Recording and Analysis of Extremely Low Frequency Signals in our Environment

Contents

Used formulaic symbols

Used abbreviations

1. Introduction
1.1 Sources of low-frequency magnetic fields
1.2 Wavelengths
1.3 Magnetic field strength
1.3.1 Field around a long electrical conductor
1.3.2 Field of the magnetic dipole
1.3.3 Field strength
1.4 Example of ELF-signals
1.5 The aim of this work

2. ELF-Signal measuring technology
2.1 Hardware to acquire ELF-Signals
2.1.1 Sensors
2.1.1.1 Use of Hall-Sensors
2.1.1.2 SQUIDs (Josephson-Effekt)
2.1.1.3 Air coils
2.1.1.3.1 Inductivity of the sensor coil
2.1.1.3.2 Linearization
2.1.1.3.2.1 Linearization with an parallel resistance
2.1.1.3.2.2 Linearization with an integrator
2.1.1.4 Ground rods
2.1.2 Analog low pass filter 6th order
2.1.2.1 Types of low pass filters
2.1.2.2 Development of Butterworth-low-pass filters in general
2.1.2.3 Designing a Butterworth low-pass filter of 6th order
2.1.2.4 Measurement results
2.1.3 Concepts for digitization of the signal
2.1.3.1 Using the sound board of a personal computer
2.1.3.2 Using the USB-Interface
2.1.3.3 Digitising and preparation of the signal
2.1.3.3.1 Sampling
2.1.3.3.2 Quantization
2.1.3.3.3 Coding
2.1.3.3.4 USB-Interface
2.1.3.3.4.1 Requirements to transfer the data into the computer
2.1.3.3.4.2 The USB-Processor
2.1.4 Power supply
2.1.5 The complete device
2.1.5.1 Sensor selector, linearizer and measurement range
2.1.5.2 Filter
2.1.5.3 Power Supply, Analog-Digital-Converting and USB-Interface
2.1.5.3.1 Software for the microcontroller which works as ADC
2.2 Software for acquiring and analyzing ELF-Signals
2.2.1 Software for acquiring ELF-Signals
2.2.1.1 The ELF-Recorder
2.2.2 Software for analyzing ELF-signals
2.2.2.1 Sample rate and frequency shifting

3. Measurements in practise
3.1 Place of receiving and installation
3.2 Recording
3.3 Causality
3.4 Bearing

4. Analysis of acquired ELF-signals
4.1 ELF immission in residential areas
4.1.1 Signals with limited local spread
4.1.1.1 Whistle
4.1.1.2 Cow
4.1.1.3 Foghorn
4.1.1.4 Owl
4.1.1.5 Locomotive
4.1.1.6 Voice
4.1.1.7 Dot matrix printers
4.1.1.8 Pan flute
4.1.1.9 Key shift
4.1.1.10 Telex
4.1.2 Signals with width local spread
4.1.2.1 Goose-Signal
4.1.2.1.1 Goose - Time signal
4.1.2.1.2 Goose – Occurance and spreading
4.1.2.1.3 Summary about the Goose-signal
4.1.2.2 Heartbeat-Signal
4.1.2.2.1 Measuring of the signal parameter
4.1.2.2.2 Regional occurrences of the Heartbeat-Signal
4.1.3 Measurements in the village "Horm" (Part of Hürtgenwald)
4.2 ELF emissions outside of residential areas
4.3 Lignite mining areas as ELF-emitters
4.4 Windmills as ELF-emitters
4.5 Household appliances as ELF-emitters
4.5.1 ELF-signal of a dishwasher
4.5.2 ELF-signal of a washing machine
4.5.3 ELF-Signal of a electrical clock
4.5.4 Typical field strengths of household appliances at mains frequency
4.5.5 Consequences from the measurements with the household devices
4.6 Other signals
4.6.1 Irregular frequency curves ("squeak signal")
4.6.2 Spontaneous onset of lines

5. Artifical ELF-Signals
5.1 Estimation of the magnetic field strength (formerly flux density)
5.2 Estimation of source properties
5.2.1 Measuring setup
5.2.2 Measuring-Setup with conductor loop
5.2.3 Measurement with ground spike
5.3 Comparison with "naturally" occurring signals

6. Considerations and hypotheses regarding the signal-origin
6.1 Anthropogenic sources
6.1.1 Appliances
6.1.2 Industrial equipment / railroad
6.1.3 High frequency waves
6.2 Natural sources

7. The effect of ELF-signals
7.1 Effect of ELF-Signals in electronic circuits
7.1.1 Influence through magnetic alternating frequencies
7.1.2 Shielding
7.2 Influence of ELF-Signals in the nature
7.3 Influence of ELF-Signals on human biology
7.3.1 Hormonal balance
7.3.2 Biorhytm
7.3.3 Immune system
7.3.4 Nervous system, behavior, psyche
7.3.5 Effect models
7.3.5.1 Body current density
7.3.5.2 Calcium
7.3.5.3 Cell membrane
7.3.5.4 Cyclotron resonance model
7.3.5.5 Direct neural effects

8. Closing remarks

Appendix
Used equipment
Source Code ELF-Recorder
References

Preamble and expression of thanks

This work is the result of curiosity and interest in technology. At first, it was an accidental discovery in 2001. This led to the desire, to learn more about ELF-signals. For that, it was necessary, to develope an inexpensive and widely available receiving-technology. The result is an ELF receiver technology, which includes hardware and software. It is designed with standard parts, which are low in prices and easy to get. Any standard PC with an USB connector and a sound card can be used for detection and analysing.

My research and development was operated part-time and now covers more than 10 years. With writing of these theses in the first version, I started in October 2008.

Thank you to my little son Fabio, who has accompanied me on some measurements and has been viewed with me many evaluations with much enthusiasm.

