Magnetic Design Formulae

Voltage-Flux Density-Frequency (Faraday's Law).
Flux density must be determined to assure proper operating level. The level of flux density changes the value of Rac, the core loss resistance, and has an effect on the permeability as shown below. Flux density can be calculated from:
Bmax=[(Erms * 108)/(4.44*A*N*f) ]
   (4.44 for sine wave, 4.0 for square wave)		 where:
Bmax=Maximum flux (gauss) density
Erms=equivalent rms voltage across coil
N=number of turns
A=core cross section (cm2)
f=frequency (hertz)
Ampere's Law
Ampere's Law relates magnetizing force to peak current, number of turns and mean magnetic path length.
H=(0.4*pi* N*I)/l where:
H=magnetizing force (oersteds)
N=number of turns
I=peak current (amperes)
l=mean magnetic path (cm)
The magnetizing force determines the estimate of flux density using the normal magnetization (B/H) curves. The relative permeability at that magnetizing force can then be determined by:
µ=B/H where:
µ=relative permeability
B=flux density (gauss)
H=magnetizing force (oersteds)
Inductance Considerations
The inductance of a wound core can be calculated from the core geometry using the following formula:
L=(0.4*pi*µ*N2*A*10-8)/l where:
L=inductance (henries)
µ=core permeability
N=number of turns
A=core across section (cm2)
l=magnetic path length(cm)

AL is the Inductance Factor of a core, and is expressed as nH/turn2 (or mH/1000 turns).
L(nH) = N2 * AL
where:
L = inductance in nH for N turns
AL = core inductance factor
Note: the manufacturer's value for ferrite cores is not suitable for RF calculations
Magnetic Formula Conversions
The following table lists conversion factors for magnetic units.
oersteds * 0.795 = amp-turns/cm
gauss * 0.0001 = tesla
mH/1000 turns * 10 = uH/100 turns
in2 * 6.425 = cm2
circ mils * 5.07 x 10-6 = cm2
watts/lb * 17.62 = mW/cm3

This page updated 23/02/11
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