Loop Antenna Characterization for ELF and SLF
Measurements
Caracterizaci
´
on de Antenas Lazo para Mediciones en ELF y SLF
G. I. Quintana
∗1
, R. Alonso
∗2
and W. G. Fano
∗3
†
Universidad de Buenos Aires, Electronic Department, Electromagnetic Radiation Laboratory
Paseo Colon 850. (1063) Buenos Aires. Argentina
1
gonza.quintana94@gmail.com
2
ninjaramiro@gmail.com
3
gustavo.fano@ieee.org
Abstract—Electromagnetic Fields are present in the Earth,
due both to natural and artificial emissions. The Electric
and Magnetic fields generated by natural events like volcanic
eruptions and earthquakes, are aspects of tectonomagnetism,
volcanomagnetism and tectonoelectricity, in the electromag-
netic spectrum from radio frequencies (RF) to submicrohertz
frequencies. This paper is dedicated to the characterization
of loop antennas for measuring electromagnetic precursors of
seismic movements and other ELF (3-30 Hz) and SLF (30-300
Hz) natural effects. The antenna factor, impedance, quality
factor Q and sensitivity of the antennas are measured. These
characteristics are of great importance in the choice of the loop
antenna to be used in the framework of the UBACyT research
proyect Study of Electromagnetic Disturbances Produced by
Seismic Movements.
Keywords: Electromagnetic Precursors, Magnetic Field,
Loop Antenna, Antenna Factor.
Resumen— Los campos electromagn
´
eticos que se encuentran
presentes en la Tierra, son debidos tanto a emisiones de
la naturaleza como producidos por el ser humano. Los
campos el
´
ectricos y magn
´
eticos que son generados por
eventos naturales como erupciones volc
´
anicas y terremotos,
son aspectos de tectomagnetismo, volcanomagnetismo y
tectoelectricidad, en el espectro electromagnetico desde
las frecuencias de radio (RF) hasta las frecuencias de los
submicrohertz. Este trabajo se dedica a la caracterizaci
´
on de
antenas lazo para medir los precursores electromagn
´
eticos
de movimientos s
´
ısmicos junto con otros efectos naturales
en ELF (3-30 Hz) y SLF (30-300 Hz). El factor de antena,
la impedancia, el factor de calidad Q y la sensibilidad de
las antenas son medidos. Estas caracter
´
ısticas son de vital
importancia para la elecci
´
on de la antena lazo a utilizar en el
marco del proyecto de investigaci
´
on de UBACyT Estudio de
Perturbaciones Electromagn
´
eticas Producidas por Movimientos
S
´
ısmicos.
Palabras clave: Precursores Electromagn
´
eticos, Campo
Magn
´
etico, Antena lazo, Factor de Antena.
I. INTRODUCTION
During the past few decades, a remarkable increase in the
quality and quantity of electromagnetic data recorded before
and during eruptions and earthquakes [1] are evidence that
seismic movements are preceded by anomalous electromag-
netic signals.
The Electromagnetic Precursors signals have been dis-
cussed in many publications [1], [2], [3] and [4]. The most
accepted theory is that electromagnetic waves are generated
as a consequence of microfractures in the rocks. The electric
charges of opposite sign, created on opposite sides of the
microfractures form electric dipoles separated by a distance
d. This separation is modulated by the mechanical vibrations
of its walls (originated by rupture of the atomic bonds),
giving rise to dipole oscillations and electromagnetic waves
[5]. This emissions are in the ELF (3-30 Hz) and TLF (<
3 Hz) range.
Another natural phenomena at ELF are the Schumann
resonances, which are electromagnetic resonances in the
cavity formed by the ionosphere and Earth’s surface (that
can be modeled as a conductor for low frequencies) excited
by lighting discharges. The first 3 peak frequencies, 7.8 Hz,
14 Hz and 20 Hz, had been measured at the location of Villa
Alpina, C
´
ordoba, Argentina [6]. This measurement had the
purpose to get evidence of electromagnetic precursors of
earthquakes in a quiet zone. This location was chosen due
to the very low artificial noise of the power lines radiation
[6].
