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Zabontova, T.M. Basics of electrodynamics and distribution of radio waves:
Educational and methodological manual / T. M. Zabontova, E. N. Meat
Cove. - N. Novgorod: Publishing House of FGOU VPO "VGAVT", 2009. - 133 p.

Content:
Static electric and magnetic fields,
Electrostatic field
Permanent electric current
Stationary magnetic field,
Movement of charged particles in permanent electrical and magnetic fields,
Electromagnetic field, Maxwell equations,
The law of electromagnetic induction,
Shift current, Maxwell equations system,
The averaged Equations of Maxwell-Lorenz in material environments,
Boundary conditions for electric and magnetic phones,
Electromagnetic waves in free space,
Flat monochromatic electromagnetic wave,
Polarization of electromagnetic waves,
Spherical electromagnetic waves in free offer,
Radiation of electromagnetic waves by an elementary vibrator,
Electromagnetic waves in homogeneous material environments,
Electromagnetic waves in a homogeneous isotropodielectric,
Electromagnetic waves in an absorption medium,
Dispersion of dielectric constant,
Distribution of packages of electromagnetic waves Group speed,
Energy Transfer Wave Package,
Dispersion and resonant absorption of molecular hydrogen
Electromagnetic waves in plasma,
Parameters of ionospheric plasma,
Electromagnetic waves in a homogeneous isotropic globe,
Electromagnetic waves in a homogeneous magnetoactive plasma,
Falling electromagnetic waves on the border of the section of homogeneous media,
Reflection and refraction of waves from the flat boundary of the section of two environments,
Reflection from perfectly conductive surface
Reflection from a nonideal conductor,
The propagation of electromagnetic waves in a smoothly inhomogeneous medium,
Smoothly inhomogeneous medium, approximation of geometric optics,
Refraction of radio waves in the Earth's atmosphere,
Reflection of radio waves from a layer of inhomogeneous plasma. .
Features of reflection of radio waves from the ionosphere when taking a magnetic field,
Interference and diffraction of electromagnetic waves,
Interference of flat monochromatic waves,
The principle of Guiggens -Frenelle -Kirhgood,
Fraunhing diffraction,
Fresnel diffraction,
Radio filter diffraction on random inhomogeneities of electronic concentration,
Distribution of radio waves in the Earth's atmosphere,
Ideal radiotrass, radio wave ranges,
The effect of the underlying surface on the distribution of radio waves,
Influence of the troposphere on the distribution of radio waves,
Distribution of radio waves in the ionosphere.

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1.1 Electromagnetic field

The electromagnetic field consists of an electric field interdependent with a magnetic field. Electric field represent electrical induction vector, functionally dependent on electric field strength vector . Magnetic field represent vector magnetic induction
, Functionally dependent on the magnetic field strength .

The vectors of the electromagnetic field in general represent a non-stationary electromagnetic vector field, which is the function of coordinates and time:

- electrical induction;

- magnetic induction.

Stationary electromagnetic vector field, is the function of coordinates and does not depend on time:

- electric field strength;

- magnetic field strength;

- electrical induction;

- magnetic induction.

The speed of propagation of electromagnetic waves in a vacuum is equal to the speed of light

c \u003d 3 · 10 8 m / s.

where λ is the wavelength, m;

T - period, p.

Frequency , Hz

c \u003d λF.

Circuit Frequency, C -1

Ω \u003d 2πF.

The larger the length of the electromagnetic wave, the less frequency. Electromagnetic waves begin with a smaller frequency, then radio waves begin with long-standing ranges, long waves, then the average waves with a larger frequency, short, ultrashort waves with even greater frequency. The radio waves follows infrared radiation with a smaller wavelength, but more frequency than that of radio waves. Visible light, begins with red waves. The names of the colors begin with the letters in order of the saying: "Every hunter wants to know where the pheasant sits." Ends visible light with purple waves. Next follow: ultraviolet, x-ray, radiation gamma and cosmic radiation.

The theory of the electromagnetic field is based on vector calculation and vector fields whose most important provisions will be considered below.

1.2 Scalar and Vector Fields

1.2.1 Potential (disgust) and vortex vector fields

Potential (daisy) fieldsstart in the source and end in stock. Vortex (solenoidal) fields do not have sources, always closed, continuous( see Figure[ 4 ] ) .

R isso - potential (dissiot) and vortex field

Circulation vector Potential field on a closed contourL.equal to zero

Flow Vector vortex field through closed the surface S.raven zero

The electrostatic field can only be a potential (disgust), the magnetic field is only vortex.

1.2.2 Gradient scalar field, Hamilton operator

The gradient (differential) of the scalar field φ is a vector showing in which direction the most rapidly increases φ equal to the largest derivative in this direction

Conditional vector or Hamilton operator

The gradient of the scalar field φ, recorded using the Hamilton operator (operator "Nabel")

The surface of the level φ contains the same values \u200b\u200bof φ \u003d const scalar field, therefore the gradient of the scalar field φ is perpendicular to the surface of the level φ and is directed towards the increase φ (see Figure [4]).

Figure - gradient of the scalar field

1.2.3 Divergence (divergence)

Danched vector field at point (x; y; z)

where
- single vectors (orts) in the directions of the axes of the coordinates x, y, z, respectively.

For vector field at point (x; y; z) Divergence (divergence) at point P equal to the stream of vector through the surfaceS, limiting volumeV divided by v when the v to zero

Divergence values \u200b\u200bat pointsP vector fields (see Figure [4]).

Figure - Divergence values

With divergence of greater zero

inside the region V. there are sources of vector field.

With negative divergence

inside the region V there are stocks of vector field.

With divergence equal to zero

from field lines are permeated areaV. or closed (vortex field).

1.2.4 Rotor (whirl)

The rotor (whirlwind) allows you to estimate the degree of rotation at some point (x; y; Z. ) Vector field

where - single vectors (orts) in the directions of the axes of the coordinates x, y, z, respectively.

For vector field at point (x; y; z) Projection of the rotor on the direction of normal to the surface, equal to the vector circulation limit around the circuit C, divided into squareΔ S.surfaces, limited by contour C, when striving Δ S.to zero.

The direction of normal is associated with the direction of bypassing the contour with the rule of the right screw.

Rotor (whirl) vector field using a Hamilton operator

Projections vector
on the axis of coordinates

If at point p the rotor is zero

,

that rotation at this point is not and the vector field is potential.

1.3 Types of charge distribution

Volumetric density of charges, CL / m 3

The charge focused in the volume V, CL

Surface naya density charges, CL / m 2

Charge focused on the surface s, cl

Linea naya density charges, CL / m

The charge of the thread , CL

Shock point charges equal to sum N charges of the ultimate magnitude

1.4 Electric field

Electric displacement vector (electrical induction) equal to the electrical constant ε 0, multiplied by a bracket in which the unit is folded with the electrical susceptibility of χ e, multiplied by the electric field strength vector

Electric constant

Vector electrical displacement (electrical induction) in substance

where ε is an absolute electrical permeability.

Vector electrical induction in vacuum

.

1.5 Magnetic Field

Vector magnetic induction is equal to magnetic constant μ 0, multiplied by a bracket in which the unit is folded with the magnetic susceptibility χ m, multiplied by the magnetic field strength vector

Magnetic constant

Vector magnetic induction in substance

where μ is an absolute magnetic permeability.

Magnetic induction vector in vacuum

1.6 Ohm Law in Differential Uniform

Ohma law for a plot of chain

U \u003d Ir.

Cone density

Express

We integrate by and we obtain the dependence of the current from the current density

Ohm's law in differential form allows you to determine the current density, a / m 2

where σ is the specific conductivity of the medium, cm / m.

2 Maxwell equations

The system of Maxwell equations in differential form describes variable electromagnetic fields

Vectors in Maxwell equations represent a non-stationary electromagnetic vector field, which is the function of the coordinates x, y, z and time t.

