Download Measurement of Weak Magnetic Fields

PIERS Proceedings, Suzhou, China, September 12–16, 2011
962
Measurement of Weak Magnetic Fields
L. Kadlcik, J. Mikulka, and E. Gescheidtova
Department of Theoretical and Experimental Electrical Engineering
Brno University of Technology, Kolejni 4, Brno 612 00, Czech Republic
Abstract— In the paper, the principle is described of measuring magnetic fields with very low
levels of magnetic induction, of the order of unities of µT. The method described in the paper
aims to ascertain the presence of a small amount of ferromagnetic material on a small area. It
can, however, be also applied when examining the homogeneity of weak magnetic fields. The
most important part of the device proposed here is the detection element, which evaluates the
changes in magnetic properties of the surrounding environment, and interacts with the given
ferromagnetic material. An integral part of the device is the demodulator, which processes
the detected signal, from which only the part carrying useful information is selected. The useful
information is deformed by convolution distortion and thus the signal must be reconstructed in an
appropriate way. The reconstruction is associated with the decoder, which facilitates obtaining
additional information in cases when the results of reconstruction are not unambiguous. A
detailed analysis of the functions of detectors working on different principles has shown that our
requirements are best satisfied by a simple ferromagnetic probe with a core of small diameter.
The detecting part is designed in the form of a pen complemented with an oscillator with a
resonance frequency of 300 kHz. The demodulator is implemented in the form of two PLL phase
detectors, which are followed by a third-order low-pass filter with a cut-off frequency of 1 kHz.
The circuitry terminates in a high-pass filter with a cut-off frequency of 0.34 Hz, which removes
the dc component of the signal. The proposed meter will be used to establish the homogeneity
of a weak magnetic field in biomedical applications.
1. INTRODUCTION
If the detector of a reading head is moved over a surface on which a thin layer of ferromagnetic
material has been deposited, then in the ideal case the amount of ferromagnetic material c along the
detector path r is a function of c(r). The sensitivity of ideal detector to the ferromagnetic material
is concentrated in one point but in practice this condition is not fulfilled. The magnetic field is
dispersed over the surrounding environment and thus an actual detector reacts to all ferromagnetic
materials present in its vicinity. This fact is described by the point spread function (PSF) h(r).
This is a spatial analogy to the Dirac pulse. The PSF of detectors actually comes close to the
Gauss curve (1), which is manifested by sloping or even overlapping signal edges,
r2
1
h (r) = K0,s √ e− 2σ2 ,
σ 2π
(1)
where K0,s is the detector sensitivity, σ is the dispersion, which gives the spread of detector sensitivity in the surrounding environment. In practice we try to design the detector such that its
point spread function is as narrow as possible, coming close to the Dirac pulse. The shape of PSF
depends, above all, on the area of the detector front; we endeavour to make this area as small
as possible. The detector behaves like a linear system: the output signal is a convolution of the
amount of ferromagnetic material and PSF
y (r) = h (r) ∗ c (r) .
(2)
In the spatial region, the detector behaves like a low-pass filter; the higher frequencies are
suppressed and this is manifested as chamfered edges of the signal. The spatial frequency response
of the distorting filter is given by the Fourier transform of PSF
+∞
Z
2 σ2
ωr
r2
1
Hr (ωr ) =
K0,r √ e− 2σ2 e−jωr dr = K0,s e− 2 .
σ 2π
(3)
−∞
Detector attenuation increases fast with increasing spatial frequency ωr ; the larger the dispersion
σ is, the lower the cut-off spatial frequency of the filter and the steeper the filter. Electronic filters
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
963
work in the time domain; for the transition from the space domain to the time domain, the law of
motion will be employed: path r equals the product of velocity v and time t
r = vt.
The frequency response of the distorting filter can then be expressed by the relation
³ω ´
1
H (ω) = Hr
,
v
v
(4)
(5)
from which it is apparent that the frequency response of the distorting filter depends on the velocity
of detector motion.
