Efficient Scalable Modeling of Double- $\pi$ Equivalent Circuit for On-Chip Spiral Inductors

This paper presents an efficient technique to generate a scalable double-pi circuit model for spiral inductors. The double-pi equivalent circuit is widely used to build an inductor library because of its high accuracy over a wide frequency range. However, direct parameter extraction for the double-pi model and scalable fitting for each parameter are complicated due to the large number of circuit elements. The proposed method performs a scalable modeling using a relatively simple single-pi model and converts the model to the double-pi model according to the physics-based conversion algorithm. For this purpose, physical relations between the single-pi and double-pi equivalent circuits for a spiral inductor have been derived. The proposed technique is verified by developing a scalable inductor library using 0.13-mum CMOS technology.