Construction and Experimental Realization of the Fractional-Order Transformer by Oustaloup Rational Approximation Method

In previous studies, there were few application circuits involving fractional-order mutual-coupling circuits. Therefore, based on the fractional mutual coupling circuit, the Oustaloup rational approximation method is proposed to construct fractional transformers. Firstly the fractional-order transformer circuit model is derived based on the fractional-order coupled inductor. And the frequency characteristics of the impedance of the fractional-order transformer under open-circuit and load conditions are analyzed. Then different orders of fractional transformers are constructed to verify the rationality of the proposed circuit by simulation. Finally, two fractional-order transformers with different orders constructed, and simulations and experiments show that the constructed circuit has good electrical approximation performance.