Induction coil sensors—a review REVIEW ARTICLE Slawomir Tumanski

Induction coil sensors—a review REVIEW ARTICLE Slawomir Tumanski
INSTITUTE OF PHYSICS PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
doi:10.1088/0957-0233/18/3/R01
Meas. Sci. Technol. 18 (2007) R31–R46
REVIEW ARTICLE
Induction coil sensors—a review
Slawomir Tumanski
Institute of Electrical Theory & Measurement, ul Koszykowa 75, 00-661 Warsaw, Poland
E-mail: [email protected]
Received 17 August 2006, in final form 7 November 2006
Published 19 January 2007
Online at stacks.iop.org/MST/18/R31
Abstract
This review describes induction coil sensors, which are also known as
search coils, pickup coils or magnetic loop sensors. The design methods for
coils with air and ferromagnetic cores are compared and summarized. The
frequency properties of coil sensors are analysed and various methods for
output signal processing are presented. Special kinds of induction sensors,
such as Rogowski coil, gradiometer sensors, vibrating coil sensors,
tangential field sensors and needle probes are described. The applications of
coil sensors as magnetic antennae are also presented.
Keywords: coil sensor, magnetic field measurement, search coil, Rogowski
coil, vibrating coil, gradiometer, integrator circuit, H-coil sensor, needle
probe method.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Induction coil sensors [1–4] (also called search coil sensors,
pickup coil sensors, magnetic antennae) are one of the oldest
and most well-known types of magnetic sensors. Their transfer
function V = f(B) results from the fundamental Faraday’s law
of induction
dH
dB
d
= −n · A ·
= −µ0 · n · A ·
(1)
V = −n ·
dt
dt
dt
where is the magnetic flux passing through a coil with an
area A and a number of turns n.
The operating principles of coil sensors are generally
known but the technical details and practical implementation
of such devices are only known to specialists. For example,
it is well known that the output signal, V, of a coil sensor
depends on the rate of change of flux density, dB/dt, which
requires integration of the output signal. However, there are
other useful methods which enable the obtaining of results
proportional to flux density, B.
It is widely known, and evident from equation (1), that a
large coil sensitivity can be obtained by using a large number
of turns n and large active area A. However, the optimization
process for coil performance, in many cases, is not as easy.
The properties of a coil sensor were described in detail
many years ago [5]. However, sensors based on the same
0957-0233/07/030031+16$30.00
© 2007 IOP Publishing Ltd
operating principle are still widely used in many applications,
especially for the detection of stray magnetic fields (potentially
dangerous for health). The induction sensor is practically
the only one that can be manufactured directly by a user
(in comparison to Hall, magnetoresistive or fluxgate-type
sensors). The method of coil manufacture is simple and
the materials (winding wire) are commonly available. Thus,
almost everyone can perform such investigations using simple
and very low-cost, yet accurate, induction coil sensors.
There are many historical examples of the renaissance of
various coil sensors. For example, the Chattock–Rogowski
coil was first described in 1887 [6, 7]. Today, this sensor
has been re-discovered as an excellent current transducer [8]
and sensor used in measurement of magnetic properties of
soft magnetic materials [9]. An old Austrian patent from 1957
[10] describing the use of a needle sensor (also called the stylus
method) for the investigation of local flux density in electrical
steel was revived several years ago for magnetic measurements
[11, 12].
The main goal of this review is to summarize the
existing knowledge about induction coil sensors, including
old, often forgotten publications as well as new developments.
Firstly, two main designs of coil sensor (with air cores and
ferromagnetic cores) are described. Then, their frequency
response is analysed taking into account the type of sensor
and their associated output electronics. Secondly, particular
Printed in the UK
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induction sensors are discussed and this is followed by a
description of the most common application of this type of
transducer: magnetic antennae. Finally, the main advantages
and disadvantages of these sensors are discussed.
2. Air coils versus ferromagnetic core coils
The relatively low sensitivity of an air coil sensor and problems
with its miniaturization can be partially overcome by the
incorporation of a ferromagnetic core, which acts as a flux
concentrator inside the coil. For a coil with a ferromagnetic
core, equation (1) can be rewritten as
dH
.
V = −µ0 · µr · n · A ·
dt
l
(2)
Modern soft magnetic materials exhibit a relative
permeability, µr, larger than 105, so this can result in a
significant increase of the sensor sensitivity. However, it
should be taken into account that the resultant permeability of
the core, µc, can be much lower than the material permeability.
This is due to the demagnetizing field effect defined by the
demagnetizing factor N, which is dependent on the geometry
of the core
µr
.
(3)
µc =
1 + N · (µr − 1)
If the permeability µr of a material is relatively large
(which is generally the case) the resultant permeability of the
core µc depends mainly on the demagnetizing factor N. Thus,
in the case of a high permeability material, the sensitivity of
the sensor depends mostly on the geometry of the core.
The demagnetizing factor N for an ellipsoidal core
depends on the core length lc and core diameter Dc according
to an approximate equation
2lc
D2
−1 .
(4)
N∼
= 2c · ln
lc
Dc
It can be derived from equation (4) that in order to obtain
a small value of N (and a large resultant permeability µc)
the core should be long and with small diameter. Let us
consider the dimensions of a search coil sensor optimized for
a large sensitivity as described in [13]. The core was prepared
from amorphous ribbon (Metglas 2714AF) with dimensions
lc = 300 mm and Dc = 10 mm (aspect ratio equal to 30).
Substituting these values into equation (4) we obtain N ∼
=
3.5 × 10−3 which means that the sensitivity is about 300 times
larger in comparison with the air-coil sensor.
Therefore, the use of a core made of a soft magnetic
material leads to a significant improvement of the sensor
sensitivity. However, this enhancement is achieved with the
sacrifice of one of the most important advantages of the aircoil sensor—the linearity. The core, even if made from
the best ferromagnetic material, introduces to the transfer
function of the sensor some nonlinear factors which depend on
temperature, frequency, flux density, etc. Additional magnetic
noise (e.g. Barkhausen noise) also decreases the resolution
of the sensor. Moreover, the ferromagnetic core alters the
distribution of the investigated magnetic field (or flux density),
which can have important consequences.
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Figure 1. The simplest coil-based sensor for flux density and
magnetic fields.
D + Di
2
Di
d
D
D - Di
2
Figure 2. Typical design of an air coil sensor (l —length of the coil,
D—outer diameter of the coil, Di—inner diameter of the coil,
d—diameter of the wire).
3. Design of the air-coil sensor
A typical design of an air-coil sensor is presented in figure 2.
