Abstract
A set of new analytical formulas is proposed for determining the geometric mean distance (GMD)for use in the Greenhouse method to calculate the inductances of three-dimensional inductors composed of on-chip interconnects. The expressions are derived using a graphical method based on the integral form of the GMD equation. The mutual inductances of coupled interconnects are computed for given layout geometries using the proposed formulas, even when the conductors are partially overlapped in different metal layers. The inductances computed using the formulas agreed well with those generated by an accurate commercial field solver, differing by less than 1% across a variety of the conductor geometries.
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