Trabajo_Final.docx

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD

ESCUELA DE CIENCIAS BASICAS, TECNOLOGIA E INGENIERIA

Teoría Electromagnética y Ondas_203058A_46

Step 5

Presenta IRMA JANETH CRUZ ANDERSSON HISNARDO PLATA SANGUINO HAROLD ALVARO GARCIA DEIBI FABIAN MUÑOZ

Tutor  OMAR LEONARDO LEYTON

Norte de Santander Mayo 2018

INTRODUCCTION

This work covers the 3 units which are based on plane and guided waves, transmission lines and phenomena such as reflection and refraction. The development focused on the conceptual and mathematical bases necessary to understand basic topics in courses such as antennas and microwaves.

Activities to develop

In this activity, the group will have to solve some practical problems using as a reference the following image.

http://www.scientechworld.com/education-software-training-and-skilldevelopment/wireless-communication/understanding-wireless-sensor-network  Retrieved

from:

Taking into account the image, solve the following problems:

1. If the signal frequency used to send the sensed parameters from the water monitoring system to the reception point is 6 MHz. how deep could the wireless transmitter be placed? How does the water behave at this frequency? Find  and  . Explain how these values could be used in the practice.

 Υ,,,   = 3 ∗10/  = 361  ∗ 10−/  = 4 ∗10−/

 = 120  377ℎ Conductividad agua dulce 10− Permitividad agua dulce  81 Permeabilidad Magnetica  = 1 First, the following contasts are considered:

 = 4 ∗10−/  = 1  = 361  ∗ 10−/  = 81  = 10−

 is found in the following way:  = √ 1 1  =  (4 ∗ 10−) ∗ (1) ∗ 361  ∗ 10−∗ (81)

The phase velocity

 = 33333333,3 / The wavelength λ is found by finding the wave number k for 6MHz:

 =    2 ∗6 ∗10  = 33333333,3

 = 1,1309733  = 2 2  = 1,1309733  = 5,5  Υ

The propagation constant  is found by means of the tangent of losses in the following way:

tan =  − 10 tan = 2 ∗ 6∗ 10 ∗  1  ∗ 10−∗ (81) 36 tan =0.03703703 " =  − 10 " = 2 ∗6 ∗10 " = 2.6525 ∗10− " ′ = tan  −   2 . 6 525 ∗10 ′ = 0.03703703  = 7.1619 ∗10−  Υ = √ 

 Υ =  ∗2 ∗ 6 ∗ 10√ (4 ∗ 10−) ∗ (1) ∗ 7.1619 ∗ 10−  2.6525 ∗10−  Υ =  ∗ 2 ∗ 6 ∗10√ (4 ∗10−) ∗ (1) ∗ (7.1619 ∗ 10−  2.6525 ∗10−)  Υ =  ∗2 ∗ 6 ∗ 10√ 8.9999 ∗10−  3.3332 ∗ 10−)  Υ =  ∗2 ∗ 6 ∗ 10 ∗ (3.0004 ∗10−  5.5544 ∗ 10−)  Υ = 0.02093  1.1311 Therefore α and β will be respectively:

 = 0.02093 Nep/m   ó  = 1.1311 /    And the maximum depth of the transmitter in the water will be:

 = 1  = 1.11311  = 0.884

=

2. If the medium has the following electromagnetic characteristics: , y . Find the losses per length unit, take into account the given frequency for the signal, how long must travel the signal to have more than 3dB of attenuation?

10− /  = 1  = 1

tan =  − 10 tan = 2 ∗6 ∗ 10 ∗  1  ∗ 10−∗(1) 36 tan =0.3

 =  − 10  = 2 ∗6 ∗10  = 2.6525 ∗10−   = tan −   2 . 6 525 ∗10  = 0.3  = 8.8419 ∗10− y = √  y =  ∗2 ∗ 6 ∗10√ (4 ∗10−) ∗ (1) ∗ (8.8416 ∗ 10−  2.6525 ∗10−) y =  ∗ 2 ∗6 ∗10√ 1.111 ∗10−  3.3332 ∗ 10−) y =  ∗2 ∗ 6∗ 10 ∗ (3.3696 ∗ 10−  4.9458 ∗ 10−) y = 0.0188 0.12703  = 0.0188 Nep/m % perdidas = 1 e−  

Propagation constant

Dimmer constant

% perdidas = 3.70% The attenuation is calculated in descibeles

/ = 8.68  / = 0.164 To have an attenuation greater than 3db the signal must travel a distance of

/ X = 3db

X =  3 / X =  3 0.164 X = 18.34

Er= E= σ= Ur= U= f= ω=

1  

σ ω*E

Tang (δ) =

=

0.3

=

0.126

8.84194E-12  

0.0001

Sm/m

y=

j

1  

6  

β =

1.25664E-06

MHz

β =

37699111.84

0.126

rad/m

376.99

Ω

0.0188

Np/m

n= n=

α= α= Perdidas por unidad de l ongitud x = 1m x= m   1.00 % Perdidas = % Perdidas =

Se càlcula la atenuaciòn en descibeles

3.70

%

αdB/m = αdB/m =

 

