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# INDUCTANCE CALCULATION

## INDUCTANCE CALCULATION

(OP)
Hello,
Can anyone tell me how to calculate coil inductance?

Thank you very much!!
Kae

### RE: INDUCTANCE CALCULATION

Static approach to calculation of the coil inductance:
L = phic/I = N x phi/I = squareN x I/(Rm x I) = SquareN/Rm
where
L is coil inductance in Henries
phic is coil flux due to I in Webers
I is coil current in Amperes
N is number of coil turns
Rm is reluctance of the coil core, in 1/Henry, which has to be calculated since it varies from a coil to coil shape. It can be
Rm = Ls/(mu x muo x S)
where
Ls is path of magnetic flux inside coil in meters
mu is relative permeability of the media in per unit
muo is vacuum permeability = 4 x PI x 10 to Exp(-7) in Henry/meter
S is coil cross-sectional area in square meters

Dynamic approach is
Ecoil(t) = L x (di/dt) in volts
or
L = Ecoil(t) / (di/dt) in Henries
where
di/di is a derivative of current according to time t

### RE: INDUCTANCE CALCULATION

Small correction (I beg your pardon):
di/di is supposed to be di/dt

### RE: INDUCTANCE CALCULATION

Additional minor correction: in JBARTOS terms "phic=phi x N"
is not a flux, but a "flux linkage"

### RE: INDUCTANCE CALCULATION

Suggestions to the previous posting marked ///\\\:
Additional minor correction: in JBARTOS terms "phic=phi x N"  is not a flux, but a "flux linkage"
///Thank you for the correction. I did not see it as the "flux." I saw it as "coil flux," which I posted, namely:
phic is coil flux due to I in Webers
In fact, the IEEE Std 100-200 "Dictionary" states:
Flux Linkages. The sum of the fluxes linking the turns forming the coil, that is, in a coil having N turns, the flux linkage is:
lambda=fi1 + fi2 + .... +fiN
where
fi1 is flux linking turn 1
fi2 is flux linking turn 2
.
fiN is flux linking Nth turn.
I see that the standard is referring to the sum as flux linkages and flux linkage. I called it the coil flux.
Also, the magnetic flux:
fiA=integral over area A of (B dot product dA)
where A is area, dA is the element of A, and B is magnetic induction at the element dA. This could be applied to the coil N times to obtain coil flux or coil flux linkages.\\\

### RE: INDUCTANCE CALCULATION

Inductance calculatio of a coil is not easy at all. Its value depends on winding geometry and on the magnetic properties of sourrounding material. All designs want a prototype for testing and correcting actions.
Nevertheless, in some particular cases, very good approaches can be got. For instance, for a single layer coil of circular turns on the free air, the inductance is approx.:

L = N^2.[R^2/(9.R+10.l)] microhenries
Where:
N:   Number of turns
R:   Half of diameter of coil between center of conductors (inches)
l:   Length of coil (inches)

More details can be found on different manuals like "Reference data for radio engineers" Howard W. Sams & Co., Inc.

Julian

### RE: INDUCTANCE CALCULATION

Suggestion: Reference:
Arthur R. Bergen "Power Systems Analysis," Prentice-Hall, Inc., Englewood Cliffs, New Jersey 07632, 1986, p. 55 indicates that
lambda=N x fi
where
lambda = flux linkages in Weber turns
fi = flux that links all the N turns of the coil
Figure 3.1 illustrates leakage fluxes in addition to the flux fi that links all the turns N. Now,
lambda= fi1 + fi2 + .. + fik + .. + fiN
where fik is the flux linking the kth turn of the coil with N turns. It appears that lambda represents flux linkages of the coil and the flux linkages form the coil flux without counting the flux leakages.

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