The operation frequency of memristor seriously affects its applications in high-frequency working conditions. In this article, a new method using a sine-based function instead of the linear term in memristor models to spread the operation frequency ranges of memristor emulators is proposed. Via using this method on a flux-controlled memristor with smooth continuous cubic function as an example, research shows that the operation frequency range of this improved flux-controlled memristor is spread greatly. In particular, the improved memristor can still display an excellent pinched hysteresis loop even when the operation frequency is up to a few gigahertz, which is higher than most of the previously reported memristor emulators. The typical dynamic characteristics and the operation frequency range of the improved memristor are studied theoretically and numerically. The circuit simulations and physical experiments agree well with the theoretical analyses, which together demonstrate the effectiveness of the proposed methodology. Then, the improved memristor is applied to realize a chaotic oscillator to show its practical applications. In addition, the new method has universality, and it can be used by many other existing memristor emulators for spreading their operation frequency ranges.

In this article, the fast-scale instability in the three-level T-type single-phase inverter feeding diode-bridge rectifier with inductive load (3TSI-DR) is studied. Simulations suggest that such fast-scale instability on switching period scale can increase the harmonic content in the 3TSI-DR, which seriously affects its stable operation. To reveal the mechanism of this fast-scale instability, the state equation of the 3TSI-DR is derived, and state variables are solved based on quasi-static approximation principle. From state equation, the 3TSI-DR is periodic time-varying and piecewise smooth, belonging to Filippov system. Accordingly, the discrete-time mapping model of the 3TSI-DR is established, Filippov method is used for obtaining monodromy matrix, and Floquet theory is applied to explore instability mechanism. Theoretical results indicate that the fast-scale instability of the 3TSI-DR is caused by period-doubling bifurcation. Moreover, the Floquet multiplier sensitivities of different circuit parameters are calculated to identify key parameters; via comparing theoretical analyses with simulations, the unstable angle ranges of the fast-scale instability are given, and the stability boundaries in various parameter spaces are discussed. All these can provide design-oriented information for optimizing the 3TSI-DR to avoid instability due to period-doubling bifurcation. Finally, experimental results agreeing with simulations are presented to verify the correctness of theoretical analyses.

In this article, the slow-scale instability occurring in the three-level T-type inverter with a passive memristive (3LT²IPM) load is investigated. The average model of the 3LT²IPM, whose coefficient matrix is nonlinear periodic time-varying, is constructed, both harmonic balance method used to calculate the approximate solution of the average model and Floquet theory used to identify the circuit dynamic states are applied to explore the mechanism of the slow-scale instability emerging in the 3LT²IPM. Theoretical results indicate that the slow-scale instability of the 3LT²IPM is caused by Hopf bifurcation emerging in a region where the frequency is higher than line frequency but much lower than switching frequency. Also, the conditions of three theoretical parameters that make the theoretical analysis results as accurate as possible are presented. Different parameters impact on the stability boundary of the 3LT²IPM in various design parameter spaces are discussed, and the Floquet multiplier sensitivity is analyzed to identify key parameters for the stability of the 3LT²IPM, which are helpful to guide parameter adjustment of the 3LT²IPM to ensure its stable operation in practice. Finally, hardware experiment is established and experimental verification is provided. Physical experiments agree well with simulations, which together demonstrate the correctness of theoretical analysis.

The proposal of the memristor, considered as the fourth basic circuit element, suggests a new possibility for the design of high-performance power electronic systems. However, it also brings new challenges. At present, more and more electrical equipment and systems have demonstrated that their external characteristics can exhibit “8”-shaped hysteresis loops and can be regard as memristive equipment and systems. In order to satisfy the requirements of controllability, flexibility, efficiently, and so on, most memristive equipment and systems are not directly connected to the power grid but instead obtain their own required powering through various forms of power electronic converters. Note that memristive loads are distinctive and demonstrate unique nonlinear behaviors. Similarly, there can be nonlinearity from the resistor (R), inductor (L), or capacitor (C) load, but there is no combination of only R, L, and C that could produce memristive characteristics. In particular, the memristance of memristive devices changes continuously during the operation process; in addition, practical power electronic systems composed of memristive devices and power supplies have strong nonlinear characteristics, which are more likely to result in various complex behaviors and are not conducive to the stable operation of the systems. Therefore, exploring complex instability behaviors of power electronic systems with strong nonlinearity in depth is necessary for better protection and utilization of memristive devices. This paper provides an outline of the status of research on complex behaviors of power electronic systems with memristive load; it is expected to provide guidance for the study of complex behavior of strongly nonlinear systems.