Nonlinear circuits with parallel-/series-connected HP-type memory elements and their characteristic analysis

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.