The resultant area of a multilayer coil sensor can be calculated
using integration [5]
D
π
1
π D 3 − Di3
A= ·
·
·
(y 2 )dy =
.
(5)
4 D − Di Di
12 D − Di
However, equation (5) is of limited accuracy. Thus, in
practice, it is better to determine the resultant area of the coil
experimentally by means of calibration in a known field. The
area of the coil can be calculated with a simplified formula
based on the assumption that its diameter is equal to mean
value Dm = (D + Di)/2, thus
π
(6)
A = · (D + Di )2 .
8
If we assume that the flux density to be measured is a sine
wave b = Bm · sin(ω · t), and the sensing coil is a ring with
diameter D, then the relation (1) can be rewritten in a form
V = 0.5 · π 2 · f · n · D 2 · B,
(7)
where f is a frequency of the measured field, n and D are
number of turns and diameter of the coil, respectively and B is
the measured flux density.
If we would like to determine the magnetic field strength
H instead of flux density B, then the equation (7) can be easily
transformed knowing that for a non-ferromagnetic medium
B = µ0 · H (µ0 = 4 · π · 10−7 H m−1) and
V = 2 × 10−7 · π 3 · f · n · D 2 · H.
(8)
Taking into account (6), equation (8) can be presented as
V =
10−7
· π 3 · f · n · (D + Di )2 · H.
2
(9)
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The number of turns depends on the diameter, d, of the
wire that is used, the packing factor k (k ≈ 0.85 [1]) and the
dimensions of the coil
l · (D − Di )
.
(10)
n=
2 · k · d2
Thus, the sensitivity S = V/H of an air-coil sensor can be
calculated as
10−7 π 3 · f · l
S=
· (D − Di ) · (D + Di )2 .
(11)
·
4
kd 2
The resolution of the coil sensor is limited by thermal
noise, VT, which depends on the resistance R of the coil, the
temperature T, the frequency bandwidth f with coefficient
equal to the Boltzmann factor kB = 1.38 × 10−23 W s K−1
VT = 2 kB · T · f · R.
(12)
Figure 3. The concept of three mutually perpendicular coils for
three-axis magnetic field measurements.
The resistance of the coil can be calculated as [14]
ρ·l
R = 4 (D − Di ) · (D + Di )
(13)
d
and the signal-to-noise ratio, SNR, of the air-coil sensor is
√
l · (D + Di ) · D 2 − Di2 · H
π 3 · 10−7
f
SNR =
·√
·
8
f
k 2 · kB · T · ρ
(14)
As can be seen from equation (14), the sensitivity
increases roughly proportionally to D3 and SNR increases
with D2, so the best way to obtain maximal sensitivity and
resolution is to increase the coil diameter D. Increasing the
coil length is less effective, because the sensitivity
increases
√
with l, while the SNR increases only with l. The sensitivity
can also be improved by an increase in the number of turns. For
example, by using wire with smaller diameter the sensitivity
increases with d2 and the SNR ratio does not depend on the
wire diameter.
Various publications discussed other geometrical factors
of the air-coil sensor. For instance, the optimum relation
between the length and the diameter of the coil can be
determined taking into account the error caused by the
inhomogeneous field. It was found [5, 15] that for l/D =
0.866 undesirable components are eliminated at the centre
of the coil. This analysis was performed for the coil with
one layer. For a multilayer coil the recommended relation is
l/D = 0.67–0.866 (0.67 for Di/D = 0 and 0.866 for Di/D =
1). The same source [5] recommends Di/D to be less than 0.3.
It can be concluded from the analysis presented above that
in order to obtain high sensitivity, the air-coil sensor should be
very large. For instance, the induction coil magnetometer
used for measurements of micropulsations of the Earth’s
magnetic field in the bandwidth of 0.001–10 Hz with resolution
1 pT–1 nT [16] have metre-range dimensions and even
hundreds of kilograms in weight. An example of a design
of such a coil sensor for such a purpose is presented in [17].
Here a coil with diameter 2 m (16 000 turns of copper wire
0.125 mm in diameter) detected micropulsation of flux density
in the bandwidth of 0.004–10 Hz. For the 1 pT field the output
signal was about 0.32 µV, whilst the thermal noise level was
about 0.1 µV.
The air-coil sensor with 10 000 turns and diameter 1 m
was used to detect the flux density of the magnetic field in the
pT range for magnetocardiograms [18].
Figure 4. An example of a pickup planar thin film coil designed for
eddy-current sensors [21].
Coil sensors are sensitive only to the flux that is
perpendicular to their main axis. Therefore, in order to
determine all directional components of the magnetic field
vector, three mutually perpendicular coils should be used
(figure 3). An example of such a low-noise three-axis search
coil magnetometer is described in [19]. Such a ‘portable’
magnetometer consists of three coils of between 19 cm and
33 cm in diameter and 4100–6500 turns with a weight
of 14 kg. It is capable of measuring the magnetic field
between 20 Hz and 20 kHz with a noise level lower than
170 dB/100 µT.
On the other hand, there are examples of extremely
small air-cored sensors. Three orthogonal coil systems with
dimensions less than 2 mm and a weight about 1 mg (40 turns)
have been used for the detection of position of small, fast
moving animals [20].
Air-coil sensors are widely used as eddy-current
proximity sensors or for eddy-current sensors for nondestructive testing (e.g. for detection of cracks). In such cases,
sensitivity is not as important as the spatial resolution and
compactness of the whole device. Such sensors are often
manufactured as a flat planar coil (made in PCB or thin
film technology [21–25]) connected to an on-chip CMOS
electronic circuit [22]. An example of such a sensor with
dimensions of 400 × 400 µm2 (7 turns) is presented in
figure 4.
For testing the spatial distribution of the magnetic field
by means of coil sensors the flexible microloop sensor array
has been developed [26]. The array consists of 16 microloop
sensors with an area of 14 × 14 mm2 and a thickness of
125 µm. Each coil has 40 turns within an area of 2 × 2 mm2.
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lc
noise [pT/ Hz]
l
10
1
Di
D
0.1
f [Hz]
Figure 5. Design of a typical ferromagnetic core coil sensor
(l—length of the coil, lc—length of the core, D—diameter of the
coil, Di—diameter of the core).
10 5
µc
µc=1/N
µr=10 5
10 4
µr=10 4
10 3
µr=10 3
10 2
µr=10 2
2lc /Di
10 1
10 2
10 3
10 4
Figure 6. The dependence of the resultant permeability of the core
on the dimensions of the core and the permeability of the material
[14].