The most important naturally occurring VLF signal is the
whistler. A whistler is created from a lightning stroke that
passes first to the ionosphere and then to the magnetosphere
above. These particles are then guided along the Earth’s
magnetic field, returning to ground to the opposite hemi-
sphere [2].
Fig. 1. Shielded loop antenna.
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Recibido: 15/06/18; Aceptado: 26/07/18
2r
1
Unshielding Loop Antenna
Receiver
Fig. 2. Unshielded loop antenna.
Due to the Electromagnetic Compatibility regulations
(EMC), measurements of Electric and Magnetic Fields are
of great importance. A very useful method for measuring
the Magnetic Field of electromagnetic waves is by means
of a loop antenna, which can be shielded or unshielded.
A shielded loop antenna can be seen in Figure 1 and an
unshielded loop in Figure 2. The radiation pattern of a loop
antenna, in which the size of the loop is much smaller than
the wavelength, is described in Figure 3. As all measure-
ments are made within the ELF and SLF ranges, Figure 3
represents the directional dependence of the received power
of the antennas used in this work.
The unshielded loop will receive the electromagnetic
radiation and the quasistatic induced noise. This noise will
typically come from fluorescent lamps, brush motors, corona
discharge from HV power lines, and the radiation from
the line scan of TV sets [7]. The shielding loop, on the
other hand, is practically insensitive to stray fields induced
noise, which is quite important as nearly all of the energy
content of long wave and medium wave interference locally
generated is quasistatic [7]. The gap observed in Figure 1 in
the shielding, prevents the currents around the loop due to
possible atmospheric effects and electrostatic discharges [8].
Magnetic loops have long been used by EMC personnel to
“sniff” out sources of emissions in circuits and equipment
[8].
In order to measure the ELF and SLF spectrum, two
circular loop antennas are constructed and compared. These
loops, together with a low noise amplifier and a computer
(using the free software GNU-Radio to compute the FFT),
allow to sense the normal component of the incident Mag-
netic Field and it’s frequency spectrum. By using an array of
three of this loops, the 3 components of
−→
B can be measured.
This paper is dedicated to the characterization and com-
parison of these two antennas. As all the measurements have
been made in the laboratory, in the absence of those unde-
sired effects, unshielded loops are used. In the future, when
using these loops for capturing electromagnetic precursors
and other natural electromagnetic emissions (as Schumann
resonances), a suitable shield will be needed to avoid the
above mentioned problems.
0.5
1
0
30
60
90
120
150
180
210
240
270
300
330
Loop
Antenna
Fig. 3. Radiation patterns of a circular short loop antenna.
II. ANTENNA FACTOR
The Antenna Factor or Correction Factor of a loop an-
tenna relates the magnitude of the incident Magnetic Field
(H) and the induced voltage (open circuit voltage) at the
antenna terminals (V). It is defined thus:
K =
H
V
A
V m
(1)
The Maxwell-Faraday Law expression in differential form
is [9]:
−→
∇ ×
−→
E = −
∂
−→
B
∂t
(2)
where:
B[T ]: is the magnetic flow density.
E[V/m]: is the electric field.
t[s]: is the time.
In order to obtain the open circuit induced voltage at the
terminals of the loop antenna, integration is performed at
both sides of eqn. (2) :
V
oc
= −
∂φ
∂t
(3)
where: φ =
R
−→
B ·
−→
ds is the magnetic flux.
Consider a short single turn loop, excited by a harmonic
electromagnetic wave as a function of time where the
wavelength of the electromagnetic wave received is much
greater than the perimeter of this loop. The magnetic flux is
then:
φ = B
Z
ds = µ
0
HA (4)
The open circuit induced voltage of N turns of the loop
antenna is [9]:
V
oc
= NAµ
0
∂H
∂t
(5)
This voltage can be written thus [10].
