ISSN:
2181-3906
2024
International scientific journal
«MODERN
SCIENCE
АND RESEARCH»
VOLUME 3 / ISSUE 2 / UIF:8.2 / MODERNSCIENCE.UZ
88
PLANE ELECTROMAGNETIC WAVE PARAMETERS.
Muhammad Islomov
Assistant
Jizzakh Polytechnic Institute, Republic of Uzbekistan, Jizzakh.
https://doi.org/10.5281/zenodo.10629568
Abstract. Nowadays, in practice, when it is required to calculate electromagnetic fields,
the use of some mathematical model is of great importance. Because, with the help of this model,
it is possible to express the propagation of electromagnetic waves in real conditions. One of them
is the plane electromagnetic wave model, which can be used to calculate many wave processes.
Let's first understand a little bit about the plane electromagnetic wave. In this, first of all, it is
necessary to learn the concept of wave front or wavy surface.
Keywords: Signal, wave, electromagnetic field, plane waves, homogeneous medium, Plane
electromagnetic wave, amplitude, Vacuum.
ПАРАМЕТРЫ ПЛОСКОЙ ЭЛЕКТРОМАГНИТНОЙ ВОЛНЫ.
Аннотация. В настоящее время на практике, когда требуется расчет
электромагнитных полей, большое значение имеет использование той или иной
математической модели. Потому что с помощью этой модели можно выразить
распространение электромагнитных волн в реальных условиях. Одной из них является
модель плоской электромагнитной волны, которую можно использовать для расчета
многих волновых процессов. Давайте сначала немного разберемся с плоской
электромагнитной волной. При этом, прежде всего, необходимо усвоить понятие
волнового фронта или волнистой поверхности.
Ключевые слова: Сигнал, волна, электромагнитное поле, плоские волны, однородная
среда, Плоская электромагнитная волна, амплитуда, Вакуум.
In practice, when the calculation of electromagnetic fields is required, the use of a
mathematical model is of great importance. Because, with the help of this model, it is possible to
express the propagation of electromagnetic waves in real conditions. One of them is the plane
electromagnetic wave model, which can be used to calculate many wave processes. Let's first
understand a little bit about the plane electromagnetic wave. In this, first of all, it is necessary to
learn the concept of wave front or wavy surface. A wavefront is a surface where the phases of the
field intensity vectors at each point have the same value.
Depending on the shape of the irradiator creating the field, the wavefront can be cylindrical,
spherical, or have another shape. It should also be noted that the wavefront generated by the
arbitrary irradiating system acquires a spherical shape at a very large distance from it. If we take a
deeper look at this situation, we can understand the following. In radio communication lines, in
almost all cases, the receiving antenna is located at a great distance. In this case, if the wavelength
of the field is ten times smaller than this distance, this situation can be considered as long-range
propagation. In practice, this condition is almost always fulfilled.
If we take into account the spherical distribution of the wave front, the receiving antenna
receives a very small part of this front equal to its size. We can always consider a very small part
ISSN:
2181-3906
2024
International scientific journal
«MODERN
SCIENCE
АND RESEARCH»
VOLUME 3 / ISSUE 2 / UIF:8.2 / MODERNSCIENCE.UZ
89
of the sphere to be flat. For this reason, the plane electromagnetic wave model is important. The
wave surface of the monochromatic field generated by the vectors is parallel to each other, or they
call the wave lying in the same plane a plane wave. A plane wave in which the values of the field
vectors are the same at all points of the wave front is called a uniform plane wave.
A plane harmonic electromagnetic wave propagating in an infinite homogeneous medium
can be represented by the following equation
z
k
j
ym
xm
m
e
e
E
y
E
x
E
−
−
+
=
)
1
1
(
The expression for instantaneous values of the field vector has the following form
( )
)
cos(
)
cos(
,
−
−
+
−
=
−
−
z
t
e
E
z
t
e
E
z
t
E
z
ym
z
xm
It is characterized by seven parameters of a plane electromagnetic wave in the state of
propagation in free space. These parameters are written separately for the cases of wave
propagation in mediums with conducting, semiconducting, and dielectric properties. As mentioned
in the previous paragraphs, the classification of the environment according to the conductivity
properties
tg δ
is done through the parameter
а
tg
=
.