Thank you also to Mrs. Anong and Jasmine Krath for their patience and understanding.

In addition, I thank Dr.-Ing. Wolfgang Jägersberg (Baesweiler) for some Tips for the Exposé and Prof. Ing. Jaromir Pistora, CSc. for his support of the lecture at the University of Ostrava at the 10th October 2006. Also thank you to Dipl.-Ing. Peter Gibbels (Langerwehe) for reviewing the manuscripts.

My thanks also to Assoc. Prof. MSc. Ján Hribik, PhD. and Prof. MSc. Daniela Durackova, PhD. for the kindly support.

But, I would particularly thank Mr. Dipl.-Geologist Kurt Diedrich (Alsdorf). Mr. Diedrich has made me aware of the issue. He provided the basic concept and made many suggestions and was authoritative actively involved in many measurements and evaluations.

Aachen, Germany, August 2015

Franz Peter Zantis

Used formulaic symbols

Abbildung in dieser Leseprobe nicht enthalten

Used abbreviations

Abbildung in dieser Leseprobe nicht enthalten

1. Introduction

Equipment and facilities in Europe operate mainly with 50 Hz alternating current. A known fact is, that these causes electric and magnetic fields with frequencies of 50 Hz in our environment - and supplementary frequency above of 50 Hz, caused by harmonics. These fields, as well as numerous other transmitters that emit fields with frequencies above of 50 Hz, cause the so-called electro smog.

Our environment is permeated by these electric and magnetic oscillations and waves. In the frequency range above the AC voltage of 50 Hz - especially in the radio frequency range, much attention from the public is given to this waves. There are lively discussions about cause and effect. Through numerous studies and publications about this type of oscillations and waves is largely known, from which sources they occur and which impact they have.

However, topic of this work are magnetic oscillations and waves in a lower frequency range; specifically in the range

Abbildung in dieser Leseprobe nicht enthalten

For simplicity, this frequency range will be called in the following "ELF -range" (ELF = E xtremely L ow F requency). For the observed oscillations and waves, the name "ELF signals" is introduced furthermore. The reason, that ELF signals has so far received little attention, is may be the fact, that they are largely obscured by the much stronger 50 Hz mains hum.

Foundations on this work are ELF-signals, which were first in the year 2000 recorded by accident from Dipl.-Geol. Kurt Diedrich. It turns out, that oscillations and waves with frequencies lower than 50 Hz (ELF-signals), are existent, detectable, albeit with very low amplitude and they are analysable and they can be cataloged.

Strange behavior of analog circuits (e.g. signal disturbances at the CMS-VDC-experiment at CERN) can now be explained with the ELF signals. Some details can be found in chapter 7.

A research revealed, that the topic ELF-signals was little or not studied to date. Also discussions with mining experts and geologists as well as the feedbacks to the papers [1], [13], [56] showed, that this oscillations are mainly unknown and no one could they explain comprehensive and satisfactorily.

In geology, certain waves for the study of the earth's crust are used. With this, it is e.g. possible to detect voids or deposits of raw materials in the upper soil layers [46]. Measurements about of the in this paper described signals, however, one can rarely find information. ELF signals could be also related to the "Brummtonphänomen (the hum phanomene)", which were discussed in the beginning of the 2000er years. On this theme, various studies and measurements were made, for example as described in [56] and [16].

The primary objective of this work is to prove the existence of the ELF signals in the specified frequency range and their composition and structure. Secondarily it goes around the origin of the signals. The in this paper described ELF-signals, were acquired, stored, analyzed and cataloged with self-developed hardware and software. The work has interdisciplinary character. For this work, knowledge and methods from physics, geology, and telecommunications are required.

The present work is based on private intitiative. It was funded by the author. Economic efficiency had not only a high priority but was a compelling need.

1.1 Sources of low-frequency magnetic fields

Numerous causes are conceivable for the emergence of low-frequency magnetic fields. Figure 1.1 gives an overview about it. It should be noted, that a magnetic field, which is caused from magnets, generates an electric field, which again generates a magnetic field.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.1: Possible sources of low-frequency magnetic fields (see text).

First it is to distinguish whether the magnetic fields occur together with an electric field. In this case the cause is a flowing electric current, or an electromagnetic wave (i.e. virtually a continuation of the flowing current in the room).

Electromagnetic fields occur, whenever electric charges move. This is for example the case, if a current flows in a conductor. In addition to the electric field always a magnetic field exists. This relationship is fixed in the first Maxwell equation. It states, that a alternating electric field, is surrounded by a ring of closed magnetic field lines:

Abbildung in dieser Leseprobe nicht enthalten

or

Abbildung in dieser Leseprobe nicht enthalten

Details about this can be taken from [57].

A high electrical voltage with low current produces a relatively strong electric field and a relatively weak magnetic field. On the other hand results a high current with low voltage to a relatively strong magnetic field and a relatively weak electric field.

Further causes which are to be considered, are the magnetic parts of the electromagnetic waves, which are spreading in the space. Considering the immense wavelengths starting with 6000 km (see section 1.2) and the assumption that the sources are on the earth, always near-field conditions has to be considered. However, it is also conceivable that the source is at a great distance from the Earth in space (universe). Then far-field conditions are assumed, in which the electric and magnetic fields are in phase and perpendicular to each other.

Only if the signal can be measured as both, as electrical field and as magnetic field, it can be assumed, that it is an electromagnetic wave (instead of a pure magnetic field).

With "caused by magnetism itself" in Figure 1.1 is meant, that the magnetic fields are not caused by an electric field, but just through magnetism self. These magnetic fields are formed, either by rotating magnets - then the magnetic field moves itself - or as by alternating interference in a static magnetic field.