Sometimes, the frequency response of the air-core sensor
is a more important factor than the sensitivity or spatial
resolution. The dimensions of the coil can be optimized for
better frequency performance. These factors are discussed in
section 5.
4. Design of ferromagnetic core coil sensor
High-permeability core coil sensors are often used in the case
when high sensitivity or dimension limitations are important.
A typical geometry of such a sensor is presented in figure 5.
The optimal value of core diameter Di has been determined
as Di ∼
= 0.3 D [14]. The length of the coil l is recommended
to be about 0.7–0.9 lc. For such coil dimensions, the output
signal V and SNR ratio at room temperature can be described
as [27]
l3
1
· H (15)
V ∼
= 0.9 × 10−5 · f · 2 · Di ·
d
ln(2 · l/Di ) − 1
√
f
1
H (16)
· l2 · l ·
SNR ∼
= 1.4 × 108 · √
ln(2 · l/Di ) − 1
f
It can be concluded from relationships (15) and (16) that
in the case of a coil sensor with a ferromagnetic core the
most efficient method of improving the sensor performance
is to make the length of the core (or rather the ratio l/Di) as
large as possible, since the sensitivity is proportional to l3.
Figure 6 presents the dependence of the resultant permeability
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1
10
100
1k
10k
100k
Figure 7. An example of the noise performance of the induction
magnetometer (after [28]).
of the core µc on the aspect ratio l/D and the core material
permeability µr (as described in [14]).
The choice of the aspect ratio of the core is very important.
The length should be sufficiently large to benefit from the
permeability of the core material. On the other hand, if the
aspect ratio is large the resultant permeability depends on the
material permeability. This may cause error resulting from
the instability of material permeability due to the changes of
temperature or applied field frequency. For large values of
material permeability the resultant permeability µc practically
does not depend on material characteristics because relation
(3) is then
1
.
(17)
N
Higher values of material permeability allow the use of
longer cores without the risk of the resultant permeability
depending on the magnetic characteristic of the material used.
As an example, let us consider a low-noise induction
magnetometer that is described in [28]. Here, the core was
prepared from amorphous ribbon (Metglas 2714AF) with
temperature-independent properties and dimensions: length
150 mm, cross-section of the order 5 × 5 mm2 (aspect ratio
of around 27). A coil of 10 000 turns was wound with a
0.15 mm diameter wire. The noise characteristic of this sensor
is presented in figure 7. The obtained noise level around
0.05 pT Hz−1/2 was found to be comparable with the values
reported for SQUID sensors.
The same authors compared the influence of the core
material. For an amorphous Metglas core the noise was
found to be 0.05 pT Hz−1/2, whilst for the same sensor with
a permalloy Supermumetal core it exhibited larger noise of
2 pT Hz−1/2. Also, a comparison of air coil and ferromagnetic
core sensors has been reported [29, 30]. Experimental results
show that well-designed ferromagnetic core induction sensors
exhibited a linearity comparable with air-core sensors.
Sensors with ferromagnetic cores are often used for
magnetic investigations in space research [31, 32]. Devices
with a core length of 51 cm and weight of 75 g (including
preamplifier) exhibited a resolution (noise level) of 2 fT Hz−1/2
[33]. In an analysis of Earth’s magnetic field (OGO search
coil experiments) the following three-axis sensors have been
used: coil 100 000 turns of 0.036 mm in diameter, core
made from nickel–iron alloy 27 cm long and square (0.6 ×
0.6 cm2) cross-section. Each sensor weighted 150 g (with half
µc ≈
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V [dB]
L
40
C0
R
R0
C
20
0
−20
f/f 0
0.01
0.1
1
10
Figure 9. Equivalent circuit of induction sensor loaded with
capacity C0 and resistance R0.
Figure 8. Typical frequency characteristic of an induction coil
sensor.
V [dB]
α =0
40
the weight being the core). The sensitivity in this case was
10 µV (nT Hz)−1 [34].
The detailed design and optimization of an extremely
sensitive three-axis search coil magnetometer for space
research is described in [35].
The coil magnetometer
developed for the scientific satellite DEMETER had a noise
level of 4 fT Hz−1/2 at 6 kHz. To obtain the desired resonance
frequency and a resistance noise above the preamplifier voltage
noise the diameter of copper wire of 71 µm and number
of turns of 12 200 were selected. The core was built from
170 mm long 50 µm thick annealed FeNiMo 15–80–5
permalloy strips, with a cross section of 4.2 mm × 4.2 mm.
The mass of the whole three-axis sensor and the bracket was
only 430 g.
There are commercially available search coil sensors. For
example, MEDA Company offers sensors with a sensitivity
of 25 mV nT−1 and noise at 10 kHz equal to 10 fT Hz−1/2
(MGCH-2 sensor with a core length about 32 cm) or at 0.2 Hz
equal to 2.5 pT Hz−1/2 (MGCH-3 sensor with a core length of
about 1 m) [36].
α1
20
0
α2 > α1
−20
fh
fl
0.01
0.1
1
f/f0
10
Figure 10. Frequency characteristics of the induction coil loaded by
the resistance R0 (the coefficient α = R/R0).
5. Frequency response of search coil sensors
The output signal increases, initially almost linearly with
the frequency of measured field, up to resonance frequency
1
.
(18)
f0 =
√
2·π · L·C
Above the resonance frequency the influence of selfcapacitance causes the output signal to drop.
Analysing the equivalent circuit of the sensor, the
sensitivity S = V/H can be expressed in the form [40]
S0
,
(19)
S=
2
α2
2
2
4
(1 + α) + β + β 2 − 2 · γ + γ
It is obvious from equation (1) that in order to obtain any
output voltage signal from the sensor the flux density must be
varying with time. Therefore, the coil sensors are capable of
measuring only dynamic (AC) magnetic fields. In the case of
the dc magnetic fields the variation of the flux density can be
‘forced’ in the sensors by moving the coil. However, the term
‘dc magnetic field’ can be understood as a relative one. By
using a sensitive amplifier and a large coil sensor it is possible
to determine low-frequency (mHz) magnetic fields [16, 17].
Thus, it is also possible to investigate quasi-static magnetic
fields with fixed-coil (unmovable) sensors.
AC magnetic fields with a frequency up to several MHz
can be investigated by means of coil sensors [37]. In
special designs, this bandwidth can be extended to GHz range
[38, 39]. An example of the typical frequency characteristic
of a coil sensor is presented in figure 8.
