We know the
meaning of Hysteresis loop or B-H curve. Let discuss in detail the Magnetic
properties of the material or in other word we can say that let discuss basic
parameters of Hysteresis loop.

Please visit
my previous blog to know more about;

Below picture shows, B-H curve (Hysteresis loop) in detail.

B-H curve |

###
**Permeability**

When a magnetic field is applied to a soft magnetic material, the resulting
flux density is composed of that of free space plus the contribution of the
aligned domains.
B = μ₀H + J or B = μ₀ (H + M)

Where; μ₀ = 4πx10¯⁷H/m,

J is the magnetic
polarization

M is the magnetization.

###
**Absolute permeability**

The ratio of flux density and applied field is called
absolute permeability.
μabsolute = B/H = μ₀ [1+(M/H)]

It is usual to express this absolute permeability as the
product of the magnetic constant of free space and the relative permeability (μᵣ).

B/H = µ₀ µᵣ

There are several versions of μᵣ depending on conditions the
index ‘r’ is generally removed and replaced by the applicable symbol e.g. μᵢ, μₐ, μΔ etc.

###
**Relative permeability**

Relative permeability shows that how the presence of a
particular material affects the relationship between flux density and magnetic
field strength. The term 'relative' arises because this permeability is defined
in relation to the permeability of a vacuum.###
**Initial
permeability**

Initial permeability describes the relative
permeability of a material at low values of Magnetic Flux
Density (below 0.1T). Low flux has the advantage that every ferrite can be
measured at that density without risk of saturation. It is helpful for the
comparison between different ferrites.
μᵢ = [(1/µ₀) x (ΔB/ΔH)] (ΔH → 0)

Initial permeability is dependent on temperature and frequency.

###
**Effective permeability**

If the air-gap is introduced in a
closed magnetic circuit, magnetic polarization becomes more difficult. As a
result, the flux density for a given magnetic field strength is lower.
Effective permeability is dependent on the initial
permeability of the soft magnetic material and the dimensions of air-gap and
circuit.

µₑ = µᵢ / {1+ [(G x µᵢ)/lₑ]}

Where;

G is the gap length and le is the effective length of
magnetic circuit. This simple formula is a good approximation only for small
air-gaps. For longer air-gaps some flux will cross the gap outside its normal
area (stray flux) causing an increase of the effective permeability.

###
**Apparent
permeability**

The definition of µₐᵨᵨ is particularly important for
specification of the permeability for coils with tubular, cylindrical and
threaded cores, since an unambiguous relationship between initial permeability
µᵢ and effective permeability μₑ is not possible on account of the high leakage
inductances. The design of the winding and the spatial correlation between coil
and core has a considerable influence on µₐᵨᵨ. A precise specification of µₐᵨᵨ
requires a precise specification of the measuring coil arrangement.
µₐᵨᵨ= L / L₀ = Inductance with core/ Inductance without core

###
**Amplitude
permeability**

It is the relationship between higher magnetic field
strength and flux densities; it is the permeability at high induction level. At
relatively low induction, it increases with H but as the magnetization reaches
saturation, it decreases with H. Helpful to find high permeability level of a
material.
µₐ = (1/µ₀)
x (^B/Ĥ)

Since the
BH loop is far from linear, values depend on the applied field peak strength.

###
**Incremental permeability**

The permeability observed when an alternating magnetic field is
superimposed on a static bias field, is called the incremental permeability.
μΔ = (1/µ₀)[ΔB/ΔH]Hᴅᴄ

If the
amplitude of the alternating field is negligibly small, the permeability is
then called the reversible permeability (μᵣₑᵥ).

###
**Complex
permeability**

To enable a better comparison of ferrite materials and their
frequency characteristics at very low field strengths (in order to take into
consideration the phase displacement between voltage and current), it is useful
to introduce μ as a complex operator, i.e. a complex permeability ͞µ, according to the following relationship:
͞µ = μs' – j . μs"

Where, in
terms of a series equivalent circuit, (see figure 5)

μs' is the
relative real (inductance) component of ͞μ and μs" is the relative
imaginary (loss) component of ͞μ.

Using the
complex permeability ͞μ, the (complex) impedance of the coil can be calculated:

͞Z = j ω ͞μ L₀

Where L₀ represents the inductance of a core of permeability μr = 1, but
with unchanged flux distribution.

Complex Permeability vs Frequency |

The region in which μ' decreases sharply and where the μ" maximum
occurs is termed the cut-off frequency fcutoff. This is inversely proportional to the initial permeability of the material (Snoek’s law).

###
**Reversible
Permeability**

In order to measure the reversible permeability μᵣₑᵥ, a small measuring alternating field is superimposed on a DC field. In this case μᵣₑᵥ is heavily dependent on Hᴅᴄ, the core geometry and the temperature.

