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Universidad Nacional Abierta y a Distancia – UNAD UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity N°1

Step Step 2- r ecogni cogni ze the electr electrod odynam ynamii c and wav wave es appli applicat catii ons

J ohn J ai ro Vale Valencia ncia R ojas C od: 9432 943264 6428 28

G r oup: up: 2030580_2 2030580_24 4

Tutor Tutor : Wilm Wi lme er H er nán nán Gutié Guti ér r ez

OPEN AND DI STANCE STANCE NATI ONAL UNI UNI VE RSI TY - UNAD Palmi Palmi r a ( V alle) lle) F ebr uar uar y of 20

Universidad Nacional Abierta y a Distancia – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity N°1

Each student in the group has to answer the following questions using academic references to support the research:

1-.) Explain the practical application of the loss tangent with an example.

Calculate the loss tangent of the dry soil at a frequency of 10kHz. Calculate again at 100MHz. Solution:

=10− ⁄ ∈=3 −  1 0 tan()= ∈ = 2∗ 10 ∗3∗ 361 ∗ 10− =60 δ=tan−(60)=89° −  1 0 tan()= ∈ = 2∗ 10 ∗3∗ 361 ∗ 10− =0006 δ=tan−(0.006)=0.3° The dry soil parameters are

There is the lost tangent to 10 kHz

Which gives an angle of losses of:

When you change the frequency to 100MHz, you get:

2.-) What kind of information give us the propagation velocity in electromagnetic waves propagation? 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.


3.-) Explain how an electromagnetic wave behaves in free space, perfect dielectrics and good conductors.

Maxwell's equations give rise to harmonic solutions which were first found by James Clerck Maxwell in 1884. Based on these solutions Maxwell predicted the existence of electromagnetic waves and discovered that signals can be transmitted over long distances without necessarily having physical means for transmission. In the year of 1887, Einrich Hertz discovered the waves predicted by Maxwell and showed that electricity can be transmitted in the form of electromagnetic waves, which propagate at the speed of light and have many of their properties. This is the principle of wireless telephony, radio, TV, telemetry, among many other wonders of modern life. It is possible to find equations that describe the behavior of fields in free space in the absence of volumetric load or electric conduction currents, under these conditions, Maxwell's equations are reduced.

4.-Using the electromagnetic spectrum, explain the practical application of every type of radiation.

Gamma rays have shorter wavelengths than R-Xs. These are the most energetic photons. Although they do not have a clear lower limit for their wavelength, it is usually accepted that they are in the frequency range: 3 EHz
Universidad Nacional Abierta y a Distancia – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity N°1 Radiación visible. Electromagnetic waves whose frequencies are between 4.6 x 1014 Hz and 6.7 x 1014 Hz constitute a region of the spectrum that is of special importance to us, since this radiation is capable of stimulating human vision, since it deals with the light waves or light. This is a very narrow region of the spectrum, so our eyes are not able to perceive most of the radiation that makes up the spectrum. The lower frequencies of the visible radiation give us the sensation of the red color. - By increasing the frequency of the waves we will have successively, those corresponding to the colors orange, yellow, green, blue, indigo, and at the end of the visible region, the color violet.

The Infrared covers the part of the spectrum from approximately 300 GHz (1 mm) to 385 THz (780 nm). It is divided into three regions : Far infrared 300GHz
The lasers are EM radiation in the range, generally, of the visible spectrum (He-Ne laser of 638 nm, Nd-YAG laser of 1.06 mμ, etc.), although they can also be located in infrared (CO2 laser of 30 μm) and even in the ultraviolet. Specific characteristics of laser light is that it is a monochromatic, coherent and collimated light. The applications are innumerable. In dentistry and other medical-surgical specialties, for readersrecorders of CD's and DVD's, etc.

Radio ondas o Radio Frecuencia (RF) refer to the portion of the EM spectrum in which EM waves can be generated by alternating currents that feed an antenna Radios waves are used for data transmission, via modulation, television, mobile phones, wireless networks, commercial broadcasting stations, amateur radio, microwave ovens, etc. Las bandas ELF, SLF, ULF y VLF, en conjunto, se conocen como Audio Frecuencia (AF).

ELF son usadas por la armada de USA para comunicarse con submarinos sumergidos. La banda VLF también se usa con el mismo propósito, pero cuando la nave se encuentra cerca de la superficie (a unos 20 m o menos). SLF es típica en líneas de transporte y distribución (50 o 60 Hz). 10 KHz es frecuente en radionavegación (banda VLF). Cocinas de inducción trabajan en el rango de 25 -40 KHz (bandas VLFLF). Las bandas LF (onda larga), MF (onda media), HF (onda corta) y VHF (FM radio y TV ), son vulgarmente conocidas como Radio Frecuencia (RF). Adem ás de en radiodifusión, otras aplicaciones

Universidad Nacional Abierta y a Distancia – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity N°1 son calentamiento por histéresis dieléctrica – soldadura, fusión y reblandecimiento de plásticos(13,56 MHz - 27,12 MHz - 40,68 MHz), calentamiento por inducción, etc.