According to (7) the output signal depends linearly on
frequency, but due to the internal resistance R, inductance L and
self-capacitance C of the sensor, the dependence V = f (f ) is
more complex. The equivalent electric circuit of an induction
sensor is presented in figure 9.
√
where
α = R/R0 , β = R · C/L, γ = f/f0 = 2 · π · f ·
√
L · C.
The absolute sensitivity S0 can be described as S0 =
2 × 10−7 · π 3 · n · D2. The graphical form of the relation (19)
is presented in figure 10.
The sensor loaded with a small resistance R0 exhibits a
frequency characteristic with a plateau between the low corner
frequency
R + R0
(20)
fl =
2·π ·L
and the high corner frequency
1
fh =
.
(21)
2 · π · R0 · C
A frequently used method for the improvement of
the sensor frequency characteristic is the connection of an
integrating transducer to the sensor output. Another method is
a load of a sensor with a very low resistance (current-to-voltage
converter). For low value of load resistance R0 (high value of
α coefficient—see figure 10) we can operate on the plateau
of frequency characteristic (in the so-called self-integration
mode).
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C
RF
R'
Bx
R1
M
+
Vout
Vin
−
R2
−
Vout
+
+
R1
−
offset
Figure 12. Typical integrating circuit for the coil signal.
Figure 11. Induction coil sensor connected to the amplifier with
negative transformer type feedback.
R1
The inductance of the sensor depends on the number of
turns, permeability and the core dimensions, according to the
following empirical formula [40]:
−3/5
l
µ0 · µc · Ac
·
.
(22)
L = n2 ·
lc
lc
The self-capacitance of the sensor strongly depends on the
construction of the coil (the application of the shield between
the coil layers significantly changes the capacitance).
The frequency characteristic below fl can be additionally
improved by incorporating a PI correction circuit (more details
are given in the next section).
A feedback circuit is another method of improvement
of the frequency characteristic of the sensor [4, 41, 42] as
presented in figure 11.
The output signal of the circuit presented in figure 11 can
be described as [41]
j · ω/ωl
RF
·
Vout = 2 · π · f · n · µ0 · µc · Ac ·
2 · π · M 1 + j · ω/ωl
1
·
· Bx .
(23)
1 + j · ω/ωh
The circuit described by equations (23) represents a highpass filter working under ω ω0, and a low-pass filter for
ω ω0. As a result, the frequency characteristic is flat
between low
1
RF
ωl =
·
(24)
M 1 + R1 /R2
and high frequency
1 + R1 /R2
ωh =
· M · ω0 .
(25)
RF
When improvement of the low-frequency characteristic
due to the feedback is not sufficient, additional suppression of
low-frequency noise is possible by introduction of RC-filters,
as is proposed in [43].
The air-core sensors, due to their relatively low
inductance, are used as large frequency bandwidth current
transducers (in the Rogowski coil configuration described
later) typically up to 1 MHz with an output integrator and up to
100 MHz with current-to-voltage output.
6. Electronic circuits connected to the coil sensors
Because the output signal of an induction coil is dependent
on the derivative of the measured value (dB/dt or dI/dt in the
case of a Rogowski coil) one of the methods of recovering the
R36
Vin
C
Vout
Figure 13. The passive integrating circuit.
R1
C
R'
−
Vout
Iin
+
Figure 14. Current-to-voltage transducer with additional frequency
correction circuit. An example described in [28] with elements:
R1 = 100 k, C = 0.22 µF, R = 47 M.
original signal is the application of an integrating transducer
[44] (figure 12).
Figure 12 presents a typical analogue integrating circuit.
The presence of the offset voltage and associated zero drift are
a significant problem in the correct design of such transducers.
For this reason, an additional potentiometer is sometimes
used for offset correction and resistor R is introduced for the
limitation of the low-frequency bandwidth. The output signal
of the integrating transducer is
T +t0
1
·
Vout = −
(Vin ) dt + V0 ,
(26)
R · C t0
where R = R1 + Rcoil. The resistance R should be sufficiently
large (as not to load the coil) as well as the capacitance C—
typical values are R1 = 10 k and C = 10 µF [44].
The amplifier can introduce several limitations at higher
frequencies.
A passive integrating circuit (figure 13)
exhibits somewhat better performance at those frequencies.
Combinations of various methods of integration (active and
passive) can be used for large bandwidth—as proposed in
[45].
Problems with the correct design of a measuring system
with an integrating transducer are often overcome by applying
low resistance loading to the coils (self-integration mode
presented in figure 10). Usually, a current-to-voltage converter
is used as an output transducer, additionally supported by
a low-frequency correction circuit. An example of such a
transducer is presented in figure 14.
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V [dB]
b
−20
a
−40
0.1
1
10
100
1k
10k
f [Hz]
Figure 15. Frequency characteristic of a coil sensor with
current-to-voltage transducer (a) and with additional correction
circuit (b).
Figure 17. An example of the coil sensor used in a digital fluxmeter
of Brockhaus.
L
ADC
−
+
AR
U2
R
C
DAC
UR2
∆f
clock
MR
∆f
I2
∆f
filter
N=2n
Figure 18. The sources of the noise in the equivalent circuit of the
coil connected to the amplifier.
Figure 16. Digital transducer of the coil sensor signal (after [48].
In the current-to-voltage transducer presented in figure 14
the correction circuit R1C is introduced to correct the
characteristic of a low-resistance loaded circuit at lower
frequencies, as illustrated in figure 15.
The above-described circuits were equipped with
analogue transducers at the output of the coil sensor. However,
it is also possible to convert the output signal to a digital
form and then to perform digital integration—several examples
of such approaches (with satisfactory results) have been
described in [46–48].
Accurate digital integration of the coil sensor signal is not
a trivial task. Also, in digital processing there are integration
zero drifts. The most frequently used method eliminating this
problem is the subtraction of the calculated average value of
the signal. The integrating period, sampling frequency and
triggering time should be carefully chosen, especially when
the exact frequency of the processed signal is unknown (which
is often the case). Moreover, the cost of a good quality data
acquisition circuit (analogue-to-digital converter) is relatively
high and the use of a PC is necessary. Therefore, in some cases
the integrating process is performed digitally by relatively
simple hardware (without a PC), consisting of analogue-todigital (ADC) and digital-to-analogue (DAC) circuits and
registers (AR and MR) as is presented in figure 16.
It is worth noting that almost all companies manufacturing
the equipment for magnetic measurements (such as Brockhaus,
LakeShore, Magnet Physik, Walker Scientific) offer digital
integrator instruments, called Fluxmeters—often equipped
with coil sensors. Figure 17 presents the coil sensor used
in this instrument.
