FIGURE 48.15 Example of how to construct a Hall effect gaussmeter. The operational amplifier and resistor Rs form a stable constant-current source for the Hall effect sensor. An instrumentation or differential amplifier amplifies and scales the Hall voltage. A load resistor is sometimes required across the Hall voltage output terminals.
The typical control current for Hall effect devices is 100 mA, but some do operate at currents as low as 1 mA. Sensitivities range from 10 mV/T to 1.4 V/T. Linearity ranges from 1/4% to 2% over their rated operating field range. The control input and the voltage output resistance are typically in the range of 1 ??to 3 ?. The sensor element is usually tiny (on the order of 10 mm square by 0.5 mm thick), and a three-axis version can be housed in a very small package. These devices are most effective for measuring flux densities ranging from 50 ??T to 30 T. Signal Conditioning
A simple Hall effect gaussmeter can be constructed using the signal conditioning circuit shown in Figure 48.15. The voltage reference, operational amplifier, and sense resistor Rs form a precision constant-current source for the Hall effect device control current Ic. For best performance, the voltage reference and Rs should be very stable with temperature and time. A general-purpose operational amplifier can be used for low control currents. A power amplifier is required for control currents above 20 mA.
The Hall voltage can be conditioned and amplified by any high input impedance (>1 k??) differential amplifier. A precision instrumentation amplifier is a good choice because it has adequate input imped-ance, its gain can be determined by a stable resistor, and the amplifier zero offset trim resistor can be used to cancel the zero offset of the Hall effect device. Some devices require a load resistor across the Hall voltage terminal to achieve optimum linearity.
The zero offset and 1/f noise of the Hall voltage amplifier limit the performance of a Hall effect gaussmeter for low field strength measurements. Sometimes, these effects can be reduced by using an ac precision current source. The ac amplitude modulated Hall voltage can then be amplified in a more favorable frequency band and synchronously detected to extract the Hall voltage signal. If the field to be measured requires this amount of signal conditioning, it probably is better to use a fluxgate magnetometer for the application.
The Magnetoresistive Gaussmeter
The magnetoresistance effect was first reported by William Thomson (Lord Kelvin) in the middle of the 19th century. He found that a magnetic field applied to a ferromagnetic material caused its resistivity to change. The amount of change depends on the magnetization magnitude and the direction in which the current used to measure resistivity is flowing. Nickel–iron alloys show the greatest change in resistivity (about 5% maximum). Figure 48.16 illustrates how the resistivity changes in Permalloy (a nickel–iron alloy) for a field applied parallel to the current flow. As magnetic field is increased, the change in resistivity increases and asymptotically approaches its maximum value when the material approaches saturation. Bozorth [6] points out that the shape of the curve and the magnitude of the change depend on the
? 1999 by CRC Press LLC
FIGURE 48.16 Change in resistivity in a ferromagnetic material. As field is applied, the resistivity changes rapidly at first. As the material approaches magnetic flux saturation, the resistivity change approaches its maximum value.
FIGURE 48.17 An AMR resistor element. During fabrication, a magnetic field is applied along the strip’s length to magnetize it and establish its easy axis. Current I is passed through the film at 45??to the easy or anisotropic axis. A magnetic field Ha applied at right angles to the magnetization vector M causes the magnetization vector to rotate and the magnetoresistance to change.
composition of the alloy. Permalloy with 80% Ni and 20% Fe provides a high magnetoresistance effect with near-zero magnetostriction and is a favorite material for magnetoresistors.
The change in resistivity in permalloy film [18] is also a function of the angle ??between the magne-tization direction and the current direction:
????????0?????m cost???
(48.40)?
where ??m is the magnetoresistivity anisotropy change and ?0 is the resistivity for ??= ??/2.
It was mentioned earlier that magnetic materials have anisotropic magnetic properties (their magnetic properties are direction dependent). The physical shape of an object (see the discussion on demagnetizing factor above) and the conditions that exist during fabrication strongly determine its anisotropic charac-teristics. A thin long film of permalloy can be made to have highly uniaxial anisotropic properties if it is exposed to a magnetizing field during deposition. This characteristic is exploited in the anisotropic magnetoresistance (AMR) sensor.
