Physics and Electrical Engineering: Earth Magnetic Field

Abstract –

The Earth is characterized by a weak magnetic field with a magnitude ranging from 25- 65. Specific sensors capable of working within the earth’s range are required to measure its field. These sensors are called Magnetometers. Various principles have been employed in measuring the earth’s magnetic field namely: Magnetic Compass, Fluxgate principle, Superconducting Quantum Interference Devices (SQUID), Fibre-optic Magnetometer, Hall Effect, Magnetoresistive effect and Lorentz Force Effect. Most recently, these magnetometers have been miniaturized to the extent that they can be fabricated into integrated circuits at very low cost and less power consumption e.g. Micro-electro-mechanical systems (MEMS) magnetic field sensor. This Paper gives an articulate insight on three main sensing technique; Fluxgate, Hall Effect and SQUID. Comparison in terms of their functionality, ease of application, realization on a chip, cost implications and Power Consumption are also highlighted.

I. Introduction

In deciding the best sensors for measuring the earth’s magnetic field a good knowledge of the behaviour and characteristics of the earth is required. The Earth’s magnetic field can be measured by specially designed sensors known as geomagnetic sensors. Geomagnetic sensors measure the earth’s magnetic fields. The direction of the earth is determined by recording the magnetic fields around its exterior. Due to the weak earth fields, measurement sensors must either have a large dynamic range or use a coil to decrease field effects. Many other features such as frequency response, size, and power consumption, are determining factors in selecting sensors for a particular application.

II. Earths Magnetic Field

Earth’s magnetic field extends from its outer core where molten iron produces a dynamo effect. This magnetic field protects Earth from the wind and high intensity rays that would certainly destroy the atmosphere and deplete the ozone layer that shields us from sun ray. This means that without Earth’s magnetic field, solar winds; streams of electrically charged particles that flow from the sun would definitely strip away the planet’s atmosphere and oceans. Hence it is of great importance to monitor little changes occurring in the earth’s field. A good analogy of earth magnetic field could be likened to a bar magnet placed within the earth at an angle tilt of 11.5° with respect to earths rotational axis. As shown in Fig 1, the white rectangular lines and the circular motion of the fields describe the way a magnetic field is produced.

There are three basic requirements to generate and ensure sustenance of the earth’s Magnetic field: a conducting liquid, convection and rotation. Earth’s outer core meets all these requirements, as opposed to other planets that may be deficient in one or two of these.

The Earth’s magnetic field is generated by electric currents due to the movement of “convection currents of molten iron in the Earth’s outer core: these currents are as a result of heat departing from the core, a natural occurrence called a geodynamo; whereby a rotating, convecting and electrically conducting fluid can preserve a magnetic field for an extended period of time. The conductive fluid in the geodynamo is liquid iron found in the outer core. The rotation of the earth causes the rotation in the iron rich outer core. This is termed Coriolis Effect- where by a mass moving in a rotating system encounters a force orthogonal to the direction of motion and to the axis of rotation. The induction equation is given by

∂B/∂t=η∇^2 B+ ∇x (vxB) (1)

Where B is the magnetic field, v is the velocity field η is the magnetic diffusivity.

At any location, the Earth’s magnetic field can be represented by three vectors. As shown in the figure below, the area labelled declination (D) is its angle relative to true North. Looking towards magnetic North, the angle the field makes with the horizontal is called the inclination. The intensity (F) of the field is described as the force exacted on a magnet by the earth.

[image: Image result for three dimensional vector diagram of the earths magnetic field]

III. Fluxgate

Fluxgate sensors were firstly developed in the 1930 and were rapidly used for many applications. Fluxgate sensors measure direct current (DC) or low-frequency alternating current (AC) magnetic fields. They are vector sensors, i.e. sensitive to the field direction in the range of up to 1 mT with achievable resolution down to 10 pT. A fluxgate magnetometer consists of a small, magnetically susceptible core encircled by two coils of wire. An alternating electrical current is passed through one coil, driving the core through a varying cycle of magnetic saturation; magnetised, unmagnetised, inversely magnetised, unmagnetised, magnetised, and so forth. This constantly changing field induces an electrical current in the second coil, and this output current is measured by a detector. For checking variations of the Earth’s field three-axis fluxgate magnetometers are mostly used employed. Figure 3. illustrates the essential elements of a fluxgate magnetometer. As in a transformer, a soft magnetic core is shrouded by a primary and a secondary coil. The primary, or excitation, coil induces a field in the core; the secondary coil measures the core’s response. When weak field H is applied, the magnetic induction exhibits a linear response

B = μH (2)

Here, μ is the permeability. In principle, μ depends on the field strength, but for weak fields, it is constant.

A fluxgate sensor comprises three main components: a ferromagnetic core, a drive coil or winding to periodically force the ferromagnetic core into magnetic saturation, and a sense winding to pick up the resulting modulated field.

IV. Hall Sensors

These are solid state devices that measure the magnetic flux density using the Hall effect and outputs a voltage proportional to the magnetic flux density.