V
oc
= Nωµ
0
HcosθA (6)
where θ is the angle between z and H and ω = 2πf.
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Using eqn. (6) and admitting that the incident magnetic
field is parallel to the antenna’s axis, the antenna factor is
obtained:
K =
1
Nωµ
0
A
(7)
which in dB is a straight line with a slope of -20 dB/decade.
As in this case the loop antenna has no ferromagnetic core,
we have µ
r
= 1.
The short loop antenna is usually a very inefficient an-
tenna [11], which can be observed by means of its Radiation
resistance in transmitting mode. However, this is not of
importance in the receiving mode, where the knowing the
antenna factor with precision takes real importance.
III. SENSITIVITY
The Sensitivity of a loop antenna states the minimum
Magnetic Field that can be measured. Thermal noise can
be expressed thus [12]:
E
a
= (4kTRa)
1/2
[V · Hz
−1/2
] (8)
where k is the Boltzmann constant, T the temperature in
Kelvin and Ra the antenna’s resistance. The Voltage induced
by a uniform Magnetic Field in a loop antenna of area A
and N turns is, from Faraday’s law
V
oc
= ωNAB [V ] (9)
Combining these two equations, the equivalent magnetic
field of the antenna’s thermal noise is:
B =
√
4kTR
NAω
[T · Hz
−1/2
] (10)
Normalizing the last result by the factor 1/f, the sensi-
tivity is [12], [13]:
S
a
=
√
4kTR
2πNA
[T · Hz
1/2
] (11)
The sensitivity is simply the magnetic field equivalent value
of the antenna’s thermal noise in a 1 Hz of bandwidth,
normalized by the factor 1/f [12]. Consequently, it gives the
minimum Magnetic Field that can be measured (Magnetic
Fields of less magnitude would be hidden by thermal noise).
IV. RESULTS
In order to measure Magnetic Fields at low frequencies,
two circular short loop antennas have been designed and
constructed (see Figure 4). For measuring the Electric Field
of the electromagnetic wave instead, short Dipole Antennas
are frequently used [14].
The characteristics of these two loops antennas, of N =
180 and N = 300 turns each, are listed in Table I. In that
table, r
c
is the conductor radius, r
l
the loop radius, µ
r
and
r
the relative permeability and permitivity, f
0
the resonance
frequency and R
DC
the antenna’s series resistance (at low
frequencies).
Fig. 4. One of the loop antennas constructed.
TABLE I
LOOP ANTENNA CHARACTERISTICS
N 180 300
r
4 4
µ
r
1 1
r
l
(m) 0.28 0.28
r
c
(mm) 0.35 0.35
f
0
(kHz) 24 17
L (mH) 64 120
R
DC
(Ω) 14.5 23.7
Fig. 5. Antenna Factor Measurement setup.
A. Antenna Factor Measurement
Using the Helmholtz coils [15] and the measurement
scheme in Figure 5, a uniform Magnetic Field is generated
in the space between the coils, in which the loop antenna is
placed.
The magnitude of this Field depends on the geometrical
characteristics of the Helmholtz coils and the current flowing
trough them. This Magnetic Field can be computed with
equation [15]:
H =
0.7154 N
h
I
r
h
(12)
where N
h
= 8 is the number of turns of each Helmholtz coil
and r
h
= 39 cm is their radius. By setting I = 20 mA, the
Magnetic Field is fixed in H = 0.2057 A/m . This Magnetic
Field induces a voltage in the antenna under test, which
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is captured by the data acquisition system of a personal
computer with the software GNU-Radio (which has been
previously calibrated) and showed in a scope. In order to
assure a constant current I, a test resistor R
p
= 56 Ω is
introduced and its voltage drop is continuously monitored.