2.1 Private cases of electromagnetic phenomena

In particular cases, the Maxwell equation can be simplified.

2.1.1 Stationary electromagnetic field

The stationary electromagnetic field is created by direct currents and is described by vector coordinate functions that do not depend on time:

Electric field strength;

Electrical induction;

Magnetic field strength;

Magnetic induction.

Vector functions do not depend on time, so the private time derivatives in Maxwell equations are zero:

The system for Maxwell's equunifies in differential form takes the form describing the stationary electromagnetic field:

2.1.2 Static Electric or Magnetic Fields

Static fields do not change over time and do not have moving charges, therefore, currents

.

The Maxwell equation system is divided into two independent system of equations. The first system characterizes the electrostatic field and is called the system of differential electrostatic equations

The second system of equations describes the magnetostatic field created by constant fixed magnets

This system of equations can be used to describe magnetic fields created by direct currents, but in areas in which the current density is zero, and which are not covered with the current (do not cover the current lines).

2.1.3 Maxwell equations in a comprehensive form

If the vectors of the electromagnetic field change over time by harmonious laws, the Maxwell equations system can be represented in a complex form that does not contain time for complex vectors

or complex amplitudes

2.1.4 Wave equations

From the Maxwell equations in a comprehensive form, expressing separately equations for complex vectors and get wave Helmholts equationsfor vectors

and complex amplitudes

where - Wave Number, D La Vacuum

.

3 Flat electromagnetic waves

At large distances from the source, the element of a spherical wave approximately can be taken flat. Flat waves cannot be created by sources, they are invented to significantly simplify the theory of electromagnetic waves in some cases.

The vectors of the electric and magnetic fields of the flat wave of the simphase and oscillate along mutually perpendicular directions in the plane perpendicular to the direction of the wave propagation. Such waves are transverse (see Figure).

Figure is an instant pattern of the distribution of electric and magnetic fields along the direction of propagation of a flat wave. In time, the pattern of the field moves in space with phase velocity V f along the z axis

The front of the wave is a geometric location of the field points with the same phase: a flat wave (see Figure) One of these surfaces is the z \u003d z 0 plane, perpendicular to the direction of the wave propagation. The field parameters when moving within the front of the wave are not changed.

The front of a flat wave is a plane perpendicular to the direction of propagation of the wave. The field parameters when moving within this plane do not change, so private derivatives in directions X and Y are zero:

In Olovnye Helmholts equationsfor flat waves become one-dimensionalfor vectors

and complex amplitudes

SOLUTION OF DIFFERENTIAL EQUATIONS FOR Vectors

where , - orts in the direction of the vectors of electrical and magnetic tensions, respectively;

A, B, C, D - coefficients.

Valid parts of vectors

Let's analyze in the first equation the first term. In the figure, we show the position of the maximum of the electric field at the time T (point A) and T + Δ t.

Figure - Position of the maximums of the electric field

During Δ t.the position of the maximum moved toΔ z,we can write down equality

A COS (ωt - kz) \u003d a COS (ωt + ωΔt - kz - k Δz),

in which the arguments are equal

ω t - kz \u003d ωt + ωΔt - kz - k Δz

0 \u003d ΩΔt - KΔz

ωΔt \u003d kΔz.

From here we get phases by the speed V f - Wave Front Spread Speed

For Vacuum

so phase speed in vacuum

Substitute constant values

therefore, in vacuo, the speed of propagation of the wave front is equal to the speed of light.

Phase speed in some environment

Phase speed does not depend on the frequency.

Amplitudes of two points at a distance of wavelength λ with phases different from 2π are equal, so equality is performed

cos (ωt - kz) \u003d cos (ωt - k (z + λ) + 2π),

in which the arguments are equal

ωt - kz \u003d ωt - k (z + λ) + 2π,

ωt - kz \u003d ωt - kz - kλ + 2π.

Reduction Ω. t - KZ.

0 = − k λ + 2π,

k λ \u003d 2 π.

Hence the length of the wave

For an arbitrary environment

,

therefore, the length of the wave

In vacuum wavelength

Wavelength in other media

Vacuum wave resistance

For dry air, the same wave resistance is accepted.

4 Distribution of radio waves

All electromagnetic waves, including radio waves apply to vacuum at a rate of 3 · 10 8 m / s.

4.1 Distribution of radio waves in free space

Distribution of radio waves in the atmosphere, along ground surface, in earth Kore, in the outer space of our galaxy and beyond the free distribution of radio waves, which we will consider.

4.1.1 Radio wave classification by range

Radio waves have a frequency range from thousands of hertz to thousands of Gigahertz: 3 · 10 3 - 3 · 10 12 Hz. Long waves have a frequency less than short waves having a greater frequency.

The use of radio waves is possible due to the transmitting device, the natural distribution environment of radio waves and the receiving device, all together forming the radio.

The earth's atmosphere and the surface are media absorbing, electrically inhomogeneous, having no conductivity constant and space, dielectric constant depending on the frequency of propagating radio waves.

Therefore, radio waves were divided into frequency ranges with approximately identical conditions for the propagation of radio waves within these frequency ranges. Frequency ranges are adopted by the International Advisory Committee on Radio (ICRC) in accordance with the Radio Regulations.

Optic waves are used for radio communications: infrared, visible and ultraviolet.

The power of electromagnetic waves depends on the frequency in the 4th degree

P ~ ω 4.

Waves with a greater frequency, but with a smaller wavelength are capable of possessing greater power.

Antennas with a narrow pattern of the orphanage have dimensions significantly exceeding the wavelength, such highly efficient antennas are easier for high frequencies.

The higher the carrier frequency, the greater the number of independent modulated channels can be transmitted by such radio waves.

4.2 Provisions from the theory of antennas

The space around the antenna is divided into three areas having a different field structure and calculated formulas: neighbor, intermediate and distant. In real communication lines, there is usually a long-distance area (Fraunhofer zone) at distances from the antenna

where L - maximum size of the radiating area of \u200b\u200bthe antenna, m;

λ - wavelength, m.

Characteristic (wave) free media resistance

Pointing vector (vector Umova - Pointing), W / m 2

where P - power, W;

r - distance from antenna to observation point, m.

where D - the directional action coefficient (CBD) antenna.

The average value of the Pointing vector in the far zone

From the relationship

express the amplitude of the magnetic field tension

Substitute

We equate the Pointing vectors

Socil

The amplitude of the electric field strength in the far zone of the antenna in the free space

The field strength in other directions is determined by the antenna pattern F (θ, α), in which the angles θ and α in the spherical coordinate system (R, θ, α) set the direction to the observation point:

5 Distribution of radio filters of various ranges

5.1 Distribution of super long and long waves

Super long waves (ADD) have a wavelength of more than 10,000 m and a frequency of less than 30 kHz. Long waves (DV) have a wavelength from 1000 to 10,000 m and a frequency of 300-30 kHz.

ADD and DV have a large wavelength, so the earth's surface is well enveloped. The conductivity currents of these radio waves significantly exceed the shift currents for all types of the earth's surface, therefore there is a slight absorption of energy when the surface wave is propagated. Therefore, ADD and DV can spread at a distance of up to 3 thousand km.

ADD and DV are weakly absorbed in the ionosphere. The lower the frequency of radio waves, the lower electronic concentration of the ionosphere is required for rotation of the radio wave to the ground. Therefore, the turn of the ADD and DV occurs in the lower border of the ionosphere (during the day in the layer D and at night in the layer E) at an altitude of 80-100 km. The troposphere on the distribution of ADD and DV practically does not affect. Around the Earth ADD and DV propagate, reflecting from the ionosphere and from the earth's surface in the spherical layer of 80-100 km between the lower boundary of the ionosphere and the earth's surface.

