Self-Resonance in Ortho-Cyclical Multilayer Air-Core Inductors: Analytical Techniques and Optimization

A multilayer air-core inductor's operational frequency limit can be known beforehand if its first self-resonance frequency can be predicted. The self-resonance frequency is due to the electrostatic capacitance stored between the turns and layers of the inductor. This article presents an analytical technique to predict the first self-resonance frequency specifically for an ortho-cyclically wound multilayer air-core inductor through electrostatic field segregations. The static capacitances between the inductor's turns and layers are segregated into vertical and horizontal electrostatic field components, and are further aggregated to predict the first self-resonance frequency. Further, a multiobjective optimization technique using the pareto-optimal fronts through key parameter variations for inductor design is presented. The analytical technique is verified with acceptable results using prototype inductors. This analytical technique and optimization can be applied in designing ortho-cyclically wound multilayer air-core inductors for low and high frequency applications.