Design of Planar Rectangular Microelectronic Inductors

TLDR

Negative mutual inductance, normally negligible in circuits, can cause inductance overestimation of up to 30 % in microelectronic coils, especially as film thickness and frequency vary. The study derives inductance equations for planar thin- or thick-film coils, comparing models that include versus exclude negative mutual inductance. A computer program was developed to calculate inductances for square and rectangular geometries, taking track width, spacing, and number of turns as inputs. Graphic results for up to 16 turns covering 3 nH to 10 µH were presented.

Abstract

Negative mutual inductance results from coupling between two conductors having current vectors in opposite directions. As a quantity in electronic circuits, negative mutual inductance is usually so much smaller in magnitude than overall inductance that it can be neglected with little effect. In the microelectronic world, however, its neglect can result in inductance values as much as 30 percent too high. This paper derives inductance equations for planar thin- or thick-film coils, comparing equations that include negative mutual inductance with those that do not. It describes a computer program developed for calculating inductances for both square and rectangular geometries, the variables considered being track width, space between tracks, and number of turns. Graphic results are presented for up to 16 turns over an inductance range of 3 nanohenries to 10 microhenries. Although details of fabrication are not included, the effects of film thickness and frequency on the mutual-inductance parameter are discussed.