Planar spiral coil inductor design

Push image to enlarge InfoThe first approximation is based on a modification of an expression developed by Wheeler; the second is derived from electromagnetic principles by approximating the sides of the spirals as current-sheets; and the third is a monomial expression derived from fitting to a large database of inductors (and the exact inductance values).
All three expressions are accurate, with typical errors of 2 – 3%, and very simple, and are therefore excellent candidates for use in design and synthesis. The thickness of the inductor has only a very small effect on inductance and will therefore be ignored.

Number of turns (n):		turns
Spacing between turns (s):		μm
Turn width (w):		μm
Outer Diameter (dout):		μm
Calculated Inner diameter (Din)		μm
Fill factor p=(Dout-Din)/(Dout+Din)		Fill factor
	Square (nH)	Hexagonal (nH)	Octagonal (nH)	Circular (nH)
Modified Wheeler
Current Sheet
Monomial Fit