The amplifier connected to the coil sensor introduces
additional noise, voltage noise and current noise, as illustrated
in figure 18. Each noise component is frequency dependent.
Analysis of the coil sensor connected to the amplifier [1]
indicates that for low frequency the thermal noise of the sensor
dominates. Above the resonance frequency the amplifier noise
dominates.
Figure 19. The sensor of a dc magnetic field with a rotating coil.
The reduction of the amplifier noise can be achieved by
the application of a HTS SQUID picovoltmeter, as it has been
reported in [48]. Indeed, the noise level of the preamplifier
was decreased to a level of 110 pV Hz−1/2, but the dynamic
performances of such a circuit deteriorated.
7. Special kinds of induction coil sensors
7.1. Moving coil sensors
One of the drawbacks of the induction coil sensor, the
sensitivity only to varying magnetic fields, can be overcome
by introducing movement to the coil. For example, if the
coil rotates (figure 19) with quartz-stabilized speed rotation
it is possible to measure dc magnetic fields with very good
accuracy. The main condition of the Faraday’s law (the
variation of the flux) is fulfilled, because the sensor area varies
as a(t) = A · cos(ω · t) and the induced voltage is
V = −Bx · n · A · sin(ω · t).
(27)
Instead of rotation it is possible to move the sensor in
other ways, the most popular being a vibrating coil. One of
the first such ideas was applied by Groszkowski, who in 1937
demonstrated the moving coil magnetometer [50]. The coil
was forced to vibrate by connecting it to a rotating eccentric
wheel.
One of the best excitation methods for vibrating a coil is by
connecting it to an oscillating element, such as a piezoelectric
R37
Review Article
oscillator
bimorph
(a)
(b)
(c)
coil
Figure 20. The vibrating cantilever magnetic field sensor (after
[52]).
Figure 22. Gradiometer coils arranged: (a) vertically,
(b) horizontally, (c) asymmetrically.
Hx1
(a)
(b)
(c)
Hext
Hx2
Figure 21. Operating principle of gradiometer sensor.
ceramic plate [51, 52]. Due to a relatively high frequency
of vibration (in the kHz range) it is possible to make a very
small sensor with a relatively good geometrical resolution.
Figure 20 presents an example of a pickup coil sensor mounted
onto a piezoelectric bimorph cantilever. The ten-turn coil,
30 µm wide and 0.8 µm thick, excited to a vibration frequency
of around 2 kHz (mechanical resonance frequency) exhibited
a sensitivity of around 18 µV/100 µT [52].
It is also possible to perform measurements by quick
removal of the coil sensor from a magnetic field (or quick
insertion into a magnetic field). Such extraction coil methods
(with the application of a digital fluxmeter with a large time
constant) enable the measurement of the dc magnetic field
according to the following relationship [53]:
(28)
V dt = −n · A · (Bx − Bo ) .
The moving coil methods are currently rarely used,
because generally there is a tendency to avoid any moving parts
in measuring instruments. For measurements of dc magnetic
field, Hall sensors and fluxgate sensors are most frequently
used.
7.2. The gradiometer sensors
The gradiometer sensors (gradient sensors) are commonly
used in SQUID magnetometers for the elimination of the
influence of ambient fields [54]. These sensors can be also
used in other applications where ambient fields disturb the
measurements, or determination of the magnetic field gradient
itself [55].
The operating principle of the gradiometer sensor is shown
in figure 21. The external magnetic field is generated by a large
and distant source (for example, the Earth’s magnetic field),
so it is assumed that this field is uniform. If two coil sensors
(with a small distance between them) are inserted into such a
field then both will sense the same magnetic field. As both
coils are connected differentially (see figure 21) the influence
of the external field is eliminated. If at the same time there is
a smaller source of magnetic field (e.g due to the human heart
investigated in magnetocardiograms) near both of the coils,
then the magnetic field in the coil placed nearer the source
is larger than in the other coil. This small difference, hence
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Figure 23. Gradiometers of a: (a) first order, (b) second order,
(c) third order.
V/V0
1
first
orde
r
0.1
sec
0.01
on
d
ord
er
0.001
1b
10b
100b
distance to
pickup coil
Figure 24. A typical response of a gradient coil sensor to the source
with a distance from the pickup coil smaller than 0.3b (b being the
distance between coils of gradiometer) (after [56]).
the gradient of the magnetic field, is therefore detected by
the gradiometer sensor. In this way it is possible to measure
a relatively small magnetic field from a local source in the
presence of a much larger magnetic field from a distant
one.
Figure 22 presents typical arrangements of the
gradiometer coils: vertical, planar and asymmetric. A welldesigned gradiometer coil should indicate zero output signal
when inserted into a uniform field. In the asymmetric
arrangement the sensing coil is smaller, hence has more turns
in order to compensate the magnetic field detected by the larger
coil.
It is possible to improve the ability to reject the
common component by employing several gradiometers.
Figure 23 presents first-order, second-order (consisting of
two gradiometers of first order) and third-order
gradiometers.
Figure 24 presents a typical response of the gradiometer
coils to a source distant from the sensor [56]. The first-order
gradiometer rejects more than 99% of the source at a distance
of 300b (where b is the distance between the single coils
of the gradiometer). For the second-order gradiometer this
distance is diminished to about 30b. It is possible to arrange
even higher order of the gradiometer (figure 23(c) presents
Review Article
dl
H
V
l
A
A
B
B
Figure 25. An example of a Rogowski coil (A, B—ends of the coil).
the gradiometer of the third order), but gradiometers of higher
order have reduced sensitivity and SNR ratio.
The quality of the gradiometer sensor is often described
by the formula
V ∝ G + β · H,
Figure 26. The application of a Rogowski coil for the determination
of H · l value.
V
(29)
where G is the gradient of the measured field and H is the
magnitude of the uniform field. In superconducting devices
it is possible to obtain a β factor as small as part-per-million.
This means that it is possible to detect magnetic fields of tens
of femtotesla in the presence of a millitesla uniform ambient
field.
7.3. The Rogowski coil
The special kind of helical coil sensor uniformly wound
on a relatively long non-magnetic circular or rectangular
strip, usually flexible (figure 25), is commonly known as the
Rogowski coil, after the description given by Rogowski and
Steinhaus in 1912 [5]. Sometimes this coil is called a Chattock
coil (or Rogowski–Chattock potentiometer, RCP). Indeed, the
operating principle of such a coil sensor was first described
by Chattock in 1887 [6] (it is not clear if Rogowski knew the
disclosure of Chattock, because in Rogowski’s article Chattock
was not cited).
