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/ = 361 ∗ 10−/ = 4 ∗10−/
= 120 377ℎ Conductividad agua dulce 10− Permitividad agua dulce 81 Permeabilidad Magnetica = 1 First, the following contasts are considered:
= 4 ∗10−/ = 1 = 361 ∗ 10−/ = 81 = 10−
is found in the following way: = √ 1 1 = (4 ∗ 10−) ∗ (1) ∗ 361 ∗ 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 = 310 = 37.5 78Ω 2 2 2 ∗ 310 = = = 310 =
ℓ = 2 ∗20 = 40
Es una linea de
40
(ℓ) = ttanan(ℓ) )(tan40)(20)) = 5050(37. (537.578 78 )(tan40)(20) = 2.6 0.50 Coeficiente de reflexion
Z Z 3 7. 5 78 310 Γ = Z Z = 37.5 78 310 = 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
