In this paper, two nonlinear circuits are constructed based on the HP‐type flux‐/ charge‐controlled memory elements in parallel and series connections. Then, the phasor method is utilized to analyze and verify the frequency doubling mechanism between pinched hysteresis loops and the applied sinusoidal excitation. The expressions of equivalent admittance (denoted as Y_M) and impedance (denoted as Z_M) for memory elements connected in parallel and series and the unified forms of which are also derived, respectively. Moreover, the mathematical models for the parallel‐/serial‐connected circuits are obtained and their characteristics are described. Meanwhile, the dual relationships, which come from the reciprocal relationship between Y_M and Z_M, are also discovered based on their models. Furthermore, the gradual steady‐state oscillation and temporal behaviors are demonstrated for two nonlinear circuits. Finally, the experimental verification shows a good agreement between theoretical analysis and experimental results.

中文翻译：

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具有并联/串联连接的HP型存储元件的非线性电路及其特性分析

本文基于并联和串联连接的HP型磁通/ 电荷控制存储元件构建了两个非线性电路 。然后，利用相量方法来分析和验证捏滞磁滞回路与所施加正弦激励之间的倍频机制。还分别导出了并联和串联连接的存储元件的等效导纳（表示为Y _M）和阻抗（表示为Z _M）的表达式，以及其统一形式。此外，并行/串行的数学模型 获得连接的电路并描述其特性。同时，还基于它们的模型发现了Y _M和Z _M之间的倒数关系的对偶关系。此外，证明了两个非线性电路的渐进稳态振荡和时间行为。最后，实验验证表明理论分析与实验结果吻合良好。