Simple accurate expressions for planar spiral inductances

Abstract

We present several new simple and accurate expres- sions for the DC inductance of square, hexagonal, octagonal, and circular spiral inductors. We evaluate the accuracy of our expressions, as well as several previously published inductance expressions, in two ways: by comparison with three-dimensional field solver predictions and by comparison with our own measure- ments, and also previously published measurements. Our simple expression matches the field solver inductance values typically within around 3%, about an order of magnitude better than the previously published expressions, which have typical errors around 20% (or more). Comparison with measured values gives similar results: our expressions (and, indeed, the field solver results) match within around 5%, compared to errors of around 20% for the previously published expressions. (We believe most of the additional errors in the comparison to published measured values is due to the variety of experimental conditions under which the inductance was measured.) Our simple expressions are accurate enough for design and optimization of inductors or of circuits incorporating inductors. Indeed, since inductor tolerance is typically on the order of sev- eral percent, "more accurate" expressions are not really needed in practice.