The latter occurs, for example if rotating ferromagnetic parts (iron parts) influences the magnetic field. Seismic processes can for example, by changing the distance between a magnetic pol and the measurement location or by shielding or focussing ​​within the earth, in relation to the earth's magnetic, cause an alternating magnetic field. In all cases of alternating magnetism an electric field is produced (current) in the environment.

1.2 Wavelengths

Because magnetic waves spread with the speed of light, the ELF-alternating fields have very large wavelengths. Just as for electromagnetic waves also applies to purely magnetic waves:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{1.1}

Where is c = Speed of light ≈ 3×108 m/s, f = Frequency in Hz, λ = Wave length

If the upper limit of the frequency range is assumed at 50 Hz, then, the shortest wavelength results from the equation above to 6000 km.

1.3 Magnetic field strength

Original the strength of the magnetic field has been described with B (induction), and H represents the magnetic field strength. In the recent literature, B is used for the magnetic field strength. H is called the magnetic excitation. This terminology is therefore used here.

1.3.1 Field around a long electrical conductor

If in a long electrical conductor flows a current of magnitude I, a magnetic field formed concentrically around the conductor (Figure 1.2). However, where the current I is an alternating current, then also the magnetic field is alternating. The strength of the magnetic field B decreases linearly with increasing distance from the conductor. Based on the Biot-Savart-rule it is (the derivation can be seen in [57]):

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.2: Concentric magnetic field around a current-carrying conductor. The strength of the magnetic field decreases here with 1 / r.

1.3.2 Field of the magnetic dipole

In Figure 1.3 is a conductor loop, lying in the xz-plane is illustrated. The magnetic field is radiated in the direction of the y-axis. It applies to the field segment dB:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{1.6}

Abbildung in dieser Leseprobe nicht enthalten

and dB consists of the components dBx and dBy. The formula for the field B is:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{1.7}

With N as number of turns and the magnetic field-constant µ0 = 4π ∙ 10-7 Vs/Am.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.3: Conductor loop in the x-z plane.

In a large distance from the magnetic source apply in consideration of Figure 1.3 and Figure 1.4 in air the educations (without derivation):

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{1.8}

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{1.9}

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.4: Situation in a big distance to a magnetic dipole-emitter (Hot Spot).

1.3.3 Field strength

It is noticeable, that the magnetic field of a long electric line, decreases in the way

H ~ 1 / r

wherein r is the distance from the source. In contrast to that, the magnetic field of a magnetic pole falls according to

H ~ 1 / r ³.

Problems in measuring magnetic fields occur, when very weak fields must be selected and measured, out of a wideband mixture. In this case, the magnetic field strengths lies in the order of a few Nano-Tesla. Sources with different magnetic field strengths are shown in Figure 1.5.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.5: Different magnetic field strength in the environment and by humans.

1.4 Example of ELF-signals

In Figure 1.6, the frequency spectrum of a recorded ELF-signal is shown as example. It was recorded at the late afternoon of the 4th March 2007, in the kitchen of the author's house in Alsdorf-Mariadorf near Aachen. The recording time was 3 hours.

On the abscissa is plotted the time. On the ordinate is the frequency. The color represents the intensity. Dark colors represents low amplitude. Red and yellow represents high amplitude.

Abbildung in dieser Leseprobe nicht enthalten

In the chart (figure 1.6), one can see clearly a line at 16,7 Hz, which comes probably from the power-supply of the railway. In the box on the right side, structures and intermittent signals can be seen.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.6: Example for recorded ELF-Signals.

1.5 The aim of this work

This work proves the existence of ELF-signals, which occur with lower frequencies than the frequencies of the power supply network. It shows how they are structured in detail, and when and where they occur. This is important if one want to estimate the effect of this signals to technical devices and environment. Also included are estimates about the field strength and assumptions about possible sources.

It describes a receiver technology for detection and digitization of weak signals with frequencies up to 25 Hz and their transmission into a personal computer, which includes hardware and software.

It is designed with standard parts, which are low in prices and easy to get. Any standard PC with an USB connector and a sound card can be used for detection and analysing.

With the help of this study, the ELF signals are now known in detail. With the help of this work one can:

- identify distortions in analog circuits caused from ELF-signals.
- be the basics for research on influence on flora and fauna through ELF-signals.

Maybe some effects which could not explained until now (announced as 'technical difficulties'), can be explained with the help of ELF-signals.

2. ELF-Signal measuring technology

For acquiring and analysis of ELF-Signals the following is to do respectively is needed:

- a sensor (hardware)
- a low pass filter (hardware)
- amplification (hardware)
- digitizing the signal (hardware)
- saving the signals on a hard disk (software)
- analyzing tools (software)

The sensor detects and provides the signal. For researching of ELF-Signals, it is necessary, to measure at different places - and maybe also time-synchronous.

So it is necessary, to use a simple construction for the sensor, which is easy to handle and not expensive. The best is, if the sensor could be manufactured in homework.

The signal has to be digitized and saved as a file on a hard disk. Before this can be done, the signal needs to be filtered and amplified to a level, which can be processed by the AD-converter.

Filtering is necessary, to beware the analogue-to-digital-converter (ADC) before signals with higher frequencies than 25 Hz. This has different advantages.

Because of the Shannon criteria it applies: the lower the upper limit frequency, the smaller can be the sampling frequency. Moreover, the ADC has a certain dynamic range. The less signal components above 25 Hz are there, the more of this dynamic range is available for the desired signal. The advantage is, that then the digital channel needs only a relatively small dynamic range (see the chapter about the low pass filter for details). Digitization with 16 bit is in this case sufficient, easy to realize and cheap.

After filtering, two different meaningful ways are possible for digitizing the signal and for saving it on a disk:

1) Digitizing under using the standard-sound-board which is in each personal computer available.
2) Digitizing under using an external AD-Converter and transfering the data through the USB-interface into the computer.

In each case, the recorded signal should be saved in a standard format. This allows to read the files with lots of available analyzing software tools.

