ASTM A340-23a

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: A340 − 23a
Standard Terminology of
Symbols and Definitions Relating to Magnetic Testing
This standard is issued under the fixed designation A340; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
In preparing this terminology standard, an attempt has been made to avoid, where possible, vector
analysis and differential equations so as to make the definitions more intelligible to the average worker
in the field of magnetic testing. In some cases, rigorous treatment has been sacrificed to secure
simplicity and clarity, but it is believed that none of the definitions will prove to be misleading.
It is the intent of this terminology standard to be consistent in the use of symbols and units with
those found in IEC 60050-221:1990 International Electrotechnical Vocabulary Chapter 221: Magnetic
materials and components. Although Committee A06 has chosen to make SI units normative, the
extensive technical and commercial literature using the older Gaussian units requires that many
definitions contain discussion about and use of both unit systems. This is not an endorsement of the
older unit system and users of this terminology are encouraged to use SI units where possible.
1. Referenced Documents A343/A343M Test Method for Alternating-Current Mag-
netic Properties of Materials at Power Frequencies Using
1.1 ASTM Standards:
Wattmeter-Ammeter-Voltmeter Method and 25-cm Ep-
stein Test Frame
This terminology is under the jurisdiction of ASTM Committee A06 on
A772/A772M Test Method for AC Magnetic Permeability of
Magnetic Properties and is the direct responsibility of Subcommittee A06.92 on
Materials Using Sinusoidal Current
Terminology and Definitions.
Current edition approved Dec. 1, 2023. Published December 2023. Originally
approved in 1949. Last previous edition approved in 2023 as A340 – 23. DOI:
2. Terminology
10.1520/A0340-23A.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
Part 1—Symbols Used in Magnetic Testing
Symbol Term B residual flux density
r
B saturation flux density
s
a cross-sectional area of B coil cf crest factor
A cross-sectional area of specimen CM cyclically magnetized condition
A' solid area d lamination thickness
B df distortion factor
magnetic flux density
D magnetic dissipation factor
m
H
magnetic induction E exciting voltage
E induced primary voltage
E induced secondary voltage
∆B excursion range of induction
B biased flux density E flux volts
f
b
f cyclic frequency in hertz
B demagnetization flux density
d
B H energy product ^ magnetomotive force
d d
(BH) maximum energy product ff form factor
max
H magnetic field strength
B incremental flux density
∆
B intrinsic flux density ∆H excursion range of magnetic field strength
i
H biasing magnetic field strength
B maximum value of magnetic flux density in a
m b
static hysteresis loop H coercive field strength
cB
H intrinsic coercive field strength
B maximum value of magnetic flux density in a
max cJ
dynamic hysteresis loop H demagnetizing field strength
d
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A340 − 23a
H incremental magnetic field strength P winding loss (copper loss)
∆ w
H ac magnetic field strength (from an assumed P exciting power
L z
peak value of magnetizing current) P specific exciting power
z (B;f)
H maximum magnetic field strength in a hyster- Q magnetic storage factor
m
m
esis loop
5 reluctance
H maximum magnetic field strength in a flux- R core resistance
max
current loop
R winding resistance
w
H ac magnetic field strength (from a measured S lamination factor (stacking factor)
p
peak value of exciting current) SCM symmetrically cyclically magnetized condition
H instantaneous magnetic field strength (coinci- T Curie temperature
t c
dent with B ) w lamination width
max
H ac magnetic field strength (from an assumed
W hysteresis energy loss
z h
peak value of exciting current) linear expansion, coefficient (average)
α¯
I ac exciting current (rms value)
∆χ incremental tolerance
I ac core loss current (rms value)
c β hysteretic angle
I constant current
dc γ loss angle
I ac magnetizing current (rms value)
m cos γ magnetic power factor
J magnetic polarization
γ proton gyromagnetic ratio
p
J residual magnetic polarization
r μ magnetic constant
J saturation magnetic polarization
s δ density
k' coupling coefficient
κ susceptibility
! flux path length
μ absolute permeability
! effective flux path length
1 μ effective circuit permeability
e
! gap length
g ac Permeabilities:
+ (also φ N ) flux linkage
μ rms amplitude permeability
a,eff
+ mutual flux linkage
m μ amplitude permeability
a
L self inductance
μ inductance permeability
L
L core inductance
1 μ L incremental inductance permeability
∆
L incremental inductance
∆ μ peak permeability
p
L intrinsic inductance
i μ incremental peak permeability
∆p
L mutual inductance
m μ instantaneous permeability
i
L initial inductance
0 μ impedance permeability
z
L series inductance
s μ incremental impedance permeability
∆z
L winding inductance
w dc Permeabilities:
m magnetic moment
μ normal permeability
M magnetization
μ differential permeability
d
M residual magnetization
r μ incremental permeability
∆
M saturation magnetization
s μ incremental intrinsic permeability
∆i
m total mass of a specimen
μ maximum permeability
m
m active mass of a specimen
1 μ initial permeability
i
N demagnetizing factor
μ relative permeability
r
N turns in a primary winding
1 μ reversible permeability
rev
N turns in a secondary winding
2 μ'/cot γ figure of merit
p magnetic pole strength
ν reluctivity
3 permeance
π the numeric 3.1416
P active (real) power
ρ resistivity
P apparent power
a φ magnetic flux
P specific apparent power
a (B;f) φN flux linkage (see +)
P core loss
c χ mass susceptibility
P specific core loss
c (B;f) χ initial susceptibility
P eddy current loss
e ω angular frequency in radians per second
P normal hysteresis core loss
h
P reactive (quadrature) power
q
P residual core loss
r
Part 2—Definition of Terms Used in Magnetic Testing
DISCUSSION—Two types of magnetic aging can be defined:
aging coefficient—the percentage change in a specific mag-
(a) Intrinsic magnetic aging due to the material as manufactured
netic property resulting from a specific aging treatment.
