Fast analytical parameters fitting of planar spiral inductors

This paper presents simple closed-form expressions for fitting measured or simulated S-parameter data to a single-pi equivalent circuit in the least-square-error sense. The presented method could be useful for quick estimation of the main equivalent parameters of a spiral inductor in a certain required frequency range. This can facilitate inductor geometry design and optimization by providing an instant insight into nature of the given S-parameters. The proposed method has been confirmed on measured S-parameters of on-chip inductor in standard CMOS technology and planar spiral inductor in package technology. The results show good agreement between the original and the fitted data.