Step 2 To recognize the electrodynamic and waves applications
Group: 203058_24
Vladimir Paredes Álvarez Selected item 1. JOSE ANGEL BOSSA DIAZ Selected item 2 Alexis Mina Selected item 3. Ricardo Cordoba Selected item 4 . Alexis Pedroza Selected item 5. .
UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA
“
UNAD”
–
School of Basic Sciences, Technology and Engineering Electromagnetic Theory and Waves 2019 16-01
Introduction En el siguiente documento, se desarrollara desarrollara la temática de la propagación de la onda electromagnética en diferentes medios, analizando así como las condiciones del medio de propagación propagació n afectan a la onda y al mismo tiempo a su transmisión, pudiendo observar diferentes clasificaciones clasificaciones de medios que por sus propiedades condicionan condicionan la transmisión de la onda electromagnética por estos y analizando diferentes conceptos generados, como atenuación, tangente de perdida, velocidad, refracción y profundidad de penetración.
Developed activity (consolidate) 1. Explain the concept of "loss tangent" applied to electromagnetic wave propagation media, and indicate how it is calculated. R//. The “loss tangent” : Also known as tan delta, is the relationship between the conduction current and the displacement through a specific medium, this relationship is constant and depends on the parameters of the medium and the frequency of the signal that apply to you The equation used to calculate it is:
tan= ∗
2. According to the "tangent of losses", how can the means of propagation be classified? R//. Basic classification for media based on the “tangent of losses ”:
Perfect dielectrics
Perfect drivers
Good insulators
Good drivers
Dissipative dielectrics
3. What concept does each of the means of propagation defined in the previous point have? R//. Concepts of each of the means of propagation: Perfect dielectrics: they do not present conduction current, therefore, they do not have losses due to Joule effect.
Tan=0⟹=0 Tan→∞⟹= Tan→0+ ⟹→0+
Perfect conductors: they do not present polarization polarization current, therefore, they do not have capacitive effects or load accumulation.
Good insulators: they present conduction current and have losses due to Joule effect, but this effect is almost negligible compared to the capacitive effect, they are also called "low loss dielectrics".
Good conductors: they present polarization current, therefore, they have capacitive or or load accumulation effects, but the conduction current and J oule losses are much more significant.
Dissipative dielectrics: they have both effects and none is negligible negligible compared to the other.
Tan→∞⟹→ 0<<
4. On what does the propagation velocity of an electromagnetic wave depend? R//. The phase velocity of electromagnetic waves depends only on the electromagnetic properties of the medium in which they propagate pro pagate 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 year 1905, by Albert Einstein. The phase velocity of an electromagnetic wave in a non-dissipative medium is:
= √ √ 1 = 1 =3×10 ⁄
The speed of electromagnetic waves in vacuum is a universal constant whose value turns out to be equal to the speed of light and is determined by: What is the relationship between the speed of propagation and the refractive index of a medium? R//. The refractive index of a substance is the ratio between the speed of of light in vacuum and the phase velocity of an electromagnetic signal in a specific medium is represented by the letter n and is given by:
=
Because the phase velocity in any medium is less than the speed of light lig ht in vacuum, the refractive index of a substance s ubstance is always an amount am ount greater than or equal to 1 In the case of perfect non-magnetic dielectrics, the refractive index remains:
= ⟹ = √ √ ⟹ =
5. What is the penetration depth of an electromagnetic wave in a medium and how can I calculate it?
= 1
R//. The penetration depth of a wave is the inverse of the attenuation constant. Since the power of a signal is i s proportional to the square of its amplitude, when the signal drops to 36% of its value, its power drops to 13%.
Conclusiones Exercises (one per student) 1. Student name: Vladimir Paredes.
A dissipative medium has the following parameters:
=3.5 =2.2 = 1.9 // ,
and
Find the wavelength and the amount of wavelengths that will penetrate a 10MHz signal.
