Electromagnetic Waves in Open Media: Propagation Parameters and Characteristics, Ejercicios de Física Matemática

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Task 1 - Electromagnetic waves in open media

Individual work format

DAVID ESTEBAN NIÑO GUERRA

Group 10

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD

Escuela de Ciencias Básicas, Tecnología e Ingeniería

Teoría Electromagnética y Ondas

Activity

Questions: (write with your own words)

1. In the context of electromagnetic waves, what is an open propagation

medium?

The electromagnetic waves do not need a material medium to propagate. This

means that electromagnetic waves can travel not only through air and solid

materials, but also through the vacuum of space.

2. Within the propagation mediums, what is mean by the tangent of losses

The loss tangent is defined as a basic measurement parameter to determine the

behavior of a medium; this can be done since it is a measure of the quality of

an insulation. The loss of tangent can be calculated using the following equation

r

𝑜

3. How is the propagation medium classified from the tangent of losses?

The propagation medium is classified as perfect dielectrics, good insulators,

dissipative dielectrics, good conductors and perfect conductors. Below is a table

with the characteristics of each one.

Media Tan(δ) δ [°]

1. Perfect dielectrics Tan(δ) = 0 δ = 0°
   2. Good insulators 0 < Tan(δ) <= 0,1 0° < δ <= 6°
2. Dissipative dielectrics 0,1 < Tan(δ) <= 10 6° < δ <= 84°
3. Good conductors Tan(δ) > 10 84°< δ < 90°
4. Perfect conductors Tan(δ) >>> 10 δ = 90° 4. What are the propagation parameters of the waves through a medium?

Propagation constant: is a measure of changes in a sinusoidal electromagnetic

wave in terms of amplitude and phase, while propagating through a medium.

This can be a transmission line or free space. The Propagation constant is a

dimensionless quantity.

Attenuation constant: The real part of the propagation constant is the

attenuation constant and is denoted by Greek lowercase letter α (alpha). It

causes a signal amplitude to decrease along a transmission line

Phase constant: it is the imaginary component of the propagation constant.

The phase constant is denoted by Greek lowercase letter β (beta) adds the

imaginary component to the propagation constant.

Exercises development

r

𝑜

− 3

6

𝐻𝑧 ∗ 80 ∗ 8 .8542x 10

− 12

Note that 𝜔 = 2 𝜋𝑓 and 𝜀 = ε

r

𝑜

Calculation:

Figure 1: operation 1 on a virtual scientific calculator.

r

𝑜

𝛿 = tan

2. According to the result obtained in point 1, classify the behavior of the chosen

medium according to one of the 5 options in Table 2 :

Table 2: Classification of propagation media.

Media Tan(δ) δ [°]

1. Perfect

dielectrics

(Not dissipative) Tan(δ) = 0 δ = 0°

2. Good

insulators

(Lost low dielectric) 0 < Tan(δ) <= 0,1 0° < δ <= 6°

3. Dissipative

dielectrics

(Dielectrics with losses) 0,1 < Tan(δ) <= 10 6° < δ <= 84°

4. Good

conductors

(Good conductors) Tan(δ) > 10 84°< δ < 90°

5. Perfect

conductors

(Perfect conductors) Tan(δ) >>> 10 δ = 90°

Interpretation: According to the concept of Tangent of losses, explain the

meaning of the value obtained for 𝑇𝑎𝑛(𝛿).

The loss tangent allows me to identify that sweet water at a frequency of 37MHz

is a good insulator, because its loss value is less than 0.1.

3. According to the classification obtained in point 2 and using Table 3 shown

below, calculate the following propagation parameters of the wave in the

chosen medium:

a. Propagation constant  (gamma).

b. Attenuation constant  (Alpha).

c. Phase constant  (Beta).

Table 3: Propagation parameters in open media.

