Step 2 To Recognize The Electrodynamic And Waves Applications 4i2m24

ELECTROMAGNETIC THEORY AND WAVES UNIT 1 - ELECTRODYNAMIC AND WAVES STEP 2 - TO RECOGNIZE THE ELECTRODYNAMIC AND WAVES APPLICATIONS

GROUP: 203058_52

COLLABORATIVE ACTIVITY

Authors: FILADELFO ATENCIO

COD: 12593519

ALEXANDER DE ARMAS ROBLE

COD: 12447197

LUIS FERNANDO BUSTAMANTE

COD: 1143944649

LUIS ALFREDO PALACIO

COD: 9295104

TUTOR: EDUARDO GUZMAN

NATIONAL UNIVERSITY OPEN AND DISTANCE-UNAD SCHOOL OF BASIC SCIENCES TECHNOLOGY AND ENGINEERING Cartagena de Indias, Colombia. October 2, 2018

INTRODUCCION

The present work is carried out in order to understand and characterize the means and waves taking into their own parameters and the interaction between them. We will present this work in three parts; firstly, a consolidated list of the answers given by the of the group is presented to the 6 questions proposed in the activity guide, such as: Concept of loss tangent by means, speed of propagation of electromagnetic waves, refractive index , flat and non-flat wave, magnetic and non-magnetic medium; In the second place we will shape the development and solution given to the 5 exercises proposed in the activity guide where we present some mathematical bases that define the behavior of electromagnetic waves; Finally we will include in this report the solution to some practical problems also proposed in the activity guide.

DEVELOPMENT OF DE ACTIVITY

Activities to develop Each student in the group has to answer the following questions using academic references to the research: Resolution of questions 1. Explain the practical application of the loss tangent with an example. The loss tangent is a measure of the state of an insulation, its magnitude depends on the type of insulation and its conditions. Its value can be affected by moisture and dirt on the surface of the insulation. Loss tangent occurs when, in an alternating current circuit, the tangent of the angle by which the actual current ing through a capacitor is out of phase with the ideal current.

In a medium that presents moisture, the loss of tangent or delta tangent increases the agreement as moisture is absorbed, as can be seen in the transformers, that although there is already a loss, when it absorbs moisture, it increases and deteriorates the conditions of its operation. Example: Calculate the tangent of freshwater losses at a frequency of 10kHz the parameters of fresh water are: 𝜎 = 10−3

𝑠𝑚 𝑚

𝜖𝑟 = 80

the tangent of losses at 5 kHz 𝜎

tan(𝛿) = 𝜔𝜖 =

10−3 1 2𝜋∗104 ∗80∗ ∗10−9 36𝜋

𝑡𝑎𝑛−1 (2.3 ∗ 101 ) = 97.23°

=

10−3 4.4∗10−5

= 2.3 ∗ 101

2. What kind of information gives us the propagation velocity in electromagnetic waves propagation?

Stiffness and density are two factors that determine the speed of propagation. James Clerk Maxwell, based on these factors, deduced that light is constituted by electromagnetic waves, calculated the rigidity measured as modulus of elasticity and the density of the electric and magnetic fields propagating through the ether. Relating the ether rigidity as electric field and density with magnetic, Maxwell showed that the speed of the waves if it exists, also concluded that electromagnetic waves are transverse, cause of electrical and magnetic phenomena

The velocity of propagation can be measured as the time necessary for a zero crossing or a maximum of the signal to occur again at the same point in space.