Solución Para calcular la longitud de onda primero se debe calcular la velocidad a la que se desplaza la onda y como conocemos las propiedades del medio la velocidad que calculamos se conoce como velocidad de fase
Pero nos dan solo el
= √ √ 1 = 3.5 = 2.=2 ∗ − ∗3.5 =8.=3.8541∗10 − 0 =989∗10 ∗ − =1.25663∗10 ∗2.2 y el
por lo que debemos calcular el y el
=2.7645∗10− = √ √ 1 = √2.7645∗10−1∗3.0989∗10− 1 − = √8.5670∗10 1 − = 9.2557∗10 =108.04∗10 /
Remplazamos los valores en la formula inicial
Con la velocidad de fase se puede calcular la longitud de onda con la formula
= 108. 0 4∗10 = 10∗101/ /
Remplazamos los valores y nos queda
=.
Para la segunda pregunta que tiene que ver con la profundidad de penetración, lo primero que debemos hacer es clasificar el medio para saber con cual formula trabajar Como vimos anteriormente los medios se clasifican con la tangente de perdida y su fórmula es
= ℴ / − = 2∗3.1.09989∗10 = 62832000∗3.1.9 /0989∗10− 9 / − = 1.91.471∗10 =975.80
Remplazamos
Como vemos que la tangente de perdida es tan grande gran de podemos afirmar que se trata de un conductor perfecto Como ya sabemos que es un conductor perfecto podemos usar la formula
= 1 == == 1 = 1 −) ∗10∗10 = 3.3.1416∗1.9∗(∗ (1.1.25663∗10 = 751 =0.01333
Teniendo en cuenta que
Remplazamos
=. 2. Student name: Jose Angel Bossa.
1.810− /
In a medium with the following characteristics, find these parameters for a 1GHz signal: a. Loss tangent. b. Propagation constant. c. Phase velocity. d. Wavelength. e. Index of refraction.
=2,5 =1.3 = ,
Explain the meaning of each found value.
a) Loss Tangent:
Be
− / =1. 3 ∗ =1. 6 336310 =2. 5 ∗ =2.2135510− / =tan1.8−10−∗ [/] =tan− (2∗110[])∗(2.2135510− [ ]) =tan=0.−70.4°01294
This angle means that material is a dielectric. b) Propagation Constant:
As the material is a dielectric, the Attenuation constant can be write as
= ∗√ √ ∗
and
And the Phase Constant as
Thus
0.166295 ∗ √ √ 2.2.5 ∗0.012916 ==29. 8 7∗0. 0 12916 = 0.0.3858 385811 // = 2 = 2 ==37.370..71834836629524 // = =0. 3 8581 3 7. 7 834 37.7834 ||=| 0.0|=.38581√ √ 1427. 1 427. 7 342 ||=37.7854
The change measure of the phase and amplitude of wave when its propagated, is 37.7854 37.785 4 c) Phase Velocity
Be
= √ √ −)(2.2135510−) =(2∗110 = (6 2832)83 1851 (851.6336310 − 307) 3 07) 6. 6 . 0 134110 134 110 = 37.37.78338 8338 − = =1.6629510/
Thus
It means that velocity of wave in that specific medium, that is an insulator (dielectric), is approximately a half of speed of light. So, this medium can act as a refraction, reflection or dispersion medium since since it changes the velocity of propagation of EM waves.
d) Wavelength
= = . = 0.0.1662 16629595 = 16.16.6295295
In relation with frequency and wavelength, it can be determinated that this wave corresponds to the Radio Spectrum, specifically to UHF. Thus, this wave changes his phase in 2π ea ch 16.6225 cm. e) Index e) Index of refraction refraction
Be
= √ √ ∗ = = √ √ 1.1.3∗2.=1.5= .8
As said in “Phase Velocity” point, this medium has a refraction characteristic. It is defined
by the index of refraction that has a medium value.
3. Student name: Alexis Mina
1.9
=14.610− /
An open medium has the following electromagnetic characteristics and
=5.5 = ,
Find the power transmitted by a 200MHz signal with a maximum electric field of 127V/m and find the skin depth of the signal. Power transmitted Calculate the loss tangent
− 14. 6 ∗10 Tan()= Tan()= = 2∗2∗10∗5.5∗ 36S/m1 ∗ 10− ∕ Tan() =2.42∗10− it is replaced
η = 8 − 2∗2∗10 2 ∗2∗10 ∗1. 9 ∗4∗10 η = 14.6∗106 2∗2∗10 2∗2∗108∗5.5∗ 361 ∗ 109 η=70.η=217.530.8 〈060085j 9°〉 Ω
Ω
Now the power is determined
(|=| 0) = 2|η| | | 127V/m 1 27V/m = 2|217.217.8| cos(69°69°) =36∕
The initial power transmitted to the medium is
it is replaced
:
Ω
Skin depth of the signal
it can be calculated by the following equation
= |1|
Since we do not have the attenuation constant, it is calculated.