Parameter

Not

dissipative

Lost low

dielectric

Dielectrics with

losses

Good

conductors

𝑜

𝑜

𝑜

𝑜

𝑟

𝑜

𝑟

𝑜

= 1 .2566x 10

− 6

T m/A

According to the value obtained in the loss tangent for the fresh water medium,

it indicates that the propagation parameters correspond to Lost low dielectric

Attention, for the calculations:

_1. Replace your values (with units) in the equation.

2. Perform the operation on a virtual scientific calculator._ __* _3. Paste the calculator image into the report.
3. Write the answer with your units._

If the image is not included, the exercise rating is 0 points.

__* You can use https://www.geogebra.org/scientific

a. Propagation constant  (gamma).

− 3

Calculation:

c. Phase constant  (Beta).

6

( 1 .2566x 10

− 6

T m/A)( 80 ∗ 8 .8542x 10

− 12

Calculation:

Sweet water

Parameter

Lost low

dielectric

Results

4. According to the results obtained in point 3 and using the following equations,

calculate the propagation characteristics of the wave in the chosen medium:

a. Propagation speed 𝒗

𝒑

𝑝

𝑝

6

𝑝

Calculation:

b. Wavelength 𝝀.

Sweet water

Propagation

characteristics

Equation Results

𝑝

𝑝

Perform the operation on a virtual scientific calculator, paste the image of the

operation on the report, then write the final result including the units.

Interpretation: According to the concepts explored, explain the meaning of the

value obtained for each of the propagation characteristics 𝑉

𝑝

, 𝜆 and 𝛿

𝑝

𝑝

is the speed with which the wave propagates, according to the value obtained

from the sweet water medium, this speed is a little more than ten percent of the

speed of light, this is due to its good insulator characteristic.

𝜆 The wavelength is the distance traveled by a periodic disturbance propagating

through a medium and is directly proportional to the frequency.

𝑝

The depth of penetration indicates the amount of the waves to propagate

through a medium

Example: One of the most common examples that you can see the use of

electromagnetic waves has to do with mobile technology.

Mobile telephony is basically made up of two main parts: a communications

network (or mobile telephone network), which is made up of antennas spread

over the earth's surface, and terminals (or mobile telephones), which allow

access to said net.

Both the antennas and the terminals are emitters-receivers of electromagnetic

waves with frequencies between 900 and 2000 MHz.

Application example

Quesada-Pé rez, M., & Maroto-Centeno, J. (2014). From Maxwell's Equations to

Free and Guided Electromagnetic Waves: An Introduction for First-year

Undergraduates. New York: Nova Science Publishers, Inc. (pp. 46 - 60).

Recovered from

https://bibliotecavirtual.unad.edu.co/login?url=http://search.ebscohost.com/lo

gin.aspx?direct=true&db=nlebk&AN=746851&lang=es&site=eds-

live&scope=site&ebv=EB&ppid=pp_

Chen, W. (2005). The Electrical Engineering Handbook. Boston: Academic Press.

(pp. 513 - 519). Recovered from

http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.co

m/login.aspx?direct=true&db=nlebk&AN=117152&lang=es&site=ehost-

live&ebv=EB&ppid=pp_

Wiley, J. & Sons Ltd. (2003). Electromagnetic Wave Propagation. Fixed

Broadband Wireless. (pp. 25 - 70). Recovered from

http://bibliotecavirtual.unad.edu.co:2048/login?url=http://search.ebscohost.co

m/login.aspx?direct=true&db=aci&AN=14505422&lang=es&site=ehost-live

Gutiérrez, W. (2017). Loss Tangent [Video]. Recovered from

http://hdl.handle.net/10596/

Leyton L., & Quintero, D. (2019). Characterization of electromagnetic waves in

open media. [Video]. Recovered from

https://repository.unad.edu.co/handle/10596/

Telefonia Movil. Aprende Como funciona. (2020). Retrieved 5 October 2020,

from https://www.areatecnologia.com/telefonia-movil.htm

References