L6.Characterization of Fero and Ferimagnetic Materials

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  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 (Mn-Zn,Ni-Zn). 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 (0.3T-0.4T compared to 1.2T-2.2T) 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 (Fe-Si) 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 Fe-Si, 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 6-1  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 Q-meter 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 fine-tune the Q-meter, 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''  
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