TPC Soft Ferrites General Characteristics

Soft Ferrites
CORE PROCESS
POWDER PROCESS
General Characteristics Process Flow Chart
Raw Material Weighing
The different raw materials (iron-oxide, manganese-oxide,
zinc-oxide,...) are entered into the process respecting the
appropriate formula.
Mixing and Pelletization
These are mixed together under precise humid conditions
in order to achieve a powder composed of pellets of a well
defined size range.
Calcination and First Milling
The pellets are calcined in a rotary kiln at about 1000°C
and then milled to a powder of small particle size.
Binder Adding and Second Milling
Organic binders and mineral components are added to the
powder, and in order to reduce its particle size and homogenize the obtained slurry, it is milled by using specific attritors.
Spray-Drying
The slurry is atomized in specific spray-driers to finally
achieve the ready-to-press ferrite powder.
Pressing
This ferrite powder is pressed into so called “green”
cores out of carbide tools.
Binder Burn-out and Sintering
The “green” cores are sintered under precisely defined
thermal (up to 1400°C) and atmospheric conditions in periodic “batch” kilns or continuous “pusher” kilns.
The sintered E- and U-cores are ground to smoothen the
interface and gapped with diamond tools upon request to
adjust the electrical characteristics.
Grinding
(E/U Cores)
Tumbling and
Coating
(Ring Cores)
The sintered ring cores are tumbled to remove sharp edges
and most frequently coated (with polyamide or parylene) to
improve dielectric insulation.
Marking and Packaging
The finished cores are cleaned and marked upon request
before being packed. Each primary packing is bar-code
labeled.
Palletizing and Shipment
After the outgoing inspection, the primary packings are
stacked up on pallets and then ready for shipment.
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Soft Ferrites
General Characteristics
• Inductance Factor: AL
1. MAGNETIC CIRCUIT
CHARACTERISTICS
• Core Factor
This parameter is defined as the sum of
various parts along the magnetic path:
C1 =
where:
A
Inductance factor is given for most magnetic circuits. It is
defined as:
(9)
AL = L2 = µ • c (nH)
N
values of the
A (mm )
-1
(1)
2.1 INITIAL PERMEABILITY: µI
It is defined as the ratio between the flux density variation
and the field variation corresponding to the origin of the
first magnetization curve within a closed ring. This applies
only to a very low amplitude of the A.C. field.
= magnetic length in mm of each portion with
constant cross section.
A = area in mm2 of the cross section of each portion.
• Permeance Factor
µi = 1 × ∆B
for small ∆H values
µ0 ∆H
In order to calculate the electromagnetic characteristics,
the core permeance factor, c, is preferred to core factor,
C1, by most designers (see AL value calculation).
It is defined as:
µ
c = —0 × 106 (nH)
(2)
C1
where: µ0 = absolute vacuum permeability.
The initial permeabilities listed on the material characteristics tables are measured on reference toroids (rectangular
toroids of 35 × 12 × 18mm), with an A.C. field amplitude
attaining peak value of ∆B = 1mT.
µi
• Other Effective Parameters
• Effective area of magnetic path: Ae =
(10)
A
A
(3)
2
• Effective magnetic path length: Ie = Ae ×
A
• Effective magnetic volume: Ve = Ae × le
(4)
Temperature (°C)
Figure 1
Note: These values are useful for core selection and calculation of hysteresis losses.
The magnetic flux density inside a ferrite core can be
described by the formula:
(6)
µ0 = absolute vacuum permeability
J = magnetic polarization of ferrite material
This relation introduces the relative permeability µ of a
ferrite material which may be defined as:
µ= 1 × B
(7)
H
µ0
Figure 2
2.2 AMPLITUDE PERMEABILITY: µa
• Inductance Formula
The inductance value of a magnetic circuit may be calculated as follows:
(8)
with L in nH, c in nH and N the number of turns.
4
fc
The cut-off frequency (Figure 2) is defined as the frequency
at which the permeability is half the initial permeability at
1-10 kHz.
where:
L = µ.c.N2
Frequency
Notes: Curie temperature Tc (Figure 1) is the temperature
at which the material looses its ferromagnetic properties.
For FERRINOX materials, this phenomenon is completely
reversible, i.e., cores cooled below the curie point recover
their magnetic properties, when brought back to room
temperature.
