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Descripción en teoria y ondas basado en las fases 4 de la universidad
Tipo: Ejercicios
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Electromagnetic Theory and Waves
Task 4 – Electromagnetic waves in guided media
Ivan Dario Gonzalez Gonzalez
Group: 202087724_
Tutor:
Noviembre 2025
Content
Introduction.............................................................................................................. 3
Objectives................................................................................................................ 4
Development of the activity ..................................................................................... 5
Objectives
General Objective:
To analyze the propagation of electromagnetic waves in guided media by calculating
electrical and propagation parameters, interpreting results through mathematical
models, and applying tools such as the Smith chart.
Specific Objectives
To identify and describe the fundamental concepts of transmission lines, including
impedance, VSWR, reflection coefficient, and propagation characteristics.
To solve application exercises involving the calculation of electrical and propagation
parameters in coaxial lines and lossless transmission lines.
To use the Smith chart and complementary digital tools to verify calculated results
and interpret the behavior of guided electromagnetic waves.
Development of the activity
a. What do you understand by transmission line? (Rudra, 2020)
A transmission line is a physical structure designed to guide electromagnetic energy
from one point to another. It ensures that signals, especially at high frequencies,
travel efficiently while controlling losses, reflections, and distortions along the path.
b. Define the electrical parameter of transmission lines: Input impedance 𝑍
(Jordan, 2016)
The input impedance 𝑍
is the effective impedance seen at the beginning of a
transmission line when it is connected to a load. It depends on the line’s length, its
characteristic impedance, and the load impedance, and it determines how a signal
enters and interacts with the line.
c. Define the electrical parameter of transmission lines: Stationary Wave Ratio
(VSWR). (Voltage Standing Wave Ratio Definition and Formula, 2012)
The VSWR is a measure of how well a transmission line is matched to its load. It
expresses the ratio between the maximum and minimum voltages along the line and
indicates the degree of signal reflection. A VSWR close to 1 means excellent
matching and minimal reflections.
d. Define the electrical parameters of transmission lines: Physical length 𝐿and
electrical length ℓ. (Steer, 2011)
The physical length 𝐿refers to the actual measurable distance of the transmission
line. The electrical length ℓ, on the other hand, describes the line length in terms of
the phase shift it produces on a signal and is usually expressed as a fraction of the
wavelength.
௦
௦
ି
ି ଷ
Loss per unit length (surface model):
ᇱ
௦
ᇱ
ି ଷ
ିସ
ି ଷ
Conductance per unit length (dielectric, per 𝜎
ௗ
ᇱ
ௗ
ln (𝑏/𝑎)
ି ଵ
ି ଵ
S/m
Propagation Constant 𝜸 = 𝜶 + 𝒋𝜷
ᇱ
ᇱ
ᇱ
ᇱ
Numerically substituting and evaluating the complex root yields:
𝛼 = ℜ(𝛾) = 0.0063964408436 Np/m
𝛽 = ℑ(𝛾) = 2.7321084850 rad/m
Converted:
dB/m
= 8.686 ⋅ 𝛼 ≈ 0.055559 dB/m
dB/km
≈ 55.56 dB/km
Characteristic impedance 𝒁 𝟎
ᇱ
ᇱ
ି
ି ଵ
Phase Rate 𝒗
𝒑
and wavelength 𝝀
Velocity:
଼
m/s ≈ 0.912ௗ𝑐
Wavelength:
଼
≈ 2.30 m
Skin Depth 𝜹y Comparison with thickness 𝒕
The Skin Depth:
Replacing:
ି
ି
m
6.11096 𝜇m
GeoGebra:
Calculation of Capacitance per Unit Length in Coaxial Line
Note. The image shows a mathematical operation performed on a calculator to
determine the capacitance per unit length C ́.
Figure 4
Calculation of Inductance per Unit Length in Coaxial Line
Note. The image shows a mathematical operation performed on a calculator to
determine the inductance per unit length L'.
2.2 The type of coax that comes closest is: RG-6/U.
Technical justification:
(2.35 mm).
The RG-6/U coaxial cable is one of the most commonly used 75-ohm transmission
lines in radio-frequency and telecommunications applications. It is widely employed
for television distribution, satellite communication, broadband internet, and RF signal
transmission due to its low attenuation over long distances. It consists of a central
copper-clad steel conductor, a dielectric insulator, a metallic shield (normally
aluminum foil and braid), and an outer protective jacket. Its geometry provides an
impedance of 75 Ω, which makes it well suited for high-frequency applications from
a few MHz to several GHz.Because of its relatively small diameter and good
shielding, RG-6/U offers a balance between flexibility, low loss, and high-frequency
performance.
Input Impedance:
The input impedance describes what the source sees looking into the line.
Because the line is long relative to the wavelength, the impedance undergoes
transformations. The calculated value:
tan 𝛽ℓ
tan 𝛽ℓ
tan 𝛽ℓ = tan(2.73𝑥1.2) = tan(3.276) ≈ −0.
Figure 5
Graphical Verification of Parameters in Smith's Chart
Note. The image shows the graphical representation in a Smith Letter to validate
theoretical calculations of input impedance, reflection coefficient, and VSWR.
Participation in the forum:
Conclusions
inductance, capacitance, losses and propagation rate) influence the
behavior of electromagnetic waves in guided media, especially in
coaxial lines.
dimensions demonstrates how these concepts are applied in real
telecommunications systems, where the correct selection and
adaptation of lines is key to minimize losses and optimize transmission.
Smith Chart Online) facilita la resolución de problemas complejos,
agiliza el proceso y brinda una representación visual que
complementa la comprensión matemática
