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2000 Sep 06 11
Philips Semiconductors
Magnetoresistive sensors for
magnetic field measurement
General
Further information for advanced users
THE 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.
LINEARIZATION
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.
RR
O
∆R
O
cos
2
α+=
sin
2
α
H
2
H
O
2
--------
for H H
O
≤=
sin
2
α 1 forH H
O
>=
RR
O
∆R
O
1
H
2
H
O
2
--------
–
for H H
0
≤+=
RR
O
for H H
O
>=
Fig.12 Linearization of the magnetoresistive effect.
handbook, halfpage
MLC125
II
Magnetization
Permalloy
Barber pole