not being in its thermodynamically stable state so that further micro-
DISCUSSION—The aging treatments usually specified for iron and steel
structural changes occur during service. Such aging is strongly depen-
are:
dent on temperature. The classic example is the aging of iron and
(a) 100 h at 150°C or
electrical steels due to the precipitation of nitrides and carbides. Other
(b) 600 h at 100°C.
examples would include amorphous, nanocrystalline materials and thin
aging, magnetic—the time dependent change in magnetic
films where residual stresses introduced during manufacturing are
properties; such changes can be due to either intrinsic or
slowly relieved during service. Ferrofluids show magnetic aging effects
extrinsic factors, are not a consequence of improper use of
due to time dependent degradation of surfactants which results in a
the material and are usually detrimental to magnetic perfor-
settling of the colloidal particles.
mance; in some instances, it may be possible to reverse the (b) Extrinsic or environmental magnetic aging due to changes in
effect of magnetic aging via heat treatment or some other the magnetic domain structure or microstructure caused by external
factors such as mechanical vibration, corrosion, irradiation, service
process, but typically the benefits are short-lived, and aging
temperature fluctuations, and external magnetic fields. Unlike intrinsic
will occur again.
A340 − 23a
magnetic aging, this type of aging can occur in materials that are
area, A—the geometric cross-sectional area of a magnetic path
otherwise thermodynamically stable.
which is perpendicular to the direction of the magnetic flux
density.
amorphous alloy—a semiprocessed alloy produced by a rapid
quenching, direct casting process resulting in metals with
B(H) loop—a hysteresis loop where the magnetic flux density
noncrystalline structure.
(B) is plotted as a function of the magnetic field strength (H).
Unless otherwise stated, it is assumed that the loop repre-
ampere-turn—the unit of magnetomotive force in the SI
sents the SCM condition and therefore has 180° rotational
system of units.
symmetry about the origin of the coordinate system.
ampere per metre, A/m—the unit of magnetic field strength in
B (H) loop—a hysteresis loop where the intrinsic flux density
i
the SI system of units.
(B ) is plotted as a function of the magnetic field strength
i
(H). Unless otherwise stated, it is assumed that the loop
NOTE 1—The term ampere-turn per metre has been used as the unit of
magnetic field strength. Further use of this term in ASTM standards is represents the SCM condition and therefore has 180° rota-
deprecated.
tional symmetry about the origin of the coordinate system.
anisotropic material—a material in which the magnetic prop-
Bloch wall—a domain wall in which the magnetic moment at
erties differ in various directions.
any point is substantially parallel to the wall surface. See
also domain wall.
anisotropy of loss—the ratio of the specific core loss measured
with flux parallel to the rolling direction to the specific core
Bohr magneton—a constant that is equal to the magnetic
loss with flux perpendicular to the rolling direction. moment of an electron because of its spin. The value of the
−21
constant is (9 274 078 × 10 erg/gauss or
P
c ~B;f! l
−24
anisotropy of loss 5 9 274 078 × 10 J/T).
P
c ~B;f! t
cgs-emu system of units—the system for measuring physical
where:
quantities in which the base units are the centimetre, gram,
P = specific core loss value with flux parallel to the
c (B;f) l
and second, and the numerical value of the magnetic
rolling direction, and
constant, μ , is unity.
P = specific core loss value with flux perpendicular to
c (B;f) t
the rolling direction.
coercive field strength, H —the absolute value of the applied
cB
magnetic field strength (H) required to restore the magnetic
DISCUSSION—This definition of anisotropy normally applies to elec-
flux density (B) to zero.
trical steels with measurements made in an Epstein frame at a flux
DISCUSSION—The symbol H has historically been used to denote the
density of 15 kG [1.5 T] and a frequency of 60 Hz (see Test Method c
coercive field strength determined from a B(H) loop. Further use of this
A343/A343M).
symbol in ASTM A06 standards is deprecated.