𝑉𝑝 =

𝑥1 − 𝑥0 ∆𝑥 = =𝜆∗𝑓 𝑡1 − 𝑡0 ∆𝑡

3. Explain how an electromagnetic wave behaves in free space, perfect dielectrics and good conductors. In the free space, the troposphere and the ionosphere are responsible for the fact that the ideal propagation model is not correct in most cases, since the orography of the soils affects the same. It is not the same when working at low frequency, which adapts to geography, that when working at high frequency, since the attenuation is very high, and the antennas must be raised more, taking into that when the propagation of the wave, there can be small obstacles that absorb energy and power. In perfect dielectrics, the tangent of losses tends to be zero, since they do not present conduction current, so their depth of penetration is infinite, the propagation is similar to that of the free space, since this is an ideal dielectric medium. In a good conductor, the conduction current is greater than the displacement current, so the energy of a wave propagating in a good conductor is fundamentally magnetic. In a good conductor, the average energy density associated with the magnetic field is greater than that associated with the electric field. It is important to keep in mind that electromagnetic energy is not transmitted inside a good conductor, it travels in the region around the driver while it only guides the waves. In a good driver the tangent of losses is very high (> 10)

4. Using the electromagnetic spectrum, explain the practical application of every type of radiation. Electromagnetic spectrum, the entire distribution of electromagnetic radiation according to frequency or wavelength. Although all electromagnetic waves travel at the speed of light in a vacuum, they do so at a wide range of frequencies, wavelengths, and photon energies. The electromagnetic spectrum comprises the span of all electromagnetic radiation and consists of many subranges, commonly referred to as portions, such as visible light or ultraviolet radiation. The various portions bear different names based on differences in behavior in the emission, transmission, and absorption of the corresponding waves and also based on their different practical applications. There are no precise accepted boundaries between any of these contiguous portions, so the ranges tend to overlap.

The entire electromagnetic spectrum, from the lowest to the highest frequency (longest to shortest wavelength), includes all radio waves (e.g., commercial radio and television, microwaves, radar), infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

Gamma rays: they are used mainly in radiotherapy or treatment of a certain type of cancer, the "pump" of Co is used as a source of radiation, due to its ability to eliminate pathogenic bacteria, also for the sterilization of instruments that can not be performed by other methods. Gamma rays through most materials and can not be reflected X-rays: its main application focuses on the field of scientific research, industry and medicine. In the medical field when an X-ray plate is taken, photographic plates, Geiger counter, scintillation detectors and semiconductor detectors are used. When negative photographic plates are used, it becomes white, where the x rays cross the soft parts of the body. and it turns black where they were stopped or absorbed by the hard parts. Ultraviolet rays: one of the applications of ultraviolet rays are photodiodes, semiconductor detectors, photomultiplier tubes, etc. In the photomultiplier tube, the absorption of a photon results in the emission of an electron, where light enters the tube through a glass or quartz window and where the emitted electrons are multiplied in chain. Infrared: There are varieties of infrared detectors such as thermal detectors or quantum detectors; where they absorb the incident radiation and the temperature of the detector increases or decreases until reaching an equilibrium with the radiation being absorbed. The most common thermal detectors are the thermopile, pyroelectric detector and bolometer. Microwave: the application that most presents this type of radiation is in ovens, taking into that its electromagnetic radiation is very high frequency, has a lot of energy and there is a very large heat transfer to food. Other microwave applications are communications and radar. Radio waves: Radio astronomy can develop on the earth's surface since the atmosphere is transparent in of radio waves. Through interferometry, it is allowed to use two or more

telescopes to create images that have the same resolution as a large one. Although radio waves are invisible to human eyes, they are applied in AM and FM broadcasting technologies, wireless networks, GPS receivers, satellite communication, etc.

5. What is the refraction index and what kind of information give us about the electromagnetic waves behavior? The refractive index of a substance is the ratio between the speed of light in vacuum and the phase velocity of an electromagnetic signal in a specific medium. It is represented by the letter n. this being a dimensionless value. 𝑛=

𝐶0 𝑉𝑃

The refractive index of a medium is a measure to know how much the speed of light (or other waves such as acoustic waves) is reduced within the medium under study. What is a plane wave and a non-plane wave and where are they used? What is a magnetic and a nonmagnetic medium and where are they used? Flat wave: It is an Electromagnetic wave in which the electric and magnetic fields remain in a plane perpendicular to the direction of propagation, and the magnetic field strength (multiplied by the impedance of space) and the electric field strength are equal.

