This is the start of a collection of Pulsed Power related formulas and calculators that I found usefull. However, whenever I could find resources on the internet already, I tried to refer to them rather than to re-invent the wheel. Consequently you might also find some of the links provided helpful.
Formulas for the Calculation of Common Inductances*)
(unless otherwise noted use SI-units in all presented formulas)
*) Planar geometries which are not very common in pulsed power systems are not covered in this table. Readers are refered to references 1, 6 and especially 8. More information on rectangular loops can be found here: http://www.qsl.net/in3otd/rlsim.html
Of course no guarantee is given for the accuracy of the listed formulaes or the calculators although I tried my best to select the formulas carefully from the literature. Please let me know when you find any mistakes.
low frequency inductance
formula
example
long, thin wire (as segment of closed circuit)
(reference 1)
conductor from parallel wires (currents in same direction) r << d
(reference 8)
return circuit of parallel wires (currents in opposite directions) r << d
(reference 1)
l
=
100
cm
w
=
2
cm
r
=
0.5
mm
L
=
1.478
μH
strip line (as segment of closed circuit)
(reference 1)
l
=
100
cm
w
=
50
cm
L
=
1.185
μH
return circuit of parallel plates (current runs in opposite directions)
The displayed equation is valid for dimensions that are entered in inches, which is taken into account in the provided calculation.
"Where great accuracy is required, a correction factor may be applied to the equation to take account of the fact that the coil is wound of spaced round wires rather than with a uniform current sheet. This correction rarely exceeds 0.5%, is greater for widely spaced turns, and increases with the number of turns." (see reference 7 for details)
D : distance between wire centers d : diameter of bare wire
(reference 9)
multi layer thin wall solenoid
N: number of turns
(reference 4)
N
=
1000
d
=
10
mm
l
=
5
cm
mr
=
1
L
=
1.645
mH
toroid
N: number of turns
(reference 4)
spiral (flat coil)
N: number of turns
(Wheeler formula)
(reference 1)
N
=
20
R
=
5
cm
w
=
2
cm
L
=
63.501
μH
windings cover entire area
(Schieber formula)
(reference 1)
N
=
20
R
=
5
cm
L
=
1.380
nH
Both formulas can also be used for printed flat coils. For the Wheeler formulas errors up to 20% have been reported. A more accurate calculation takes the ratio between coil radius, R, and winding-thickness, w, into account (Grover method). See reference 1 for details.
conical coils
The inductance of conical coils is calculated from the geometric sum of the helical and the planar contribution. See reference 5 for details.
LH : inductance of equivalent helical coil LP : inductance of equivalent planar coil
(reference 5)
References:
1) F.W. Grover, Inductance Calculations, Dover Publications, Mineola, 2004.
2) home.san.rr.com/nessengr/techdata/inductance/induc.html
3) H. Stöcker,Taschenbuch der Physik, Verlag Harri Deutsch, Frankfurt/Main, 1994, p. 334 (f = 1).
4) Formelsammlung Passive Bauelemente, www.iwe.uni-karlsruhe.de/download/WWW_PB_WET_FS.pdf
5) Herb's Tesla Page (Design Page), http://home.wtal.de/herbs_teslapage/design.html#des-2pri
6) University of Missouri-Rolla, Electromagnetic Compatibility Laboratory, www.emclab.umr.edu/new-induct, 2001.
7) F.E. Terman, Radio Engineers' Handbook, McGraw-Hill, New York, 1943, p.53.
8) F.W. Grover, Inductance Calculations, Dover Publications, Mineola, 2004, p.37.
9) F.E. Terman, Radio Engineers' Handbook, McGraw-Hill, New York, 1943, p.60.
