FIGURE 48.20 Typical AMR bridge sensor transfer functions. The sensitivity of an AMR bridge can be adjusted by changing its bias field. Increases in sensitivity are accompanied by corresponding decreases in range.
As Equation 48.44 shows, the polarity of the transfer function is determined by the polarity of (Hk + Hb). If the sensor is exposed to an external field that is strong enough to reverse this field, then the transfer function polarity will reverse. To overcome this ambiguity, the polarity should be established prior to making a measurement. This can be accomplished by momentarily applying a strong magnetic field along the easy axis of the AMR bridge. Some commercial AMR bridges come with a built-in method for performing this action.
Figure 48.21 is a block diagram for a signal conditioner that takes advantage of the bias field polarity flipping property to eliminate zero offset errors and low frequency 1/f noise. A square wave oscillator is used to alternately change the direction of the bias field and thus the polarity of the transfer function. The duration of the current used to set the bias field direction should be short in order to minimize power consumption. The amplitude of the ac signal from the bridge is proportional to the field magnitude, and its phase relative to the oscillator gives the field direction. This signal can be amplified and then phase-detected to extract the field-related voltage. Optionally, the output signal can be fed back through a coil that produces a magnetic field opposing the field being measured. This feedback arrangement makes the AMR bridge a null detector and minimizes the influence of changes in its transfer function on overall performance. Of course, the added circuitry increases the size, cost, and complexity of the instrument.
48.4 Scalar Magnetometers
Scalar magnetometers measure the magnitude of the magnetic field vector by exploiting the atomic and nuclear properties of matter. The two most widely used scalar magnetometers are the proton precession and the optically pumped magnetometer. When operated under the right conditions, these instruments have extremely high resolution and accuracy and are relatively insensitive to orientation. They both have several common operating limitations. The instruments require the magnetic field to be uniform throughout the sensing element volume. They have a limited magnetic field magnitude measurement range: typically 20 ??T to 100 ?T. And they have limitations with respect to the orientation of the magnetic field vector relative to the sensor element.
? 1999 by CRC Press LLC
FIGURE 48.21 Example AMR gaussmeter. The magnetization direction can be alternately flipped to eliminate zero offset. The resulting ac signal can then be amplified and synchronously phase-detected to recover the field-related signal. Optionally, the range and stability of the AMR gaussmeter can be increased by connecting the output voltage through a resistor to a feedback coil that produces a field that nulls the applied field.
The proton precession magnetometer uses a strong magnetic field to polarize the protons in a hydro-carbon and then detects the precession frequency of the protons while they decay to the nonpolarized state after the polarizing field is turned off. The precession frequency is proportional to the magnitude of any ambient magnetic field that is present after the polarizing field is removed. This sampling of the magnetic field strength through the polarize-listen sequence makes the proton precession magnetometer response very slow. Maximum rates of only a few samples per second are typical. Because of its dependence on atomic constants, the proton precession magnetometer is the primary standard for calibrating systems used to generate magnetic fields and calibrate magnetometers.
The optically pumped magnetometer is based on the Zeeman effect. Zeeman discovered that applying a field to atoms, which are emitting or absorbing light, will cause the spectral lines of the atoms to split into a set of new spectral lines that are much closer together than the normal lines. The energy-related frequency interval between these hyperfine lines is proportional to the magnitude of the applied field. These energy levels represent the only possible energy states that an atom can possess. The optically pumped magnetometer exploits this characteristic by optically stimulating atoms to produce an overpopulated energy state in one of the hyperfine spectral lines and then causing the energy state to depopulate using an RF magnetic field. The RF frequency required to depopulate the energy state is equal to the spectral difference of the hyperfine lines produced by a magnetic field and, therefore, is proportional to the magnetic field strength. The optically pumped magnetometer can be used to sample the magnetic
? 1999 by CRC Press LLC
FIGURE 48.22 Nuclear precession. A spinning proton with angular momentum L and magnetic moment ??, when subjected to a magnetic field Ha, will precess about the field at an angular rate ?? equal to ??Ha/L.
field at a much higher rate than the proton precession magnetometer and generally can achieve a higher resolution. The sample rate and instrument resolution are interdependent.
The Proton Precession Magnetometer
The proton precession magnetometer works on the principle that a spinning nucleus, which has both angular momentum L and a magnetic moment ?? ???
??p, will precess about a magnetic field like a gyroscope,
as shown in Figure 48.22. The precession frequency ?? is proportional to the applied field. When the magnetic field ??Ha is applied to the nucleus, it will produce a torque:?
r r
r
T????????Ha
(48.47)
on the nucleus. Because the nucleus has angular momentum, this torque will cause the nucleus to precess about the direction of the field. At equilibrium, the relationship between the torque, precession rate, and angular momentum is:
?????
r
Ha
???????
r
L
r
(48.48)
Solving for the magnitude of the (Larmor) precession frequency, one finds that:
????????????????L Ha Ha ????????????????
(48.49)
where ??is called the gyromagnetic ratio and equals (2.6751526 ??0.0000008) ??10–8 T–1 s–1.
Figure 48.23 is a block diagram of a proton precession magnetometer. The sensor is a container of hydrocarbon rich in free hydrogen nuclei. A solenoid wrapped around the container is used to both polarize the nuclei and detect the precession caused by the ambient field. Before the polarizing field is applied, the magnetic moments of the nuclei are randomly oriented, and the net magnetization is zero. Application of the polarizing field (typically 3 mT to 10 mT) causes the nuclei to precess about the field. The precession axis can be parallel or antiparallel (nuclear magnetic moment pointing in the direction of the field) to the applied field. From a quantum mechanical standpoint, the antiparallel state is a lower energy level than the parallel state. In the absence of thermal agitation, which causes collisions between atoms, the fluid would remain unmagnetized. When a collision occurs, the parallel precession-axis nuclei lose energy and switch to the antiparallel state. After a short time, there are more nuclei with magnetic
? 1999 by CRC Press LLC
FIGURE 48.23 Typical proton precession magnetometer. A polarizing field is applied to the hydrocarbon when S1 is closed. The amplifier input is shorted to prevent switching transients from overdriving it. After a few seconds, S1 is opened and the coil is connected to the signal processor to measure the Larmor frequency.
moments pointing in the direction of the field than away from it, and the fluid reaches an equilibrium magnetization M0. The equation that relates magnetization buildup to time is:
M ??t???M ?????e t ?
1
0
????e
(48.50)
where ?e is the spin-lattice relaxation time.
The equilibrium magnetization is based on thermodynamic considerations. From Boltzmann statistics for a system with spins of 1/2:
np e2?? Ha kT ??n
a
(48.51)
where np is the number of precession spin axes parallel to Ha, na is the number of precession spin axes
antiparallel to Ha, k is Boltzmann’s constant, and T is temperature (kelvin). If n is the number of magnetic moments per unit volume, then:
n n ??????
n n ???????H kT
1 2 ???e a ?????
(48.52)
? 1999 by CRC Press LLC
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