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In this paper, the fractional-order statespace averaging model of the Buck-Boost DC/DC converter in discontinuous conduction mode is presented based on the theory of fractional calculus. The order of the model can be considered as an extra parameter, and this extra parameter has a significantly influence on the performance of the model. The quiescent operation point of the fractional-order model is not only related to the switching time period, the duty ratio, and the inductance value, but also related to the inductor order. The amplitude of the output voltage, the inductor current, and the inductor current ripple increase with the decreasing of the inductor order. Subsequently, some low-frequency characteristics, such as the line-tooutput transfer function and the control-to-output transfer function of the fractional-order model, are derived from alternating current components of the fractionalorder state-space averaging model. And the results suggest that transfer functions are not only relative to the inductor order, but also have intimate correlation to the capacitor order. Fractional-order models can increase the flexibility and degrees of freedom by means of fractional parameters. Numerical and circuit simulations are presented to demonstrate the correctness of the fractional-order model and the efficiency of the proposed theoretical analysis. These simulation results indicate that the fractional-order model has a certain theoretical and practical significance for the design and performance analysis of DC/DC converter.

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Summary 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 YM) and impedance (denoted as ZM) 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 YM and ZM, 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.

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