The induced voltage is used as the output signal of the
Rogowski coil. But the principle of operation of this sensor
is based on Ampere’s law rather than Faraday’s law. If the
coil of length l is inserted into a magnetic field then the output
voltage is the sum of voltages induced in each turn (all turns
are connected in series)
d dφ
·
V =
−n ·
dl dt
B
d
n
= µ0 · · A ·
·
(H ) dl · cos(α).
(30)
l
dt A
The output signal of the Rogowski coil depends on the
number of turns per unit length n/l and the cross section
area, A, of the coil. A correctly designed and manufactured
Rogowski coil inserted in the magnetic field at fixed points
A–B should give the same output signal independent of the
shape of the coil between the points A and B. A coil with
connected ends (length A–B equal to zero) should have zero
output signal.
One of the important applications of the Rogowski–
Chattock coil is the coil in the device for testing of magnetic
materials known as a SST (single sheet tester) [8, 57, 58]. In
such a device it is quite difficult to use Ampere’s law (H · l =
I
Figure 27. The Rogowski coil as a current sensor.
I · n) for the determination of the magnetic field strength H
(from the magnetizing current I), because the mean length l
of the magnetic path is not exactly known (in comparison to
a closed circuit system). But if the RCP coil is used we can
assume that the output signal of this coil is proportional to the
magnetic field strength between the points A–B
d
n
(31)
V = µ0 · · A · (H · lAB ) .
l
dt
The RCP coil can be used to determine the H · l value, that
is the difference of magnetic potentials. The application of the
coil to direct measurements of H (for fixed value of length
lAB) is not convenient, because the output signal is relatively
small and integration of the output voltage is required. For
this reason, the compensation method shown in figure 26 is
more often used. In such a method the output signal of the
RCP coil is utilized as the signal for the feedback circuit for
the current exciting the correction coils. Due to the negative
feedback circuit the output signal of the coil is equal to zero,
which means that all magnetic field components in the air gaps
and the yoke are compensated and
H · lAB − n · I = 0.
(32)
Thus, the magnetic field strength can be determined directly
from the magnetizing current because the other parameters
(lAB and n) are known.
The most important application of the Rogowski coil is for
current measurements [59–63]. When the coil wraps around
a current conducting wire (figure 27) the output signal of the
sensor is
n
dI
(33)
V = µ0 · A · .
l
dt
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Review Article
Figure 29. An example of a spherical coil sensor.
Hx
Figure 28. An example of the Rogowski coil current sensor—model
8000 of Rocoil [68].
The Rogowski coil used as a current sensor enables
measurements of very high values of current (including
plasma current measurements in space [32]). Due to the
relatively small inductance of such sensors they can be used to
measure the transient current of pulse times down to several
nanoseconds [63]. Other advantages of the Rogowski coil as a
current sensor in comparison with current transformers are as
follows: excellent linearity (lack of saturating core), no danger
of opening the second winding of the current transformer
and low construction costs. Therefore, the Rogowski current
sensor in many applications has effectively substituted current
transformers. The application of the Rogowski coil for
current measurements is so wide that recently Analog Devices
equipped the energy transducer (model AD7763) with an
integrating circuit for connecting the coil current sensors.
Although the Rogowski coil seems to be relatively
simple in design, careful and accurate preparation is strongly
recommended to obtain the expected performance [64–66].
First, it is important to ensure the uniformity of the winding (for
perfectly uniform winding the output signal does not depend on
the path the coil follows around the current-carrying conductor
or on the position of the conductor). Special methods and
machines for the manufacture of Rogowski coils have been
proposed [65–67]. The output signal, thus also the sensitivity,
can be increased by increasing the area of the turn, but for
correct operation (according to Ampere’s law) it is required
to ensure the homogeneity of the flux in each turn. For this
reason, the coil is wound on a thin strip with a small crosssectional area. Also, the positioning of the return loop is
important—both terminals should be at the same end of the
coil. When the coil is wound on a coaxial cable the central
conductor can be used as the return path [64].
There are several manufacturers offering various types of
Rogowski coils or Rogowski coil current sensors. Figure 28
shows an example of the Rogowski coil transducer (coil and
integrator transducer) of Rocoil Rogowski Coils Ltd [68].
7.4. The flux ball sensor
It is quite difficult to manufacture a coil sensor with sufficient
sensitivity and small dimensions for measurements of local
magnetic fields.
If the investigated magnetic field is
inhomogeneous, then the sensor averages the magnetic field
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Figure 30. An example of a typical H-coil sensor.
over the area of the coil. Axially symmetric coils inserted into
an inhomogeneous field are insensitive to all even gradients.
As described in section 3, for certain coil dimensions (l/D ≈
0.67) the odd gradients can also be eliminated.
Brown and Sweer [69] demonstrated that the volume
averaging of the field over the interior of any sphere centred at
a point is equal to the value of the magnetic field at this point.
Thus, a spherical coil measures the field value at its centre. An
example of a design of such a spherical coil sensor is shown
in figure 29.
7.5. Tangential field sensor (H-coil sensor)
Measurements of the magnetic field strength in magnetic
materials (for example electrical steel sheet) utilize the fact
that the magnetic field inside the magnetic materials is the
same as the tangential field component directly above this
material. Thus, a flat coil called an H-coil is often used for the
measurements of the magnetic field strength [70, 71].
The coil sensor for the measurement of the tangential
component should be as thin as possible. This is in conflict
with the requirement for the optimum sensitivity of the sensor,
which depends on the cross-section area of the coil. A
typical coil sensor with a thickness of 0.5 mm and an area of
25 mm × 25 mm wound with a wire of 0.05 mm in diameter
(about 400 turns) exhibits a sensitivity of around 3 µV (A m)−1
[72].
In order to obtain sufficient sensitivity the coil sensor is
manufactured with a thickness of about 0.5 mm or more. Thus,
the axis of the coil is somewhat distanced from the magnetic
material surface under investigation. Nakata [71] proposed a
two-coil system where the value of the magnetic field directly
at the surface can be extrapolated from two results. This
idea has been tested numerically and experimentally [73].
It was shown that such a method enables the determination
of the magnetic field on the magnetic material surface even
if the sensor is at a distance of more than 1 mm from this
surface. Additionally it was proposed to enhance the two-coil
method by application of up to four parallel (or perpendicular)
sensors. An example of such a multi-coil sensor is shown in
figure 31(b).
Review Article
(a)
(b)
Figure 31. Two examples of a coil sensor for two components of
magnetic field: (a) two perpendicular H-coils wound around the
same former, (b) four separate coils allowing double-coil
measurements.
