Electrical equivalent circuit for frequency dependant impedance: minimum lumped elements for a given precision [SMPS transformer]

At high frequency, due to the skin and proximity effects, the inductance and resistance of wound components become frequency dependent: impedances proportional to the square root of frequency are often encountered. Such behaviour is tricky to represent accurately by an electrical equivalent circuit. This well-known problem is referenced as "half order system" representation. In this paper, it is shown how to design a circuit, made of constant resistances and inductances, which behaves as the leakage inductor of an SMPS transformer. Attention is paid to minimise the component number, necessary to reach a given accuracy and a given frequency range.