2. PERMEABILITY
B = µ0 • H + J
TC
(5)
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In the case of magnetization by a large amplitude sine
field, permeability µa is defined as the ratio between the
inductance peak value B and the field peak value H, with
no D.C. magnetic field applied.
ˆ
µa = 1 • B
(11)
µ0
ˆ
H
Amplitude permeability variation versus B or H is given for
each FERRINOX material in the FERRITE MATERIALS
section.
Soft Ferrites
General Characteristics
2.3 EFFECTIVE PERMEABILITY: µe
If a small airgap is created in a closed magnetic circuit,
manufactured from material with a permeability µ, the
resulting permeability will be smaller than µ due to the
reluctance increase in the airgap. This permeability of the
magnetic circuit system is called effective permeability.
In more general terms, it is the permeability that an
homogeneous hypothetical material must have in order
to get the same total reluctance as a core manufactured
with several materials where the magnetic leakage flux is
negligible (the same dimensions are assumed).
thus:
µe =
or
A
µe = µ1 • L2 •
N
0
A
µ.A
2.4 REVERSIBLE PERMEABILITY: µrev
µrev is defined as the ratio between the flux density variation ∆B and the corresponding field variation for a very
low amplitude A.C. field and a superimposed D.C. field H0:
103 (12)
∆B
µrev= 1 • ∆H
µ0   H0
l = l + ε
µe µ
le
(17)
This permeability µrev can therefore be compared, to initial
permeability µi or to the effective permeability µe corresponding a low level A.C. field. But the difference arises
from the fact that for measurement of µi or µe the core must
not previously have been subjected to the influence of any
large amplitude field while for the measurement of µrev the
core is assumed to have been previously magnetized.
(13)
(µ is the permeability of each material constituting the
magnetic circuit).
An interesting specific case is that of an average length and
constant section circuit made of a material of permeability µ
and an airgap length of ε<< l e (valid for ε<0.005 l e ).
Equation (13) becomes:
Note: These formulas are valid only when the magnetic
flux section in the airgap remains roughly the same
as in the magnetic core. Conversely, when the airgap length ε is no longer negligible, it is necessary
to take into account a factor β, which corresponds
to the flux expansion in this airgap.
Note for designers: Useful AL versus airgap curves are
given for E, U, RM and FM cores.
3. HYSTERESIS LOOP
The static hysteresis loop, (BH) curves (Figure 4), are
obtained by measuring the resulting flux density B inside
the core under test for increasing values of H field until
saturation.
(14)
Note: For a given core, when µe decreases, the acceptable
peak value of magnetic field increases (Figure 3).
B
µe
Br
H
Hc
H
Figure 4
Figure 3
Two types of µ e may be calculated:
The effect permeability for low level (corresponding to
∆B < 1mT, µ=µi ):
l = l + ε
µe µi le
(15)
The effective permeability for a high amplitude A.C. field
(µ=µa ):
l = l + ε
µe µa le
Notes: For each FERRINOX material, measurements were
made on reference toroids (previously demagnetized)
at 25°C and 100°C.
Remanent flux density Br is defined as the intersection of the hysteresis loop with B axis (H = 0). Br is an
important factor for unipolar operating systems.
Coercive force Hc is the intersection of the hysteresis
loop with H axis (B = 0). It is representative of static
hysteresis loss of the considered material, which is
recorded in the FERRITE MATERIALS section.
(16)
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Soft Ferrites
General Characteristics
3.1 PLOTTING THE CURVES B=ƒ(H)
• Eddy currents,
• Hysteresis,
• Magnetic drag (residual losses)
(18)
Rt = RF + Rh +Rr
In this case, it is also possible to define loss coefficients
F, h and r by using the Jordan formulas.
The static B(H) (Figure 5) curves are given on the specific
sheets pertaining to the characteristics of the various
FERRINOX materials. They are obtained by measuring the
induction B with an analog integrator on the reference
toroid (30 x 20 x 8mm) at temperature of 25°C and 100°C.
ƒ2
ƒ
ƒ
• L + h • Ni •
•L + r •
•L
800
800
8002
Rt = F•
The first magnetization curves are established on previously demagnetized toroids and for increasing values of
field H.
L
Inductance in henrys
ƒ
Frequency in hertz
i
RMS current intensity (in amperes) in the coil
Length of the line of mean force
N
Number of turns of the coil
F, h, r Loss coefficients due to eddy currents, hysteresis,
and residual losses for a frequency of 800 Hz and measured at a specify frequency, field and temperature.