2.1 Hardware to acquire ELF-Signals

2.1.1 Sensors

There are numerous options for receiving magnetic fields. In the following, two of these will briefly mentioned and the third, then used, discussed in detail.

2.1.1.1 Use of Hall-Sensors

In principle, magnetic fields can be measured with Hall sensors. These are semiconductor devices, that convert magnetic field into an electrical voltage. The sensitivity of commercially available types is between about 7.5 to 10.6 mV / mT at a frequency range up to 100 kHz. The advantage here is the frequency-linear behavior. However, for the fields which are to measure, the sensitivity is not sufficient.

2.1.1.2 SQUIDs (Josephson-Effekt)

With the Josephson effect, it is possible to measure very small magnetic fields [58]. However, the needed operation-temperatures are just above the absolute zero point. A commercial SQUID sensor has indeed, an extremely fine measuring range. But it is expensive and therefore for private measuring of ELF signals in big areas not suitable.

2.1.1.3 Air coils

Another particularly reasonable method to measure the magnetic field, is the use of the law of induction. Here the fact is used, that alternating magnetic fields induce a voltage in a coil. The voltage height is proportional to the strenght of the magnetic field. According to Faraday's law, a voltage is induced in a conducting loop if the magnetic field, which is in the conducting loop, is changing. In the second Maxwell equation, the relationships are described mathematically:

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.1: Principle of induction.

It is up to the terminals of the coil a voltage, which is proportional to the effective magnetic field intensity and the number of turns.

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.2}

with uind the induced voltage [V], Φ the magnetic flux [Vs], N the number of turns of the coil

The voltage which is tapped at the terminals, corresponds to the derivative of the magnetic flux through the coil with respect to time.

Abbildung in dieser Leseprobe nicht enthalten

with B magnetic field strength, φ phase angle, w angular frequency; w =2 p f

A higher output voltage can be realized, by increasing the area A or the number of turns N.

Because of the differential-relation (inner derivation) the voltage changes proportional to the frequency of a stationary alternating magnetic field. A sinusoidal alternating magnetic field, passes vertically through an air-coil. Then, the effective induced voltage at the coil is:

Uind = 2π f ·N · B · A Eq.{2.3}

N turns of the coil, f frequency of the magnetic alternating field in Hz, B magnetic field strength in Tesla (T), A cross section area of the coil in m²

The output voltages are low in weak fields. It is possible to increase the output voltage, by increasing the area A and the number of turns N.

As can be seen from the equation {2.3}, is further apparent, the induced voltage does not depend only on the magnetic flux density, but also on the frequency. At a constant field strength, the voltage from the coil increases linearly with frequency.

After changing the formula, to get the magnetic field strength B, equation {2.4} appears. The magnetic field strength can be determined by measuring the induced voltage.

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.4}

An air-core coil can thus be used as a sensor for detecting magnetic fields. Major advantages are, that the parts are easy to get, the easy production as well as the natural exclusion of DC fields. However, a disadvantage is the linear frequency dependence.

Empirical tests with different coil types were made. If the equation {2.4} is changed according to the output voltage Uind, it can be seen, that the output voltage increases in proportion to the area A, which is defined by the coil. Thus, experiments were conducted with very large coils. But this turned out to be unsuitable for practical use. The problem in these large coils is the mechanical stability. The coil shown in Figure 2.3 provided high output voltages, but the frame caused strong interference from vibration due to insufficient stability. The relationship between the antenna-noise-voltage and the antenna-area is qualitatively illustrated in figure 2.2.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.2: Antenna noise-voltage in relation to the antenna area.

Empirical tests finally showed, that the best results was supplied, by an air coil according to Figure 2.4. It is a flat air-core coil with 4000 windings with a diameter of 40 cm.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.3: Experiment with a particularly large coil (Photo: K. Diedrich).

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.4a: The sensor used: air coil with 4000 windings and a diameter of 40 cm. The (parasitic) DC resistance is 1720 ohms (Photo: K. Diedrich).

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.4b: Self-made winder (Photo: H.-W.Atzenhöfer)

2.1.1.3.1 Inductivity of the sensor coil

As already stated, the used receiving coils are coreless flat coils, which have a high parasitic ohmic resistance Rl, due to the high number of turns. This must be considered when determining the inductivity. This resistor is connected in series with the coil as shown in Figure 2.5. In it, all active power losses are represented. For the air coils which are used here, this resistor is on the first view, the ohmic resistance of the winding wire. Although other parasitic components such as capacities exists and needs to be noticed, it will play rarely a role in the low frequency range.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.5: A coil can be regarded as an ideal inductance with a in series-connected parasitic resistive.

To determine the inductance with simplest equipment, but as exactly as possible, the measurement was carried out with three different measuring methods:

- The current-voltage measurement method
- The resonance measurement method
- "Decreasing-current" method

Details about that can be found in [26] and [27]. In [57] is given, as an approximation for the inductance of a wire ring (in air):

Abbildung in dieser Leseprobe nicht enthalten

If to the equation the number of turns N is added, then it is obtained for the inductivity of the coil from figure 2.4:

Abbildung in dieser Leseprobe nicht enthalten

This value is close to the measured value of 11.5 H. The calculation of the resonance frequency of parallel and series resonant circuits is done with the Thomson's formula:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.6}

With the measured inductance of L = 11.5 H, the relationship of the resonance frequency in dependence on the terminal-capacity is like in the figure 2.6. The terminal-capacity must be sufficiently small, to have enough distance, between the resonance frequency of the receiving-circuit and the acquired ELF-signals. Figure 2.6 shows the behaviour. In this case, already at a terminal-capacity of 10 nF, a value which should be easy to guarantee with the chosen technique, the resonant frequency is in a sufficient distance from the frequency of the signals which are to be detect.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.6: Relation between terminal capacity and resonance frequency.

