10

MAGNETIC POWDER CORES

TECHNICAL DATA

MAGNETIC POWDER CORES

TECHNICAL DATA

The inductance of a wound core at a given number of turns is calculated using the following formula.

L

L

= inductance( μH)

μ

= core permeability

N

= number of turns

A

= mean magnetic path length(cm)

N

0.4 μ

=

2

10

-3

Ampere’s Law

Faraday’s Law

Magnetic Design Formulas

Inductance of a Wound Core

Ampere’s Law and Faraday’s Law show the relations of permeability, flux density and magnetizing force of a wound core.

H

= magnetizing force(oersteds)

N

= number of turns

l

= peak magnetizing current(amperes)

= mean magnetic path length(cm)

f

= frequency(hertz)

Permeability - Flux Density - Magnetizing Force

Inductor specification

a) Formula to calculate L at 0Ampere

b) Determine DC magnetizing force (H) by using Ampere’s law to achieve the roll off.

H = 0.4 Nl /

H = 0.4 3.14 22 10 / 6.35 = 43.5(Oe)

The magnetizing force(dc bias) is 43.5 oersteds, yielding 64% of initial permeability. See on page 11.

The inductance at 10Ampere will decrease the inductance by 64% compared with 0Ampere.

Therefore, L( 10A) = 76 0.64

= 48.6 ( μH)

solution

- Core : CM270125

- Number of Windings : 22Turns

- Current : DC 10Amperes

Inductance Calculation by Permeability vs DC Bias Curves

H

Nl

0.4

=

=

8

4.44fAN

μ

B

=

H

For toroidal powder cores, the effective area(A) is the same as the cross sectional

area. By definition and Ampere’s Law, the effective magnetic path length is the ratio

of ampere-turns(NI) to the average magnetizing force. Using Ampere’s Law and

averaging the magnetizing force gives the formula for effective path length.

Mean Magnetic Path Length

(OD - ID)

OD

ID

()

=

ln

Q

= quality factor

= 2 frequency (hertz)

L

= inductance (henries)

Q

L

=

Powder cores have low hysteresis loss, minimizing signal distortion, and low residual loss. The total core loss at low flux densities is the

sum of three frequency dependent losses of hysteresis loss, residual loss, and eddy current loss. The core loss is calculated from the

following Legg’s equation.

When a varying magnetic field passes through the core, eddy currents are induced in it. Joule heat loss by these currents is called eddy

current loss. Hysteresis loss is due to the irreversible behavior in the hysteresis curve and equal to the enclosed area of the loop.

The other core loss is called residual loss.

Where

= core loss resistance (ohms)

a

= hysteresis loss coefficient

c

= residual loss coefficient

e

= eddy current loss coefficient

Eddy current loss

Core Loss

Residual loss

Hysteresis loss

Total loss factor

2

L

=

OD = outside diameter of core (cm)

ID = inside diameter of core (cm)

A

= core cross section (effective area)

= mean magnetic path length (cm)

The Q factor is defined as the ratio of reactance to the effective resistance for an inductor and thus indicates its quality. The Q of wound core can

be calculated using the following formula, when neglecting the effects of self-resonance caused by the distributed capacitance resulting from the

differential voltage between adjacent turns.

Q Factor