超越阻抗可加性：忆阻器关联的系统性非线性视角
Beyond Impedance Additivity: A Systematic Nonlinear Perspective on Memristor Associations
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中文总结 AI 辅助
本研究从非线性视角系统考察忆阻器与无源元件串联时的阻抗可加性，发现表观等效电路仅在特定参数范围有效，且有效参数被重整化，为等效电路模型的适用边界提供了指南。
中文摘要 AI 辅助
我们研究了在包含忆阻器件与电阻、电容或电感串联的交流电路中，叠加原理和阻抗可加性的有效性。虽然阻抗的串联关联是线性电路理论的基石，但其对具有记忆的非线性系统的适用性在很大程度上尚未被探索。利用一个状态相关的忆阻模型，我们在正弦激励下数值分析了稳态电流响应，并表征了由此产生的谐波谱、伯德图和奈奎斯特图。为了评估基波响应是否仍可通过等效电路框架来解释，我们引入了表观忆阻器的概念，其有效参数直接从复合阻抗中提取。我们表明，尽管在选定的参数范围内，基波谐波可以被表观等效电路精确复现，但有效参数与孤立忆阻器的参数存在显著差异，揭示了由与无源元件耦合引起的重整化效应。更重要的是，我们识别出表观电路描述完全失效的参数区域，特别是对于电容和电感耦合系统，这表明复合阻抗通常不能表示为独立阻抗之和。这些结果为在具有记忆功能的电子系统中使用等效电路模型设定了边界，并为解释具有记忆的非线性器件中的阻抗谱提供了实用指南。
英文摘要
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.
发表机构
- Federal University of São Carlos（圣卡洛斯联邦大学）
- Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）
- University of Richmond（里士满大学）
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