There are two basic types of detector [1]: induction detector operating on the principle of Faraday’s induction law, and inductive detector, which detects the presence of ferromagnetic material
by changing the detector coil inductance. In the course of motion over a magnetized material, alternating voltage is induced in the induction coil, whose waveform corresponds to the distribution
of magnetic induction. The principle is simple but inapplicable in our case; the induction near the
surface of ferromagnetic layer is very low, lower than the induction of the Earth’s magnetic field. To
obtain a signal whose level would make it applicable, the coil surface would have to be large, which
is in contradiction with the demand for low dispersion. Common detectors of weak magnetic fields
are single and double ferromagnetic probes [1, 2]. The field coil and the current source are intentionally designed such that the core is being oversaturated. The waveform of magnetic induction is
detected by the coil winding, in which the voltage induced passes through a band-pass filter tuned
to the second harmonic. The voltage after the band-pass filter is rectified. The spectrum does not
contain the even harmonics and thus there is zero voltage on the probe output. If the coil core is
inserted into an external magnetic field, its intensity in the half-wave of one polarity will be added
up with the magnetic field of the field coil and subtracted in the other half-wave. The core in one
half-wave will thus be oversaturated more than in the other. The waveform of magnetic induction
in the core will be asymmetrical, and so will the waveform of induced voltage [2]. The asymmetrical
waveform contains the even harmonics; the second harmonic passes through the band-pass filter
and is rectified by a rectifier. On the probe output there will be a voltage whose magnitude depends
on the induction of external magnetic field. The band-pass filter must be sufficiently selective because we try to extract from the induced voltage the second harmonic in the presence of the much
more pronounced fundamental frequency [2]. The sensitivity of the simple ferromagnetic probe is
sufficient for our purposes. When testing the function of the meter we have fabricated we used as
a reference detector the FLC 100 ferromagnetic probe manufactured by Stefan Meyer Instruments.
The manufacturers claim that a magnetic field of 50 µT induction will change the voltage on the
probe output by 1 V.
2. DESIGN AND IMPLEMENTATION OF THE SENSOR
The fabricated device consists of an appropriate detector, demodulator, reconstruction circuit, and
decoder, as shown in Fig. 1.
2.1. Detector
In the design of the sensor the detection element chosen was the oscillator, which is an LC circuit
complemented with an amplifier, which makes up for the energy losses and thus the circuit becomes
a source of permanent oscillations. A positive feedback guarantees that the amplitude and phase
conditions are fulfilled. In the design of the oscillator we endeavoured to minimize the effect of
Figure 1: Block diagram.
PIERS Proceedings, Suzhou, China, September 12–16, 2011
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Figure 2: Schematic of detection oscillator.
surrounding signals. The barrier capacitances of the semiconductor employed mistune the supply
voltage, which results in parasitic frequency modulation. This may lead to a feedback being formed
through the supply voltage distribution, and the circuit need not be stable. Large capacitances will
be used in the LC circuit and this will reduce the proportion of barrier capacitances in the total
capacitance. We also tried hard to make the coupling between the circuit and the amplifier as loose
as possible — the LC circuit is connected via a capacitive divider.
Both the coil inductance and the capacitance of the capacitors employed are temperaturedependent. The temperature dependence of the capacitance is primarily given by the type of
capacitor dielectric [3, 4]. The temperature dependence of the inductance is given by the thermal
expansivity of the coil and also by the temperature dependence of the permeability of its core.
The temperature dependence of the frequency will be reduced if the thermal coefficients of the
capacitance and of the inductance compensate each other. If the oscillator amplifier is excited up
to the non-linear part of its transfer characteristic, the oscillator may be pulled by an interfering
signal. Interference propagating through the supply voltage distribution can be prevented by an LC
low-pass filter. For the convolution distortion to be attenuated as much as possible it is necessary
to choose the detector with the narrowest possible spatial pulse response; the response width is
directly proportional to the size of the detection area. The oscillator is assembled using SMD
components on a small board, which is connected to the demodulator by a coaxial cable (shielded
two-wire line) terminating in a connector.
2.2. Demodulator
An integral part of the device is the demodulator, which processes the signal detected, from which
only the part that carries useful information is selected. This information is deformed by convolution
distortion so that the signal must first be reconstructed in an appropriate way.
The phase detector measures the phase shift between two signals and produces a voltage on its
output a certain characteristic of which (the mean value, for example) corresponds to this phase
shift. The phase detector output signal is usually rectangular and the information about the phase
shift is carried by the mean value, which we obtain by filtering. In the simplest case the loop
filter is a first-order low-pass filter [5, 6]. The transfer function of the filter markedly influences the
dynamic properties of PLL.