NOTE 2—The IEC defines a similar term called the loss anisotropy
factor. It is however calculated differently and is not numerically equal to
DISCUSSION—The coercive field strength monotonically increases
the above definition.
with increasing maximum magnetic field strength (H ) reaching a
m
maximum or limiting value termed the coercivity. Unless it is known
anisotropy of permeability—the ratio of relative peak perme-
that the material has been magnetized to saturation, the term coercive
ability measured with flux parallel to the rolling direction to
field strength is preferred.
the relative peak permeability measured with flux perpen-
DISCUSSION—The coercive field strength is not completely described
dicular to the rolling direction.
without knowing the maximum magnetic flux density (B ) or maxi-
m
μ
prl mum magnetic field strength (H ) used in the measurement.
m
anisotropy of permeability 5
μ
prt
coercive field strength, intrinsic, H —the absolute value of
cJ
where:
the applied magnetic field strength (H) required to restore
μ = relative peak permeability value with flux parallel to
either the magnetic polarization (J) or magnetization (M) to
prl
the rolling direction, and
zero.
μ = relative peak permeability value with flux perpendicu-
prt DISCUSSION—The symbol H has historically been used to denote the
ci
lar to the rolling direction.
intrinsic coercive field strength determined from a B (H) loop. Further
i
use of this symbol in ASTM A06 standards is deprecated.
DISCUSSION—This definition of anisotropy normally applies to elec-
DISCUSSION—The intrinsic coercive field strength monotonically
trical steels with measurements made in an Epstein frame at a flux
increases with increasing maximum magnetic field strength (H )
density of 15 kG [1.5 T] and a frequency of 60 Hz (see Test Method
m
reaching a maximum or limiting value termed the intrinsic coercivity.
A343/A343M).
Unless it is known that the material has been magnetized to saturation,
antiferromagnetic material—a feebly magnetic material in the term intrinsic coercive field strength is preferred.
which almost equal magnetic moments are lined up antipar-
DISCUSSION—The measured value of intrinsic coercive field strength
allel to each other. Its susceptibility increases as the tem-
will be the same whether it is measured from a magnetic polarization
perature is raised until a critical (Neél) temperature is
J(H) or a magnetization M(H) hysteresis loop and will always be
reached; above this temperature the material becomes para-
numerically larger than the coercive field strength (H ) measured from
cB
magnetic. a magnetic flux density B(H) hysteresis loop.
A340 − 23a
DISCUSSION—The intrinsic coercive field strength is not completely
core loss density—the active power (watts) expended in a
described without knowing the maximum magnetic polarization, maxi-
magnetic core in which there is a cyclically varying mag-
mum magnetization or maximum magnetic field strength (H ) used in
m
netic flux density of a specified maximum value, B, at a
the measurement.
specified frequency, f, divided by the effective volume of the
core.
coercivity—see coercive field strength.
DISCUSSION—This parameter is normally used only for non-laminated
coercivity, intrinsic—see coercive field strength, intrinsic.
cores such as ferrite and powdered cores.
coercivity, normal—this term is used exclusively in the
core plate—a generic term for any insulating material, formed
permanent magnet industry to denote the coercivity (H ) to
cB metallurigically or applied externally as a thin surface
distinguish it from the intrinsic coercivity (H ). The use of
coating, on sheet or strip stock used in the construction of
cJ
the word “normal” does not imply anything about the
laminated and tape wound cores.
symmetry of the hysteresis loop of the material being tested.
coupling coefficient, k'—the ratio of the mutual inductance
commutation curve—see normal magnetization curve.
between two windings and the geometric mean of the
individual self-inductances of the windings.
core, laminated—a magnetic component constructed by
stacking suitably thin pieces of magnetic material which are
crest factor, cf—the ratio of the peak value of a waveform to
stamped, sheared, or milled from sheet or strip material.
its rms value.
Individual pieces usually have an insulating surface coating
=
DISCUSSION—For a sinusoidal waveform, the crest factor is 2.
to minimize eddy current losses in the assembled core.
Curie temperature, T —the temperature above which a fer-
c
core, mated—two or more magnetic core segments assembled
romagnetic or ferrimagnetic material becomes paramagnetic.
with the magnetic flux path perpendicular to the mating
current, ac core loss, I —the rms value of the in-phase
surface.
c
component (with respect to the induced voltage) of the
core, powder (dust)—a magnetic core comprised of small
exciting current supplied to a coil which is linked with a
particles of electrically insulated metallic ferromagnetic
ferromagnetic core.
material. These cores are characterized by low hysteresis and
current, ac exciting, I—the rms value of the total current
eddy current losses.
supplied to a coil that is linked with a ferromagnetic core.
core, tape-wound—a magnetic component constructed by the
DISCUSSION—Exciting current is measured under the condition that
spiral winding of strip material onto a suitable mandrel. The
any other coil linking the same core carries no current.
strip material usually has an insulating surface coating which
current, ac, magnetizing, I —the rms value of the magnetiz-
m
reduces interlaminar eddy current losses in the finished core.
ing component (lagging with respect to applied voltage) of
core loss, P —the active power (watts) absorbed in a ferro-
the exciting current supplied to a coil that is linked with a
c
magnetic or ferrimagnetic material in which there is a time
ferromagnetic core.
varying magnetic flux density; in electrical steel technology,
current, dc, I —a steady-state dc current. A dc current
dc
the core loss is sometimes referred to as the iron loss.
flowing in an inductor winding will produce a unidirectional
DISCUSSION—Although core loss is almost entirely due to eddy
magnetic field in the magnetic material.
currents generated in the vicinity of moving magnetic domain walls, it
is customary to consider the core loss to be the sum of three losses, the
customary units—a set of industry-unique units from the
hysteresis loss (P ), the eddy current loss (P ), and the residual core
h e
cgs-emu system of units and U.S. inch-pound systems and
loss (P ), all of which have different functional dependencies on
r
frequency for a given material and specimen. This separation of losses units derived from the two systems.
is useful in both practical applications and in modeling of the core loss.
