Equivalent Circuit Analysis of RF-Integrated Inductors with/without Ferromagnetic Material

In this paper, the detailed procedure to extract π-type equivalent circuit parameters of RF-integrated spiral inductors with/without ferromagnetic material is presented. RF-integrated spiral inductors have been fabricated and the Tohoku University group (TU) and The Tokyo Institute of Technology group (TIT) separately acquired equivalent circuit parameters of an air-core spiral. The S-parameters were measured to extract the equivalent circuit parameters. The extracted parameters were perfectly identical. Extended 3D EM simulation clarified the effectiveness of ferromagnetic materials up to 5 GHz as well as the wave shortening effect by the permittivity of Si beyond the 10 GHz range. The 3D-EM-simulated parameters conformed to the extracted parameters in the low frequency range.