2.1.1.3.2 Linearization

It is desirable, if the sensor provides a signal-voltage, where the amplitude depend only on the magnetic field strength B and not on the frequency. Then, it is without further calculations, just with the help of a frequency analysis of the coil voltage possible, to get an indication of the strength of the magnetic fields related on the frequencies. The two linearization methods

- Linearization with an parallel resistance and
- Linearization with an integrator

were taken into account.

2.1.1.3.2.1 Linearization with an parallel resistance

In the simplest method for linearization of the frequency response, use is made of the frequency dependence of the inductive reactance. These is calculated according to the formula

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.7}

It can be seen: It increases linearly with the frequency. If now a resistor is switched parallel, then a voltage divider arises, which divides the with the frequency increasing voltage linear down. This is indicated in figure 2.7.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.7: Schematic diagram respectively principle of linearization using a parallel-resistor at an ideal coil.

The result is shown in Figure 2.8: The induced voltage Vind(f), which would be measured without the shunt resistor, increases continues, linear with the frequency. The linearized voltage Umss(f), however, increases up to a certain value, and then remains, regardless of the frequency at a constant value. Theoretically, the frequency can be increased to any value, without of influence to the frequency-linearity. But, in practice, in the high frequency range, very own laws apply. These can be completely ignored, since in the current case only low frequency fields are considered.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.8: The output of the coil-voltage with linearization resistor (Umess) and without linearization resistor (Uind).

The area at the lower end of the frequency scale is notable: since the parallel resistor is a passive component, it cannot increase the voltage. At very low frequencies inevitably hardly voltage is induced. However, there is a relationship between the value of resistance and the start of the linear range. The lower the resistance, the smaller the lower limit frequency, but the lower the voltage is, which will be achieved. The relationship between resistance and lower cut-off frequency (-3dB) frequency is (the parasitic coil resistance is not considered):

Abbildung in dieser Leseprobe nicht enthalten

At the frequency f, the resistance R is equal to the inductance of the coil. When measuring weak fields, every small amount of sensitivity should be exploited. This means: the resistor R must be as large as possible, without the risk, of restrictions into the linearization. In practice, the parasitic coil resistance must be taken in consider. It cannot be neglected and makes it more complicate.

For the ELF receiver coil from figure 2.4, the linearization is be to consider, using a parallel resistor.

This coil has a number of turns of 4000, an inductance of 11.5 H and a parasitic DC resistance of 1720 Ω. To achieve a linearization at a frequency beginning at 1 Hz, the parallel resistor must be, under using an ideal coil:

Abbildung in dieser Leseprobe nicht enthalten

This would result in a voltage division of about 1:25. This deteriorated tremendously the signal-to-noise ratio and thus the possible sensitivity. In fact, this value for the parallel resistor cannot be used with the specified coil. The reason becomes clear, with the equivalent circuit from figure 2.9.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.9 Test of the linearization with parallel resistance at a practical coil.

With this constellation, the -3dB-frequency has a value of:

Abbildung in dieser Leseprobe nicht enthalten

Compared to an ideal coil, the output voltage is again smaller with the factor

Abbildung in dieser Leseprobe nicht enthalten

However, even with a high-quality coil, where the DC-resistance is negligible, a low resistance for the linearization arises to another problem:

the lower the resistance, the greater the current which is flowing through the measuring coil. This in turn generates a magnetic field, which is in opposite directions to the field, which is to measure. It weakens the field which is to measured and thus, it distorted the measurement result.

If the measuring-coil is close to the source, then it "feels" the weakening magnetic field, attracts a slightly higher current (provided that the source can deliver this) and compensates this magnetic field weakening.

But, if the probe is in a sufficiently distant from the source, then it weakens the magnetic field in their environment, and the source is not affected. In the neighborhood of the source it therefore the measurement error leads to zero, while further away - in the far field - it can alter the magnitude of the measurement result.

So, a small linearization resistance, not only alters the measurement results in the far field, also the error is largely indeterminable and not correctable.

2.1.1.3.2.2 Linearization with an integrator

To avoid the disadvantages of linearization caused by a shunt resistor, an active element is needed. With an active integrator, the frequency response can be linearized down to very low frequencies. The better the frequency response correction, the less is the influence of the frequency on the measurement accuracy.

For the amount of the transfer function of the integrator from Figure 2.10 is, respectively according to [39]:

Abbildung in dieser Leseprobe nicht enthalten

For the complete transfer function, including coil-integrator then applies involving equation {2.3}:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.8}

In a real operational amplifier occur errors, caused through the bias current and the offset voltage. To eliminate the error due to the input bias current, one can, as suggested in [39], and to see in figure 2.10, connect the positive input of the integrator via a resistor R2 ≈ R1 to ground. But, the also in a real operational amplifier existing offset current drift and resulting offset voltage, cannot be compensated. In use of operational amplifiers with field effect transistors in the input stage, the bias current is so small, that it is only necessary to compensate the offset voltage.

As can be seen, the transfer function is now independent of the frequency. If dimensions and number of turns of the coil are fixed, it results with the components R1 and C1 the constant term

Abbildung in dieser Leseprobe nicht enthalten

With these two components, it can be determined the frequency-independent gain for the described application. For the integrator shown in Figure 2.10 this term has a value of

Abbildung in dieser Leseprobe nicht enthalten

The smaller the values ​​for the resistor R1 and the capacitor C1, the higher the reachable frequency-independent output voltage. Because of the finite open-loop gain of real operational amplifiers, the deepest frequency which can be linearized, may be increased. The circuit in figure 2.10 has no offset compensation. But this is mandatory. Otherwise, the output voltage drifts to the positive or negative supply voltage.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.10: An example for a coil with a downstream integrator for linearization. R2 is only required to compensate deficiencies of real operational amplifiers. An offset-compensation is not shown, but it is mandatory.