1.
The following formulas are the expressions of plane electromagnetic wave parameters.
2.
γ – complex coefficient of wave propagation. This math parameter is used to simplify and
transform expressions
j
+
=
α – attenuation coefficient. This parameter shows the decay of the energy that occurs when
the wave travels a distance of 1 m.
−
+
=
м
tg
а
а
1
1
1
*
2
*
*
2
β – phase coefficient. This quantity represents the angle by which the wave changes its
phase when it travels a distance of 1 m.
+
+
=
м
tg
а
а
1
1
1
*
2
*
*
2
v
f
– phase velocity. This parameter represents the speed of movement of the wavy
surface, in other words, it shows the speed of oscillation of the field vector.
=
с
м
ф
v
g
– group speed. This parameter shows the speed of energy propagation
ISSN:
2181-3906
2024
International scientific journal
«MODERN
SCIENCE
АND RESEARCH»
VOLUME 3 / ISSUE 2 / UIF:8.2 / MODERNSCIENCE.UZ
90
=
=
с
м
d
d
Г
0
λ – wavelength. This parameter shows the distance traveled by the wave during one
complete cycle
м
2
=
Z
c
– characteristic resistance of the environment. This parameter is determined by the ratio
of the complex amplitudes of the field vectors
Ом
H
E
Z
c
=
In the vacuum state, the characteristic resistance of the medium is equal to 120p Ohm.
For real environments, it has a complex character and can be defined as follows
Ом
e
Z
Z
j
c
c
=
(
)
Ом
Z
а
а
c
cos
=
From the above, it can be understood that a flat electromagnetic wave can be
generated only in a limited part of space. However, in solving many practical problems,
the external field is assumed to be completely flat at all points in space.
This facilitates the solution of electrodynamic problems.
REFERENCES
1.
Islomov, M., & Irisboyev, F. (2023). IOT (INTERNET OF THINGS) TECHNOLOGIES
OF INTERNET DEVICES. Modern Science and Research, 2(9), 220-223.
2.
Islomov, M. (2023). CALCULATION OF SIGNAL DISPERSION IN OPTICAL
FIBER. Modern Science and Research, 2(10), 127–129.
3.
Boymirzayevich,
I.
F.,
&
Husniddin
o'g'li,
I.
M.
(2023).
INTERNET
QURILMALARINING IOT (INTERNET OF THINGS) TEXNOLOGIYALARI.
4.
Isaev R.I., Atametov R.K., Radjapova R.N. Telekommunikatsiya uzatish tizimlari. -«Fan
va texnologiya», 2011. — 520 bet.
5.
Sifrovыe i analogovыe sistemы peredachi: Uchebnik dlya vuzov/ V.I. Ivanov, V.N.
Gordienko, G.N. Popov, R.I. Isaev i dr.; Pod red. V.I. Ivanova.- 2-e izd. –M.: Goryachaya
liniya – Telekom, 2003.
6.
ITU-T Manual, 2009, Malkom Jonson. – Optical fiberes, cables and systems. 293 p.
7.
Sklyarov O. K. Volokonno - opticheskie seti i sistemы svyazi: Uchebnoe posobie. 2e izd.,
ster. — SPb.: Izdatelstvo «Lan», 2010. — 272 s.
8.
Islomov, M. (2023). CALCULATION OF SIGNAL DISPERSION IN OPTICAL
FIBER.
Modern Science and Research
,
2
(10), 127-129.
ISSN:
2181-3906
2024
International scientific journal
«MODERN
SCIENCE
АND RESEARCH»
VOLUME 3 / ISSUE 2 / UIF:8.2 / MODERNSCIENCE.UZ
91
9.
