the resource handbook of electronics, 8353ch 09
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Whitaker, Jerry C. Inductors and Magnetic Properties
The Resource Handbook of Electronics.Ed. Jerry C. Whitaker
Boca Raton: CRC Press LLC, 2001
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Chapter
9Inductors and Magnetic Properties
9.1 Introduction
The elemental magnetic particle is the spinning electron. In magnetic materials, such
as iron, cobalt, and nickel, the electrons in the third shell of the atom are the source of
magnetic properties. If the spins are arranged to be parallel, the atom and its associ-
ated domains or clusters of the material will exhibit a magnetic field. The magnetic
field of a magnetized bar has lines of magnetic force that extend between the ends,
one called the north pole and the other the south pole, as shown in Figure 9.1a. The
lines of force of a magnetic field are calledmagnetic flux lines.
9.1.1 Electromagnetism
A current flowing in a conductor produces a magnetic field surrounding the wire as
shown in Figure 9.2a. In a coil or solenoid, the direction of the magnetic field relative
to the electron flow ( to +) is shown in Figure 9.2b. The attraction and repulsion be-
tween two iron-core electromagnetic solenoids driven by direct currents is similar to
that of two permanent magnets.
The process of magnetizing and demagnetizing an iron-core solenoid using a cur-
rent being applied to a surrounding coil can be shown graphically as a plot of the mag-
netizing field strength and the resultant magnetization of the material, called a hyster-
esis loop(Figure 9.3). It will be found that the point where the field is reduced to zero, a
small amount of magnetization, calledremnance, remains.
9.1.2 Magnetic Shielding
In effect, the shielding of components and circuits from magnetic fields is accom-plished by the introduction of a magnetic short circuit in the path between the field
source and the area to be protected. The flux from a field can be redirected to flow in a
partition or shield of magnetic material, rather than in the normal distribution pattern
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between north and south poles. The effectiveness of shielding depends primarily upon
the thickness of the shield, the material, and the strength of the interfering field.
Some alloys are more effective than iron. However, many are less effective at high
flux levels. Two or more layers of shielding, insulated to prevent circulating currents
from magnetization of theshielding, areused in low-level audio,video,anddata appli-
cations.
9.2 Inductors and TransformersInductors are passive components in which voltage leads current by nearly 90 over a
wide range of frequencies. Inductors are usually coils of wire wound in the form of a
cylinder. The current through each turn of wire creates a magnetic field that passes
through every turn of wire in the coil. When the current changes, a voltage is induced
Figure 9.1 Theproperties of magnetism: (a) lines offorce surrounding a bar magnet, (b)relation of compass poles to the earths magnetic field.
Figure 9.2 Magnetic field surrounding a current-carrying conductor: (a) Compass atright indicates thepolarity and direction of a magnetic field circling a conductor carrying
direct current. Iindicates the direction of electron flow. Note: The convention for flow ofelectricity is from+ to, the reverse ofthe actualflow. (b) Directionof magnetic field foracoil or solenoid.
(a) (b)
(a) (b)
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in the wire and every other wire in the changing magnetic field. The voltage induced
in the same wire that carries the changing current is determined by the inductance of
the coil, and the voltage induced in the other wire is determined by the mutual induc-
tance between the two coils. A transformer has at least two coils of wire closely cou-
pled by the common magnetic core, which contains most of the magnetic field within
the transformer.
Inductorsand transformersvarywidely insize,weighingless than 1 g ormore than 1
ton, and have specifications ranging nearly as wide.
9.2.1 Losses in Inductors and TransformersInductors have resistive losses because of the resistance of the copper wire used to
wind the coil. An additional loss occurs because the changing magnetic f ield causes
eddy currents to flow in every conductive material in the magnetic field. Using thin
magnetic laminations or powdered magnetic material reduces these currents.
Losses in inductors are measured by the Q, or quality, factor of the coil at a test fre-
quency. Losses in transformersaresometimesgiven as a specific insertionloss in deci-
bels. Losses in power transformers are given as core loss in watts when there is no load
connectedandas a regulation in percent, measured as therelativevoltage drop foreach
secondary winding when a rated load is connected.