Communication lines for ADD and DV have the high stability of the electric field strength. During the day and the year, the value of the signal changes little, and also not subjected to random changes. Therefore, ADD and DV are widely used in navigation systems.

A limited frequency range (3-300 kHz) ADD and DV does not allow to place even one television channel for which the 8 MHz band is required.

A large wavelength of ADD and DV dictates the use of cumbersome antennas.

Despite the shortcomings, ADD and DV are used in radio navigation, radio broadcasting, radiotelephone and telegraph communications, including underwater objects, since these and optical waves are weakly absorbed in sea water.

5.2 Distribution of medium waves

The average waves (SV) have a wavelength from 100 to 1,000 m, the frequency of 300 kHz to 3 MHz (0.3 - 3 MHz). Earth and ionospheric CV, which are used primarily in broadcasting can be distributed.

Earth SV-Radiolines are limited to a length of not more than 1000 km due to the essential absorption of the Red Ground surface.

The ionospheric is capable of reflected from the layer E ionospheres. Through the lowest layerD. ionosphere, appearing only during the day, sv pass and strongly absorbed in it,virtually excluding communication during the day. Therefore, at night in the ionosphere, the absorption of SV significantly decreasesand distances of large 1000 km from the transmitter communicationrestores.

Due to the interference of the ionospheric waves, or (and at night) with the earth's waves, random signments of the signal arise (Feding). Antifiling antennas are pressed to the earth's surface maximum focus chart to combat fadingand cross-modulation on sv.

5.3 Spreading short waves

Short waves (kV) have a wavelength from 10 to 100 m (10 times shorter than medium waves), a frequency of 3 to 30 MHz (10 times the frequency of SV). KV are used primarily for broadcasting.

KV strongly absorbed by the earth and poorly enveloped the surface of the Earth, so the earth kV applies only to several tens of kilometers.

KV test the absorption and pass in the lowest layers of the ionosphere D and E, but reflected from the layerF.

The calculation of the SV communication lines is to compile the schedule of working frequencies depending on the time of day (wave schedule).

5.4 Features of the propagation of ultrashort waves

Ultra-screwed waves (VHF) have a wavelength of less than 10 m and frequency of more than 30 MHz. In the light of the bottom, the VHF borders from the KV, and from above with infrared waves. The ionosphere for VHF is transparent, so the VHF lines are used mainly within the limits of direct visibility.

VHF has a large frequency range capable of transmitting significant amounts of information. On meter and decimeter waves, you can place 297 television channels. In the entire shortwave range there are only 3 television channels, and in all sv bands none.

The development of mobile and satellite communications, the Internet and other of the above reasons cause radio engineering to switch to higher frequencies, so VHF is becoming increasingly important.

5.4.1 Distribution of ultrashort waves within the limits of direct visibility

VHF communication lines operating within the limits of direct visibility:

VHF and television broadcasting;

Radar stations (radar);

Radio relay communication lines (RPL);

Communication with space objects;

Mobile connection.

5.4.2 Distribution of VHF for the horizon

Far distribution of VHF in the horizon line occurs in the following ways:

Due to the scattering on the heterogeneities of the troposphere;

Superfractions in the troposphere;

Dispersion on the heterogeneities of the ionosphere;

Due to the reflection from the layers of the ionosphere F 2 and E S;

- due to the reflection from meteor traces;

Thanks to the increase in the obstacle (see Figure)

Figure - Distribution of radio waves when an obstacle enhancing

List of conventional designations, symbols, units and terms

D, B - electrical and magnetic induction vectors

E, H - Electric and Magnetic Tensions Vectors

I (R, T) - Electric Current

j (R, T) - vector density electric current

P-power electromagnetic field

M - magnetization vector

P - electric polarization vector

q - Electric charge

ε, μ - absolute dielectric and magnetic permeability

ε 0, μ 0 - dielectric and magnetic constant

ε R, μ R - relative dielectric and magnetic permeability

P - Pointing vector (vector Umova - Pointing)

ρ, ξ, τ - the density of volume, surface and linear charge

Σ - Specific medium conductivity

φ - scalar electrostatic potential

χ e, χ m - electric and magnetic susceptibility

W - Electromagnetic Field Energy

W E, W M - electric and magnetic energy

w detergent electromagnetic field

w E, W M - electric and magnetic energy density

k - wave number

SDV - super long waves

DV - Long Waves

SV - medium waves

KV - Short Waves

VHF - Ultra-Court Waves

RLS - Radar Station

RRL - Radio Line

D - directional coefficient (CBD) antenna

G - antenna amplification coefficient

F (θ, α) - antenna pattern diagram

R 0 - Land Radius (6371 km)

Z 0 - wave resistance of free space

List of sources used

1.Electrodynamics and distribution of radio waves: studies. Manual / L.A. Bokov, V.A. Zamotrinsky, A.E. Mandel. - Tomsk: Tomsk. State University of UPR systems. and electronics, 2013. - 410 p.

2.Morozov A.V. Electrodynamics and radio wave: Tutorial for Higher. military studies. Institutions / Morozov A.V., N. N., Shmakov N. P. - M.: Radio Engineering, 2007. - 408 p.

3.Yamanov D.N. Basics of electrodynamics and distribution of radio waves. Part I. Basics of electrodynamics: Texts of lectures. - M.: MSTU GA, 2002. - 80 s.

4.Panko V.S. Lectures in the course "Electrodynamics and distribution of radio waves".

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1 Federal Agency for Education State educational institution Higher vocational education "North-Western State Correspondence Technical University" Department of Radio Engineering Electrodynamics and distribution of radio waves Educational and methodical complex Institute of Radio Electronics Specialty of the preparation of a graduate specialist: Radio Engineering Direction of bachelor's preparation: Radio Engineering St. Petersburg Publisher NTPU 009

2 Approved by the Editorial Publishing Council of the University of UDC Electrodynamics and the distribution of radio waves: Techmetic complex / Sost. L.Ya. Rhodes, D.A. Cleaners. St. Petersburg: Publishing House of SZTU, p. Training and metodology complex (UMC) is designed in accordance with the requirements of state educational standards of higher professional education. The CMDs consider the issues of the theory of the electromagnetic field, the main methods of solving applied tasks Electrodynamics in relation to the propagation of electromagnetic waves in guide systems and radio waves on natural highways. The CMD is intended for students of the specialty, studying the discipline "Electrodynamics and the spread of radio waves", and bachelors of technology and technology in the direction of the same discipline. Considered at the meeting of the Department of Radio Engineering G., approved by the Methodological Commission of the Radio Electronics Institute of Reviews: Department of Radio Engineering NWTU (Head. Department of G.I. Khudyakov, Dr. Tech. Sciences, prof.); V.S. Kalashnikov, Dr. Tehn. Sciences, prof., Ch. Scientific Sot. VNIIR. Compilers: L.Ya. Rhodes, Cand. tehn Sciences, Doc.; YES. Cleaners, cand. tehn Sciences, Doc. Northwest State Cam technical University, 008 Rhodes L.Ya., Chistyakov D.A., 008

3 1. Information on discipline 1.1. The preface electrodynamics and the spread of radio waves (ED and RRV) refers to the disciplines of the negotiation cycle. Its volume on state educational standard (State) is 170 hours. It includes two interrelated parts: part 1 - actually electrodynamics (theoretical electrodynamics) and part - the propagation of radio waves (applied electrodynamics). This discipline is basic for modern radio engineering. The purpose of studying discipline is the acquisition by students of theoretical knowledge and skills of solving problems in the field of electromagnetic field theory, features of the interaction of electromagnetic waves with various physical environments, the propagation of radio waves along the guide systems and on natural routes. The tasks of studying the discipline assimilation of the main provisions of electrodynamics and the characteristics of the propagation of radio waves. As a result of studying discipline, the student must master knowledge of discipline formed at several levels: to have an idea: about the philosophical interpretation of the concept of "electromagnetic field", on the history of the development of electromagnetism, on the relationship of electrical, magnetic and optical phenomena, about the vector nature of electromagnetic and optical Fields, on radio wave ranges used in the technique, the main features of the distribution of radio waves on natural highways. Know: Maxwell equations in integral and differential forms, the physical meaning of all the terms included in these equations; Mechanisms of the effect of Earth and the Earth's atmosphere on the distribution of radio waves of various ranges. 3.

