At what frequencies should air-core magnetics be used?

TLDR: The boundary between the magnetic core and air core regimes has not yet been theoretically identified, and intermediate frequency ranges (i.e. 5 to 30 MHz) see both cored and air-core examples as discussed by the authors .

Abstract: Magnetic components for power conversion (inductors & transformers) are often designed with magnetic cores, which add core loss but reduce the required number of turns, copper loss, and usually total loss. At very high frequencies, poor core materials make this tradeoff less advantageous and air-core magnetic components are often preferred. The boundary between the magnetic-core and air-core regimes has not yet been theoretically identified, and intermediate frequency ranges (i.e. 5 to 30 MHz) see both cored and air-core examples. In this work, we calculate an expression that suggests that, based on the properties of currently available magnetic materials, cored inductors can outperform their air-core counterparts up to 60 MHz, well into the VHF range. We experimentally demonstrate this boundary frequency by comparing the quality factors of optimized cored and air-core toroidal inductors. Formally demonstrating the advantage of cored over air-core inductors even at tens of MHz suggests more advantageous designs for applications at ISM bands (6.78, 13.56, 27.12 MHz) and other RF applications.