Abbildung in dieser Leseprobe nicht enthalten

Figure2.11: Modified circuit from Figure 2.17 for the practical use with the coil from figure 2.4.

Is the round flat coil from figure 2.4 linearized through the circuit from figure 2.10, then, the calculated behaviour is according to figure 2.10. The frequency-independent output voltage reaches a value of almost 230 mV at a field strength of 10 μT. The deepest yet linearized frequency is determined among other things by the values ​​of the operational amplifier used. To reach the frequency down to 1 Hz, the operational amplifier must achieve a gain of 723.

In fact, the circuit shown in figure 2.10 is unsuitable for practical use, because due to the voltage-offset, the integrator does not behave stable. In the best case, the output voltage contains a constant DC component and in the worst case the output voltage runs against the positive or negative supply voltage. To prevent this or at least to reduce, it is essential to limit the gain of the integrator. In the circuit shown in figure 2.11, a non-inverting amplifier is arranged behind the inverting integrator. The output of the amplifier has a feedback to the input of the integrator. This prevents, that the output voltage drifts to the positive or negative supply voltage. As an integrator behaves as a low pass, it does not affect the lower frequencies. However, caused by the feedback, the lower frequency limit of the overall system increases.

In practical tests with a rotating magnet (figure 2.13), the behavior which is shown in figure 2.14 has been occurred. The lowest frequencies are not satisfactorily received.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.12: The calculated linearization of the coil described using the circuit of Figure 2.10. The ordinate axis shows the gain A of the integrator divided through 100 and the output voltage of the coil and of the integrator in volts. At a constant magnetic field strength, the level of the output signal is independent of the frequency.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.13: Practical measurement setup. A rotating magnet (Magnet) is located inside of the coil (Spule). With the help of the motor (Motor), the rotation-frequency of the magnet can be infinitely varied.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.14: The transmission curve of the circuit from figure 2.11, measured with the setup of Figure 2.13. The second (bold) curve is a moving-average over two measurements.

Figure 2.15 shows another example for an linearization-circuit. In this case with no need for a feedback-loop. There, a special operational amplifier (OP277) is used, wherein the compensation resistor from the positive input to ground, is, according to [38], not necessary or even disruptive. The term for amplification has here a value of

Abbildung in dieser Leseprobe nicht enthalten

To reduce the offset problem, the resistance R2 is connected in parallel with the capacitor C1. This results for the integrator to a maximum gain of

Abbildung in dieser Leseprobe nicht enthalten

and theoretically for the transmission behavior as shown in Figure 2.16.

A second operational amplifiers of the same type causes an amplification by a factor of 10.

The compensation of the offset voltage of the operational amplifier can be adjusted with the potentiometers P1 and P2. All components must be temperature stable. Otherwise it can be, that changes in temperature causes DC voltages at the output. The missing of a feedback enables a deeper lower cutoff frequency. This is an advantage. However, compared with the circuit from figure 2.11, must be done a calibration for each stage.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.15: An example for a coil with a integrator for linearization and possibility for offset compensation. The operational amplifier OP277 does not need a resistor to compensate the bias current.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.16: Calculated transfer-characteristic of the coil from figure 2.4 with integrator of figure 2.15 (without following amplifier).

In all examples (circuits of figure 2.10, 2.11 and 2.15), the gains are much lower than the open loop gain of the operational amplifier, which thus have no influence on the transmission characteristic. This is (with the operational amplifier OP277) in figure 2.17 clearly to see.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.17: Gain characteristic in the use of the operational amplifier OPA277 for the circuit of figure 2.11 (1) and 2.15 (2) compared to the open loop gain (G).

The practical measurement of the circuit in figure 2.15 (only integrator-part without amplification) showed the behavior in figure 2.18. The measurement setup corresponded to figure 2.13. Compared to the circuit from 2.11 it shows a significantly lower low frequency limit.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.18: Transfer-characteristic of circuit in figure 2.15

In the first version of the equipment, this circuit was mounted in the housing of the coil (figure 2.19). So with this, the coil is an active sensor. It was connected to the receiver via a 4-wire cable (+15V, -15V, GND, Signal out). This allows long cable length between coil and receiver.

This was described in 2010 in [8]. In a publication from 2014 [40] the same principle is used and explained.

In the newer version of the equipment, the linearization circuit is inside the receiver. This could be made because of two reasons:

- because of their very big wavelength, the received signals pass everything - also big walls; so the sensor coil can be placed close to the receiver
- the new version of the equipment do not need much power, so it can be used offline.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.19: linearization-circuit of figure 2.15 mounted in the coil-housing.

2.1.1.4 Ground rods

Ground rods can be used to detect ground currents. With this it is possible to find out, if signals which are detected with the coil, results from ground currents. The receiver is designed to make measurements with ground rods instead of the coil.

2.1.2 Analog low pass filter 6th order

Today, filtering of signals is realized in the digital way. However there are applications, which need the filtering before the analogue-to-digital-converter. One of this application is the acquisition of ELF-signals, how it is described e.g. in [1] and [2]. Would the signal, which is coming from the antenna, digitized without filtering, then, almost the whole dynamic range of the A/D-converter must be used for the 50-Hz-hum of the main power supply. For the relevant ELF-signal only a few bits at the end of the scale (near the LSB) can be used. This results in a poor signal-noise-relation. The frequency-diagram in figure 2.20 results from a measurement inside of a house. The 50-Hz-hum from the power supply is in this case round about 41 dB stronger than the ELF-signals below this frequency.

The solution of this problem offers an analogue low-pass-filter with strong slope. The cut-off-frequency must be placed with enough distance to the 50-Hz-hum. With this configuration, the 50-Hz-hum-signal is suppressed and only the ELF-signals goes to the A/D-converter. Much more of the dynamic range of the A/D-converter can be used for digitalization the ELF-signals.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.20: The difference in the dynamic range between the 50-Hz-hum of the power supply and the ELF-signals (left of the 50-Hz-Peak) is 40.94 dB.