4 be able to: convert Maxwell equations to equations of electrical and magnetostatics, stationary electrical and magnetic fields, into wave equations for the electromagnetic field vectors, vector and scalar potentials; Formulate the task (select the model) to calculate the parameters of a particular radio. Get the skills: solutions to the problems of electrodynamics methods: separation of variables, delayed potentials, scalar and vector integrals of Kirchhoff; selection of type, sizes and calculation of parameters of guide systems (electromagnetic energy transmission lines); calculating the characteristics of the emission of elementary emitters and real antennas; Selection of the model and determination of the nature and degree of influence of the radio wave propagation route on the characteristics of a particular radio system. The study of the discipline "Electrodynamics and distribution of radio waves" requires the development of a number of preceding disciplines. These include: mathematics (ranks, differential and integral calculation, vector field theory, solving differential equations); physics (electricity and magnetism, electrodynamics); Informatics (methods of algorithm, numerical solutions). In turn, the ED and RRV course underlies all the disciplines that determine the professional training of a specialist in the field of radio engineering: the basics of chains theory, radio equipment and signals, microwave and antenna devices, receiving and signal processing devices, generation and signal generation devices, radio engineering systems et al. Content, volume and procedure for studying the materials of the course "Electrodynamics and distribution of radio waves" in accordance with the requirements of the State are set out in the "Working Program" submitted in the "Information Resources" heading. There is also a "thematic plan", containing information on the types of reports on topics. four

5 1 .. The content of discipline and types academic work The content of the discipline in accordance with the state in the course "Electrodynamics and the spread of radio waves" should be studied by the following dydactic units: integral and differential equations of electromagnetism; Complete system of Maxwell equations, boundary conditions; Energy of the electromagnetic field; Umova-Pointing theorem; boundary problems of electrodynamics; analytical and numerical methods for solving boundary tasks; Electromagnetic waves in various environments; electrodynamic potentials; Electromagnetic waves in guide systems; electromagnetic oscillations in bulk resonators; excitation of electromagnetic fields given sources; radiation of electromagnetic waves in free space; Theorem of delayed potentials; the propagation of electromagnetic waves near the surface of the Earth; Tropospheric distribution of radio waves; the spread of radio waves in the conditions of rough terrain and in the presence of obstacles; Models and methods for calculating radiobrass volume of discipline and types of academic work Just hours Type of study Form of training Full-time Overcordinated Correspondence Total laboriousness of discipline (USD) 170 Work under the guidance of the teacher (RPRP) including audited activities: lectures Practical lessons (PZ) Laboratory work (LR) Number of hours of working using dot Independent work student

6 Intermediate monitoring, the number of test work is a test type of final control (exam), the number of student's academic work species, the current control of academic performance and intermediate certification is two test work (for part-time and correspondence forms of training); - Tests (training by themes, Lubogogogogo discipline sections, questions for self-test, etc.); - one offset (on the laboratory work of part 1 - electrodynamics); -Wall exam .. Working training materials.1. Work program (170 hours) Part 1 - electrodynamics.1.1. Section 1. Integral and differential equations of electromagnetism Basic concepts and definitions (4 hours) [1], with basic concepts and definitions, the materiality of the electromagnetic field, the vectors of the electromagnetic field, the classification of media in electrodynamics. Maxwell equations are fundamental electrodynamic equations (1 hour.) [1], from the Maxwell equation in integral and differential forms and their physical meaning. Electric current continuity equation. Third-party electric and magnetic currents and charges. The complete system of EMF equations in symmetric and asymmetric forms. Maxwell's equations for harmony- 6

7 wicker dependence of electromagnetic processes. Complex dielectric permeability of media. The principle of the permutation duality of the Maxwell equations. Energy characteristics of EMF (6 hours) [1], with a balance of energy in EMF: Localization, movement and transformation of energy. Energy characteristics in the harmonious dependence of electromagnetic processes on time. Electromagnetic waves - the form of existence of EMF (6 hours) [1], with wave equations for EMF vectors. Electrodynamic potentials. Wave equations for electrodynamic potentials. Wave equations in comprehensive form. Private types of EMF equations (4 hours) [3], with an electrostatic field: charge system, dipole, container, conductors and dielectrics in an electrostatic field. Stationary field: current system, magnetic dipole, inductance. Quasistationary field: from Maxwell equations to chain theory..1 .. section. Boundary problems of electrodynamics The main methods for solving the problems of electrodynamics (8 hours) [1], p. 1-7 Domestic and external electrodynamic tasks. Edge conditions and radiation condition. The uniqueness of solving the problems of electrodynamics. The principle of superposition solutions, reciprocity theorem, equivalence theorem. Strict methods of solving: delaying potentials, separation of variables, Kirchhof. Approximate methods of solution: geometric and wave optics, edge waves, geometric diffraction theory, modeling. 7.

8 Flat electromagnetic waves (EMV) (10 hours) [1], p. 7-4 General properties wave processes. Flat homogeneous electromagnetic waves in a homogeneous limitless isotropic medium. Waves in dielectric, semiconductor and explorer. Spherical EMV in infinite homogeneous media. EMV radiation (1 hour) [1], with the types of elementary emitters. Radiation of the system of specified currents. Elementary electric emitter: EMF vectors, radiation function, power and radiation resistance. Elementary magnetic emitter. Guygens element. Flat EMV in an inhomogeneous medium (10 hours) [3], with electromagnetic waves and optical rays. Boundary conditions for the vectors of the electromagnetic field. Reflection and refraction of electromagnetic waves on the flat boundary of the media partition. The laws of Snellulus and Frenelly Formulas. The concepts of bruteter angles, complete internal reflection, surface effect Section 3. EMV in guide systems. Electromagnetic oscillations in bulk resonators. Guided EMV and guide systems. Waveguides (16 hours) [1], with General On guide systems and railway waves. Hollow metal waveguides: rectangular, round. The structure of the electromagnetic field, the main types of waves, phase and group velocity, the wavelength in the waveguide, the characteristic resistance, the attenuation of the electromag- 8

9 thread waves, excitation and communication of waveguides, choosing a waveguide size for work on a given type of waves. Coaxial and two-wire transmission lines (4 hours.) [3], p. 4-9 Features of the waves of type t and the main parameters of the waves in the coaxial and two-wire transmission line. Phase constant, phase speed, group speed, wavelength in line, wave resistance. The range of single-mode coaxial line. Volume resonators (8 hours) [3], with a segment of a guide structure as a resonator. General Theory Volume resonators based on rectangular, cylindrical and coaxial waveguides. Own frequency and quality of resonators. Excitement of resonators. Part of the distribution of radio waves.1.4. Section 4. Distribution of EMV near the ground surface. Influence of obstacles. Basic concepts and definitions (4 hours), p. 4-7 Basic concepts and definitions in the theory of RRV. The role and place of issues of distribution of radio waves in the preparation of radio engineers. The history of the development of the RRV theory. Radio wave classification in frequency ranges and distribution methods on natural routes. The distribution of radio waves in the free space (10 hours), with an electromagnetic field of isotropic and directed emitters in free space. Equations of the perfect radio communications for emitters 9