DISCUSSION—Examples of customary units used in ASTM A06
standards include:
DISCUSSION—For the purpose of grading magnetic materials, the core
Quantity
loss is normally measured in the symmetrically cyclically magnetized
Quantity Name Symbol Unit Name Unit Symbol
(SCM) condition using a sine flux waveform, or the results are
mathematically corrected for deviations from the sinusoidal condition.
Magnetic field strength H oersted Oe
Magnetic flux density B gauss G
core loss, incremental, P —the core loss in a magnetic
c∆ Specific core loss P watt/pound W/lb
c(B;f)
material when the material is subjected simultaneously to a
cyclically magnetized condition, CM—a magnetic material is
dc biasing magnetic field and an alternating magnetic field.
in a cyclically magnetized condition when, after having been
core loss, residual, P —also called the anomalous or excess subjected to a sufficient number of identical cycles of
r
loss, the portion of the core loss, P , which cannot be magnetizing field, it follows identical hysteresis or flux-
c
attributed to hysteresis or classical eddy current losses. current loops on successive cycles which are not symmetri-
cal with respect to the origin of the axes.
core loss, specific, P —the active power (watts) expended
c(B;f)
per unit mass of magnetic material in which there is a demagnetization curve, normal—the portion of a normal
cyclically varying magnetic flux density of a specified hysteresis loop that lies in the second quadrant, that is,
maximum value, B, at a specified frequency, f. between H = 0 and the coercive field strength H .
cB
A340 − 23a
demagnetization curve, intrinsic—the portion of an intrinsic analysis or direct measurement E , E , E , and so forth are
1 2 3
hysteresis loop (either B , J or M vs H) that lies in the second the effective values of the pure sinusoidal harmonic compo-
i
quadrant, that is, between H = 0 and the intrinsic coercive nents of a distorted voltage waveform, then the distortion
field strength H . factor is the ratio of the root mean square of the second and
cJ
all higher harmonic components to the fundamental compo-
demagnetizing factor, N—the ratio of the self-demagnetizing
nent.
magnetic field strength to the magnetization (M). It is a
2 2 2 1/2
df 5 @E 1E 1E 1···# E
dimensionless quantity ranging in value from 0 to 1 and 2 3 4 1
DISCUSSION—There are no dc components (E ) in the distortion
depends on the specimen geometry, dimensions, and the
factor.
magnetic susceptibility of the material.
DISCUSSION—The demagnetizing factor has a single calculable value
domains, ferromagnetic—magnetized regions, either macro-
only when the sample is an ellipsoid (usually an ellipsoid of revolution)
scopic or microscopic in size, within ferromagnetic materi-
or has the value zero (for a closed uniform magnetic circuit). Approxi-
als. Each domain, in itself, is magnetized to magnetic
mate values are available as the result of calculations or measurements.
saturation at all times, and the saturation magnetization is
For demagnetization factors derived from measurements, one might
unidirectional within the domain.
encounter the symbols N for ballistic measurements, N for fluxmetric
b f
measurements, and N for magnetometric measurements. Additional
m
domain wall—a boundary region between two adjacent do-
descriptors, used less frequently, define the direction of measurement,
mains within which the orientation of the magnetic moment
that is, N , N , and N .
x y z
of one domain changes into a different orientation of the
demagnetizing field strength, H —a magnetic field strength
d
magnetic moment in the other domain.
applied in such a direction as to reduce the magnetic flux
density in a magnetized body. See demagnetization curve. eddy current—an electric current developed in a material as a
result of induced voltages developed in the material.
density, δ—the ratio of mass to volume of a material. In the
3 3
cgs-emu system of units, g/cm . In SI units, kg/m .
electrical steel—a term used commercially to designate strip
or sheet used in electrical applications and historically has
diamagnetic material—a material whose relative permeabil-
referred to flat-rolled, low-carbon steels or alloyed steels
ity is less than unity.
with silicon or aluminum, or both. Common types of
DISCUSSION—The intrinsic flux density, B , is oppositely directly to
i
electrical steels used in the industry are grain-oriented
the applied magnetic field strength H.
electrical steel, nonoriented electrical steel, and magnetic
disaccommodation—a time dependent change of magnetic
lamination steel.
properties, especially the initial permeability, that occurs
electrical steel, grain oriented—a flat-rolled silicon-iron alloy
after demagnetization of a magnetic material. This change is
usually containing approximately 3 % silicon, having en-
usually due to the motion of point defects such as vacancies
hanced magnetic properties in the direction of rolling and
and interstitial atoms, occurs over a time period measured in
normally used in transformer cores.
seconds or minutes, and is reversible by demagnetization. It
is a different phenomenon than magnetic aging which (a)
electrical steel, nonoriented—a flat-rolled silicon-iron or
typically involves the clustering of impurity atoms or pre-
silicon-aluminum-iron alloy containing 0.0 to 3.5 % silicon
cipitation of a new phase, (b) occurs over a much longer time
and 0.0 to 1.0 % aluminum and having similar core loss in
period (normally weeks or months at room temperature), and
all directions.
