks and AI systems. Finally, the application circuits reveal that even within the same circuit, varying memristor placements can lead to distinct topological configurations and divergent nonlinear output behaviors. This phenomenon further validates the unique characteristics of memristors as an emerging field. These findings establish a solid theoretical and experimental foundation for future exploration and development of memristive systems, including next-generation neural networks, artificial intelligence applications, and aerospace technologies.