The demodulator supply voltage is 12 V; an IC3 stabilizer produces a smooth stable supply
voltage for PLL. Connectors for the supply intake have intentionally a great number of pins; at the
prototype stage its further extension was taken into account, in which case some further circuits
might also require different supply voltages. The prototype can be further extended.
3. EXPERIMENTAL RESULTS
The device was implemented according to the description given above. The detection coil itself is
a winding of several tens of turns on a ferrite core of 2 mm in diameter; it is placed on the detector
board and connected to the oscillator. An implemented device is shown in Fig. 5.
The reference detector employed to test the function of the whole facility was the FLC 100
ferromagnetic probe (Stefan Meyer Instruments). The manufacturers claim that a magnetic field
of 50 µT induction generates on the probe output a voltage change of 1 V [7].
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
965
Figure 3: Block diagram of phase lock.
Figure 4: Schematic of demodulator.
Figure 5: Implemented device.
In the verification, we used a substance with a deposited layer of ferromagnetic ink, which was
magnetized by applying a strong permanent magnet. On the reference probe output we obtained
a signal with 20 mV amplitude. This means that the magnetic induction of magnetized ink is
1 µT. With the bar code not applied, the detection oscillator oscillates on the frequency f1 =
(311698 ± 95) Hz. Applying one wide bar of magnetic ink directly to the front of the detection coil
core of the designed detector reduced the frequency by f = (97 ± 5) Hz, or f = (−312 ± 16) ppm.
The results of measuring on the demodulator are as follows. At rest the control voltage VCO
Uf1 = (2.196 ± 0.002 V).
After applying a 5 mm wide magnetic bar the voltage drops by Uf = (−2.95 ± 0.45) mV, i.e.,
Uf = (−1340 ± 210) ppm.
After amplification, the amplitude swing of the signal acquires a value of ca. 1 V (Fig. 6 in [20]).
The convolution distortion can be observed clearly on the signal. If the detection is performed by
the edge of the coil core, the amplitude swing of the signal is smaller (approximately 0.7 V, Fig. 7
in [21]), but the convolution detection is manifested to a lesser extent (because the surface of the
edge is smaller). The output signal exhibits 50 Hz mains interference, as can be seen from the
voltage waveforms in Fig. 6.
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PIERS Proceedings, Suzhou, China, September 12–16, 2011
Figure 6: Output signal of demodulator.
4. CONCLUSION
The device described in the paper can be used with advantage to establish the presence of a
small amount of ferromagnetic material. It can also be used to examine the homogeneity of weak
magnetic fields. The most important part of the device is the detection element, which assesses
the changes in the magnetic properties of the surrounding environment when the element is moved
over a source of magnetic field, and which interacts with the ferromagnetic material present. A
simple ferromagnetic probe, FLC 100 (Stefan Meyer Instruments), can be used to this purpose
but the detection is not very sharp. Detection by the detection oscillator that we designed and
implemented is sharper but still leaves scope for improvement. It would be of advantage to use a
coil core of less than 2 mm in diameter.
ACKNOWLEDGMENT
This work was supported within the framework of projects No. 102/11/0318 of the Grant Agency
of the Czech Republic and the research plan MSM 0021630516.
REFERENCES
1. Draxler, K., P. Kaspar, and P. Ripka, Magnetické prvky a měřenı́, CVUT, Praha, 1999 (in
Czech).
2. Dufek, M., J. Hrabak, and Z. Trnka, Magneticka merenı́, SNTL, Praha, 1964 (in Czech).
3. Shellhammer, S., D. Goren, and T. Pavlidis, “Novel signal-processing techniques in Barcode
scanning,” IEEE Robotics & Automation Magazine, Vol. 6, 57–65, 1999.
4. Smith, J., Modern Communication Circuits, McGraw-Hill Book Company, New York, 1986.
5. Curtin, M. and P. O’Brien, “Phase locked loops for high-frequency receivers and
transmitters — Part 3,” Analog Dialogue [online], Vol. 33, No. 1, 18–22, 1999.
URL: http://www.analog.com/library/analogdialogue/cd/vol33n1.pdf.
6. NXP
Semiconductors,
HEF4046B
Phase-locked
Loop
[online],
URL:
<www.nxp.com/documents/data sheet/HEF4046B.pdf>.
7. Stefan Mayer Instruments, Magnetic Field Sensor FLC 100 [online], URL:
<http://www.stefan-mayer.com/Data%20sheet%20FLC%20100.pdf>32.