Non flat wave: It is a wave whose equal phase points are not found in a plane in space. the non-flat waves are: Spherical and cylindrical waves: Spherical waves:

The wave fronts are concentric spheres, centered at the point where the disturbance originated. Naturally, there are non-elementary spherical waves in which the amplitude or intensity is not the same in all directions, because the source of disturbance produces different effects, depending on the direction. Such is the case, for example, with the sound wave coming from a cornet or with the EM waves radiated by directional or sectorial antennas, used in cellular telephony, in which the "Directivity" (relation between the maximum power density and the power density). average on a sphere) is a parameter ≥ 1 that measures the degree of anisotropy of the radiation. In the socalled "far-field" region, the EM waves radiated by an antenna are assumed to be spherical, which behave locally as flat .

Cylindrical waves:

Wave fronts are surfaces parallel to a line. In elementary cylindrical waves the fields depend only on the distance ρ to a reference axis. Magnetic medium: The magnetization of a material depends on the applied magnetic field. However, unlike dielectrics, which all respond in the same way (although to a greater or lesser extent) to an external electric field, the materials respond differently to magnetic fields. Therefore, they can be classified in different types:

Diamagnetic: They are materials (mercury, silver, lead, water) in which there is a very weak magnetization that goes in the opposite direction to the applied magnetic field. This causes them to be repelled by the magnets (but very slightly)

Paramagnetic: They are materials (aluminum, gold, magnesium, air, palladium) that when an external magnetic field is applied, a very weak magnetization appears in them in the same sense of the applied field.

Ferromagnetic: They are metallic materials (iron, Cobalt, Nickel.) That can present a magnetization in the absence of external field (magnets) and that respond to external fields with a high additional magnetization in the same sense of the applied field. Ferrimagnetic or ferrite (iron ferrite) They are oxides such as magnetite that have magnetic properties similar to ferromagnets, although as they are oxides they have a much lower electrical conductivity than ferromagnetic ones, which are metals.

Non-magnetic medium: It does not affect the age of the magnetic field lines. Example: the vacuum. Choose one of the followi

6. What is a plane wave and a non-plane wave and where are they used? What is a magnetic and a nonmagnetic medium and where are they used? A flat wave or also called one-dimensional wave, is a wave of constant frequency whose wave fronts are parallel planes of constant amplitude normal to the velocity vector, they propagate in a single direction along the space and an example are the waves in the springs or on the strings, another uses the field produced by an antenna that is approximately flat in a far field region. A non-planar or spherical wave is a three-dimensional wave whose wavefronts for an observer at rest are concentric spheres. An example of these are the waves in the water produced by a disturbance of a specific object When the magnetic field and the electromagnetic field are perpendicular to the direction of propagation, they have the same magnitude and phase in planes orthogonal to it, this being in the presence of a flat electromagnetic wave. For its analysis it is enough to know the shape of the electric field since the magnetic field is easy to extract from Maxwell's equations. The flat wave is more used to study models of electromagnetic phenomena, since from its form, the different scenarios and phenomena that can be presented in a study can be modeled easier, less information is needed, and it is easier to model.

Choose one of the following problems, solve it and share the solution in the forum. Problem 1 Developed by: FILADELFO ATENCIO A dissipative medium has the following parameters: 𝜀𝑟 = 4.5, 𝜇𝑟 = 1.2 and 𝜎 = 1.2 𝑆/𝑚 Find the wavelength and the amount of wavelengths that will penetrate a 6MHz signal. Solution: Parameters

𝜀𝑟 = 4.5 𝜇𝑟 = 1.2 𝜎 = 1.2 𝑆/𝑚 6MHz signal Loss tangent: 𝜎 1.2 10000000 = = = 502.53 𝜀 ∗ 𝜔 ∗ 𝜀0 4.5 ∗ (6.03 ∗ 107 ) ∗ (8.8 ∗ 10−12 ) 19899

