2000 Sep 06 16
Philips Semiconductors
Magnetoresistive sensors for
magnetic field measurement General
sinφ= (6)
where |Hy|≤|H0+H
x
| and Hxand Hyare the components
of the external field. In the simplest case Hx = 0, the volt-
ages Ux and Uy become:
Ux=ρ
⊥
l (7)
Uy=ρ
⊥
l (8)
(Note: if Hx= 0, then H0 must be replaced by
H0+H
x
/cos φ).
Neglecting the constant part in Ux, there are two main
differences between Ux and Uy:
1. The magnetoresistive signal Ux depends on the
square of Hy/H0, whereas the Hall voltageUyis linear
for Hy « H0.
2. The ratio of their maximum values is L/w; the Hall
voltage is much smaller as in most cases L » w.
Magnetization of the thin layer
The magnetic field is in reality slightly more complicated
than given in equation (6). There are two solutions for
angle φ:
φ1 < 90˚ and φ2 > 90˚ (with φ1+φ2 = 180˚ for Hx=0).
Replacing φ by 180˚ -φ has no influence on Ux except to
change the sign of the Hall voltage and also that of most
linearized magnetoresistive sensors.
Therefore, to avoid ambiguity either a short pulse of a
proper field in the x-axis (|Hx|>H
k
) with the correct sign
must be applied, which will switch the magnetization into
the desired state, or a stabilizing field Hst in the
x-direction can be used. With the exception of Hy « H0, it
is advisable to use a stabilizing field as in this case, Hx
values are not affected by the non-ideal behaviour of the
layer or restricted by the so-called ‘blocking curve’.
Theminimum value of Hst depends on the structure of the
sensitive layer and has to be of the order of Hk, as an
insufficient value will produce an open characteristic
(hysteresis) of the sensor. An easy axis in the y-direction
leads to a sensor of higher sensitivity, as then
Ho=H
k−H
d
.
Linearization
As shown, the basic magnetoresistor has a square
resistance-field (R-H) dependence, so a simple
magnetoresistive element cannot be used directly for
linear field measurements. A magnetic biasing field can
be used to solve this problem, but a better solution is
linearization using barber-poles (described later).
Nevertheless plain elements are useful for applications
using strong magnetic fields which saturate the sensor,
where the actual valueof the field is not being measured,
suchas for angle measurement. In this case, the direction
of the magnetization is parallelto the field and the sensor
signal can be described by a cos2α function.
Sensors with inclined elements
Sensorscan also be linearized by rotating the current path,
by using resistive elements inclined at an angle θ, as
shown in Fig.18. An actual device uses four inclined
resistive elements, two pairs each with opposite
inclinations, in a bridge.
The magnetic behaviour of such is pattern is more
complicatedas Mois determined by the angle of inclination
θ, anisotropy, demagnetization and bias field (if present).
Linearity is at its maximum forφ + θ≈ 45˚, which can be
achieved through proper selection ofθ.
A stabilization field (Hst) in the x-direction may be
necessaryfor some applications, as this arrangement only
works properly in one magnetization state.
Hy
HoHx
cosφ
------------
+
--------------------------
L
wt
------
1∆ρ
ρ
-------
1H
y
H
0
-------
2
–
+
1
t
---
∆ρ
ρ
-------
H
y
H
0
-------
1H
y
H
0
⁄()
2
–
Fig.18 Current rotation by inclined elements
(current and magnetization shown in
quiescent state).
handbook, halfpage
MBH613
M0
M0
Ι
Ι
ϑ
ϑ
ϕ
ϕ