10 different types. Guiggens-Fresnel principle. Fresnel zones in free space. The essential and minimum area of \u200b\u200bspace when distributing radio waves. Transmission loss when distributing radio waves in free space. The effect of the surface of the Earth on the spread of radio waves (18 hours), with the electrical parameters of the earth's surface. The formulation and general solution of the problem of diffraction of radio waves around a homogeneous spherical earth surface. Analysis of the overall solution of the problem: the effect of electrical parameters of the surface of the earth and the distance between the corresponding points by the magnitude and behavior of the multiplier of weakening in space. The distance of the direct visibility and calculation of the multiplier of weakening in the area of \u200b\u200bthe line of sight. Interference formulas. The limits of the applicability of the interference formulas. Calculation of a multiplier of weakening in the shadow and half zones. Reflection of radio waves from the surface of the Earth, a significant and minimum area of \u200b\u200bthe reflective surface. Accounting for the effects of the curvature of the earth's surface when reflecting radio waves. The effect of the heterogeneity of the electrical parameters of the earth's surface on the distribution of radio waves along it. The effect of irregularities of the surface of the earth on the spread of radio waves. Relay criterion. General information about the distribution of radio waves near statistically uneven surfaces Section 5. Effect of Earth's atmosphere on radio wave. The effect of land troposphere on radio wave spread (10 hours), with the composition and structure of the atmosphere of the Earth. Electromagnetic parameters of the troposphere, stratosphere and ionosphere. Refraction of radio waves in the troposphere and the ionosphere. The equation of the trajectory of the wave and the radius of the curvature of the beam. Types of radio wave refraction in the troposphere. Equivalent land radius. The process of education and parameters of tropospheric waveguides. 10

11 The influence of the Earth's ionosphere on the distribution of radio waves (8 hours), with the path of radio waves in the ionosphere. Reflection of radio waves from the ionosphere. Critical and maximum frequency. Phase and group rates of radio wave in the ionosphere. The effect of the magnetic field of the Earth on the distribution of radio waves in the ionosphere. Scattering and absorption of radio waves in the troposphere and the ionosphere. Methods experimental research Tripospophers and ionospheres Section 6. Models and methods for calculating radiotrass. Radioline various destination. Ranges of used frequencies (8 hours), from line of broadcasting, television, radio communications, radar, radio navigation, radio control and telemetry. Purpose of radiolines, ranges of used frequencies and features of the propagation of radio waves of these ranges on the radio route. Methods for calculating various radiolines, with a methodology for calculating radiolines for various purposes and various radio wave ranges. eleven

12 .. Themed discipline plan..1. Thematic plan of discipline for students of full-time education of training sections and the number of hours of full-time education Types of classes (hours) Lectures of PZ (C) LP Audit. Dot audit. Dot audit. Dot self-work tests types of control test work abstracts lp Course work Total section 1. Integral and differential equations of electromagnetism 1.1 Basic concepts and definitions 3 1. Maxwell equations Fundamental equations of electrodynamics Energy characteristics of the electromagnetic field (EMF) Electromagnetic waves The form of existence of EMF private types of EMF equations 7 section. Boundary Objectives of electrodynamics 8.1 Basic methods for solving electrodynamic problems 9. Flat electromagnetic waves (EMV) in a homogeneous medium 10.3 Spherical EMV in limitless media. EMV Radiation Flat EMV in an inhomogeneous medium 1 Section 3. EMV in guide systems. Electromagnetic oscillations in volume resonators guided EMV and guide systems. Waveguides Coaxial and two-wire transmission lines Volume resonators Section 4. Distribution of 4 EMV near the surface of the Earth. Effect of obstacles Basic concepts and definitions

13 18 4. DISTRIBUTION OF RADIVETS IN THE SPACE EFFECT OF THE EARTH SURFACE FOR RADIOVAL DISTRIBUTION 0 SECTION 5. EFFECT OF THE EARTH ENGERSFER ON THE DISTRIBUTION OF RADIOVAGE INFLUENCE OF EARTH TRAPRIFERS FOR RADIVE DISTRIBUTION 5. Effect of Earth's ionospheres on the distribution of radio waves 3 Section 6. Models and methods for calculating radio radiolines destination. Ranges of the used frequencies 5 6. Methods for calculating various radiolines Thematic discipline plan for students of part-time learning for training sections and the number of hours on day form Types of classes (clock) Lecture of PZ LR Audit. Dot audit. Dot audit. Dot Samost. Work tests Types of control of counter. Works of PZ LR Course. Works Total Section 1. Integral and Differential Equations Electromagna-1 Tismism Basic Concepts and Definitions of the Maxwell Equation - Fundamental Equations of Electrodynamics Energy Characteristics of the Electromagnetic Field (EMF) Electromagnetic Waves-Formation EMF Private Types of EMF Equations 4 7 Section. Boundary problems of electrodynamics Basic methods for solving electrodynamic problems Flat electromagnetic waves (EMV) in a uniform medium spherical EMV in infinite homogeneous media. EMV flat EMV radiation in an inhomogeneous environment

14 1 Section 3. EMV in guide systems. Electromagnetic oscillations in bulk resonators Guided electromagnetic waves and guide systems. Waveguides Coaxial and two-wire transmission lines Volume resonators Section 4. Distribution of electromagnetic waves near the ground surface. Influence of obstacles Basic concepts and definitions of radio wave in the free space Effect of Earth's surface on the spread of radio waves SECTION 5. Effect of Earth's atmosphere on the spread of radio waves The effect of the Earth's distribution on the spread of radio waves The effect of the Earth's ionosphere on the distribution of radio waves Section 6. Models and methods for calculating radiolirass of various purposes. Ranges of used frequencies. Methods for calculating various radiolines Themed discipline plan for students of correspondence formation of training sections and the number of hours of full-time education. Dot audit. Dot audit. Dot Independent Work Tests Tests Control Types of Control Works Essays LR Coursework Just Section 1. Integral and Differential Equations of Electromagnetism 1.1 Basic Concepts and Definitions 3 1. Maxwell Equations Fundamental Equations Electrodynamics Energy Characteristics of the Electromagnetic Field (EMF)

15 5 1.4 Electromagnetic Waves Form of EMF existence Private types of EMF equations section. Boundary problems of electrodynamics Basic methods for solving electrodynamics problems 9. Flat electromagnetic waves (EMV) in a uniform medium spherical EMV in limitless media. EMV flat EMV radiation in an inhomogeneous medium Section 3. EMV in guide 3 systems. Electromagnetic oscillations in volume resonators guided EMV and guide systems. Waves coaxial and two-wire transmission lines Volume resonators Section 4. Distribution of 4 EMV near the surface of the Earth. Influence of obstacles Basic concepts and definitions of radio wave in the free space Effect of Earth's surface on the distribution of radio waves SECTION 5. Effect of atmosphere 5 Earth on the distribution of radio waves Influence of the Earth's propagation on the distribution of radio waves 5. Effect of Earth's ionospheres on the distribution of radio waves 3 Section 6. Models and methods for calculating radio Radio various destination. Ranges of used frequencies 5 6. Methods for calculating various radar

16 .3. Structural and logical diagram of discipline Electrodynamics and distribution of radio waves Section 1 Integral and differential equations Section Boundary tasks Electro- Section 3 Electromagnetic waves in guides Section 4 Distribution of electromagnetic waves near Section 5 Effect of Earth's atmosphere for distribution Section 6 Models and methods for calculating RA-basic concepts and definitions of maxwell-fundamental basic methods for solving problems Electrodi-guided electromagnetic waves and basic concepts and determination of the Earth's troposphere on the distribution of various destination radiolines. Energy characteristics ELECTRICAL ELECTROMATIC Waves Spherical Electromagnetic Waves in Non-Comaxial and Two-Water Transmission Distribution In Free Pro Influence of Earth's Ionosphere Distribution Methods for Calculation of Different Ra-Electromagnetic Waves Shape Support Sole Electromagnetic Volume Resonators Earth Effect Effect on the distribution of the distribution of radio waves in cosmic private types of equations of electromag

