ME 421G Alexandru Damoc, Muhamad Amru Eldan, Yazan Alshawa
Characterization of Fero and Ferimagnetic materials under “Small signal”
regime
Purpose of the experiment
This experiment emphasises the behaviour in frequency of magnetic cores made out of fero and ferimagnetic materials, used in inductors and used
under “small signal” regime.
Theoretical Background
When a fero or ferimagnetic material is placed in a magnetic field of intensity H, they will interract and as a result, in the respective material magnetic induction B appears. Some losses appear also: losses through currents Foucault, losses through the hysteresis, through magnetization or through magnetic resonance.
0 0
m
j
B B j e H H
is the relative complex magnetic permeability of the material
δ
m
is the loss angle
μ´ is the real part of
, it increases the induction of the coil by a number of μ´ times at the same
geometrical dimensions (it characterises the material from the pov of magnetization properties)
μ”characterises the material from the
pov of losses that appear When talking about alternative magnetic fields applied to a magnetic material, there are two functioning regimes. 
The “small signal” regime with reduced amplitude of the alternative field H
~
applied, overlapped or not, on a continuous field H
=

The “big signal” regime in which the value of the field is enough for the material to describe a
hysteresis cycle
Characterising feromagnetic materials under “small signal” regime
In order to characterise a
FEROMAGNETIC
material under “small signal” regime (B
~
<1 mT), we consider 2 coils with the same geometry of the winding (preferably with a toroid form, in order to neglect the dispersion field) and the same number of turns. The first coil is built on a nonmagnetic support, while the second one is built on a magnetic core of the same dimensions with the support of the first coil, made out of the feromagnetic material to be studied.
Fig.1
Graphic model of the two coils and the equivalent electric circuit
ME 421G Alexandru Damoc, Muhamad Amru Eldan, Yazan Alshawa
In order to define them, we write the impedances of the two coils:
Z
0
= r
0
+ jωL
0
; Z
m
= r
0
+ jωL = r
0
+ ω
L
0
= r
0
+ ω
L
0
+ jω
L
0
= r + jω
L
0
Where: r
0
is the resistance of losses through Joule effect, proximity, dielectrics etc in the winding r
m
is the resistance of losses due to the presence of the magnetic core r is the equivalent series resistance of the coil with magn. core r = r
0
+ r
m
= r
0
ω
L
0
L
0
is the inductance of the coil without magn. core L is the inductance of the coil with magn. core
μ
is the (initial) complex permeability of the core
2
is the frequency of measurement
The quality factor of the feromagnetic material Q
m
is :
00
bmb
Q QQQ Q
where Q
0
and Q
b
are the quality factors of the coils w/o and w/ magn. core
000 0
bm
L LQ ; Qr r r
If the measurement is done at a specific frequency
2
, L
0
, L, r
0
,r,
can be computed using the formula :
00 0
r r L j j L L
Characterising ferimagnetic materials under “small signal” regime
The general chimical structure of ferites is
Me
2+
O
2
Fe
3+
O
32
where
Me
is a bivalent metal (Mn, Zn, Ni, Cd) or an equiv. metalic combination (MnZn,NiZn). Campared to the feromagnetic materials, ferites have the following advantages:
o
bigger electrical resistivity
o
more stable magnetic characteristics at mechanical stress (shocks,vibrations,etc) There are also disadvantages, compared to the feromagnetic materials
o
smaller relative magnetic permeability
o
smaller saturation of the magnetic induction (0.3T0.4T compared to 1.2T2.2T)
o
lower Curie temperature and a more pronounced dependency of magn. characteristics to the temperature
o
hard to mecanically mould
r
m
ME 421G Alexandru Damoc, Muhamad Amru Eldan, Yazan Alshawa
In order to study ferimagnetic materials, toroid
shaped cores will be measured, “bowl” and ”bar”types.
For any shape of the magnetic core, the “effective”
measurements must be done (dimensions l
e
, A
e
and the
permeability μ
e
) of an hypothetic magnetic core with the core constants C
1
and C
2
.
1 2 2 2
e i e ii ie i e i
l l l l C C A A A A
Using these relations, we can define further measures:
212
e
C l ;C
12
e
C A ;C
1
eii i i
C ;l A
Losses in the ferimagnetic core
These losses depend on the apex induction
ˆ
B
applied to the material (losses through hysteresis) and on the frequency (losses through Foucault currents). Furthermore, at low frequency and small field
0 0
ˆ
f , B
, residual losses are defined, which are a property of the material.
Fig.2
The loss factor
(tgδ
m
/μ’
) dependancy as a function of frequency
ME 421G Alexandru Damoc, Muhamad Amru Eldan, Yazan Alshawa
Description of laboratory proceedings:
6.1. Dependancy of the complex relative magnetic permeability of feromagnetic materials with respect to the frequency
In order to characterise a feromagnetic material (FeSi) under small signal regime (B
~
< 1mT), we use 3 coils with the same geometry and number of the windings.
L
m
has a magnetic core made out of FeSi, E+I interwinded sheets
L
md
is different to
L
m
only in the way the sheets have been introduced. Between the sheets E and I there is an
air gap
L
m0
is identical to the other two, but it has
no
magnetic core 
we connect, in turns, the terminals of the measuring RLC bridge to the coils L
m
, L
md
, respectively L
m0

by varying the frequency according to those in
Table 61
we fill in the data table
for calculus, we used :
Q
m
= μ'
/
μ’’
Q
mef
(f) =
μ'
ef
/ μ''
ef
00 0
r r L j j L L
6.2. Dependancy of the complex relative magnetic permeability of ferites with respect to the frequency
We determined the inductances and equivalent resistances of
L
m1
(coil with core) and of
L
01
(coil identical to
L
m1
but without core), at different frequencies. By determining the parasitic capacity of the coil and the correction factor at the measured frequencies, we could analyze the behaviour of the ferite core in the frequency domain, using the Qmeter BM 560 Tesla, and filling in the
Table 6.2
: 
we press the button between the 550 kHz and 1.1 MHz frequencies and in order to finetune the Qmeter, we rotate the frequency knob until we reach 800, respectively 1000 KHz 
we rotate the capacitance knob while visualising on the screen the maximum capacities, which are at resonance, at the 2 set frequencies 
the parasitic capacity is calculated using the formula :
2 21 1 2 22 22 1
v v P
f C f C C f f

using the RLC bridge, we made the measurements for inductances and equivalent resistances necessary to fill in the data
Table 6.3
for calculus, we used:
21
1
m p
k L C
101
' m
LkL
1 0101
'' m
R R L
Q
m
= μ'
/
μ''