Fundamentals of electrodynamics and radio wave propagation. Electrodynamics and radio wave propagation

Article

• djvu format
• size 922.8 KB
• added February 05, 2010

Zaboronkova, T. M. Fundamentals of electrodynamics and radio wave propagation:
educational manual / T. M. Zaboronkova, E. N. Myasni-
cov. - N. Novgorod: Publishing house of the Federal State Educational Institution of Higher Professional Education "VGAVT", 2009. - 133 p.

Content:
Static electric and magnetic fields,
Electrostatic field
Direct electric current
Stationary magnetic field,
Movement of charged particles in constant electric and magnetic fields,
Electromagnetic field, Maxwell's equations,
Law of electromagnetic induction,
Displacement current, Maxwell's system of equations,
Averaged Maxwell–Lorentz equations in material media,
Boundary conditions for electric and magnetic fields,
Electromagnetic waves in free space,
Plane monochromatic electromagnetic wave,
Polarization of electromagnetic waves,
Spherical electromagnetic waves in free space,
Emission of electromagnetic waves by an elementary vibrator,
Electromagnetic waves in homogeneous material media,
Electromagnetic waves in a homogeneous isotropic dielectric,
Electromagnetic waves in a medium with absorption,
Dielectric constant dispersion,
Propagation of electromagnetic wave packets group velocity,
Transfer of energy by a wave packet,
Dispersion and resonance absorption of molecular gas
Electromagnetic waves in plasma,
Ionospheric plasma parameters,
Electromagnetic waves in a homogeneous isotropic plasma,
Electromagnetic waves in a homogeneous magnetoactive plasma,
The incidence of electromagnetic waves at the interface between homogeneous media,
Reflection and refraction of waves from a flat interface between two media,
Reflection from a perfectly conducting surface,
Reflection from an imperfect conductor,
Propagation of electromagnetic waves in a smoothly inhomogeneous medium,
Smoothly inhomogeneous medium, geometric optics approximation,
Refraction of radio waves in the Earth's atmosphere,
Reflection of radio waves from a layer of inhomogeneous plasma. ,
Features of the reflection of radio waves from the ionosphere when taking into account the magnetic field,
Interference and diffraction of electromagnetic waves,
Interference of plane monochromatic waves,
Huygens-Fresnel-Kirchhoff principle,
Fraunhofer diffraction,
Fresnel diffraction,
Diffraction of radio waves by random inhomogeneities of electron density,
Propagation of radio waves in the Earth's atmosphere,
Ideal radio path, radio wave ranges,
The influence of the underlying surface on the propagation of radio waves,
The influence of the troposphere on the propagation of radio waves,
Propagation of radio waves in the ionosphere.

Related sections

see also

Babaenko L.A. Electrodynamics and propagation of radio waves, part 1

• pdf format
• size 582.45 KB
• added September 06, 2011

St. Petersburg State Pedagogical University textbook 2006. 55 pages. part 1 Lecture notes (part I) corresponds to the group of sections of the discipline “Electrodynamics and radio wave propagation” of the bachelor’s training areas 552500 “Radio Engineering”, as well as the specialty 2015000 “Household Radio-Electronic Equipment”. The basic equations of electrodynamics, boundary conditions for electromagnetic field vectors, energy characteristics, static and stationary...

Babaenko L.A. Electrodynamics and radio wave propagation, part 2

• pdf format
• size 509.49 KB
• added September 06, 2011

St. Petersburg State Pedagogical University textbook 2006. 42 pages. part 2 Lecture notes (part 2) correspond to the group of sections of the discipline “Electrodynamics and radio wave propagation” of the bachelor’s training areas 552500 “Radio Engineering”, as well as the specialty 2015000 “Household Radio-Electronic Equipment”. Statement of problems of electrodynamics, electromagnetic waves in various media, Wave phenomena at the interface between two media are considered. Intended for students...

Babaenko L.A. Electrodynamics and propagation of radio waves, part 3

• pdf format
• size 529.18 KB
• added September 06, 2011

St. Petersburg State Pedagogical University textbook 2006. 49 pages. part 3 L.A. Babenko. Electrodynamics and radio wave propagation. Basic equations of electrodynamics. Static and stationary fields. Lecture notes. Part 3 Lecture notes (Part 3) corresponds to the group of sections of the discipline “Electrodynamics and radio wave propagation” of bachelor’s training areas 552500 “Radio Engineering”, as well as specialty 2015000 “Household Radio-Electronic Equipment”. Consider...

Baskakov S.I. Electrodynamics and radio wave propagation. (textbook + problem book)

• djvu format
• size 12.97 MB
• added March 11, 2010

Two files: textbook and problem book. 1. Baskakov. Electrodynamics and radio wave propagation. 1992. 2. Baskakov. Collection of problems for the course "Electrodynamics and radio wave propagation". 1981 1. Baskakov. Electrodynamics and radio wave propagation: The fundamentals of macroscopic electrodynamics, the theory of plane electromagnetic waves in various media, methods for calculating waveguide and oscillatory systems, as well as devices for emitting and receiving electromagnetic waves are presented...