###
**Power loss**

It should be considered for high frequency/excitation application. It is the
addition of Hysteresis losses, Eddy current losses and Residual losses. It
should be <1.
PL = Physteresis +
Peddy current + Presidual

###
**Saturation
flux density**

It is how much magnetic flux the magnetic core can handle
before becoming saturated and not able to hold any more. It should be high. Use
minimum number of turns in winding.###
**Remanence**

The magnetic flux density remaining in a material, especially
a ferromagnetic material, after removal of the magnetizing field. It
measures the strongest magnetic field ferrite can produce. There should be low
retentive. So, ferrite should not magnetize easily without the application of
magnetic field. ###
**Coercivity**

It is the magnetizing field strength required to bring the
magnetic flux density of a magnetized material to zero. It should be low, so
that it requires low magnetic field thus low opposite current to bring it back
to the non-magnetic state.###
**Hysteresis Material constant**

It is useful for
estimating ferrite core losses. It is a constant that represents hysteresis loss when a
magnetic material is operating in the Rayleigh region (low magnetic field region
- behaviour of magnetic materials at low field). It should be less.
Hysteresis
Constant is given by: ηв = (Δ tanδm) / [μe × Δ(^B)]

###
**Disaccommodation Factor**

Disaccommodation occurs in
ferrites and is the reduction of permeability with time after a core is
demagnetized. This demagnetization can be caused by heating above the Curie
point by applying an alternating current of diminishing amplitude or
by mechanically shocking the core. The value of dis-accommodation per unit
permeability is called disaccommodation factor. It is a
gradual decrease in permeability. It should be low and should be <2.
DF = (µ₁ -µ₂)/
[log₁₀ (t₂/t₁)] (1/µ₁²) (t₂>t₁)

Where;

µ₁ = resulting complete demagnetization, the magnetic permeability after
the passing of t₁ seconds.

µ₂ = resulting complete demagnetization, the magnetic permeability after
the passing of t₂ seconds.

###
**Curie temperature**

The
transition temperature above which a ferrite loses its ferromagnetic
properties. It should be high.###
**Resistivity**

High resistivity makes eddy current losses extremely low
at high frequencies. Resistivity depends on temperature and measuring
frequency. Ferrite has DC resistivity in the crystallites of the order of 10⁻³Ωm
for a MnZn type ferrite, and approx. 30 Ωm for a NiZn ferrite.###
**Relative loss factor**

With
the frequency increase, core loss is generated by the changing magnetic ﬂux
field within a material.
Core-loss factor, is defined as the ratio of core-loss
resistance to reactance, and consists of three components; namely, hysteresis
loss, eddy-current loss and residual loss.

Addition of an air gap to a magnetic circuit changes the values of its
loss factor and effective permeability. The amounts of change are nearly
proportional to each other.

It should
be less.

This factor is defined as the loss angle tangent divided by
permeability, Relative loss factor = tanδ/μᵢ

The loss angle tangent, tanδ, is decreased by an air gap in
proportion to the ratio of permeability’s before and after air gap presence.

tanδₑ = (tanδ/µᵢ) µₑ

Where;

tanδ and μᵢ : permeability and loss angle tangent without an
air-gap μₑ.

tanδₑ: permeability and loss angle tangent with an air-gap.

Hence, the relative loss factor, tanδ/μᵢ does not depend on
air gap size, when the air-gap is small.

###
**Quality
Factor**

It is the reciprocal of loss angle tangent.
Q = ωL/R˪ = 1/tanδ = reactance / resistance

Temperature
factor of permeability

Temperature coefficient is defined as the change of initial permeability per °C over a prescribed temperature range. Temperature factor of permeability is defined as the value of temperature coefficient, per unit permeability. The measured value should be less.

Temperature coefficient is defined as the change of initial permeability per °C over a prescribed temperature range. Temperature factor of permeability is defined as the value of temperature coefficient, per unit permeability. The measured value should be less.

It is the ratio of “Temperature factor for initial magnetic
permeability” to the “initial magnetic permeability“.

αµ = αµ₁/µ₁ = [(µ₂-µ₁)/µ₁] [1/(T₂-T₁)] (T₂>T₁)

αµγ = [(µ₂-µ₁)/µ₁²] [1/(T₂-T₁)] (T₂>T₁)

where,

µ₁ = initial magnetic permeability at temperature T₁

µ₂ = initial magnetic permeability at temperature T₂

###
**Density**

It is calculated by;
d = W / V (g/cm³)

Where;

W = Magnetic core weight

V= Magnetic core volume

###

Magnetic properties of material help us to select perfect material according to application. Even in the case of failure of application we can analysis the material properties and cause of failure easily we can find. Also, it helps us to find maximum working limit of a material.

## 3 Comments

Write CommentsWonderful read, was looking for beta-zone permeability temperature coefficient; came across https://www.mag-inc.com/design/design-guides/designing-with-magnetic-cores-at-high-temperatures which is mainly on design philosophy and https://nvlpubs.nist.gov/nistpubs/bulletin/07/nbsbulletinv7n1p71_A2b.pdf original publish of Temp Coefficient of Resistance, both in line with this page.

ReplyHe just didn`t mention the magnetostriction!!!!

ReplyThanks for suggesting Magnetostriction, I missed to write in the article. I will update it in my article.

ReplyMainly the shape change is due to sintering. But there is little bit effect on dimension during magnetization. You can avoid it by proper heat control.

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