Amorphous Wire Magnetic Field and D.C. Current Sensor Based on the. Inverse Wiedemann Effect. E.Pulido, R.P. del Real, F.Conde, G.Rivero, M.VBzquez, ...
EEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 6, NOVEMBER 1991
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Amorphous Wire Magnetic Field and D.C. Current Sensor Based on the Inverse Wiedemann Effect E.Pulido, R.P. del Real, F.Conde, G.Rivero, M.VBzquez, E.Ascasibar, A.Hemando. Instituto de Magnetism0 Aplicado. Lab. "Salvador Velayos" Renfe - Complutense Univ. Apdo. 155, Las Rozas 28230 Madrid - Spain
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Abstract The magnetic field sensor presented here is based on the Inverse Wiedemann Effect (IWE) on amorphous wires. The external magnetic d.c. field to be detected, changes the time symmetry of the output voltage induced in a pick-up coil, creating even harmonics. The results of our measurements show important advantages in sensitivity and working frequencies, mainly due to the core's geometry. INlROWCIlON
METALLIC glasses are well known soft magnetic materials [ 11. Their application in stress, torque and magnetic field sensors has been widely developed [2-4]. In the present work, we have studied the application of amorphous wires with helical anisotropy as magnetic field sensors using the Inverse Wiedemann Effect (WE). Previously, amorphous ribbons have been used in a similar way [5]. Let us consider an a.c. current flowing through a twisted amorphous wire. When the current sense changes, the induced circular magnetic field is inverted and, for a well-defined critical value of this field, a switching of the magnetization occurs [6,7].
w
5
3 E
0 0
The switching of the magnetization's longitudinal component induces a voltage in a pick-up coil wound around the wire. This induced voltage shows a series of narrow switching peaks, periodically spaced along the time axis. The effect of an extemal magnetic d.c. field, or a d.c. current flowing through the wire, will be a change in the time symmetry of these peaks (see Fig. l), thus creating a second harmonic signal. The detection and measurement of this even harmonic signal amplitude allows one to obtain the value of the external magnetic field. The significant advantage of the wire's cylindrical geometry when adjusted to the twist symmetry, and the sharp definition of the switching peaks, show the promising future of the IWE in amorphous wires as magnetic field detectors. ExpERlMENTAL
Two magnetic field sensors, based on the property described previously, have been built. The core in both cases is a wire of nominal composition Fe77.5Si7.5B15 , obtained by the in-water-quenching technique, each being 12 cm long. In the first sensor as-cast wire has been used, while the wire of the second one has been current annealed with a 500 mA current for 1 minute. The average diameter of the wires is 125 pm. The magnetostriction constant h of the as-cast wire is 2 8 ~ 1 0 - ~and , its shear modulus is 6x1010 Nm-2. During all the measurements, the wires were clamped under a 52.36 rad/m twist. The extemal magnetic d.c. field to be measured was applied by Helmholtz coils. Using an HP 35660A Dynamic Signal Analyzer we studied the first and second harmonic sensor output induced in a 2000-turn pick up coil for intensities of the exciting a.c. current from 25 mA to 50 mA versus applied field from 0 to 0.07 mT (see Fig. 2). The fundamental frequency was varied from 40 to 5000 Hz.
ro
t9 (hlmholtz coils)
Start: 0 s
Stop:
4 ms
Fig. 1. Voltage output of the pick-up coil: a) under zero applied magndc field, Hz ,b) under Hz # 0 .
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0018-9464/91$01.00 0 1991 IEEE
Fig. 2. Experimental setup.
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If we define the sensor's sensitivity, S,as: RESIJi,TSAhDDIscussION
Fig. 3 shows the second harmonic voltage versus applied d.c. field for both sensors. The current intensity flowing through the wire was 50 mA and its frequency was 360Hz. We observe that in the case of annealed wire the amplitude of the second harmonic signal is larger than for the as-cast wire. The same measurement carried out for a lower frequency (40 'Hz)showed very similar output signals from the as-cast and annealed samples; for higher frequencies (1 - 5 KHz) the second harmonic curves split considerably, being the output voltage of the sensor with annealed wire higher than the signal of the Sensor with as-cast wire. In both cases it is easy to see two usable linear regions for the detection of magnetic fields in two different ranges: approximately 0 0.02 mT and 0.02 - 0.05 mT. Measurements were also carried out with a 25 mA a.c. current flowing through the wires. A lower second harmonic signal was obtained for the same extemal magnetic field range (0 - 0.05 mT) in both devices. Therefore, we focused our measurements on highzr currents (40 - 80 mA).