𝛿=

𝜔 = 2𝜋𝑓 = 2𝜋 ∗ (6 ∗ 106 ) = 12000000𝝅 = 37699111.843 𝛽 = 𝑗√𝜋𝑓𝜎𝜇0 = 𝑗√𝜋 ∗ (6 ∗ 106 ) ∗ (1.2) ∗ (4𝜋 ∗ 10−7 ) = 𝜆=

2𝜋 𝛽

=

2𝜋 6𝜋𝑗 5

5

= 3𝑗 m

𝛼 = √𝜋𝑓𝜎μ0 = √𝜋 ∗ (6 ∗ 106 ) ∗ (1.2) ∗ (4𝜋 ∗ 10−7 ) = 𝛿𝑝 =

1

1

100

= 5.33 = 533 = 0.1876 𝑐𝑚 𝛼

𝛿𝑝(𝜆) =

0.1876 5 3𝑗

6𝝅√2𝑗 5

1407

= 12500𝑗

6𝝅√2 5

= 5.33𝑁𝑝/𝑚

Problem 2 Developed by: ALEXANDER DE ARMAS In a medium with the following characteristics: 𝜀𝑟 = 4, 𝜇𝑟 = 1.6 and 𝜎 = 2.3𝑥10−4 𝑆/𝑚 Find these parameters for a 300MHz signal: a. Loss tangent. b. Propagation constant. c. Phase velocity. d. Wavelength. e. Index of refraction. Explain the meaning of each found value.

Solution: Development Parameters: εr = 4 μr = 1.6 σ = 2.3x10−4

S m

f = 300MHz

Loss tangent. first the angular frequency is calculated 𝜔 = 2𝜋𝑓 = 2𝜋 ∗ 3 ∗ 108 𝐻𝑧 = 1884955592.15388 then the absolute electrical permittivity is calculated 𝜀 = 𝜀𝑟 ∗ 𝜀0 where 𝜀0 is the electric permittivity of the vacuum 𝜀0 = 8.8541878176 ∗ 10−12 𝜀 = 4 ∗ 8.8541878176 ∗ 10−12 = 3.54167512704 ∗ 10−11 Now the lost tangent is calculated σ σ Tan (δ) = δ = Tan−1 ( ) ωε ωε σ Tan (δ) = ωε Tan (δ) =

2.3x10−4 1884955592.15388 ∗ 3.54167512704 ∗ 10−11

Tan (δ) = 0.0034452281852 σ δ = Tan−1 ( ) ωε δ = Tan−1 (

2.3x10−4 ) 1884955592.15388 ∗ 3.54167512704 ∗ 10−11

𝛿 = 0.197396253° With these values, it is evaluated in the table to determine the characteristics of the medium. MEDIUM

Tan(δ)

δ

Not dissipative

Tan(δ) = 0

0°

Low loss dielectric

0 < Tan(δ) <= 0.1

0° < δ <= 6°

Dielectric with losses

0.1 < Tan(δ) < 10

6° < δ <= 84°

Good drivers

Tan(δ) >= 10

δ >= 84°

Perfect drivers

Tan(δ) >>> 10

δ = 90°

The characteristic medium is low loss dielectric.

Propagation constant. 𝜇𝑟 = 1.6 𝜇0 = 4𝜋 ∗ 10−7 𝜇 = 𝜇𝑟 ∗ 𝜇0 = 1.6 ∗ 4𝜋 ∗ 10−7 𝜇 = 2.0106192982975 ∗ 10−6 𝜀 = 3.54167512704 ∗ 10−11