The basic resistor element in an AMR is a thin rectangular shaped film as shown in Figure 48.17. One axis, called the anisotropy or easy axis, has a much higher susceptibility to magnetization than the other two. The easy axis is normally along the length of the film. Because of its thinness, the axis normal to the film has virtually no magnetic susceptibility. The axis transverse to the easy axis (across the width) has very little susceptibility as well.
A bias field Hb is used to saturate the magnetization along the easy axis and establish the magnetization direction for zero external field. For a simplified analysis, the film can be modeled as a single domain.
? 1999 by CRC Press LLC
FIGURE 48.18 Magnetoresistor construction. (a) A typical AMR element consists of multiple strips of permalloy connected together in a serpentine pattern. Current shunts force the current to flow through the permalloy at 45??to the easy axis. (b) A close-up view.
The effect of an external field in the plane of the film and normal to the anisotropy axis is to rotate the magnetization vector and, according to Equation 48.40, change the resistivity. Kwiatkowski and Tumanski [19] stated that the change in resistance of the film can be approximated by Equation 48.41:
?
?????????????
?R?R m h 2?
cos 2??
?h ??h2 ?
1 sin 2
???
1?
?????cos2??
(48.41)
where ha is the normalized externally applied field (i.e., ha = Ha/Hk), Rs is the nominal resistance, and
??m/??is the maximum resistivity change. Hk is the anisotropy field. Optimum linear performance is obtained when ??= ??/4 and Equation 48.41 reduces to:
????
1
??R ??R m???H ??H?Ha
s
k
b
(48.42)
The anisotropy field is given by:
Hk???Hk ???NM s?
0
2
(48.43)
2
where Hk0 is the film anisotropy field, N is the demagnetizing factor (??thickness(t)/width(w)) and Ms is the saturation magnetization.
An AMR is constructed using long thin film segments of deposited permalloy. During deposition, a magnetic field is applied along the length of the film to establish its easy axis of magnetization. The shape of the film also favors the length as an easy axis. As shown in Figure 48.18, a series of these permalloy films is connected together to form the magnetoresistor. The current is forced to flow at a 45??angle to the easy axis by depositing thin strips of highly conductive material (e.g., gold) across the permalloy film. The level of magnetization of the film is controlled by a bias field that is created through the deposition of a thin layer of cobalt over the resistors, which is then magnetized parallel to the easy axis of the permalloy.
? 1999 by CRC Press LLC
FIGURE 48.19 AMR bridge sensor. In an AMR bridge, the current shunts of resistors A and D are the same and reversed from B and C. Thus, the resistors on diagonal legs of the bridge have the same response to an applied field and opposite that of the other diagonal pair. Bridge leg resistance varies from 1 k??to 100 k??.
A typical AMR sensor suitable for a gaussmeter or magnetometer consists of four AMRs connected in a Wheatstone bridge as shown in Figure 48.19. The transfer function polarity of the A and D resistors is made to be opposite that of the B and C resistors by rotating the current shunt 90?. This complimentary arrangement enhances the output voltage signal for a given field by a factor of four over a single resistor. Kwiatkowski and Tumanski [19] showed that the transfer function for the bridge configuration is described by:
v?IRs cos2 ??
m
?????
a
1 h2 ??h ???a
(48.44)
Where:
cos2????
H ?H ???NM??? 2
k 0
2 k
s 2
(48.45)
2 H H
H
h ?? a a
H ?H
(48.46)
k b
For best linearity, Ha < 0.1 Hk. The linearity of the bridge can be controlled during fabrication by adjusting the l/w ratio and Hk0. The bias field can also be used to optimize linearity and establish the measurement field range. Some transfer functions for a typical AMR bridge [20] are shown in Figure 48.20. A more comprehensive discussion of AMR theory can be found in [21–23]. Signal Conditioning
Conventional Wheatstone bridge signal conditioning circuits can be used to process the AMR bridge. The bridge sensitivity and zero offset are proportional to the bridge voltage, so it is important to use a well-regulated supply with low noise and good temperature stability.
? 1999 by CRC Press LLC
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