UHF, SHF y EHF, popularmente se conocen como Microondas (MO). La telefonía móvil (GSM, DCS y UMTS 14) opera en esta franja del e spectro frecuencial. Otras aplicaciones: hornos microondas (2,45 GHz), radares para control policial de tráfico (10 GHz), radares de aeropuertos (15-100 GHz), Wi-Fi 15, 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. The inverse of the refractive index is also a characteristic parameter of the different means of propagation and is called speed factor: Because the phase velocity in any medium is less than the speed of light in vacuum, the refractive index of a substance is always an amount greater than or equal to 1.

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? Why do we use plane waves to explain practical models associated to electromagnetic phenomenon?

plane wave By extension, the term is also used to describe waves that are approximately flat in a localized region of space. For example, a source of electromagnetic waves such as an a ntenna produces a field that is approximately flat in a far field region. That is to say that, at a distance far from the source, the waves emitted are approximately flat and can be considered as such electrodynamics are used to easily model the behavior of the wave.

non-plane wave magnetic medium it is a device that stores information in the middle of magnetic waves. Magnetic media are hard drives, 3 1/2 "discs, audio cassettes or cassettes.


Choose one of the following problems, solve it and share the solution in the forum. Perform a critical analysis on the group members’ contributions and reply this in the forum.

 =4  =1.6 =2.310− /

In a medium with the following characteristics, find these parameters for a 90MHz signal:     

Loss tangent. Propagation constant Phase velocity. Wavelength. Index of refraction. Explain the meaning of each found value.

Solution

LOSS TANGENT

−  2, 3 ∗ 10 tan() =  = 2∗ 9 ∗4∗ 361 ∗ 10− 2, 3∗ 10−− 1 8∗ 9 ∗ 10  36 2,531441 3∗ 10− 500000000 0.531441 00023 500000000 500000000∗0. 0 0023 531441

,

y


115000 531441 =0.21639 δ=tan− 0.21639=12.4 R/. - tangente de perdida es de

12.4°

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; The IEEE 4002001.20 standard illustrates the basic elements that must be taken into account when evaluating the quality of power cable insulation through the tangent of losses.

PROPAGATION CONSTANT Solution

= (+) =2∗9  =1.6 =2.3+10−  =4 =  2∗9 ∗1. 6 ∗4∗10(2.310− +2∗9 ∗4∗ 361 ∗10−) 531441 +10− ∗2.3) =  2 ∗4∗9 ∗10 ∗1.6(500000000 531441 +10− ∗2.3) =  9 ∗10 ∗12.8(500000000


531441 +10− ∗2.3) =√ 12.8   9 ∗10 (500000000 531441 +10− ∗2. 3)= =√ 12.8 √  9 ∗10 (500000000 = 6.1222 (0.001062882+0.00023) =2 6.1222 =24743080.49 =24743080.49 (0.001062882+0.00023) =7732679.89 (0.001062882+0.00023)  =0.00023    ℎ ℎ =0.001063  attenuation constant

As can be seen in the complete solution, the constant α is related to an attenuation of the amplitude of the wave as a function of distance; while the constant β is related to the phase gain as a function of distance. These are called attenuation constant and phase constant, respectively. The phase constant is measured in radians per unit of length, while the attenuation constant is measured in units inverse to the unit of length.


PHASE VELOCITY. Solution

 = √        ℎ  3∗10   =4  3∗10  = √ 4 =150000000 150000000  where

The phase velocity of electromagnetic waves depends exclusively on the electromagnetic properties of the medium in which they propagate and not on the relative displacement between observers, which clearly violates the laws of mechanics known. This observation gave rise to the so -called special theory of relativity, whose fundamental statement was published, in the y ear 1905, by Albert Einstein.

WAVELENGTH. Solution

=    ∗ = 90∗103 −   = 90000 − =. / . 

Universidad Nacional Abierta y a Distancia – UNAD Escuela de Ciencias Básicas Tecnologías e Ingenierías-ECBTI Curso: Teoria electromagnetica y Ondas Unity N°1 For a constant time, space points that have the same field magnitude are separated by a distance such that the phase gain is equivalent to π radians

INDEX OF REFRACTION. Solution

=   ∗ =    /.

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. 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

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