Philips Magnetoresistive Sensor User Manual
Page 11
2000 Sep 06
11
Philips Semiconductors
Magnetoresistive sensors for
magnetic field measurement
General
Further information for advanced users
T
HE
MR
EFFECT
In sensors employing the MR effect, the resistance of the
sensor under the influence of a magnetic field changes as
it is moved through an angle
α
as given by:
(2)
It can be shown that
(3)
and
(4)
where H
o
can be regarded as a material constant
comprising the so called demagnetizing and anisotropic
fields.
Applying equations (3) and (4) to equation (2) leads to:
(5)
(6)
which clearly shows the non-linear nature of the MR effect.
More detailed information on the derivation of the formulae
for the MR effect can be found in Appendix 1.
L
INEARIZATION
The magnetoresistive effect can be linearized by
depositing aluminium stripes (Barber poles), on top of the
permalloy strip at an angle of 45
°
to the strip axis (see
Fig.12). As aluminium has a much higher conductivity than
permalloy, the effect of the Barber poles is to rotate the
current direction through 45
°
(the current flow assumes a
‘saw-tooth’ shape), effectively changing the rotation angle
of the magnetization relative to the current from
α
to
α −
45
°
.
A Wheatstone bridge configuration is also used for
linearized applications. In one pair of diagonally opposed
elements, the Barber poles are at +45
°
to the strip axis,
while in another pair they are at
−
45
°
. A resistance
increase in one pair of elements due to an external
magnetic field is thus ‘matched’ by a decrease in
resistance of equal magnitude in the other pair.
The resulting bridge imbalance is then a linear function of
the amplitude of the external magnetic field in the plane of
the permalloy strips, normal to the strip axis.
R
R
O
∆
R
O
cos
2
α
+
=
sin
2
α
H
2
H
O
2
-------- for H
H
O
≤
=
sin
2
α
1 for H
H
O
>
=
R
R
O
∆
R
O
1
H
2
H
O
2
--------
–
for H
H
0
≤
+
=
R
R
O
for H
H
O
>
=
Fig.12 Linearization of the magnetoresistive effect.
handbook, halfpage
MLC125
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I
I
Magnetization
Permalloy
Barber pole