2.1.2.1 Types of low pass filters

The question is, which characteristics the filter must have. To be sure, that no signals will missed, it would be good, if the filter can pass all frequencies until close to 25 Hz. However, the 50-Hz-hum of the power supply must be surpressed very strong. To do this, a low-pass-filter with high slope is necessary.

However, especially steep filter, like the Chebychev-type, causes errors - depending on the design - in the pass band or stop band. The reason for that is the fact, that Chebyshev-filters have a marked non-linear group delay and so, an extremely non-linear phase-characteristic. If the signal must be analysed also in the time domain, only the Bessel-filter can deliver a relevant result. This kind of filter is optimised for constant group delay. However, the transfer characteristic from the pass-band too the stop-band is comparatively width.

The compromise is the filter with Butterworth-characteristic. Just as the Chebyshev-filter, it has not a constant group delay, but it causes no error in the pass band - and has relatively strong steepness anyway. If it is planned, to make the analysis preferably in the frequency range, the Butterworth-filter is the right selection.

As closer the cut-off frequency is placed to 50 Hz, as more steepness is needed. In general applies for the steepness of the transfer characteristics depending from the filter-order:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.9}

Figure 2.21 shows the transfer characteristic of optimized low pass filters. The optimization is relevant for the range around of the cut off frequency. Of course, in width-band-view, equation 2.9 is relevant.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.21: Qualitative comparison of the transfer characteristics of optimized filters 4. order: 1 Bessel, 2 Butterworth, 3 Chebycev (Source: [3])

2.1.2.2 Development of Butterworth-low-pass filters in general

To optimize a filter it must be at least of the order 2. Second-order Low pass filters of type Butterworth can be designed like described in [3]. According to the "Sallen-Key-Concept". Each filter needs one operational amplifier, two resistors and two capacitors.

Higher order filters can be constructed through series circuits. Two filters of second order in series delivers a filter of fourth order. Three filters of second order in series delivers a filter of sixth order. When dimensioning must be noted, however, that the individual filter curves multiplied together gives the total transfer-characteristic. Two low pass filters with the cutoff frequency fc in series delivers a low pass filter with a cutoff frequency which is lower than fc. A filter higher order, which is constructed from several single filters, requires therefore a certain dimensioning of the whole filter.

The transfer characteristic of a Butterworth low-pass filter of sixth order is calculated in generally:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.10}

The variable s stands for the frequency-dependence. If a filter of sixth order is builded from three filter of second order, the characteristic of each filter is:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.11}

Now a circuit must be found, which allows to realize the corresponding curves. The easiest way to create a low pass filter of second order, offers the Sallen-Key-Filter corresponding to Figure 2.22.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.22: Sallen-Key low pass filter of second order.

The transfer characteristic of this filter is (under condition "Butterworth-behave"):

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.12}

The component values can be calculated by comparing coefficients with Eq.{2.11}.

Abbildung in dieser Leseprobe nicht enthalten

To obtain real values, the condition [Abbildung in dieser Leseprobe nicht enthalten]must be fulfilled. Therefore, at first the capacitors are to be chosen. Then, the calculation of the resistors can be done.

A filter of 6th order can be designed by three filter of 2nd order, which are serially connected. The overall transfer function is the result from the product of the single transfer functions of each filter.

To make the calculation easier, one can use a worksheet like it is described in [3]. Alternatively a special filter-calculation-program can be used. An example for that is the program “Filter Pro” from Texas Instruments (Figure 2.23). After selecting the filter-type and entering of the parameters, the program offers a circuit diagram and the transfer-characteristic. As one can see, in this case, the transmission curve (green curve) is not completely flat - although, the type "Butterworth" was selected.

Abbildung in dieser Leseprobe nicht enthalten

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.23: Filter design with the program "Filter Pro" from Texas Instruments (above) and the result (left, see text).

Green: transfer characteristic

Red: phase response

Black: group delay

2.1.2.3 Designing a Butterworth low-pass filter of 6th order

According to equation {2.9}, the steepness of a filter of 6th order is 36 dB/Octave. If the cut off frequency is 25 Hz, the 50 Hz hum of the power network, which bother the measurement, is reduced by 36 dB. Based on the task to filter out ELF-signals just before the line frequency and under considering of figure 2.20, is the result compared to the unfiltered A/D conversion, a dynamic improvement of these 36 dB. With the help of [4], the attenuation of the 50-Hz-hum is reduced to the factor:

Abbildung in dieser Leseprobe nicht enthalten

If the cut off frequency is 20 Hz, the 50-Hz-hum is even reduced to 46 dB (see figure 2.23, green line), which is equivalent to an attenuation-factor of nearly 200. However, in this case, the ELF-signals are transferred then only until nearly 20 Hz without damping - what means error free in the frequency range. This cut off frequency (20 Hz) was selected, because for the intensity of the 50-Hz-hum, the damping of 36 dB is not enough. The fact, that this filter reduces the 25 Hz about 11 dB, must be considered if necessary.

Figure 2.24 shows the circuit diagram of the designed Butterworth-Low Pass filter of 6th order with a cut off frequency of 20 Hz. It is build up with three filters of 2nd order. The first operational amplifier (OP1.1) is just for pre amplification of the incoming signal to the factor 4,5.

The filter itself is designed with the operational amplifiers from OP1.2 to OP1.4. The selected type OPA4227 from Texas Instruments has an extreme low offset-voltage and its very low temperature dependence. Maybe even C7 can be leaved out, so that the passband range begins with 0 Hz (DC). This can certain be made with adding an offset adjustment (not in the circuit diagram), which must be connected at OP1.4.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.24: Circuit diagram of the low pass filter of 6th order designed according to Sallen-Key (see [19]). The first operational amplifier (OP1.1) is for separating and input-amplification. The real filter is designed with the operational amplifiers OP1.2, OP1.3 and OP1.4.

