Optimal Design of Single-Layer and Multi-Layer Air-Core Inductors Considering Uncertainty Factors

Air-core inductors are key components in power converters and measurement equipment. To optimally design inductors, their self-resonant frequency (SRF) as a result of inherent stray capacitance should be accurately estimated. This paper presents optimal design procedures for air-core inductors, considering constraints such as SRF and inductor volume. To this end, a methodology is proposed to estimate the variability of stray capacitances, accounting for various uncertainty factors. Specifically, for single-layer air-core inductors, an empirical expression is adopted and experimentally verified to provide better predictions compared to the commonly used physical-based approach. For multi-layer air-core inductors, an enhanced analytical approach based on the energy-conservation method is proposed, which considers the impact of five influence factors. Two key factors (the proximity effect and the variation of turn length) are investigated by FEM simulations and incorporated into the enhanced models. The other three factors (the effective permittivity of the wire insulation coating, the winding tightness, and the electric field path assumption) are taken into account as uncertainty factors, leading to statistical estimates of the stray capacitance and SRF. Finally, two samples are fabricated for single- and multi-layer air-core inductors, which agree well with the design specifications, proving the effectiveness of the proposed design methodology.