chapter 12: applications of soft magnets€¦ · chapter 12: applications of soft magnets 1. losses...
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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: [email protected]
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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.