-0.164

Para tener una atenuacion superior a

3

db, la señal de be recorrer una

αdB/m X=

-3

db

X=

-3

X=

-3.00 -0.164

X=

18.34

db αdB/m

m

 = 300Ω

3. In the buildings have an intrinsic impedance of   and the signal has a power of . Fin the reflected and transmitted power to the buildings. Air impedance Intrinsic impedance

Reflection coefficient Reflectance Transmittance Reflected power Transmitted power

100/  = = 120  300Ω 

r =  −+ = − + = 0.114 < 180 R = || = 0.114 = 0.0129 = 1.29% T = 1   = 1  1.29% = 98.71% |−| = 1.29% ∗100/2 = 1.29/2 + = 98.71% ∗100/2 = 98.71/2

Coeficiente de reflexiòn

Γ=

N1 =

120

N2 =

300

P= R= T=

100.00

Impedancia del aire

p

Impedancia intrinsica mW/m2

Potencia Reflactancia Transmitancia

-

Potencia reflejada

+

Potencia transmitida

| P1  | = | P1  | =

Γ=

N2 - N1

-76.99

=

N2 + N1

Γ=

-0.114

R= R=

|Γ| 1.29%

%

T=

1- R

=

2

676.99

<

180.00

=

0.0129

°

98.71%

| P1  | =

-

1.29%

*

100.00

mW/m2

=

1.29

mW/m2

+

98.71%

*

100.00

mW/m2

=

98.71

mW/m2

| P1  | =

75Ω

4. A near monitoring station has put  coaxial transmission line with a length of 20 m and is terminated with an antenna of . If the relative permittivity of the line is 2.56 and the frequency is 3.0 GHz, find the input impedance to the line, the reflection coefficient at the load, the reflection coefficient at the input, and the SWR on the line. Impedancia de entrada

 =     tan(ℓ) tan(ℓ) Donde

 = 50Ω

37.5  78Ω

ℓ = 20   = 310  = 37.5  78Ω   2    2    2  ∗ 310  =  =  = 310 = 

ℓ = 2 ∗20 = 40

 Es una linea de

40  

(ℓ)  =     ttanan(ℓ) )(tan40)(20))   = 5050(37. (537.578 78 )(tan40)(20)  = 2.6  0.50 Coeficiente de reflexion

   Z    Z   3 7. 5  78  310   Γ = Z  Z = 37.5  78  310 = 5.8  10.42 = 0.63.

SWR

 = 11  = 11 0.0.6633 = 4,40

5. In the monitoring station, there is a radio transmitter connected to an antenna having an impedance  with a  coaxial cable. If the  transmitter can deliver  when connected to a  load, how much power is delivered to the antenna?

50

80  40 30   = (1 |Γ|2) 

50

50

El coeficiente de reflexion en la carga es

40  50 =  30  40 Γ =     = 8800  40  50 130 40  4000 Γ = 550018500 Γ = 0.297  0.216 Donde |Γ |  = (0.297)  (0. 2 16)  = 0.134 La Potencia Resulta

 = (1 |Γ|)  = (1 0.134) ∗ 30 = 25.98

CONCLUSIONS

Se abarcaron las temáticas estudiadas en las unidades 1, 2 y 3, donde se trataron los temas, Electrodinámica y ondas, Ondas en medios abiertos y cerrados y Ondas electromagnéticas en medios guiados y radiación. Se desarrollaron 5 ejercicios donde se abarcan los temas anteriormente mencionados, así mismo se baso su desarrollo en las referencias compartidas por el curso.

REFERENCES 











Gutiérrez, W. (2017). Loss Tangent [Video]. Retrieved from http://hdl.handle.net/10596/13139 ́ Quesada-Pe rez, M., & Maroto-Centeno, J. A. (2014). From Maxwell's Equations to Free and Guided Electromagnetic Waves: An Introduction for First-year Undergraduates. New York: Nova Science Publishers, Inc, 49-80 Retrieved from http://bibliotecavirtual.unad.edu.co:2051/login.aspx?direct=true&db =nlebk&AN=746851&lang=es&site=eds-live&ebv=EB&ppid=pp_49 Chen, W. (2005). The Electrical Engineering Handbook. Boston: Academic Press, 519-524. Retrieved from http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebs cohost.com/login.aspx?direct=true&db=nlebk&AN=117152&lang=es &site=ehost-live&ebv=EB&ppid=pp_519 Chen, W. (2005). The Electrical Engineering Handbook. Boston: Academic Press, 525-551. Retrieved from http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebs cohost.com/login.aspx?direct=true&db=nlebk&AN=117152&lang=es &site=ehost-live&ebv=EB&ppid=pp_525 Joines, W. T., Bernhard, J. T., & Palmer, W. D. (2012). Microwave Transmission Line Circuits. Boston: Artech House, 23-68. Retrieved from http://bibliotecavirtual.unad.edu.co:2051/login.aspx?direct=true&db =nlebk&AN=753581&lang=es&site=eds-live&ebv=EB&ppid=pp_23 Hierauf, S. C. (2011). Understanding Signal Integrity. Boston: Artech House, Inc. Chapter 6, 7, 11. Retrieved from http://bibliotecavirtual.unad.edu.co:2051/login.aspx?direct=true&db =nlebk&AN=345692&lang=es&site=eds-live&ebv=EB&ppid=pp_49