Apr 182012
 


Info This is an popular coil geometri used in todays wireless charger circuits.
The formula used in this calculation is based on the
Harold A. Wheeler approximations
for air core flat spiral coil inductor.

…where:

  • L = inductance in μH
  • Di = inner diameter in inches.
  • s = distance between windings in inches
  • w = wire diameter in inches
  • N = number of turns

1 inch = 0,0254m=2,54cm = 25,4mm.
This formula applies at ‘low’ frequencies (<30MHz)
using enameled copper wire. Some people call it "magnet
wire".

Click on image to enlarge

Flat spiral coil inductor example

Please note that the outer and inner diameter is measured from the center of the wire.
Flat spiral coil dimensions drawing

Dimensions

Coil inner diameter (Di):
Number of turns (N):
Wire Diameter (w):
Spacing between turns (s):
Inductance (L):
Outer diameter (Do):
Wire lenght (Wl):
      

image

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Apr 172012
 


Push image to enlarge
Square planar spiral coil Hexagon spiral coil inductor Octagon spiral coil inductor Sircular spiral coil inductor
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.
Notes:
Fill in appropriate values in the white fields.Then push “calculate”.
1μm =0.001mm
1μm =0.00003937007874015748 inch
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)
  Square Hexagonal Octagonal Circular
Modified Wheeler nH nH nH nH
Current Sheet nH nH nH nH
Monomial Fit nH nH nH nH

 

Reference:
S.S. Mohan, M. Hershenson, S.P. Boyd and T.H. Lee
Simple Accurate Expressions for Planar Spiral Inductances
IEEE Journal of Solid-State Circuits, Oct. 1999, pp. 1419-24.
For multilayer spiral pcb coils see here:
A new calculation for designing multilayer planar spiral inductors

image
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