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Chapter 12: Applications of Soft Magnets

1. Losses

2. Materials

3. Static Applications

4. Low-frequency Applications

5. High-frequency Applications

Comments and corrections please: jcoey@tcd.ie

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Further reading

• C.W. Chen, Magnetism and Metallurgy of Soft Magnetic Materials, Dover: 1983An excellent monograph which contains a wealth of detailed and reliable information on almost every aspect of soft magnets.

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Ni-Fe/Fe-Co (heads)

Fe-Si

Fe-Si (oriented)

Ni-Fe/Fe-Co

Amorphous

Others

Others

Alnico

Sm-CoNd-Fe-B

Hard ferrite

Co- ! Fe 2 O 3

(tapes, floppy discs)

CrO2 (tapes)

Iron (tapes)

Co-Cr (hard discs)

Soft ferrite

Others

Iron

Soft Magnets

HardMagnets

MagneticRecording

Magnet applications; A 30 B! market

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Figure 12.1 Hysteresis in a soft magnetic material. B(H)

and J(H) are indistinguishable in small fields.

! Minimal hysteresis.! High polarization! Largest possible permeability

B = µ0µrH

102 < µr < 106

µr " !

B ≈ J (= µ0M)

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skin depth

Bd = µ0µrH

Electrical steel; " = 0.5 µ# m, µr = 10,000

$s = 0.36 mm at 50 Hz; $s = 3.6 µm at 500 kHz

µr decreases with increasing frequency; 106 to 102

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Pan

f

Phy

Pan

P/f

Phy

Ped

Hysteresis loss per cycle is the area of the

B(H) loop

%H

Reduction of eddy-current losses by lamination

Figure 12.2 Total loss per cycle showing the three

contributions

1. Losses

! 1/n2

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t

d

H

Figure 12.3 Pry and Bean model for movement of uniformly-spaced domain walls.

Currents are induced in the vicinity of the walls, as shown by the dashed lines.

Reduces to zero as d/t & 0

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Figure 12.4 Total loss per kg for permalloy at differentfrequencies. Thickness is 350 µm

Figure 12.5 Progress during the 20th Century.

a) Losses in transformer cores

b) Initial static permeability

Losses are double in a rotating field.

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12.1.2 High-frequency losses.

Complex permeability µ = µ’ - iµ”

h = h0exp i't

b = b0exp i('t-$) real parts are h(t), b(t)

µ = (b/h) exp -i$

= (b/h) [cos$ - i sin$ ]

Re(µh) is the time dependent flux densityb(t) = h0[µ’cos't + µ”sin't] Losses are proportional to µ”

Quality factor Q = µ’/ µ” = cot$

Loss angle

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A Fourier integral

The Fourier components are

General time-dependent response

Real and imaginary parts of µ are related via the Kramers-Kronig relations

Rate of energy dissipation P = h(t) db(t)/dt = h02cos't (-µ’ 'sin't + µ”'cos't) (sc=0, (c2=1/2

P = (1/2)µ”'h02

Losses are +ve, hence the - sign in the defn

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Hs

h

M

Ms

m

Precession of the

magnetization

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Snoek’s relation

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Figure 12.6 Real and imaginary parts of the susceptibilities ) and *. The peak

is at the ferromagnetic resonance frequency

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Figure 12.7 Global market for soft magnetic materials.

The pie represents about 10 B$ per annum

12.2 Soft Magnetic Materials

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[100] roll direction

(011) plane

Goss texture of grain-oriented silicon steel

Iron-rich edge of the Fe-Si phase diagram

Figure 12.8 Losses as a function of operating induction

for grain-oriented silicon steel

At % Si

Wt % Si

L

TC

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Figure 12.9 Frequency response of some Ni-Zn ferrites

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Magnetic shielding, The shielding ratio R is Hout/Hin

HoutHin

12.3 Static Applications

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Figure 12.10 A laboratory electromagnet

Tapered pole pieces; 55°

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Figure 12.11 Types of cores. The powder core has been

sectioned to indicate its internal structure.

Stacked laminations Tape-wound core Powder core

Ferrite E-core

12.4 Low Frequency Applications

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Figure 12.12 Two electric motor designs: a) an induction motor with a squirrel-cage winding and b) a 3/4

variable reluctance motor

"

#

$

$

#

"

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Figure 12.13 A fluxgate magnetometer. a) Schematic b) operating principle

~

V

H

H

B

Hexc

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Figure 12.14 A surface accoustic wave delay line

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a a’

b b’

A magnetic amplifier

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An assortment of soft magnetic components made from Finemet

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A pulse transformer

Figure 12.15 A wire loop antenna, and am equivalent ferrite rod

with a much smaller cross section.

12.5 High Frequency Applications

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Q = '0/+'

A C-core with an airgap

Figure 12.16 An LC filter circuit, and the pass band.

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Figure 12.17 Absorption and transmission for left- and

right-polarized radiation

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Figure 12.18 A plane-polarised wave is decomposed into the sum of two, counter-rotating

circularly-polarized waves (a) which become dephased because they propagate at differentvelocities (b) through the magnetized ferrite. The Faraday rotation , is non- reciprocal - independent

of direction of propagation.

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Figure 12.19 A waveguide propagating a TE01 mode. Filling the upper half with YIG

magnetized vertically absorbs the microwaves for one direction of propagation, but not the

other.

YIG

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Figure 12.20 A four-port circulator a) illustrates the principle, b) shows the sense of

propagation and c) is the logic table. $antenna #receiver "load % transmitter.

%

#

$ "

0100%

0010"

0001#

1000$

%"#$ In out

45°

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A resonant microwave filter. The device transmits a

signal in a narrow frequency range, around the

ferromagnetic resonance frequency of the YIG sphere.