(c) the changes are not reversible by demagnetization.
emu—the notation emu is an indicator of electromagnetic
dissipation factor, magnetic, D —the tangent of the hyster-
m
units. When used in conjunction with magnetic moment, m,
etic angle that is equal to the ratio of the core loss current, I ,
c
it denotes units of ergs per oersted, erg/Oe. A moment of 1
to the magnetizing current, I . Thus:
m
erg/Oe is produced by a current of 10 amperes (1 abampere)
D 5 tan β 5 cot γ 5 I /I 5 ωL /R 5 I/Q
m c m 1 1 m flowing in a loop of area 1 cm . The work done to rotate a
DISCUSSION—This dissipation factor is also given by the ratio of the
moment of 1 erg/Oe from parallel to perpendicular in a
energy dissipated in the core per cycle of a periodic SCM excitation
uniform field of 1 Oe is 1 erg. The conversion to the SI units
(hysteresis and eddy current heat loss) to 2π times the maximum energy
of magnetic moment J/T (joule/tesla) or A m is given by:
stored in the core.
erg/Oe cgs 2 emu 10 amperes cm cgs 2 emu
~ ! ~ !
distortion, harmonic—the departure of any periodically vary-
[ 5 10 (1)
J/T ~SI! A m ~SI!
ing waveform from a pure sinusoidal waveform.
DISCUSSION—The distorted waveform that is symmetrical about the
Magnetization, M, the magnetic moment per unit volume,
3 3
zero amplitude axis and is most frequently encountered in magnetic
has units erg/(Oe-cm ), often expressed as emu/cm .
testing contains only the odd harmonic components, that is
fundamental, 3rd harmonic, 5th harmonic, and so forth. Nonsymmetri-
energy product—the product of the coordinate values of any
cal distorted waveforms must contain some even harmonic
point on a normal demagnetization curve. This is also called
components, in addition to the fundamental and, perhaps, some odd
the BH product. In the cgs-emu system of units the energy
harmonic components.
product is expressed in units of gauss-oersted. In the SI
distortion factor, df—a numerical measure of the distortion in system of units, the energy product is expressed in units of
any ac nonsinusoidal waveform. For example, if by Fourier joule per cubic metre.
A340 − 23a
DISCUSSION—Although the energy product is mathematically
flux density, biased, B —the value of the dc magnetic flux
b
negative, it is customary to express it as a positive number.
density around which cyclic flux density changes are occur-
ring in a magnetic material simultaneously subjected to both
energy-product curve, magnetic—the curve obtained by
a cyclic and a dc biasing field; the biased flux density is a
plotting the product of the corresponding coordinates, B and
d
function of the incremental magnetic field strength, H , and
∆
H , of points on the demagnetization curve as abscissa
d
is not determined by the normal magnetization curve.
against the magnetic flux density, B , as ordinates.
d
DISCUSSION—The maximum value of the energy product, (BH) ,
max
flux density, demagnetization, B —the magnetic flux density
d
corresponds to the maximum value of the external energy.
at any point on any normal demagnetization curve in a
DISCUSSION—The demagnetization curve is plotted to the left of the magnetic material.
vertical axis and usually the energy-product curve to the right.
DISCUSSION—Although it is customary to consider the demagnetiza-
tion curve to lie entirely within the second quadrant, there is an
energy product, maximum (BH) —for a given demagneti-
max
increasing tendency to continue the curve into the third quadrant when
zation curve, the maximum value of the energy product. The
measuring high coercivity permanent magnets.
maximum energy product is an important figure of merit for
flux density, incremental, B —one half the algebraic differ-
permanent magnets. ∆
ence of the extreme values of the magnetic flux density
equipment test level accuracy—(1) For a single test
during a cycle in a magnetic material that is subjected
equipment, using a large group of test specimens, the
simultaneously to a biasing magnetizing field and a sym-
average percentage of test deviation from the correct average
metrically cyclically varying magnetizing field; twice the
value. (2) The average percentage deviation from the aver-
incremental flux density is indicated by the symbol ∆B, thus:
age value obtained from similar tests, on the same test
B 5 ∆B/2
∆
specimen or specimens, when measured with a number of
other test equipments that have previously been proven to
flux density, intrinsic, B —the vector difference between the
i
have both suitable reproducibility of measurement and test magnetic flux density in a magnetic material and the
level, and whose calibrations and quality have general
magnetic flux density that would exist in a vacuum under the
acceptance for standardization purposes and where better influence of the same magnetic field strength when measure-
equipment for establishing the absolute accuracy of test is
ments are made using cgs-emu units. This is expressed by
not available. the equation:
B 5 B 2 H
exciting current, ac, I—see current, ac exciting. i
exciting voltage, E—the ac rms voltage across a winding
This term is not defined or used in the SI system of units
linking the flux of a magnetic core. The voltage across the
where the magnetic polarization (J) is instead used. The
winding equals that across the assumed parallel combination
use of the term intrinsic flux density should be restricted
of core inductance L , and core resistance, R .