17 .4. A temporary schedule for studying the discipline (for students engaged in the use of dot) The name of the section (themes) The duration of the study of the section (themes) 1 section 1. Integral and differential 7 days. Equations of electrodynamics section. Boundary problems of electrodynamics 9 days. 3 Section 3. Electromagnetic waves in guide systems. Electromagnetic oscillations in volume resonators 7 days. 4 Section 4. Distribution of electromagnetic 7 days. Waves near the surface of the Earth 5 Section 5. Effect of Earth's atmosphere for distribution of 4 days. Radio films 6 Section 6. Models and methods for calculating radiotrass 4 days. 7 Examination of 1 day. 8 DN test work. TOTAL.5. Practical block.5.1. Practical practical classes ( full-time Learning) 4 days Number and name Theme Topic.3 Spherical EMV in limitless environments. EMV Radiation Topic 3.1 Guide EMV and Guide Systems. Waveguides Topic 4. Distribution of radio waves in free space Solution of radiation problems EMV Elementary electric and magnetic dipoles Determination of the size of waveguides and characteristics of EMF in rectangular and round waveguides Determination of the parameters of radio communication lines in free (cosmic) space Name of practical classes Number of hours Theme 4.3 - Calculation of EMF tension on

18 The surface of the Earth on the spread of radio waves of Diolines, passing near the surface of the Earth practical classes (correspondence and part-time forms of training). Practical classes for students of these forms of training by work plans are not provided ... 5 .. Laboratory works Laboratory work (full-time learning) Number and name of the section (themes) section. Boundary problems of electrodynamics Theme .. Flat electromagnetic waves Theme.4. Flat EMV in an inhomogeneous medium Section 3. EMV in guide systems. Electromagnetic oscillations in bulk resonators Topic 3.1. Guides EMV and guide systems theme 3.3. Volume Resonators Name of laboratory work Research of polarization of the electromagnetic field The study of the reflection and refraction of flat EMV on the flat boundary of the section of two homogeneous dielectric environments Investigation of the main wave in the floor of a rectangular metallic waveguide Study of the electromagnetic field in a cylindrical volume resonator

19 Section 4. Distribution of EMV near the surface of the Earth Theme 4 .. Distribution of radio waves in free space Theme 4.3. Effect of Earth's surface on the spread of radio waves. Study of the area of \u200b\u200bspace that has a significant effect on the spread of radio waves in a homogeneous environment. Study of the effect of the surface of the Earth's spread of radio waves 4 4 Laboratory works ( part-time Learning) Number and name of the section (Topics) Section. Boundary problems of electrodynamics Theme .. Flat electromagnetic waves Theme.4. Flat EMV in an inhomogeneous medium Section 3. EMV in guide systems. Electromagnetic oscillations in bulk resonators Topic 3.1. Guides EMV and guide systems theme 3.3. Volume Resonators Name of laboratory work Research of polarization of the electromagnetic field The study of the reflection and refraction of flat EMV on the flat boundary of the section of two homogeneous dielectric environments Investigation of the main wave in the floor of a rectangular metallic waveguide Study of the electromagnetic field in a cylindrical volume resonator

20 Section 4. Distribution of EMV near the surface of the Earth Theme 4. The propagation of radio waves in the free space Theme 4.3. The effect of the surface of the Earth on the spread of radio waves. Study of the area of \u200b\u200bspace that has a significant effect on the spread of radio waves in a homogeneous medium. Study of the effect of the earth's surface on the distribution of radio waves 4 4 Laboratory works (correspondence formation) The number and name of the section (themes) section. Boundary problems of electrodynamics Theme .. Flat electromagnetic waves Theme.4. Flat EMV in an inhomogeneous medium Section 3. EMV in guide systems. Electromagnetic oscillations in bulk resonators Topic 3.1. Guides EMV and guide systems theme 3.3. Volume Resonators Name of laboratory work Study of the polarization of the electromagnetic field The study of the reflection and refraction of flat EMV on the flat boundary of the section of two homogeneous dielectric environments Investigation of the main wave in the floor of a rectangular metal waveguide. Study of the electromagnetic field in a cylindrical volume resonator Number of hours 4

21 Section 4. Distribution of EMV near the surface of the Earth Theme 4 .. The propagation of radio waves in the free space Theme 4.3. Effect of Earth's surface on the spread of radio waves. Study of the area of \u200b\u200bspace that has a significant effect on the spread of radio waves in a homogeneous environment. Study of the effect of the surface of the earth on radio wave .6. Ballery rating system for assessing knowledge When using dot discipline Electrodynamics and propagation of radio waves, as mentioned above, consists of two parts. The study of the first part of the course (electrodynamics) is carried out in the fifth semester and ending with the exam. The first part of the course contains three sections (twelve topics), when learning which you need to perform the first testconsisting of two tasks. Each topic in the reference abstract ends with a list of issues for self-test, which should be considered as training tests with an open task. After studying each topic, it is necessary to answer the questions of training tests of the current (intermediate) control containing five questions. The study of each section ends with an answer to the Questions of the Front Control Test, containing ten questions. The numbers of the corresponding tests are summarized. The definition of rating points is made as follows: - for the correct answer to the question of the test of the frontier control - the score; - For the correctly solved problem - 0 points. With successful work with the materials of the first part of the course, the student can get x10x3 + 0x \u003d 100 points. Overcoming the threshold of 70 points, as well as the execution of the laboratory cycle on sections and 3 during the examination session and obtaining for 5

22 couples on laboratory work, ensures the admission to the exam. Studying the second part of the course is carried out in the sixth semester and ends with the exam. The second part of the course consists of three sections (seven topics), when studying which you need to perform a second test work, consisting of two tasks. Each topic in the reference abstract ends with questions for self-test, which should be considered as training tests with an open task. After studying each topic, you must answer questions training test The current (intermediate) control consisting of five questions. The study of each section ends with an answer to the Questions of the Front Control Test, containing ten questions. The numbers of the corresponding tests are summarized. Determining rating points when studying the second part of the course is made in the same way as the first part. With successful work with the materials of the second part of the course, the student can get x10x3 + 0x \u003d 100 points. Overcoming the threshold of 75 points and the execution of the laboratory cycle during the examination session provides admission to the exam. 3. Discipline information resources 3.1. Bibliographic list of the main: 1. Kalashnikov, V.S. Electrodynamics and distribution of radio waves (electrodynamics): letters. Lectures / V.S. Kalashnikov, L.Ya. Rhodes. SPb.: Edvo SZTU, Rhodes, L.Ya. Electrodynamics and radio wave distribution (radio wave): studies. - Method. Complex: studies. Deposit / L.Ya. Rhodes. - SPb.: Publishing house SZTU, Krasyuk, N.P. Electrodynamics and distribution of radio waves: studies. Manual for universities / N.P. Krasyuk, N.D. Dymovich. - M.: Higher. Shk., Additional: 6

23 4. Petrov, B.M. Electrodynamics and distribution of radio waves: studies. For universities / B.M. Petrov. -R ed., sn. M.: Hotline Telecom, Krasyuk, N.P. Distribution of VHF in an inhomogeneous troposphere: studies. Manual / N.P. Krasyuk, L.Ya. Rhodes. L.: SPI, Chistyakov, D. A. Laws and equations of electrodynamics as a consequence of the Maxwell equations: Abstract of lectures / D.A. Cleaners. SPb.: SPI, clean, D.A. Basics of electrodynamics in tasks with solutions: Pisch. Lectures / D.A. Cleaners. SPb.: SPI, clean, D.A. Equations Maxwell Physical Axioms of electrodynamics: letters. Lectures / D.A. Cleaners. St. Petersburg: SPI, in electronic library SZTU at the address there are sources from the bibliographic list below the numbers: 1 ;; Support (scenario educational process) The discipline of electrodynamics and the spread of radio waves, as mentioned above, is a fundamental discipline and is entirely based on courses of physics and higher Mathematics. In this regard, proceeding to its study, it is necessary to restore the main information from the second part of the course general physics (electricity and magnetism) and the following sections of the highest mathematics: equations of mathematical physics, vector analysis, field theory. The main purpose of the discipline is the study of the Maxwell equations, their physical meaning and the use of these equations for solving applied problems of radiophysics and radio engineering. The technique and the sequence of study of the discipline correspond to the list of those thematic plan. The material of each topic is saturated with mathematical ratios, the physical interpretation of which is often quite complex, therefore the study of the material requires serious, thoughtful work. 7.