V=td
dB
dt
V= 21 td
dB
dt
Figure 33. Reference levels of the magnetic field recommended by
ICNIRP [79].
8. Coil sensor used as a magnetic antenna
fields is their primary application, the importance of which
is heightened due to the need for stray field investigations,
especially for electromagnetic compatibility and protection
against dangerous magnetic fields in the human environment.
University laboratories are often visited by ordinary
people, who live near transformer stations or power
transmission lines. They may wonder if such close proximity
to such sources of magnetic fields can be potentially dangerous
for their health, and so they have a genuine interest in the
measurement of magnetic field intensities.
It is possible to do these measurements yourself. It is
sufficient, for example, to wind 100 turns of a copper wire
on a non-magnetic tube (5–10 cm diameter) (figure 1) and to
measure the induced voltage. Then, if for instance f = 50 Hz,
n = 100 and D = 10 cm we obtain (according to relations
(7) and (8)) a simple expression for output voltage: V (V) ∼
=
246.5 B (T) or V (V) ∼
= 0.3096 × 10−3 H (A m−1). Of
course, there are many commercially available professional
measuring instruments using similar methods. Figure 33
shows the limits for exposure to time-varying magnetic fields
recommended by ICNIRP (International Commission on NonIonizing Radiation Protection) and WHO (World Health
Organization) [79].
Moreover, starting from 2006 all products indicated
by the CE sign should fulfil European Standard
EN 50366:2003 ‘Household and similar appliances—
Electromagnetic Fields—Methods for evaluation and
measurements’. Figure 34 presents the professional measuring
instrument of Narda [80] designed for the determination of
electromagnetic compatibility conditions according to the
European Standard EN 50366.
The European Standard EN 50366 requires that the
magnetic field value should be isotropic. As the coil sensor
detects the magnetic field only in one direction, a three-coil
system (shown in figure 3) should be used and then the value
of magnetic field should be determined as
b(t) = bx2 (t) + by2 (t) + bz2 (t).
(35)
Similar to other magnetic field sensors, coil sensors are often
used for measurements of non-magnetic values. They are used
in non-destructive testing (NDT), as proximity sensors, current
sensors, reading heads etc. However, the detection of magnetic
For investigations of magnetic pollution (magnetic smog) the
author designed and constructed a magnetometer consisting
of an air-coil sensor (figure 35) and amplifier/frequency
correction system (figure 36). The coil was wound onto a
t
d
d
Figure 32. Two methods of local flux density measurements:
micro-holes method and needle method.
7.6. The needle sensors (B-coil sensors)
When it was necessary to determine the local value of the flux
density in electrical steel sheet practically only one method
was available (apart from the optical Kerr method): to drill
two micro-holes (with diameter 0.2–0.5 mm) and to wind oneor more-turn coil (figure 32(a)).
However, drilling such small holes in relatively hard
material is not easy. Moreover, this method is destructive.
In order to avoid these problems, several years ago Japanese
researchers [11, 74, 75] returned to an old Austrian patent of
Werner [10]. Werner proposed to form a one-turn coil by using
two pairs of needles, but the application of his invention was
difficult, due to relatively small (less than mV) output signal of
the sensor. Experimental and theoretical analyses [11, 12, 74–
78] proved that today this method can be used with satisfactory
results. It is sufficient to use one pair of needles to form a halfturn coil sensor where the induced voltage is described by the
following relation:
1
dB
·t ·d ·
,
(34)
2
dt
where t is the thickness of the steel sheet and d is the distance
between the needles.
Although the needle method is not as accurate as the
micro-holes method, it is widely used for flux density
measurements, especially in two-dimensional testing of
electrical steel sheets. To ensure correct contact with the
insulated surface of the sample the needle tip should be
specially prepared [78].
V ≈
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Review Article
Bx
preamaplifier
filter 50 Hz
filter 150 Hz
amaplifier
I/U
I/U converter
converter
integration
output
Figure 37. Block diagram of the induction magnetometer.
ferrite
core
Vout
loop coil
feedback
coil
Figure 38. The loop sensor with feedback coil MHz range
application [4].
Table 1. Performances of constructed sensor.
Figure 34. An example of a search coil magnetometer used for
testing electromagnetic compatibility (with permission of Narda
Company).
Figure 35. The air-coil sensor designed for investigations of
magnetic pollution.
Figure 36. Frequency characteristics of the constructed sensor.
ring with a diameter of 60 mm and a width of 35 mm using
a wire of 0.1 mm diameter. There were 70 000 turns and
the coil was divided into seven sections with 10 000 turns
each. The frequency characteristics of this sensor are shown in
figure 36, and the summary of sensor performance is shown in
table 1.
R42
n
D
(mm)
R
(k)
L
(H)
S/f (mV µT−1)
for 50 Hz
fo
(Hz)
10 000
20 000
30 000
40 000
50 000
60 000
70 000
130
140
147
156
165
173
181
8.8
18.2
28.1
38.6
54.1
66
82
19
76
168
303
473
673
932
45
95
150
210
270
330
380
450
430
410
410
380
350
300
The block diagram of the constructed magnetometer
is presented in figure 37. Two notch filters (50 Hz and
150 Hz) have been used for the elimination of the power
frequency components. The tuned integration circuit (for
voltage coil input) or current-to-voltage converter (for current
coil input) can be selected by the investigator. Due to the high
sensitivity of the sensor the smallest attainable sensitivity of
the magnetometer was found to be 0.1 pT.
By applying the special design of a sensor and electronics
it is possible to extend the working range towards high
frequencies, to the MHz range. Cavoit [4] designed a large
primary shorted coil (with small capacity and high resonance
frequency) coupled to a toroidal ferrite core bearing a winding
(figure 38). Prototypes of such sensors, used for radar and
space probes, worked at a frequency range of 0.1–50 MHz.
The interest in the measurement of high frequency
magnetic fields (up to several GHz) grew with the latest
rapid development of high frequency applications, for example
mobile phones and their antennae. The inductive sensor can
also be used in this range of frequencies, although several
additional problems can occur [81]. The dimensions of the
sensor should be smaller than the wavelength of the measured
field. Therefore, typically measuring instruments are equipped
with several sensors. An example of a high frequency field
sensor is presented in figure 39. Additional problems arise
from the fact that in a high frequency electromagnetic field
it is rather difficult to separate the electric and magnetic
components (especially near the source of the field).