The Hall Effect is coined after Edwin Hall, who in 1879 discovered that “a voltage potential develops across a current-carrying conductive plate when a magnetic field passes through the plate in a direction perpendicular to the plane of the plate”. as illustrated in the lower part of figure 7.

[image: Figure 1. The Hall effect and the Lorentz force. Hall effect sensors, sensor hall.]

Figure1.The Hall Effect refers to the detectable voltage when applied current is influenced by a perpendicular magnetic field.

The basic principle behind the Hall Effect is the Lorentz force, which is illustrated in the upper part of figure 7. Where an electron moves along a direction, v, perpendicular to the applied magnetic field, B, experiencing a force, F, called Lorentz force that is normal to both the applied field and the current flow.

V. Superconducting Quantum Interference Device (Squid)

At temperatures approaching absolute zero, certain materials undergo a transition to what is known as the superconducting state. Below this temperature, known as the transition temperature, the material is characterized by a complete lack of electrical resistance.

Until 1986, the critical temperature of all known materials was pretty low and liquid helium had to be used for cooling. Unfortunately, liquid helium is expensive and difficult to handle. In 1986 “High-Temperature Superconducting“ materials were discovered by Müller and Bednorz .These materials can be cooled with cheap and easy-to-handle liquid nitrogen, thus making them more accessible outside the laboratory. Figure below shows the main components of a SQUID sensor.

[image: C:UsersAKUPUOMEDesktopwinter semester 2019-2020Sensor sciencerfsqdpre_579.jpg]

Superconducting Quantum-Interference-Devices are the most sensitive sensors for magnetic fields. Their operation is based on the idea of superconducting loops containing Josephson junctions, which make clever use of properties which are specific for superconductors: zero electrical resistance, expulsion of magnetic fields and quantization of magnetic flux. There are two main types of SQUID namely: DC and radio frequency (RF) . The major difference being that the DC type may offer lower noise when compared to RF type. Figure Below shows an Electrical schematic of a SQUID where Ib is the bias current, I0 is the critical current, ɸ is the flux threading and V is the voltage response to that flux. The X-symbols represent Josephson junctions.

[image: https://upload.wikimedia.org/wikipedia/commons/7/71/SQUID_IV.jpg]

The sensitivity of SQUID devices is best discussed in terms of the energy sensitivity:

EN= Linput I2N =

Where Linput is the input inductance of the device, I2N is the current noise, and ɸ2N is the flux sensitivity. EN is often expressed in terms of Planck’s constant h =6.6*10−34 J/Hz.

Discussion And Comparison

For Specific application requirements some sensors may be preferred to the others. Fluxgate sensors are more sensitive than other solid-state devices like the Hall-effect sensors. Fluxgates also measure the direction of the field. The fluxgate sensors have no moving parts and are “more sensitive to the measured field and less sensitive to vibrations and thermal changes”. Fluxgate sensors are cheaper than SQUIDS and do not require the use of liquid helium. The main fields of application are: geophysical measurements; space research; identification, location and compasses; and measurement of electrical current. However they are Large in Size and power consuming.

Hall Effect sensors in contrast are much smaller with lesser power consumption. They have become popular in smartphones and handy devices. These magnetometers are what enable the phone’s compass to function. As technology improves, Hall-effect IC’s are finding their way into many modern household appliances; Washers, Dryers, Ovens and Refrigerators among others. However they suffer from Piezo Effect and are more appropriate for in-plane sensing. They can be affected by the input current and the self-excited zero potential during manufacture. Their ease of incorporation into integrated circuits with different technologies makes them more advantageous compared to other techniques.

SQUID’s sensors are by far the most sensitive and reliable magnetometer, having the extra ability to make measurements where other methodologies fail. However, they are not used frequently due to their complex design process, large size, their operation at low temperatures and cost implications. They are mostly used in detection of gravity waves, Refrigeration and most recently bio-magnetic evaluation of human heart and brain.

Conclusion

With the extensive variety of solutions available for sensing the Earth’s magnetic field, designers can select optimal technologies and packages to achieve their commercial and engineering goals. There always remain the same critical factors that must be considered, such as cost, power consumption resolution, accuracy, reliability, and durability, which largely determine the type of sensors that would be used in any application. Hall-effect technology, with its contactless magnetic sensing, provides exceptional value also the ease of its incorporation into integrated circuits with different technologies makes it more suitable for home friendly applications. Fluxgate Sensors are also used because they are highly sensitive, affordable, Compact, have the ability to precisely measure low DC fields and rugged enough to withstand harsh conditions. Squids on the other hand are the most sensitive of all Sensors but are much more expensive. Therefore a form of trade off has to be done in choosing a particular sensor over the other. The sensing techniques (sensors) can also be combined to achieve a particular application need. Correction and compensation circuitry must be incorporated into the sensor to ensure greater efficiency and resolution. It is also important to note that the sensitivity range for each type of sensor is somewhat influenced by the readout electronics they comprise.

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