Philips Magnetoresistive Sensor manual Further information for advanced users

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°.

2000 Sep 06

Philips Semiconductors

Magnetoresistive sensors for

magnetic field measurement

Further information for advanced users

THE MR EFFECT

General

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:				handbook, halfpage	Barber pole
R = RO + ΔRO cos2 α
				(2)
It can be shown that				I	I
sin	2	α =	H2	(3)
			------- for H ≤ HO		MLC125
			HO2
and					Permalloy
					Magnetization
sin2 α = 1 for H > HO				(4)

where Ho can be regarded as a material constant
comprising the so called demagnetizing and anisotropic
fields.	Fig.12 Linearization of the magnetoresistive effect.

Applying equations (3) and (4) to equation (2) leads to:

R	= RO	⎛	H2 ⎞	(5)	A Wheatstone bridge configuration is also used for
		+ ΔRO ⎜1	–-------⎟for H ≤ H0
		⎝	H2 ⎠		linearized applications. In one pair of diagonally opposed
			O
R = RO for H > HO				(6)	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.

11