1 1
to cgs-emu measurements.
feebly magnetic material—a material generally classified as
flux density, maximum—(1)B the maximum value of mag-
m
“nonmagnetic,” whose maximum normal permeability is
netic flux density, B, in a static hysteresis loop. The tip of this
less than 4.
loop has the coordinates B and H , which occur simulta-
m m
neously in time. (2)B the maximum value of magnetic
max
ferrimagnetic material—a material whose atomic magnetic
flux density, B, in a dynamic hysteresis loop. The tip of this
moments are both ordered and anti-parallel but being un-
loop has the coordinates B and H which may or may
max max
equal in magnitude produce a net magnetization in one
not occur simultaneously in time; B may occur later than
max
direction.
H (especially at low magnetic flux densities).
max
ferrite—a term referring to magnetic oxides in general, and
DISCUSSION—The maximum flux density is not synonymous with
especially to material having the formula M O Fe O , where saturation flux density (B ). It is a magnetic test parameter, not a
2 3 s
physical property.
M is a divalent metal ion or a combination of such ions.
Certain ferrites, magnetically “soft” in character, are useful
flux density, open circuit—the magnetic flux density that
for core applications at radio and higher frequencies because
remains in a magnetic material in an open magnetic circuit
of their advantageous magnetic properties and high volume
after the applied magnetic field strength is reduced to zero.
resistivity. Other ferrites, magnetically “hard” in character,
have desirable permanent magnet properties. flux density, remanent—the magnetic flux density that re-
mains in a magnetic material or magnetic circuit after the
ferromagnetic material—a material whose magnetic mo-
applied magnetic field strength is reduced to zero.
ments are ordered and parallel producing magnetization in
DISCUSSION—If there are no self-demagnetizing fields in the magnetic
one direction.
circuit, such as when the circuit is closed, the remanent flux density will
equal the residual flux density, B ; if self-demagnetizing fields are
r
figure of merit, magnetic, μ'/cot γ—the ratio of the real part of
present, such as in a circuit with a non-magnetic gap, the remanent flux
the complex relative permeability to the dissipation factor of
density will be less than the residual flux density.
a ferromagnetic material.
flux density, residual, B —the value of magnetic flux density
DISCUSSION—The figure of merit index of the magnetic efficiency of
r
the core in various ac electromagnetic devices. (B) corresponding to zero magnetic field strength (H) in a
A340 − 23a
symmetrically cyclically magnetized material not subject to gap length, ℓ —the distance that the flux transverses in the
g
a self-demagnetization field. central region of a gap in a core having an “air” (nonmag-
netic) gap in the flux path may be considered unity in the
DISCUSSION—The residual flux density is not completely described
without specifying either the maximum magnetic flux density or
gap.
maximum magnetic field strength used in the measurement. The
gauss (plural gausses), G—the unit of magnetic flux density
residual flux density will monotonically increase with increasing
applied magnetic field strength reaching a maximum or limiting value.
in the cgs-emu system of units. The gauss is equal to 1
−4
NOTE 3—This term replaces the historically used term residual maxwell per square centimetre or 10 tesla. See magnetic
induction.
flux density.
NOTE 4—The IEC uses the term remanent flux density instead of
residual flux density. The term remanent flux density is used in ASTM gilbert, Gb—the unit of magnetomotive force in the cgs-emu
standards to denote the magnetic flux density remaining in a magnetic
system of units. The gilbert is a magnetomotive force of
material or circuit when self-demagnetization fields are present.
4π/10 ampere-turns. See magnetomotive force.
flux linkage, +—the sum of all flux lines in a coil.
gyromagnetic ratio, proton, γ —the ratio of the magnetic
p
+ 5 φ 1φ 1φ 1···φ
moment of a hydrogen nucleus to its angular momentum.
1 2 3 N
DISCUSSION—The gyromagnetic ratio is used to calculate the mag-
where:
netic field from a measured resonance frequency when using the
φ = flux linking turn 1; nuclear magnetic resonance technique. The relationship is:
φ = flux linking turn 2, and so forth; and
B 5 ~2πf/γ ! gausses 5 ~2 π f / γ ! × 10 teslas
p p
φ = flux linking the Nth turn.