For gapped cores, with µe effective permeability, the
preceding formula becomes:
B
1/µ
/l
1/µa
/l
1/µ
Without Airgap
With Airgap
2
Rt = F • µe • ƒ • L + h • µe2 • Ni • ƒ • L + r • µe • ƒ • L (20)
µi
µi
800
8002
µ2
800
i
H
4.1 LOSSES AT LOW INDUCTION LEVEL
Figure 5
• Loss angle δ and loss angle tangent
3.2 SATURATION INDUCTION
Induction B in the magnetic circuit is given by the conventional formula:
B = µ0 • H + J
J being the magnetic moment per unit of volume.
The term 4πJ comes from the magnetic material. As
soon as it reaches saturation, 4πJ becomes constant
and equal to 4πJs, which correspond to the saturation
induction BS.
However, as the value of BS is only obtained with a very
important field H, we give in the FERRINOX MATERIALS
section THE VALUES OF B corresponding to a rather
high specified field, this in order to give an idea of the
inductions which can be obtained in practice.
Saturation magnetization varies with temperature and
becomes zero at the Curie point. In the FERRINOX
MATERIALS section the values of B are given for 25°C
and 100°C, which correspond to the normal temperature
range of utilization of transformers.
4. LOSSES
Only losses caused by ferrite magnetic core will be considered here.
When the core flux density is low enough (e.g., several
mT), the series resistance, equivalent to the total losses
Rt in the core, can be reduced to a sum of three terms
RF, Rh and Rr, corresponding respectively to the loss
resistance caused by:
The phase shift angle between induction and field within a
closed magnetic circuit is designated by δ. This applies to
low values of the magnetic field, assumed to be sinusoidal.
tgδ = Rts
LS
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(21)
U=Zl
Ls l
FRESNEL
DIAGRAM
l
Rts l
Figure 6
Considering the series configuration (Figure 6), a coil
including a ferrite core may be represented by an ideal
inductance LS (without losses) and by a resistance Rts
corresponding to the total losses in the core.
I
Ls
Rts
U
Figure 7
6
(19)
Soft Ferrites
General Characteristics
The representation suggests that the material permeability
must be considered as a complex value called complex
permeability µ :
• Quality Factor: Q
It is given by the inverse of the loss angle tangent:
1
Q=
tgδ
µ = µ's - jµ"s
with
µ's = real permeability (µi or µe)
thus
= j c N2 (µ's - jµ"s)
(24)
= µ"s c N2 + j µ's c N2 (25)
Ls = µ's c N2
(26)
Rts = µ"s c N2 (27)
( = 2 π f = pulsation)
Figure 8 shows an example of Z curve versus frequency.
Z (Ω)
|Z| =
L
2
s
2
2 + Rts
200
100
Rts = f(µ"s)
Ls = f(µ's)
3
10
It should be noted that this quality factor is only equal to
that measured on the system including a winding associated to a ferrite magnetic circuit if the losses resulting from
the winding itself (ohmic resistance, eddy currents in the
wire, distributed capacity) are negligible, conversely, the
latter should be taken into account.
(22)
µ"s = imaginary permeability due to loss
resistance.
For each FERRINOX material used for noise suppression
filters, µ's and µ"s curves versus frequency are given in
the FERRINOX MATERIALS section.
Consequently, the resulting impedance of the coil may
be expressed by the following formula (if copper losses
negligible):
(23)
Z = Rts + jLs = J µ c N2
Frequency (MHz)
Figure 8
• Loss Factor: tgδ/µ
The loss factor is reduced by an airgap based on the ratio
of permeabilities before and after airgap presence: consequently for small airgap cores, the ratio tgδ/µ factor or loss
factor does not depend on the airgap (under constant
magnetic induction).
Depending on frequency, tgδ/µ versus f curves are given
for each FERRINOX material in FERRINOX MATERIALS
section. The maximum practical operating frequency of a
selected material is almost entirely controlled by the rapid
increase of the loss factor.
This factor is, therefore, ideal for assessing a material
under high frequencies.
