# Magnetic properties of the material

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.

Below picture shows, B-H curve (Hysteresis loop) in detail. B-H curve
Below are the magnetic properties of the material;

### 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. Comparison of hysteresis loops for a ferrite core with and without an air gap

### 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
Figure at above shows the characteristic shape of the curves of μ' and μ" as functions of the frequency, using a NiZn material as an example. The real component μ' is constant at low frequencies, attains a maximum at higher frequencies and then drops in approximately inverse proportion to f. At the same time, μ" rises steeply from a very small value at low frequencies to attain a distinct maximum and, past this, also drops as the frequency is further increased.
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.

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

### Conclusion

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.