24 3..1. Basic concepts and definitions in electrodynamics The basic concepts and definitions are set forth in the pages when studying this section, it is necessary to understand the purpose of the discipline in the preparation of radio engineers, the place and task of it in the system. modern ideas Natural science, turning special attention to the materiality of the electromagnetic field. It must be assimilated that the electromagnetic field in all its manifestations is fully characterized by two basic and four additional vectors. The electromagnetic field exists and is considered in various media that are classified by the character of the dependence of their electromagnetic parameters on the time, spatial coordinates, the values \u200b\u200band direction of the vectors of the electromagnetic field existing in this environment. All mathematical ratios of this course are recorded in units "C". Questions for self-test 1. What are the main features of the electromagnetic field confirming its materiality?. What is the physical meaning of vectors characterizing the electromagnetic field? 3. What kind of material equations for the vectors of the electromagnetic field are there? 4. What are the classifications of environments, are used in electrodynamics? 3 ... Maxwell Equations - Fundamental Equations of Electrodynamics The content of this section is presented in the pages it is necessary to pay attention to the fact that the Maxwell equations are the result of the generalization of a large number physical lawsare fundamental dependence of macroscopic electrodynamics, allowing to obtain all the main relationships of the theory of electromagnet- 8

25th field. It should be understood that the sources of the electromagnetic field are electrically charged particles or moving, or at rest. In practical applications, a harmonic dependence on the time of the values \u200b\u200bincluded in the Maxwell equations are often used, so it is convenient to use a symbolic method for their presentation. Questions for self-test 1. What experimental laws underlie the Maxwell equations?. What is the physical meaning of the offset current? 3. What is the physical meaning of the Maxwell equations in integral and differential forms? 4. What is the difference between symmetric and asymmetric forms of recording Maxwell equations? Energy Specifications EMF The content of this section is set out in the pages of the electromagnetic field as the type of matter has a certain energy. For him, the law of conservation is fair. Analytical representation of this law is the equation of the balance of electromagnetic energy - the Umov - Pointing theorem. Questions for self-test 1. What energy components may include an electromagnetic field energy balance equation?. Record the expression for the Pointing vector in the case of harmonic fields in time of electromagnetic waves - the form of existence of EMF The content of this section is given in the pages from the Maxwell equations it follows that the electromagnetic field may be su- 9

26 exist in the form of electromagnetic waves. Adequate relationships describing the wave character of the electromagnetic field are wave equations - differential equations in second-order private derivatives, which can be obtained directly from the equations of Maxwell - differential equations in the private derivatives of the first order. To solve various kinds of applied tasks, wave equations for field vectors and wave equations for electrodynamic potentials are used. With the harmonious dependence of electrodynamic processes on time, the form of recording and solving the wave equations is significantly simplified. Questions for self-test 1. What types of wave equations are used to solve the problems of electrodynamics?. What is the meaning of the calibration ratio? 3. What is the difference between the Dalamber equations and the Helmholtz from the generalized wave equation? 4. Does the difference between the vector potential and the hertz vector in the case of a harmonic electromagnetic field? Private types of EMF equations The content of this section is given in the page of the equation of stationary and static fields, are obtained as special cases from the equations of electrodynamics - the Maxwell equations, provided that the sources of the electromagnetic field are either stationary (independent of time), or, moreover, still (Static). Stationary and static fields are material; For them, the law of conservation and conversion of energy is carried out, but they do not wear a wave nature and in equations describing their behavior, does not contain temporal dependence (for example, the Poisson and Laplace equations). Questions for self-test 10

27 1. Under what conditions, the Maxwell equations system disintegrates on the electrical and magnetostatic system of equations?. What is the difference between stationary and static fields? 3. What is determined by the energy of the electrostatic field? 4. Record the second order equations in private derivatives for static and stationary fields. 5. What methods are used to solve electrostatic problems? Basic methods for solving electrodynamic problems The content of this section is set out in pages 1 7. When mastering this section, it is necessary to study the features of the wording and solving the internal and external problems of electrodynamics, turning special attention to the wording of the uniqueness of the solution of electrodynamic problems for limited and limited spaces of space, the basic principles and theorems used in constructing solutions of practical problems. Examine strict and approximate decision methods, given that the results of solutions by any strict methods coincide, while the results of the solution of the problem obtained by various approximate methods differ from each other. Questions for self-test 1. How are the internal and external problems of electrodynamics formulate?. What is the role of radiation conditions when solving external tasks? 3. How is the uniqueness theorem for solving electrodynamics problems is formulated? 4. Under what conditions is the principle of superposition of solutions? 5. What environments is performed by the reciprocity theorem and what is its essence? 6. What is the role of the equivalence theorem for external problems of electrodynamics? 7. What is the basis of solving problems by the method of delayed potential

28 cyals? 8. Under what conditions can the Kirchhoff method be considered as a strict solution method? 9. Word the applicability of geometric and wave optics methods. 10. What is the essence of the methods of edge waves and the geometric theory of diffraction? 11. What is the essence of the method of electrodynamic modeling? Flat electromagnetic waves (EMV) The content of the section is presented in on pages 7 4. In this section, it is necessary to pay attention to the fact that the concepts of phase and amplitude wave fronts are introduced to characterize any wave process. In the general case, phase fronts may have an arbitrary form, but the main are: flat, cylindrical and spherical. For the characteristics of vector wave processes, in addition to amplitude, phases and frequency of oscillations, the concept of polarization is introduced. It is necessary to study all existing species of polarization of electromagnetic waves. Here, the solution of the Helmholtz equations for the vectors of the electromagnetic field in the form of flat waves should be considered, paying attention to various mathematical forms of writing expressions, the mutual orientation of the tensions of electric and magnetic fields and the Pointing vector, as well as the relationship between them and the electromagnetic parameters of the medium. The features of the propagation of a flat wave in a dielectric, semiconductor and conductor should be studied, turning attention to the specifics of the propagation of a flat wave in media with conductivity (exponential decrease in amplitude, the appearance of phase shift and dispersion). Questions for self-test 1. What is the difference between wave processes from vibrational processes in radio circuits? one