Dolukhanov M.P. Radio propagation

• djvu format
• size 3.81 MB
• added January 06, 2009

Publishing house "Svyaz", Moscow 1972. In the book, along with general questions propagation of radio waves, propagation over flat and smooth spherical surfaces of the Earth and over uneven terrain is considered in detail; the influence of the troposphere on the propagation of ground waves is analyzed; The processes of propagation of tropospheric waves and absorption of radio waves in the troposphere are considered. The issues of the structure of the ionosphere and the propagation of radio waves in it are presented. More...

Lectures - Electrodynamics and radio wave propagation

Article

• doc format
• size 1.98 MB
• added December 26, 2009

Vladimirsky State University(VlSU). Teacher: Gavrilov V. M. 184 pages. Electromagnetic field and environmental parameters. Basic equations of electrodynamics. Border conditions. Electromagnetic field energy. Electrodynamic potentials of a harmonic field. Plane electromagnetic waves. Propagation of radio waves in various environments. Wave phenomena at the interface between two media. Surface effect. Elementary emitters. Key points...

Transcript

1 FEDERAL AGENCY FOR EDUCATION State educational institution of higher education vocational education"NORTH-WESTERN STATE CORRESPONDENCE TECHNICAL UNIVERSITY" Department of Radio Engineering ELECTRODYNAMICS AND RADIO WAVE PROPAGATION EDUCATIONAL AND METHODICAL COMPLEX Institute of Radio Electronics Specialty of training of a certified specialist: radio engineering Field of bachelor's training: radio engineering St. Petersburg Publishing house SZTU 009

2 Approved by the editorial and publishing council of the UDC University Electrodynamics and propagation of radio waves: educational and methodological complex / comp. L.Ya. Rhodes, D.A. Chistyakov. SPb.: Publishing house of North-West Technical University, p. Training and metodology complex(UMK) was developed in accordance with the requirements of state educational standards of higher professional education. The educational complex covers issues of the theory of the electromagnetic field, the main methods for solving applied problems electrodynamics in relation to the propagation of electromagnetic waves in guiding systems and radio waves along natural paths. The educational complex is intended for students of the specialty studying the discipline “Electrodynamics and radio wave propagation”, and bachelors of engineering and technology in the field studying the same discipline. Considered at a meeting of the Department of Radio Engineering of the city, approved by the methodological commission of the Institute of Radio Electronics of the city Reviewers: Department of Radio Engineering of North-West Technical University (head of the department G.I. Khudyakov, Dr. Tech.. sciences, prof.); V.S. Kalashnikov, Doctor of Engineering. sciences, prof., ch. scientific co-workers VNIIRA. Compiled by: L.Ya. Rhodes, Ph.D. tech. Sciences, Associate Professor; YES. Chistyakov, Ph.D. tech. Sciences, Associate Professor Northwestern State Correspondence Technical University, 008 Rhodes L.Ya., Chistyakov D.A., 008

3 1. Information about the discipline 1.1. Preface Electrodynamics and radio wave propagation (ED and RW) belong to the disciplines of the general professional cycle. Its volume according to the state educational standard (GOS) is 170 hours. It includes two interrelated parts: part 1 - electrodynamics itself (theoretical electrodynamics) and part - the propagation of radio waves (applied electrodynamics). This discipline is basic for modern radio engineering. The purpose of studying the discipline is for students to acquire theoretical knowledge and skills in solving problems in the field of electromagnetic field theory, features of the interaction of electromagnetic waves with various physical media, the propagation of radio waves along guide systems and on natural paths. The objectives of studying the discipline are to master the basic principles of electrodynamics and the features of radio wave propagation. As a result of studying the discipline, the student must master knowledge of the discipline, formed at several levels: Have an idea: about the philosophical interpretation of the concept of “electromagnetic field”, about the history of the development of the doctrine of electromagnetism, about the relationship of electrical, magnetic and optical phenomena, about the vector nature of electromagnetic and optical fields, about the ranges of radio waves used in technology, the main features of the propagation of radio waves along natural paths. Know: Maxwell's equations in integral and differential forms, the physical meaning of all terms included in these equations; mechanisms of influence of the Earth and the Earth's atmosphere on the propagation of radio waves of various ranges. 3

