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This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters. [ABSTRACT FROM AUTHOR]

The Caputo–Fabrizio (C–F) definition, which solves the singularity problem in the Caputo definition, has been preliminarily applied in the field of circuit system modeling. However, the complex characteristics of the C–F definition-based circuit systems are still understudied. Therefore, this paper proposes a C–F definition-based fractional-order RLC (CF-FORLC) circuit model and analyzes its basic characteristics. First, the effects of different component orders on the performance parameters including the impedance, quality factor, and bandwidth are analyzed, which gives insights into the design of CF-FORLC. Then, the analytical solutions and the frequency-domain characteristics of CF-FORLC with different capacitance and inductance orders under arbitrary input are derived. Finally, the data of actual circuits are fitted to obtain the parameters of the CF-FORLC model, and the orders of the C–F definition-based capacitors and inductors are estimated. The results of the comparative experiments show that the proposed modeling scheme can improve the consistency of the dynamic performance of the model with that of the actual circuit. In addition, the proposed CF-FORLC model shows higher accuracy and flexibility with more adjustable parameters. [ABSTRACT FROM AUTHOR]