29. What additional characteristic is entered to describe vector wave processes? 3. What types of polarization are considered to be considered in the tasks of electrodynamics? 4. What are the main properties of a flat wave? 5. What character carries a wave number in different environments? 6. What are the features of the spread of a flat wave in conductivity environments? 7. What is the nature of the dispersion phenomenon when the flat wave is propagated in the semiconducting medium? 8. What does the nonlinearity and anisotropy of the medium lead to the spread of a flat wave? Spherical EMV in infinite homogeneous media. EMV radiation The content of this section is given in on the pages when studying this section, it is necessary to understand the formulation of the problem of radiation of electromagnetic waves, as well as the fact that radiation is created only by electrical charges moving with acceleration. It is necessary to assimilate the purpose of the introduction of the concept of elementary emitter, the types of models of elementary emitters and methods for calculating their characteristics. Attention should be paid to the features of the distribution of the electromagnetic field of the elementary emitter in space, depending on the distance and the angular coordinates, to learn the features of the behavior of Pointing vector. It is also necessary to know the main technical characteristics of emitters, such as a radiation diagram, power and resistance of radiation, directional coefficient. Questions for self-test 1. What is the purpose of introducing the concept of an elementary emitter? 13

thirty . How is the problem of radiation of electromagnetic waves formulad? 3. What solution method is used to calculate the emission of an elementary electric dipole? 4. Name the characteristic zones of the space and the separation criteria, in which it is customary to consider the radiation field. 5. Describe the energy properties of the field emitted by the elementary emitter. 6. What characteristics are characteristic of the elementary emitter as an antenna? 7. What models are used to describe the elementary magnetic emitter? 8. Compare the radiating ability of elementary electrical and magnetic emitters. 9. What species has a Guygens element diagram? Flat EMV In an inhomogeneous medium The content of this section is presented in on the pages when studying this section, the student must understand the formulation of the problem of reflection and refraction of the flat electromagnetic wave on the flat boundary of the media section and the physics of phenomena on the interface. It is necessary to know the method of obtaining relations for the electromagnetic field vectors at the interface, turning attention to the scope of use of boundary conditions. It should also be studied the content and meaning of such concepts as an angle of complete internal reflection, the corner of the Brewer, the surface effect. Questions for self-test 1. What is the reflection physics, and refractive to a flat wave on the interface of the media section? How the electrodynamic task is formulated for reflection and pre-14

31 Plugging a flat wave on the interface interface? 3. What is the meaning of the introduction of boundary conditions? 4. How is the polarization of an electromagnetic wave falling on the edge of the media section? 5. What is the physical meaning of the phenomenon of full polarization? 6. What is understood by the skin-layer thick? 7. Connect the behavior of the module, and the phase of the reflection coefficient when the flat wave falls on the interface in the function from the angle of the incidence of the guide EMV and guide systems. Waveguides The content of this section is given in the pages in this section, existing types of guide systems, types and main features of electromagnetic waves propagating in them should consider the solution of the wave equation for rectangular and round waveguides. It is necessary to understand the main parameters characterizing the work of the waveguide: the critical wavelength, the wavelength in the waveguide, phase and group velocity, the characteristic resistance of the waveguide. It is necessary to know and be able to portray graphically the structure of the main types of oscillations in the rectangular and round waveguide, as well as be able to choose the size of the waveguide to work on a given type of oscillations. It should also have an idea of \u200b\u200bthe distribution of currents on the walls of the waveguide and the excitation and communication systems of waveguides. Questions for self-test 1. Name the currently existing types of guide systems .. What is the difference between electric, magnetic and transverse electromagnetic waves in the transmission lines? 3. What types of waves can be distributed in waveguides, coaxial and wired transmission lines? 4. Formulate the formulation of the problem of distribution of electromag - 15

32 thread waves in the waveguide. 5. What boundary conditions are used in solving the wave equation in the floor of the metal waveguide? 6. In what limits may change the phase and group velocity of electromagnetic waves in the waveguide? 7. What type of oscillations is customary called the main? 8. Based on which conditions, the selection of the cross-sectional size of the waveguide is made? 9. Word requirements for electromagnetic oscillations in a waveguide coaxial and two-wire transmission lines The content of the section is represented in page 4 9. In this section, it is necessary to study the basic concepts related to transverse electromagnetic waves, pay attention to the features of the distribution of the electromagnetic wave along the transmission line and in its cross-sections. You should also be able to record expressions for the basic parameters characterizing the data of the transmission line: wave resistance, power tank and inductance, attenuation coefficient, the value of the portable power. Questions for self-test 1. Word the basic properties of the transverse wave in the transmission lines. Picture a picture of the power lines of the electromagnetic wave in the cross-sectional plane of coaxial and two-wire transmission lines. 3. Record the expressions for the main parameters of the transmission lines under consideration. Volume resonators The content of this section is represented in on the pages when studying this section, it is necessary to understand the appointment and constraint.

33 Restructive features of various types of volume resonators. To get acquainted with the method of solving a wave equation for a volume resonator, built on the basis of a rectangular waveguide, types and structure of the simplest types of oscillations in it, as well as with methods for calculating the main parameters of the resonator. The main types of oscillations in cylindrical volume resonators should be known, ways to determine their own resonant frequency, quality and resonator sizes, excitation methods. Questions for self-test 1. What types of volume resonators are used in ultrahigh frequency techniques?. What types of oscillations can exist in bulk resonators? 3. How is the solidness of the volume resonator determined? 4. What considerations are the dimensions of volume resonators built on the basis of rectangular and round waveguides? 5. What excitation systems of resonators are used in practice? The main concepts and definitions in the RRV theory The content of this section is represented in page 4. In this section, it is necessary to pay attention to the role of Russian scientists in the development of the theory and development of technology of radio broadcasting systems, radio communications, television, radar. It should be remembered that at present all over the world has been adopted a decimal system for dividing the frequency range of waves on subbands. It is necessary to have an idea of \u200b\u200bthe features of the propagation of radio waves of these subbands. Questions for self-test 1. What subbands are separated by the entire range of radio waves?. What are the features of the distribution of radio waves of various subbands? 17.

34 Distribution of radio waves in the free space The content of this section is presented in the pages in this section you should pay attention to the energy relationships in the propagation of radio waves of non-directional and directed emitters in free space. It is necessary to be able to derive and analyze the equation of the ideal radio; Using the Guiggens-Fresnel principle, to build the Fresnel zones and determine the essential and minimum area of \u200b\u200bspace affecting the spread of radio waves. It is also necessary to draw attention to the fact that even when the radio wave of radio waves, the electromagnetic field stream is weakened in the free space with distance. You should be able to explain the physics of this phenomenon and write down a mathematical expression for the transfer loss in free space. Questions for self-test 1. How to determine the density of the energy flow and the intensity of the field of non-directional and directed emitters in free space?. How is the principle of Guiggens-Fresnel formulated? 3. How are Fresnel zones are built when RVV in free space is built? 4. What considerations determine a significant and minimum area affecting RRV in free space? 5. How to explain the process of weakening the electromagnetic field in free space? The effect of the surface of the Earth on the distribution of radio films The content of this section is presented in the pages in this section it is necessary to assimilate that the surface of the Earth has a significant impact on RRV. This influence is taken into account by the introduction of a multiplier of the weakening of the free space field, which is calculated based on the specific type of radio painter. You need to know the electromagnetic parameters 18

35 main varieties of the earth's surface. To determine the impact factor, it is necessary to solve the complex problem of radio wave diffraction around the real surface of the Earth. It should be borne in mind that at present this task is even in the most strict formulation, does not take into account the irregularities of the earth's surface and is solved for a smooth spherical surface. Received, even with such a formulation of the problem, expressions, are extremely complex and calculated a multiplier of weakening are possible only with the use of computers, therefore, in engineering practice, for some radiostrass, approximate solutions based on interference formulas in the illuminated area and a single diffraction formula in the area are used. Deep shadow. To account for the effect of the real distribution of land parameters along the radiosses and irregularities of its surface also apply approximated methods. Attention should be paid to the phenomena: coastal refraction (curvature of the electromagnetic wave trajectories); The effect of amplification of the electromagnetic field due to obstacles; On the hopping change in the size of the electromagnetic field during the transition through the border of the portions of the track with various electromagnetic parameters. Irregularities on the surface of the Earth are randomly distributed, which leads to the need to apply methods mathematical statistics In the study of radio wave propagation processes over similar uneven surfaces. Questions for self-test 1. How do the effect of the earth's surface on RRV? What electromagnetic parameters are the surface of the earth? 3. How do the problem of diffraction of radio waves around the earth's surface? 4. What characteristic areas of space are made to allocate when measured

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