𝛾 = 𝑗𝜔 ∗ √𝜇𝜀 𝛾 = 𝑗 ∗ 1884955592.15 ∗ √2.01 ∗ 10−6 ∗ 3.54 ∗ 10−11 𝛾 = 15.90𝑗

Phase velocity. 𝑽𝒑 = 𝑉𝑝 =

𝟏 √𝝁𝜺 1 √2.0106192982975 ∗ 10−6

𝑉𝑝 = 118503374.077681

∗ 3.54167512704 ∗ 10−11

𝑚 𝑠

Wavelength. 𝜆=

𝑉𝑝 𝑓

𝑚 118503374.077681 𝑠 𝜆= = 0.3950112469256 𝑚 3 ∗ 108 𝐻𝑧 𝜆 = 0.3950112469256 𝑚

Index of refraction. 𝑛=

𝐶0 3 ∗ 108 𝑚/𝑠 = = 2.53 𝑉𝑃 118503374.077681 𝑚/𝑠

𝑛 = 2.53

Explain the meaning of each found value. Loss tangent 𝑇𝑎𝑛 (𝛿) = 0.0034 𝛿 = 0.197°

It is the relation between the conduction current (𝐽 = 𝜎𝐸) and the displacement current (𝐽𝑑 =

𝑑𝐷 ) 𝑑𝑡

in a specific medium; this value depends on the parameters of the medium and the

frequency of the applied signal.

In conductive materials it tends to be very high 𝑇𝑎𝑛 (𝛿) → ∞; while in dielectric media the behavior is opposite 𝑇𝑎𝑛 (𝛿) → 0. The value of the loss tangent is a measure of the quality of an insulation; the lower the conduction current compared to the displacement current, the better the quality of the electrical insulation.

Propagation constant 𝛾 = 15.9𝑗 The propagation constant of a sinusoidal electromagnetic wave is a measure of the change experienced by the amplitude and phase of the wave as it propagates in a given direction. The quantity that is measured can be the voltage, the current in a circuit or a field vector, such as the electric field strength or the flux density. The propagation constant measures the change per unit length, but has no dimensions.

Phase velocity 𝑉𝑝 = 118503374.077 𝑚/𝑠 Is the speed at which the phase of the wave propagates in space. The phase velocity is given in of the wavelength λ (lambda) and the time period T. 𝜆 𝑇 The velocity of propagation can be measured as the time necessary for a zero crossing or a 𝑉𝑝 =

maximum of the signal to occur again at the same point in space.

Wavelength 𝜆 = 0.395 𝑚 It is the real distance that a wave travels in a certain interval of time. That time interval is the interval between two consecutive maximums of some physical property of the wave. Index of refraction 𝑛 = 2.53 It is the relationship between the speed of light in vacuum and the phase velocity of an electromagnetic signal in a specific medium. It is represented by the letter n. Because the phase velocity in any medium is less than the speed of light in a vacuum, the refractive index of a substance is always an amount greater than or equal to 1 (𝑛 > = 1)

Exercise 5 Developed by: LUIS ALFREDO PALACIO

For a 1GHz signal, traveling in seawater find the attenuation per length unit. How long does the signal have to travel, in order to have an attenuation greater than 3dB? the attenuation constant is: 𝛼 = √𝜋 ∙ 𝑓 ∙ 𝜇 ∙ 𝜎 So, for the sea water it is: 𝜎=4 𝜇=1 𝑓 = 1𝐺𝐻𝑧 We substitute and solve: 𝛼 = √𝜋 ∗ (1) ∗ (1) ∗ 4 𝛼 = √4𝜋 = √12.57 𝛼 = 3.54 𝑁𝑝/𝑚 The wave for an attenuation of 3dB is: 𝑒 𝛼𝑧 =

1 2

𝑒 −𝛼𝑧 = 2 𝑧=

1 𝛼 ∗ ln(2)

𝑧 = 1.51𝑚𝑚

CONCUSIONS

The investigation and realization of this work has led us to the following conclusions:

- It is important to appropriate the concepts and skills necessary to solve the problems raised for this activity - It was understood that in order to characterize a medium, it is very important to know the tangent of losses - The required variables were identified to find the depth of penetration of a signal such as conductivity, electrical permissiveness and magnetic permeability - It was realized that as the conductivity of a material decreases the depth of penetration increases.

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