Islomov, M., & Irisboyev, F. (2023). IOT (INTERNET OF THINGS) TECHNOLOGIES
OF INTERNET DEVICES. Modern Science and Research, 2(9), 220–223. Retrieved from
https://inlibrary.uz/index.php/science-research/article/view/24108
10.
Islomov, M. (2023). CALCULATION OF SIGNAL DISPERSION IN OPTICAL
FIBER. Modern
Science
and
Research, 2(10),
127–129.
Retrieved
from
https://inlibrary.uz/index.php/science-research/article/view/25048
11.
Mirzaev, U., Abdullaev, E., Kholdarov, B., Mamatkulov, B., & Mustafoev, A. (2023).
Development of a mathematical model for the analysis of different load modes of operation
of induction motors. In E3S Web of Conferences (Vol. 461, p. 01075). EDP Sciences
12.
J.T., M., & F.B., I. (2023). VOLATILE AND NON-VOLATILE MEMORY DEVICES.
Modern Science and Research, 2(10), 116–119.
13.
Ж.
Метинкулов
ИСПОЛЬЗОВАНИЕ
МИКРОКОНТРОЛЛЕРОВ
ДЛЯ
УПРАВЛЕНИЯ НАПРЯЖЕНИЕМ Vol. SCIENTIFIC APPROACH TO THE
MODERN EDUCATION SYSTEM 2 No. 20 (2023):
14.
Ирисбоев, Ф. Б., Эшонкулов, А. А. У., & Исломов, М. Х. У. (2022). ПОКАЗАТЕЛИ
МНОГОКАСКАДНЫХ УСИЛИТЕЛЕЙ.
Universum: технические науки
, (11-3 (104)),
5-8.
15.
Islomov, M., & Irisboyev, F. (2023). IOT (INTERNET OF THINGS) TECHNOLOGIES
OF INTERNET DEVICES.
Modern Science and Research
,
2
(9), 220-223.
16.
Irisboyev, F. (2022). ELEKTR SIGNALLAR KUCHAYTIRGICHLARI VA ULARNING
ASOSIY PARAMETRLARI VA TAVSIFLARI.
Евразийский журнал академических
исследований
,
2
(11), 190-193.
17.
Irisboyev,
F.
(2022).
YARIMO
‘TKAZGICHLI
MODDALARDAN
TAYYORLANADIGAN
KUCHAYTIRGICHLARNING
PARAMETRLARI
VA
XARAKTERISTIKALARI.
Science and innovation
,
1
(A6), 374-377.
18.
Irisboyev, F. B. (2022). ELEKTRON ZANJIRLAR VA MIKROSXEMOTEXNIKA
QURILMALARINING ASOSLARI.
Academic research in educational sciences
,
3
(10),
15-19.
19.
Irisboyev, F. (2024). CLUSTERS OF SELENIUM ATOMS IN THE SILICON
LATTICE.
Ilm-fan va ta'lim
,
2
(1 (16)).
20.
Irisboyev, F. (2024). ASYNCHRONOUS MACHINE TYPES, STRUCTURE AND
PRINCIPLE OF OPERATION.
Ilm-fan va ta'lim
,
2
(1 (16)).
21.
Irisboyev, F. (2023). THE INPUTS ARE ON INSERTED SILICON NON-BALANCED
PROCESSES.
Modern Science and Research
,
2
(10), 120-122.
22.
Boymirzayevich, I. F. (2023). THE INPUTS ARE ON INSERTED SILICON NON-
BALANCED PROCESSES.
23.
Islomov, M., & Nasriddinov, A. (2024). INTERNET NARSALAR OLDIDA BIZNI
NIMA KUTMOQDA.
Ilm-fan va ta'lim
,
2
(1 (16)).
24.
Irisboyev, F. (2022). PARAMETERS AND CHARACTERISTICS OF AMPLIFIERS
MADE OF SEMICONDUCTOR MATERIALS.
Science and Innovation
,
1
(6), 374-377.
