Behavioral Model of Inductors via Physics-Informed Circuit Synthesis and Modified Vector Fitting

This paper proposes a physics-informed circuit synthesis method to obtain behavioral models of inductors, the parameters of which are determined by a modified vector fitting (MVF) routine. Although the vector fitting (VF) algorithm provides accurate numerical approximation of virtually any frequency response in form of poles and residues, the most common circuit synthesis methods often lead to unphysical electrical parameters (e.g. negative resistances), which correctly fit frequency responses, but cannot be used in common time-domain simulators such as Matlab Simulink. On the contrary, the methodology here proposed specifically for inductors produces circuit models with physical, easily interpretable circuit elements, such as the low-frequency functional inductance, the winding capacitance responsible for self-resonance frequency (SRF), and additional physical components to correctly fit multiple resonances. The proposed method is experimentally compared with a straightforward equation-based method and the original VF method in terms of accuracy, simplicity, and compatibility with common, commercial circuit solvers.