S=AV2O/WXt (1) where V2" is the voltage amplitude of the second hmonic signal and HeXt is the extemal magnetic d.c. field, Fig. 4 shows sensitivity versus the wire's current frequency for both sensors, along the first working region (0 - 0.02 mT). while Fig. 5 depicts the same for the second region (0.02 0.05 mT). In both figures we observe a higher sensitivity for the sensor with a current annealed core (i. e. with a working frequency of 4 KHz we obtain over 20 V/mT for the first range). /
Current annealed wire e...
0 0
0 ' '0
0 0
0
0 0
Fig. 5. Sensitivity vs. current frequency. Magnetic field range: 0.02 0.05 mT.
As cast wire 0 .-
Current Int: 50 mA (Ims) Current freq: 360 Hz
cp
c CY.... 0.00 0.02
,I.
I I I . , I . I I I I I 1 . , I I . I . . , I . , . . l . I . I I I , , , , . . , , , .
0.06
0.04
o.io
0.08
Applied field (mT) Fig. 3. Secund harmonic voltage amplitude vs. applied mametic field. x
a c
Current annealed wire
Fig. 6 shows for the sensor with current annealed wire the amplitude of the second harmonic of the excitation frequency (RB), when exposed to a square-wave field (RA) with peakpeak amplitude of 20 UTand 0.12 Hz frequency; the working conditions were 500 Hz current frequency and 50 mA current intensity through the wire.
As cast wire
jp Current intensity : 50 mA
(rms)
Frequency (KHz) Fig. 4. Sensitivity vs. current frequency. Magnetic field range:
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0 0.02 mT.
Fig. 6. Signal output (RB) .The sensor is exposed to a 20 pT zquarewave applied field with frequency 0.12 Hz (RA).
THEORETICALCONSIDERATIONS
In this theoretical study we will suppose HQ homogeneous, restricting ourselves to a cylindrical region of the wire. Let us assume that the voltage in Fig. la can be taken as a chain of pulses alternatively opposed, with a width z and amplitude a; then, V(t) admits a Fourier expansion such as:
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V(t) = C (2a/xn) sin(onz) cos(ont) (2) 2n+ 1 When a longitudinal d.c. magnetic field is applied, the value of the resulting field in the easy axis direction and positive sense is: (q+ Hz) cos d 4 , while in the negative sense is: - Hz) cos d 4 (seeFig. 7). Without an extemal magnetic field, the magnetization switch will occur for a critical value & of the field induced by the current flowing through the wire; this switching w;ll start at a value of time t,. When the external field is applied (see Fig. lb). the positivebnegative sense switching field is then reached at a time value (k +At). In a similar way, the negative-topositive switching field is obtained at a lower H+, that is, at (k+ x/w - At). For H z cc &, At is: (3) At = Hz/ (oH+~cos(o~)) is the amplitude of the current induced field. where bo
1
/
EASY AXIS
V(t)=Z(ai-a2cosnx) (2.")sin(nw) [cos(onAt)cos(wnt) + n= 1 + sin(onAt) sin(wnt)] (9) From (9). the amplitude of the second hannonic results: V2" = [(ai - a2) / x] cos(2wAt) sin(202) (10) In our approximation we supposed OAT to be very small; this is reasonable if HZ c< (see (3)). ~ 2 =" [(ai - a21 /XI sin(2m)
(11)
Using (4) to (8) we get a1 - a2 = 2Mscos(7d4) NS At 2 0 sin(ok)/(z cos(ok)) (12) From (3): ai - a2 = 2MScos(lc/4)NS 2W HZ & /(COS((.&) A Hao) (13) Using (6):
f (h+Hz)w4
02 = A /
[Heo cos(d4) (1-(& / HQO COS(^/^))^)'^] (14)
If we suppose H,
