Resistance Variations in High-Frequency Inductors Considering Induced Fields Among Conductors

In the high-frequency alternating current (ac) fields, both skin effect and proximity effect account for the significant part of losses in an inductor. In particular, serious losses between multiple wires occur due to the proximity effect. A stranded wire has two or more strands with twisted structure so that the analysis of stranded wire-wound inductors requires lots of computational time for detailed discretization in finite element analysis (FEA). The analytical method can be alternatively used to help achieve fast (real-time) estimation by reducing the complexity of the original model. However, the proximity effect cannot be accurately predicted due to induced fields by eddy current from adjacent conductors (strands and wires). In this article, induced fields among adjacent conductors are discussed for the accurate analytical calculation. The concepts of a complex permeability and homogenization can help improve the estimation of frequency-dependent resistance in an inductor. The proposed estimation is verified and compared with the computed value by FEA and measurement data with a spiral inductor.