Calculation of the loss factor of a gapped circuit is done
merely by multiplying the material loss factor by the actual
permeability of the circuit.
tgδ
• µe
(28)
tgδe =
µ
(29)
4.2 LOSSES AT HIGH FLUX DENSITY
LEVEL
In SMPS application, mainly for power transformer
design, approximate total ferrite losses at the working
point need to be known by the designer in order to:
• Integrate them into the efficiency coefficient calculation,
• Take into consideration for heat dissipation (i.e., cooling
systems).
Generally, power losses are characterized by three parameters:
• Peak induction level Bˆ
• Frequency f
• Temperature T
Approximate PL may be obtained by the following formula
(valid only for specified typical operating range):
PL = K • ƒm • Bn
where K is the material factor (depending on temperature T)
1.3 < m < 1.6
2 < n < 2.6
Notes for designers: The total losses curves (in Watts) of
the magnetic circuit are given at different temperature,
frequency and flux density for E, U, RM and FM cores.
Please refer to CORE DATA in CORES FOR POWER
APPLICATION section.
The power losses curves (in mW/cm3) of power ferrite
materials are given at different temperature, frequency
and flux density in the FERRINOX MATERIALS section.
5. OTHER CHARACTERISTICS
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• Density
Between 4 and 5 depending on the material grades. FERRINOX A and B materials generally have values between
4.7 and 4.9 (see Materials Characteristics tables).
• Specific Heat
From 20°C to 300°C, specific heat ranges between 0.5
and 0.8 Joule/g/°C (0.12 and 0.2 cal/g/°C). For example,
FERRINOX B1 specific heat is about 0.75 J/g/°C.
• Linear Expansion Factor
From 20°C to 300°C, the increase of any of the core
dimensions by unit of length and by the ratio ∆ ranges
∆
between 7.5 to 10 × 10-6K-1.
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Soft Ferrites
General Characteristics
• Mechanical Properties
Young’s modulus of elasticity
Ultimate tensile strength
Ultimate compressive strength
• Dielectric Constant (or permittivity)
80 to 150.10 N/m
30 to 70.106 N/m2
200 to 800.106 N/m2
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• Resistivity
FERRINOX materials are high resistivity, non metallic,
ferromagnetic substances which are developed in
response to the unacceptably high losses due to eddy
currents, occurring at high frequencies in ferromagnetic
materials.
This resistivity varies with applied field, temperature, and
frequency. Generally, for FERRINOX materials B, it
decreases slightly as frequency increases.
In practice, FERRINOX cores behave like semiconductors.
With D.C. current, their resistivity varies with the measuring
voltage (decreases slightly under constant voltage).
An accurate measurement of a core resistivity cannot be
done without prior metallization (with silver, or preferably,
with indium-gallium alloy) due to the difficulty in achieving
a perfect contact between the electrodes and the core.
It is also recommended to carefully lap the faces before
metallization in order to lay bare the core of the material
before depositing the metal layer. Actually, after noticeable
firing in some case, the resistivity of the rough surface of
a core differs from that of the inside. This is particularly
true for FERRINOX B due to slight superficial oxidation.
The characteristic tables of the materials indicate the mean
resistivity values for the various FERRINOX materials
measured at low frequency and with a low field.
The relative permittivity value for FERRINOX B materials
is high at low frequencies and generally decreases as
frequency increases. Thus for these materials permittivity
is between 1 - 1.5 × 105 at 1 kHz; at 1 MHz its value can
still exceed 0.5 × 105. At high frequency for all materials,
it reaches a value between 10 and 20.
• Magnetostriction
Magnetostriction is an elastic deformation phenomenon
which accompanies magnetization.
Linear magnetostriction is defined as the relative variation
of the part length under the influence of magnetic field.
When the variation is measured in the magnetization
direction, we have longitudinal magnetostriction.
λ = ∆
Generally, this coefficient is negative for all FERRINOX
materials, i.e., these materials contract in the magnetization direction. The absolute value increase with magnetization (at the beginning λ is more or less proportional to
the square of magnetization) up to a maximum value λs
corresponding to saturation.
The value of λs for the various FERRINOX materials is
generally very low, between 0 and -1 × 106 for B materials.
Magnetostriction effects appear in power transformer as
an audible hum, particularly in U shaped cores without airgaps. It is, therefore, recommended to secure the cores
tightly and to use cores with airgaps whenever possible.
• Thermal Conductivity
It is equal to about 10 × 103 cal/cm/s/°C or 4W/m/°C.
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