N
where:
DISCUSSION—When the coupling coefficient, k', is less than unity, the
f = resonance frequency in cycles per second (hertz) and
flux linkage equals the product of the average flux linking the turns and
γ = gyromagnetic ratio (the accepted value at present for
p
the total number of turns. When the coupling coefficient is equal to
4 −1 −1
water is 2.675 12 × 10 gauss s ).
unity, the flux linkage equals the product of the total flux linking the
coil and the total number of turns.
henry (plural henries), H—the unit of self- or mutual
inductance. The henry is the inductance of a circuit in which
flux linkage, mutual, + —the flux linkage existing between
m
a voltage of 1 V is induced by a uniform rate of change 1 A/s
two windings on a magnetic circuit. Mutual linkage is
in the circuit. Alternatively, it is the inductance of a circuit in
maximum when the coupling coefficient is unity.
which an electric current of 1 A/s produces a flux linkage of
flux path length, ℓ—the distance along a flux loop.
one weber turn (Wb turn) or 10 maxwell-turns. See
inductance, mutual, and inductance, self.
flux path length, effective, ℓ —the calculated length of the
flux paths in a magnetic core, which is used in the calcula-
hertz, Hz—the unit of cyclic frequency, f.
tions of certain magnetic parameters.
hysteresis energy loss, W —the energy expended in a single
h
flux volts, E —the voltage induced in a winding of a magnetic
excursion around a static B(H) loop. The energy dissipated is
f
component when the magnetic material is subjected to the integrated area enclosed by the loop and manifests itself
repeated magnetization under SCM or CM conditions.
as heat.
For the cgs-emu system of units, the hysteresis loss is
−8
E = 4.443 B A'Nf × 10 V (SCM excitation)
f max
expressed as:
E = 2.221 ∆ BA' Nf × 10 V (CM excitation)
f
E = 1.1107 E
f avg
W 5 rHdB
h
4π
which:
2 where:
A' = solid cross-sectional area of the core in cm ,
W = hysteresis loss, ergs/cm /cycle,
N = number of winding turns, and h
H = magnetic field strength, Oe, and
f = the frequency in hertz.
B = magnetic flux density, G.
form factor, ff—the ratio of the rms value of a periodically
For the SI system of units, the hysteresis loss is expressed as:
alternating quantity to its average absolute value.
W 5 rHdB (2)
h
DISCUSSION—For a sinusoidal variation, the form factor is:
where:
π/2=2 5 1.1107
W = hysteresis loss, J/m /cycle,
h
frequency, angular, ω—the number of radians per second H = magnetic field strength, A/m, and
B = magnetic flux density, T.
traversed by a rotating vector that represents any periodically
varying quantity.
hysteresis loop—a close curve obtained from measurements
DISCUSSION—Angular frequency, ω, is equal to 2π times the cyclic
on a ferromagnetic or ferrimagnetic material by plotting
frequency, f.
corresponding values of magnetic flux density (B), intrinsic
frequency, cyclic, f—the number of hertz (cycles/second) of a flux density (B ), magnetic polarization (J), or magnetization
i
periodic quantity. (M) on the vertical axis and magnetic field strength (H) on
A340 − 23a
the horizontal axis when the material is passing through a dinate system when measured in the SCM condition. His-
complete cycle of applied magnetic field strength. They are torically this term has been most often applied to a B(H) loop
commonly referred to as the B(H), B (H), J(H), and M(H) although its use is not restricted to this loop. This term is
i
loops respectively. seldom used today.
hysteresis loop, biased—an incremental hysteresis loop that
hysteresis loop, saturation—also called the major hysteresis
lies entirely in any one quadrant.
loop, it is the normal hysteresis loop obtained when the
DISCUSSION—In this case, both of the limiting values of H and B are
maximum applied magnetic field strength is sufficient to
in the same direction.
cause magnetic saturation of the material.
hysteresis loop, dynamic—a hysteresis loop obtained when
hysteresis loop, static—a hysteresis loop obtained when the
the measurement is conducted at a magnetic field strength
measurement is conducted at a magnetic field strength rate of
rate of change that is sufficiently high that eddy currents
change that is sufficiently slow that eddy currents do not
affect the loop shape. It is also commonly referred to as an
affect the loop shape. This is also commonly referred to as a
a-c hysteresis loop. It has been less commonly called a
d-c hysteresis loop.
flux-current loop.
DISCUSSION—The size and shape of a dynamic hysteresis loop for a
hysteresis loss, P —the active power (watts) absorbed in a
h
given maximum magnetic flux density depends on several factors such
ferromagnetic or ferrimagnetic material as a result of mag-
as the magnetizing waveform and frequency, specimen dimensions, and
netic hysteresis. It is equal to the product of the hysteresis
electrical resistivity. Knowledge of these factors is required to properly
energy loss W and frequency.
interpret the loop. h
hysteresis loop, dynamic, normal—the dynamic hysteresis
hysteresis loss, rotational—the active power (watts) absorbed
loop obtained when the magnetic material is symmetrically in a ferromagnetic or ferrimagnetic material when subjected
cyclically magnetized (that is, no dc bias present). to a constant magnetic field, the direction of which rotates
DISCUSSION—The area enclosed by the normal dynamic hysteresis
with respect to the material, either in a continuously cyclic or
loop is proportional to the core loss.
in a repeated oscillatory manner.