So
= ( ) = = 2∗ ∗ 2 ∗ 10 ∗ 1.9∗4∗107(14.6∗10− 2∗2∗10 ∗5.5∗ 361 ∗ 10−) =0.001617513.5408758 =0.0016175 ∕ = |0.0.00161751 ∕| | ∕ = 61618.8.23 4. Student name: Ricardo Cordoba.
For a medium with the same electromagnetic characteristics than the third problem, find the losses per length unit for a 400MHz signal. If the original signal has an electric field of 120Vrms/m. Find the losses in watts when the signal travels travel s 20m in the medium. Solution: As the statement tells me that the characteristics of the medium are the same as the previous problem, we must bear in mind that: , and The first thing I do is ca calculate lculate the tangent of losses to discriminate the medium mediu m like this: Knowing that: y so:
=5.5 =1.9 =14.610− / / =5. 5 ∗ ∗ 10− ⁄ =2∗4×10 − 14. 6 10 = ∗ ⟹= 2∗4×10 // ∗ 5. 5/∗ 361 × 10− ⁄ =.×−
The medium is a low loss dielectric so the intrinsic impedance is given by:
− 4×10 = ⟹ = 5.5∗ 361 × 10− =.
− 14. 6 10 2∗160.−7495⁄ =.= 2⟹=. ⟹ = ×
The attenuation constant is:
=1 − % =1 −∗.× % =1 %=.=.%
As the losses in units of length are requested,
From the above we can deduce that in this medium for each meter traveled, 0.2% of the power is lost. Therefore if a 20m run is made:
− % =1 −∗∗.× % =1 %=.=.%
| ⁄ | 120 1 20 = |160.160.7495|495| ⟹ =. ⁄ ∗ 0.0.0458 =. =89.58⁄ 0⁄ 45833
Now the initial power is:
The losses therefore are:
5. Student name: Alexis Pedroza.
For a 400MHz 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? 5. Para una señal de 400MHz, viajando en agua de mar, encuentre la atenuación por unidad de longitud. ¿Cuánto tiempo tiene que viajar la señal para tener una atenuación mayor que 3dB?.
Solucionando: 1.
Tangente de Perdidas:
Siendo: Ɛ0= 8,8541878
x 10 -12
∗=8∗10 =4
= Ɛr =
80
708,33 x 10-12 = 4x108 Hz =2
Ɛ = Ɛr * Ɛ0 =
∗=1.78 tan(n() = 1.478 =2.25 tan−(2.2.25)5) =66,04 Tan(Ᵹ ) = 2.25
Para este ejercicio tenemos un medio dieléctrico disipativos.
Calculo de permeabilidad:
= ∗
= , − = =,−
= ( ) == 1.78 == (1.1.25710−) (25.25.13310 ) =3158,841
Obteniendo la propagación Constante, para dieléctrico disipativos.
= 3158. 3158.841(41.78)
Siendo A= 64.059 atenuación constante. B= 98.62 i
Se tiene:
=64, = 98.60259
para la atenuación constante.
