Philips Magnetoresistive Sensor manual Magnetization of the thin layer, Linearization

where Hy≤ H0 + Hx and Hx and Hy are the components of the external field. In the simplest case Hx = 0, the volt- ages Ux and Uy become:

Philips Semiconductors

Magnetoresistive sensors for

magnetic field measurement

General

sinφ = --------------------------	Hy
	Hx
Ho
	+ ------------
	cosφ

Ux = ρ⊥l	⎛ L	⎞ ⎛	1 +	⎛ Δρ⎞ ⎛		1	⎛ Hy⎞ 2⎞⎞
	-----			------	⎠ ⎝		– ------	⎠⎠
	⎝ wt⎠ ⎝			⎝ ρ			⎝ H0⎠

resistance-field (R-H) dependence, so a simple

(6)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 value of the field is not being measured,

(7)such as for angle measurement. In this case, the direction of the magnetization is parallel to the field and the sensor signal can be described by a cos2α function.

Uy = ρ⊥l	⎛ 1⎞ ⎛ Δρ⎞ ⎛ Hy⎞				1	–(H		⁄ H	)	2	(8)
	--	------	------	⎠			y
	⎝ t	⎠ ⎝ ρ	⎠ ⎝ H					0
			0

(Note: if Hx = 0, then H0 must be replaced by H0 + Hx/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 voltage Uy is 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 > Hk) 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

Sensors with inclined elements

Sensors can 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 complicated as Mo is determined by the angle of inclination θ, anisotropy, demagnetization and bias field (if present). Linearity is at its maximum for φ + θ ≈ 45˚, which can be achieved through proper selection of θ.

A stabilization field (Hst) in the x-direction may be necessary for some applications, as this arrangement only works properly in one magnetization state.

handbook, halfpage	M0	ϕ
ϑ

Ι

ϑ

ϕ

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’.

M0

Ι

MBH613

The minimum 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 = Hk − Hd.

Fig.18 Current rotation by inclined elements (current and magnetization shown in quiescent state).

Linearization

As shown, the basic magnetoresistor has a square

2000 Sep 06 16