Coil sensor antennas can be used as pickup coil sensors for
the detection of metal objects [82, 83]. An example of such
Review Article
1/ f
µV
Figure 39. Magnetic field sensor for the frequency bandwidth of
0.6–2 GHz.
In the first [93], thin strips cut from amorphous materials
are magnetized by the field emitted from the transmitter
antenna. Due to the nonlinearity of the magnetic properties
the output signal contains harmonics of the predetermined
frequency detectable by the receiver antenna.
Recently, a more efficient magneto-acoustic system was
proposed by Herzer [94]. The label is prepared as a strip made
from magnetostricitve amorphous material. A transmitter
produces pulses of frequency of 58 kHz, 2 ms on and 20 ms off.
The vibrating amorphous strip generates a signal of frequency
of 58 kHz, which is detected by the receiving antenna. The
system is synchronized, so the antenna is active only during
the pause, and therefore the influence of background noise is
decreased.
In both systems the activation or deactivation of the marker
is realized by an additional strip made from a semi-hard
magnetic material. After demagnetization of this initially
magnetized element, the frequency generated by the label
changes and it is not detected by the receiver antenna, thus
deactivation is achieved.
9. Conclusion
Figure 40. An induction search coil as a tool for the detection of
metal objects (with permission of DCG Detector Center).
A
B
transmitter
synchronization
receiver
Figure 41. Magnetic article surveillance system: (A) magnetic
harmonic system, (B) magneto-acoustic system.
a device is shown in figure 40. Practically almost all mine
detectors use coil sensors [84, 85, 86]. Especially important
are applications of magnetic sensors in water environment,
for submarine communication and location of submarines
[87, 88].
Induction coil sensors are commonly used in geophysics,
for the observation of magnetic anomaly and low-frequency
fields. An interesting application of such investigations is the
possibility of prognosis of earthquake events, probably due to
the signals generated by piezoelectric rock formation before
the earthquake [89–92].
Great commercial success can be noted in the application
of magnetic antennae in magnetic article surveillance systems
(figure 41). Two main types of such systems are used.
The induction sensors used for magnetic field measurements
(and indirectly other quantities such as for example current)
have been known for many years. Today, they are still in
common use for their important advantages: simplicity of
operation and design, wide frequency bandwidth and large
dynamics.
The performance of the induction coil sensor can be
precisely calculated due to the simplicity of the transfer
function V = f (B).
All factors (number of turns
and cross-section area) can be accurately determined and
because function V = f (B) does not include material
factors (potentially influenced by external conditions such as
temperature) their dependence is excellently linear without
upper limit (without saturation).
Because of the absence of any magnetic elements and
excitation currents, the sensor practically does not disturb
the measured magnetic field (as compared for instance with
fluxgate sensors).
The case of a coil sensor with ferromagnetic core is
more complicated, because the permeability depends on the
magnetic field value and/or temperature. Despite this, if the
core is well designed, then these influences can be significantly
reduced.
However, the coil sensors also exhibit some shortcomings.
First, they are sensitive only to ac magnetic fields, although
quasi-static magnetic fields (of frequencies down to mHz
range) can be measured. One notable inconvenience is that
the output signal does not depend on the magnetic field value
but on the derivative of this field dB/dt or dH/dt. Therefore,
the output signal is frequency dependent. Moreover, it is
necessary to connect an integrating circuit to the sensor, which
can introduce additional errors of signal processing.
It is rather difficult to miniaturize the induction coil
sensors because their sensitivity depends on the sensor area (or
the length of the core). Nevertheless, micro-coil sensors with
dimensions less than 1 mm that have been prepared through
the use of thin film techniques are reported.
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Review Article
Magnetic Sensor
FLUXGATE
Detectable Filed Range
1nT
1 µT
1 mT
1T
SQUID
1 fT/ Hz
NUCLEAR PRECESSION
SEARCH COIL
EARTH'S FIELD
MR
COIL
SQUID
FIBER-OPTIC
OPTICALLY PUMPED
OPTICALLY PUMPED
1 pT/ Hz
HALL
1 nT/ Hz
Figure 43. Typical resolution of various magnetic field sensors.
AMR SENSORS
FLUX-GATE
MAGNETOTRANSISTOR
MAGNETO-OPTICAL
HALL-EFFECT
GMR SENSORS
Examples of modern sensors and applications presented
in this review demonstrate that inductive sensors still play a
very important role in measuring technology.
Figure 42. The typical field range of various magnetic field
sensors.
References
Two methods are used for the output electronic circuit: the
integrator circuit and the current-to-voltage transducer (selfintegration mode). Although digital integration techniques
are developed and commonly used, the analogue techniques,
especially current-to-voltage transducers, are often applied due
to their simplicity and good dynamics.
Certain old inventions, such as the Chattock–Rogowski
coil or the needle method, are today successfully re-utilized.
The importance of the coil sensor has also increased recently,
because it is easy to measure stray fields generated by electrical
devices (to meet electromagnetic compatibility requirements).
The induction coil sensors with ferromagnetic core
prepared from modern amorphous materials exhibit sensitivity
comparable to the sensitivity of SQUID sensors. But low
magnetic field applications (at less than pT level) can be better
served by using SQUID methods. On the other hand, it is
more convenient to use the Hall sensors for large magnetic
fields (above 1 mT).
Also other competitive sensors (flux-gate sensors for fields
below around 100 µT and magnetoresistive sensors for fields
above around 100 µT) are ‘winners’ in many applications—
especially when miniaturization is required. For example, a
spectacular ‘defeat’ was the substitution of inductive reading
heads in hard drives by magnetoresistive sensors [95].
From the comparison presented in figure 42 it would be
possible to conclude that the coil sensor is ‘the best’ because
it covers the whole detectable field range. But in practice
we should also compare other parameters, such as frequency
range and dimensions. If we are not limited to the dimensions
(for example in geophysical investigations) it is assumed that
inductive sensors are more sensitive than fluxgates starting
from the frequencies of about 0.003 Hz [3]. But if we compare
the sensors of the same dimensions this border is shifted to
about 10 Hz [27].
In most sensors, the practical limit of the resolution
depends on the possibility of achieving the noise floor. In
the comparison of various magnetic field sensors, Prance
et al [3] estimated these noise levels as: ∼50 fT Hz−1/2 for
SQUID, <100 fT Hz−1/2 for induction coil, ∼100 fT Hz−1/2 for
fluxgates, ∼1 pT Hz−1/2 for optically pumped magnetometers,
∼100 pT Hz−1/2 for magnetoresistive sensors and ∼10 nT
Hz−1/2 for Hall sensors. This comparison is presented in
figure 43.
R44
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