hysteresis loop, incremental—the hysteresis loop, nonsym-
hysteresis, magnetic—the property of a ferromagnetic or
metrical with respect to the axes, exhibited by a magnetic
ferrimagnetic material where the magnetic flux density (B),
material in a cyclically magnetized condition while under
magnetic polarization (J), and magnetization (M) depend on
the influence of a static (dc) biasing field.
the prior history of magnetization. It is due to a lag in these
DISCUSSION—The limiting values of H may have opposite polarity,
parameters with respect to the applied magnetic field
but definitely have different maximum absolute values. An incremental
strength resulting from magnetic domain behavior. It mani-
loop may be initiated at either some point on a normal hysteresis loop
or at some point on the normal magnetization curve. fests itself by irreversibility of magnetization (the param-
eters will have more than one possible value at a given
hysteresis loop, intrinsic—the B (H) and J(H) loops are often
i
magnetic field strength) and energy dissipation during the
referred to as intrinsic hysteresis loops since they represent
magnetization cycle.
the contribution of the magnetic material to the observed
magnetic flux density. That is the contribution of the
hysteretic angle, magnetic, β—the mean angle by which the
magnetic field strength (H) due to the applied magnetic field
fundamental component of exciting current leads the funda-
has been removed. In the cgs-emu system of units the
mental component of magnetizing current, I , in an inductor
m
relationship between B and B is given by:
i having a ferromagnetic core.
DISCUSSION—Because of hysteresis, the instantaneous value of the
B 5 B 2 H
i
hysteretic angle will vary during the cycle of SCM excitation. However,
In the SI system of units, the relationship between B and J
β is taken to be the mean effective value of this angle.
is given by:
inductance, core, L —the effective parallel circuit inductance
J 5 B 2 μ H
o
of a ferromagnetic core based upon a hypothetical nonresis-
tive path that is exclusively considered to carry the magne-
where μ denotes the magnetic constant. The difference
o
tizing current, I .
between the B(H) loop and the intrinsic hysteresis loop m
DISCUSSION—The product I ωL equals the quadrature power deliv-
is usually negligible for soft magnetic materials. For per- m 1
ered to the core.
manent magnet materials, the difference can be substan-
tial and both the B(H) loop and intrinsic hysteresis
inductance, incremental, L —the self-inductance of an elec-
∆
loop (B (H) or J(H) depending on the system of units)
i trical circuit when the ferromagnetic core has an ac cyclic
are used in magnetic system design and specification.
magnetization produced by specified values of both ac and
dc components of the exciting current.
hysteresis loop, minor—a hysteresis loop obtained when the
maximum applied magnetic field strength is less than that
inductance, initial, L —the limiting value of the core
required to cause magnetic saturation of the material. This
inductance, L reached in a ferromagnetic core when, under
loop can be either symmetrical or asymmetrical.
ac symmetrical cyclic excitation, the magnetizing current
hysteresis loop, normal—a hysteresis loop which has 180° has been progressively and gradually reduced from a com-
rotational symmetry with respect to the origin of the coor- paratively high value to a zero value.
A340 − 23a
DISCUSSION—Initial inductance may be obtained by highly sensitive
di/dt = time rate of change of the current.
ASTM bridge methods working in the range in which μ is a linear
L
function of H. A series of decreasing values of μ is measured and
DISCUSSION—If ferromagnetic material or eddy currents are present,
L
plotted versus corresponding values of magnetizing current, I (or
the self-inductance must be regarded as a function of the circuit current,
m
other suitable excitation parameter), and the data extrapolated to zero
its rate of change, and the magnetic history of the material. Thus:
excitation. See permeability, initial dynamic.
e 5 2 ~d ~Li! / dt! 5 2@L~di/dt!1i~dL/dt!#
inductance, intrinsic (ferric), L —that portion of the self-
i
inductance, series, L —the effective series ac self-inductance
s
inductance which is due to the intrinsic flux density in a
exhibited by an inductor having a ferromagnetic core and
ferromagnetic core.
subjected to an SCM excitation after the core has been
DISCUSSION—It is determined at a specified value of the magnetizing
demagnetized.
current.
DISCUSSION—The value of series inductance is a function of the level
inductance, mutual, L —the common property of two elec-
m
of excitation.
trical circuits that determines the flux linkage in one circuit
inductance, winding, L —the linear inductance of the mag-
(the secondary) produced by a given current in the other
w
netizing winding as a result of the flux caused by the ac
circuit (the primary). The mutual inductance, L , is defined
m
symmetrical cyclic magnetization exciting current, I. The
by the equation:
flux linking the winding is that flux outside of the ferromag-
L 5 + I
m 2 1
netic core material.
where:
induction, B—see magnetic induction (flux density).
+ = flux linkage in the secondary and
induction, biased—see flux density, biased.
I = current in the primary, assuming no current in the
induction, incremental—see flux density, incremental.
secondary.
induction, intrinsic—see flux density, intrinsic.
DISCUSSION—If + is in maxwell-turns and I is in amperes, then the
2 1
mutual inductance
...