La atenuación en decibeles por unidad de longitud queda de la siguiente manera:
= 8.68 = 556.032
Para tener una atenuación mayor mayor de -3dB, la señal debe recorrer una distancia de:
3 = 3 = 3 = 556.032 =5.3910−
Conclusions (one per student) Conclusion 1: Student name Conclusion 2: Student name Conclusion 3: Student name Conclusion 4: Student name Conclusion 5: Alexis Pedroza, los medios físicos donde se propaga o transmite una señal u onda, influyen en la señal de todas las formas, pudiendo afectar el tiempo de transmisión, los datos transmitidos y la distancia de recepción de la misma. Por lo tanto, analizar esto permite que la transmisión de señales en las comunicaciones comunicaciones electrónicas sea efectiva y se conozca con anterioridad sus limitaciones. Pudiendo conocer el campo de cobertura y todas sus atenuaciones. ... The conclusions should be written with their own words and should focus on the concepts explored, learned, discovered discovered and practiced in the development of the activity, it is suggested to present a conclusion by topic, the result of learning obtained as evidence of conceptual assimilation. To obtain a good writing it is suggested to read the written several times, correcting and adjusting the text until obtaining a clear and coherent postulate. Avoid superficiality and simplicity.
References (one per student) Bibliography 1: JOSE ANGEL BOSSA
Wiley J. & Sons Ltd. (2003). Electromagnetic Wave Propagation. Fixed Broadband Wireless. 25-70. Retrieved fromhttp://bibliotecavir from http://bibliotecavirtual.unad.edu. tual.unad.edu.co:2048/login co:2048/login?url=http://searc ?url=http://search.ebscoho h.ebscohost.com/l st.com/l ogin.aspx?direct=true&db ogin.aspx?di rect=true&db=aci&AN=145 =aci&AN=14505422&lang= 05422&lang=es&site=eho es&site=ehost-live st-live Chen, W. (2005). The Electrical Engineering Handbook. Handbook. Boston: Academic Press, 519524. Retrieved fromhttp://bibliotecavir from http://bibliotecavirtual.unad.edu. tual.unad.edu.co:2048/login co:2048/login?url=http://searc ?url=http://search.ebscoho h.ebscohost.com/l st.com/l ogin.aspx?direct=true&db ogin.aspx?di rect=true&db=nlebk&AN=11 =nlebk&AN=117152&lang=e 7152&lang=es&site=ehos s&site=ehosttlive&ebv=EB&ppid=pp_519
Bibliography 2: Jose Angel Bossa
Wiley J. & Sons Ltd. (2003). Electromagnetic Wave Propagation. Fixed Broadband Wireless. 25-70. Retrieved fromhttp://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.com/login.aspx?direc from http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.com/login.aspx?direc t=true&db=aci&AN=14505422&lang=es&site=ehost-live
Chen, W. (2005). The Electrical Engineering Handbook. Boston: Academic Press, 519-524. Retrieved fromhttp://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.com/login.aspx?direc from http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.com/login.aspx?direc t=true&db=nlebk&AN=117152&lang=es&site=ehost-live&ebv=EB&ppid=pp_519
Bibliography 3: Alexis Mina catedra.ing. (s.f). Obtenido de https://catedra.ing.unlp.edu.ar/electrotecnia/camposyo/PropOndasPlanas.pdf https://catedra.ing.unlp.edu.ar/electrotecnia/camposyo/PropOndasPlanas.pdf wikilengua. ((s.f)). Obtenido de http://www.wikilengua.org/index.php/Terminesp:medida_de_la_tangente_d http://www.wikilengua.org/index.php/Termin esp:medida_de_la_tangente_del_%C3%A1ngulo_de_p%C3%A el_%C3%A1ngulo_de_p%C3%A 9rdidas
Bibliography 4: Ricardo Cordoba
Paz. P, A., (2013). Electrodinámicas y Ondas. Electromagnetismo para ingeniería electrónica (pp. 196-199). Cali, Colombia: Editorial. Sello Editorial Javeriano. Retrieved from: http://www.academia.edu/15 http://www.aca demia.edu/15312004/Electr 312004/Electromagnetism omagnetismo o Bibliography 5: Alexis Pedroza: Alejandro paz parra, 2013. Electromagnetismo para javeriana. ingeniería electrónica, campos y ondas. Pp(197-243).Colombia:
https://es.scribd.com/do https://es.scribd.com/document/364 cument/364143165/Elec 143165/Electromagnetism tromagnetismo-Para-Ingenieria-El o-Para-Ingenieria-ElectronicaectronicaCampos-y-Ondas-1ra-Edicio Campos-y-Ondas-1ra-Edicion-Alejandro-Paz-Par n-Alejandro-Paz-Parra ra …
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