As I = 20 mA, this peak voltage drop should always be
V
p
= 1.12 V .
The frequency of this current, and therefore of the Mag-
netic Field, is swept from 5 Hz to 10 kHz and the different
amplitudes captured in the scope of the software GNU-Radio
are noted.
As the Magnetic Field H is fixed, using eqn. (1), the fre-
quency response of the Antenna Factor of the two antennas
is computed. This measurement and the theoretical curves
are compared in the Figures 6 and 7.
Fig. 6. Antenna Factor of the loop with 300 turns.
Fig. 7. Antenna Factor with the loop of 180 turns.
It can be seen from Figure 6 that the measured Antenna
Factor for N = 300 turns follows well the theoretical
curve for frequencies of up to 2 kHz. As we move towards
the system’s resonance frequency, the rate of increase of
the reactance of the coils is increased, which triggers the
induced voltage. As the Magnetic Field H continues being
constant this results in a decrease of the Antenna Factor, as
can be seen in Figure 6.
In contrast, the above mentioned effect can’t be seen in
Figure 7 as the resonance frequency of this loop antenna is
higher than of the larger one.
B. Antenna Impedance Measurements
The frequency response of the antenna impedance, both
the resistance and the reactance, for the two loops are
measured with a Gwinstek LCR-819 LCR-meter. These
results are shown in Figure 8 y 9.
It can be seen that the antennas behave as inductors in the
range of frequencies of interest, as their reactance augments
linearly with frequency. However, the resistance rises for
frequencies near 500 Hz. To explain this phenomena, the
behavior of the impedance’s resistive part of a long wire,
which is detailed in [16], is examined. The general expres-
sion for the interior impedance of a long straight wire is:
Z
wire
=
L
p
jωµ/(σ + jω)
2πa
I
0
(γa)
I
1
(γa)
(13)
where γ ≈
√
jωµσ is the propagation constant, I
0
and I
1
are the modified Bessel functions, a is the wire’s radius and
L is its length.
At low frequencies, where the wire radius is small compared
with the wave’s depth of penetration, the expression of eqn.
(13) is reduced to [16]:
Z
wire
≈
L
πa
2
σ
+ jω
µL
8π
(14)
This equation can be used to estimate theoretically the
loops resistances at low frequencies. The antennas under
test were constructed with a copper cable of diameter 0.7
mm. Considering µ = µ
0
and σ
Cu
= 5.96 10
7
S/m, the
impedance of two long wires (of the same length that the
loops) at low frequencies are then
Z
N=180
≈ 13.8 Ω + j ω 15.84 µH (15)
Z
N=300
≈ 23 Ω + j ω 26.4 µH (16)
It can be seen that the resistances obtained with equation
13 are practically equal to the measured 14, 5 Ω and 23, 7 Ω
at low frequencies. In addition, the contribution of the
internal impedance to the total inductance of the loop is
negligible for low frequencies.
At higher frequencies the depth of penetration gets smaller,
which causes the wire’s resistance to increase as the con-
ducting area is reduced (this is known as Skin Effect). When
the depth of penetration is small compared to the radius of
the wire, eqn. (13) is reduced to
Z
wire
≈
1
2πa
r
ωµ
2σ
+
j
2πa
r
ωµ
2σ
(17)
For a copper wire of 0.7 mm of diameter the increase of
the resistance starts being detected at frequencies from 10 to
100 kHz, which are much higher frequencies than the 500
Hz at which this effect is seen in Figure 8. However, eqn.
(17) stands for a straight long wire, which is not our case.
In coiled-wire inductors, Skin Effect is enhanced by the
Proximity Effect. The magnetic flux through a conductor
turn generated by the current in an adjacent turn produces a
circulating current or Eddy current in the conductor which
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results in an increase of the wire’s resistance [17].
Additionally, a radial resistivity gradient (high resistivity at
the outer side and low resistivity at the inner one) develops
in the bent wire. This is consequence of both the difference
in conduction paths between wire ends and the rearrange
of the microcrystals at the material’s bulk due to stretching
[17].