Transformer loss heats the transformer and raises its temperature. For this reason,
transformers are rated in watts or volt-amperes and with a temperature code designat-
ing the maximum hotspot temperature allowable for continued safe long-term opera-tion. For example,class A denotes 105C safe operating temperature.Thevolt-ampere
rating of a power transformer must be always larger than the dc power output from the
rectifier circuit connected because volt-amperes, the product of the rms currents and
Figure 9.3 Graph of the magnetic hysteresis loop resulting from magnetization and de-magnetization of iron. The dashed line is a plot of the induction from the initial magneti-zation. Thesolid line shows a reversalof thefieldand a return to theinitialmagnetizationvalue. Ris theremainingmagnetization (remnance) whenthe field isreduced tozero.
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rms voltages in the transformer, are larger by a factor of about 1.6 than the product of
the dc voltages and currents.Inductorsalso have capacitance between thewires of thecoil, whichcauses thecoil
to have a self-resonance between the winding capacitance and the self-inductance of
the coil. Circuits are normally designed so that this resonance is outside of the fre-
quency range of interest. Transformers are similarly limited. They also have capaci-
tance to the other winding(s), which causes stray coupling. An electrostatic shield be-
tween windings reduces this problem.
9.2.2 Air-Core Inductors
Air-core inductors are used primarily in radio frequency applications because of the
need for values of inductance in the microhenry or lower range. The usual construc-
tion is a multilayer coil made self-supporting with adhesive-covered wire. An inner
diameter of 2 times coil length and an outer diameter 2 times as large yields maxi-mum Q, which is also proportional to coil weight.
9.2.3 Ferromagnetic Cores
Ferromagnetic materials have a permeability much higher than air or vacuum and
cause a proportionally higher inductance of a coil that has all its magnetic flux in this
material. Ferromagnetic materials in audio and power transformers or inductors usu-
ally are made of silicon steel laminations stamped in the forms of letters E or I (Figure
9.4). At higher frequencies, powdered ferric oxide is used. The continued magnetiza-
tion and remagnetization of silicon steel and similar materials in opposite directions
does not follow the same path in both directions but encloses an area in the magneti-
zation curve and causes a hysteresis loss at each pass, or twice per ac cycle.
All ferromagnetic materials show the same behavior; only the numbers for perme-ability, core loss, saturation flux density, and other characteristics are different. The
properties of some common magnetic materials and alloys are given in Table 9.1.
9.2.4 Shielding
Transformers and coils radiate magnetic fields that can induce voltages in other
nearby circuits. Similarly, coils and transformers can develop voltages in their wind-
ings when subjected to magnetic fields from another transformer, motor, or power cir-
cuit. Steel mounting frames or chassis conduct these fields, offering less reluctance
than air.
The simplest way to reduce the stray magnetic field from a power transformer is to
wrap a copperstripas wideas thecoilofwirearoundthe transformerenclosingall three
legs of the core. Shielding occurs by having a short circuit turn in the stray magnetic
field outside of the core.
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Figure 9.4 Physical construction of a power transformer: (a) E-shaped device with thelow- andhigh-voltage windings stacked asshown,(b) constructionusinga boxcore withphysical separation between the low- and high-voltage windings.
(a)
(b)
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Table 9.1 Properties of Magnetic Materials and Magnetic Alloys (From[1]. Used with permission.)
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9.3 References
1. Whitaker, Jerry C. (ed.), The Electronics Handbook, CRC Press, Boca Raton, FL,1996.
9.4 Bibliography
Benson, K. Blair, and Jerry C. Whitaker, Television and Audio Handbook for Techni-cians and Engineers, McGraw-Hill, New York, NY, 1990.
Benson, K.Blair,AudioEngineeringHandbook, McGraw-Hill,New York,NY, 1988.Whitaker, Jerry C., Television Engineers Field Manual, McGraw-Hill, New York,
NY, 2000.
9.5 Tabular Data
Table9.2 MagneticPropertiesof Transformer Steels (From[1]. Usedwithpermission.)
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Table 9.3 Characteristics of High-Permeability Materials (From[1]. Used with permission.)
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Table 9.4 Characteristics of Permanent Magnet Alloys (From[1]. Used with permission.)
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Table 9.5 Properties of Antiferromagnetic Compounds (From[1]. Used with permis-sion.)
Table 9.6 Saturation Constants for Magnetic Substances (From[1]. Used with permis-sion.)
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Table 9.7 Saturation ConstantsandCurie Pointsof Ferromagnetic Elements (From[1].Used with permission.)