2.1.2.4 Measurement results

The filter does not show the ideal Butterworth behavior. This can be seen in more detail after measuring the transfer-characteristics (figure 2.25, measured with equipment <2>, <3> and <4>). This measuring is made without the capacity at the output of the circuit (C7). However the desired cut off frequency matches very good the 20 Hz. The reason for that inaccuracy in the transfer characteristic is the tolerance of the component-values. The values for the resistors are selected from the E12-series. The values for the capacitors are selected from the E6-series. For the planned application this does not matter.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.25: Transfer-characteristic of the filter from figure 2.10.

2.1.3 Concepts for digitization of the signal

After passing the filter, the signal must be digitized. The amplitude of the signals is typically weak. The absolute value is not known. The system must be sufficient sensitive.

With the delivered data of the system it should be possible to show the signal independent from the form of the curve.

It must be possible, to do acquisition of the elf-signals at many places at the same time. The hardware should be easy to build and cheap. Moreover it must work with any standard personal computer. Most PCs work with MS-Windows operating systems. So the program must run under Windows.

In principle two different meaningful ways are possible for digitizing the signal and save it on a disk:

1. Digitizing under using the sound-board and the A/D-converter on it, which is in each personal computer available.
2. Digitizing under using an external A/D-converter and transferring the data through the USB-interface into the computer.

2.1.3.1 Using the sound board of a personal computer

Very first tests in the way similar to 1) was made in the year 2000 and published in the year 2003 [56, 57]. A better version is described in detail in [8] and [14]. This equipment was used for several measurements in the years 2003 to 2011 and also during the setup in chapter 5. It was changed in 2012 to an equipment which is power-supplied by the USB-Port, and which is independent from the transfer-curve of the onboard sound card. Just a few facts about this topic hereinafter.

The problem in this case is, that it is not sure, whether the sound board in a personal computer can process signals in the ELF range. Typically this sound boards are designed for audio signals like music or speech. So, before the sound board of a computer can be used for recording of ELF-signals, it is necessary to measure the transfer characteristic. With this data an adaption must be designed with hardware or software. This has to be done for each computer which is used for ELF-recording. This is uncomfortable and result easy to errors.

On the other hand, commercial sound boards in personal computers have a 16-Bit-Analog-Digital-converter already implemented. This makes the handling easy.

To solve the problem with the unknown frequency-characteristics of the sound board, a modulation can be used. For example an AM-signal with a carrier-frequency which lies in the middle of the audio range, can be used. It is very likely, that in the middle of the audio range the transfer characteristic of an audio sound board is straight.

The block diagram for this solution is shown in figure 2.36. The modulated signal, which goes to the sound board is shown in figure 2.27. Assumption: In the surrounding of 200 Hz, each standard sound card has a linear frequency response. According e.g. to [9], the bandwidth B of an AM-signal is:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.13}

Whereby fmax is the highest frequency which modulates the carrier. So here it is

Abbildung in dieser Leseprobe nicht enthalten

So the used band starts at 175 Hz and it stops at 225 Hz. It can be assumed that any standard soundboard has a linear frequency response in this range. With this concept there is no limit of the low frequencies. Details to the AM-modulation can be found in [9].

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.26: Concept under using the sound board of an personal computer

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.27: Amplitude modulated (AM) signal. The carrier is modulated with the ELF-Signal.

Test with this concept has been made. The used self made board is shown in [8]. A real disadvantage is the fact, that through the modulation, the dynamic range is restricted. The dynamic range results from the allowed modulation factor m. The modulation index is defined as the ratio, between the highest and the lowest amplitude value of the (upper) envelope of the AM-signal.

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.14}

Theoretically m can go from 0 to 100 % (see [9]). In practice it is necessary to have a good distance from 100%. Otherwise there is a danger of over-modulation and resulting signal-distortion. The signal-noise-ratio depends also on the amplitude of the carrier. The higher the amplitude, the more better is the signal-noise-ratio on the transmission way. However there is a limit, because most commercial sound boards can handle input voltages up to 2 Vss. To make sure, that any sound board can be used, without signal distortion, the amplitude of the carrier should not exceed 1 Vss.

Of course, in the computer the data must be demodulated by software. In [8] is a very simple way described with which ELF-signals can be demodulated without Hilbert transformation. However, this requires that the sampling frequency is at least 5 times higher than according to Shannon necessary (see [65] or see later in this chapter).

For those in [8] described methods of "peak tracking", an amplitude error is present. In the worst case, the peak value occurs exact between two samples. In figure 2.28, one can see, that the peak value of a 2p-function occurs at p /2. The maximum error appears, if the next sample value is 1/2 × fS before or after the peak value. For the relative value of the error one can write:

[Abbildung in dieser Leseprobe nicht enthalten]Eq.{2.15}

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.28: Estimation of the maximum possible error, with demodulation through peak tracking. With constant carrier frequency, the used sample frequency is crucial factor for the error.

The declaration of the formula-statement will be more clear with the help of the diagram in figure 2.29. As expected, the error is as smaller, the higher the sampling rate is and/or the lower the carrier frequency is. The minimum value of the carrier frequency is in turn determined by the behavior of the transmission channel in general or specific case and the expected frequency of the desired signal. The 1%- accuracy-line can be calculated as follows:

Abbildung in dieser Leseprobe nicht enthalten

The sine value 0.99 exists also for an argument which is smaller than pi / 2 - i.e. before the maximum of the function. The result of the above equation, therefore, leads to a negative frequency-ratio. Because of the symmetry around the point pi / 2 one can also write the following:

[...]