This two effects drag the increase of the antenna’s resis-
tance to lower frequencies, therefore providing a theoretical
explanation of Figure 8.
Fig. 8. Resistance of the two Loop Antennas.
Fig. 9. Reactance of the two Loop Antennas.
The Quality Factor, which is defined as
ω L
R
[18] is plotted
in Figure 10. The Q increases with frequency up to 20
(for N=180) or 30 (for N=300), due to the increase of the
resistance of the loop antennas with frequency.
1)
C. Sensitivity of the Antennas
The Sensitivity of three different antennas, the two previ-
ous circular loops and one rectangular loop antenna, which
was used in [6] to measure the Schumann Resonance, have
been computed using eqn. (11). The results are listed in
Table II, being Ra the series antenna resistance, A the loop
area, r
c
the conductor radius and Sa the sensitivity.
Fig. 10. Quality Factor Q as a function frequency.
TABLE II
SENSITIVITY OF THE THREE LOOP ANTENNAS
N Ra[Ω] A[m
2
] r
c
[mm] Sa[pT Hz
1/2
]
180 14.5 0.2463 0.35 1.68
300 23.75 0.2463 0.35 1.28
100000 16k 64 · 10
−4
0.12 3.86
The sensitivity values of the loop antennas, as these
are going to be used to measure seismic electromagnetic
precursors and Schumann resonances, should enable them
to capture Magnetic Fields of tens of pico Tesla.
Considering a bandwidth of 1 Hz, the minimum Magnetic
Field that can be measured with the 180 and 300 turns
loops is 1.68 pT and 1.28 pT, respectively. Hence, the two
constructed loops are capable of measuring these natural
effects, being the larger loop fitter than the smaller, as its
sensitivity is lower. Moreover, as these two have a lower
sensitivity than the loop used in [6], they should also be
used to measure Schumann resonances (in conjunction with
a proper high gain and low noise amplifier).
V. CONCLUSIONS
Two circular loop antennas, one with 180 and the other
with 300 turns, have been constructed and characterized,
in order to test their fitness for measuring low amplitude
magnetic fields at ELF. As the only difference between them
is the number of turns, the one with more turns has a bigger
inductance (providing though a higher amplification of the
signal under test) but has a larger series-resistance in return.
In order to make precise measurements, the loops have been
calibrated using a pair of Helmholtz coils [15] and their
antenna factor have been measured for frequencies up to
10 kHz. These measurements are in agreement with the
theoretical Antenna Factor curves.
Additionally, the antenna impedance of the two loops
have been measured in a wide frequency range (from ELF
to VLF). It is concluded that the loops can be used as
measuring devices for frequencies lower than 1 kHz. For
higher frequencies, as a consequence of the skin effect
enhanced by the proximity effect, the antenna resistance
grows and the Q-factor stagnates. This, added to the fact
that the loop approaches its resonance, makes the antenna to
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stop behaving as a an inductor, making it though unsuitable
for measuring magnetic fields.
Finally, the sensitivity of the two loop antennas have been
computed and compared to the sensitivity of the antenna
used in [6] and to the expected amplitude of the magnetic
seismic precursors. As the minimum Magnetic Field that
can be captured with each loop is lower than those naturally
induced fields, it is then concluded that the coils are fit to be
used in the UBACyT project Study of Electromagnetic Dis-
turbances Produced by Seismic Movements, which is being
carried out by the Electromagnetic Radiation Laboratory, in
conjunction with other laboratories of this University. As the
300 turns coils has been showed to have lower sensitivity
than the one with 180 turns and as it provides a higher signal
amplification, the authors conclude that the larger loop is
preferable to the smaller one.
ACKNOWLEDGMENT
The authors would like to thank to the University of
Buenos Aires and to the UBACyT research grants.
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