4 Be able to: convert Maxwell’s equations into equations of electro- and magnetostatics, stationary electric and magnetic fields, into wave equations for electromagnetic field vectors, vector and scalar potentials; formulate a problem (select a model) to calculate the parameters of a specific radio link. Gain skills: solving problems of electrodynamics using methods: separation of variables, retarded potentials, scalar and vector Kirchhoff integrals; selection of type, dimensions and calculation of parameters of guide systems (electromagnetic energy transmission lines); calculation of radiation characteristics of elementary emitters and real antennas; choosing a model and determining the nature and degree of influence of the radio wave propagation path on the characteristics of a particular radio system. Studying the discipline “Electrodynamics and radio wave propagation” requires mastering a number of previous disciplines. These include: mathematics (series, differential and integral calculus, vector field theory, solution of differential equations); physics (electricity and magnetism, electrodynamics); computer science (algorithmization methods, numerical solution methods). In turn, the course of ED and RRR lies at the basis of all disciplines that determine vocational training specialist in the field of radio engineering: fundamentals of circuit theory, radio circuits and signals, microwave devices and antennas, signal receiving and processing devices, signal generation and conditioning devices, radio systems, etc. Content, scope and order of studying the course materials “Electrodynamics and radio wave propagation” in accordance with the requirements of the State Standards, they are set out in the “Work Program”, presented in the heading “Information Resources”. There is also a “Thematic Plan” containing information about the types of reporting by topic. 4

5 1.. Contents of the discipline and types of academic work Contents of the discipline In accordance with the State Standards, the following didactic units should be studied in the course “Electrodynamics and Propagation of Radio Waves”: integral and differential equations of electromagnetism; complete system of Maxwell's equations, boundary conditions; electromagnetic field energy; Umov-Poynting theorem; boundary value problems of electrodynamics; analytical and numerical methods for solving boundary value problems; electromagnetic waves in various media; electrodynamic potentials; electromagnetic waves in guiding systems; electromagnetic oscillations in volumetric resonators; excitation of electromagnetic fields by specified sources; radiation of electromagnetic waves into free space; retarded potential theorem; propagation of electromagnetic waves near the Earth's surface; tropospheric propagation of radio waves; propagation of radio waves in rough terrain and in the presence of obstacles; models and methods for calculating radio paths Scope of the discipline and types of academic work Total hours Type of academic work Form of training Full-time Part-time Part-time Correspondence Total labor intensity of the discipline (OTD) 170 Work under the guidance of a teacher (RpRP) Including classroom lessons: Lectures Practical lessons(PL) Laboratory work (LR) Number of hours of work using DOT Student’s independent work

6 Intermediate control, quantity Test work - Test Type of final control (exam), quantity List of types of student's educational work, ongoing monitoring of progress and intermediate certification - two tests (for full-time and correspondence forms of study); -tests (training tests on topics, milestone tests on discipline sections, self-test questions, etc.); - one test (for laboratory work part 1 - electrodynamics); -two exams. 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, materiality of the electromagnetic field, electromagnetic field vectors, classification of media in electrodynamics. Maxwell's equations - fundamental equations of electrodynamics (1 hour) [1], with Maxwell's equations in integral and differential forms and their physical meaning. Continuity equation for electric current. Third-party electric and magnetic currents and charges. A complete system of EMF equations in symmetric and asymmetric forms. Maxwell's equations at harmonic 6

7 logical dependence of electromagnetic processes on time. Complex dielectric constant of media. The principle of commutative duality of Maxwell's equations. Energy characteristics of EMF (6 hours) [1], with Energy balance in EMF: localization, movement and energy transformations. Energy characteristics for the harmonic dependence of electromagnetic processes on time. Electromagnetic waves - a form of existence of EMF (6 hours) [1], with Wave equations for EMF vectors. Electrodynamic potentials. Wave equations for electrodynamic potentials. Wave equations in complex form. Particular types of EMF equations (4 hours) [3], with Electrostatic field: system of charges, dipole, capacitance, conductors and dielectrics in an electrostatic field. Stationary field: current system, magnetic dipole, inductance. Quasistationary field: from Maxwell's equations to circuit theory..1.. Section. Boundary value problems of electrodynamics Basic methods for solving problems of electrodynamics (8 hours) [1], p. 1-7 Internal and external problems of electrodynamics. Boundary conditions and radiation condition. Uniqueness of solutions to electrodynamics problems. Principle of superposition of solutions, reciprocity theorem, equivalence theorem. Rigorous methods for solving: retarded potentials, separation of variables, Kirchhoff. Approximate solution methods: geometric and wave optics, edge waves, geometric diffraction theory, modeling. 7

8 Plane electromagnetic waves (EMW) (10 hours) [1], p. 7-4 General properties of wave processes. Plane homogeneous electromagnetic waves in a homogeneous infinite isotropic medium. Waves in a dielectric, semiconductor and conductor. Spherical electromagnetic waves in boundless homogeneous media. Electromagnetic waves radiation (1 hour) [1], with Types of elementary emitters. Radiation of a system of specified currents. Elementary electrical emitter: components of EMF vectors, directivity function, power and radiation resistance. Elementary magnetic emitter. Huygens element. Flat electromagnetic waves in an inhomogeneous medium (10 hours) [3], with Electromagnetic waves and optical rays. Boundary conditions for electromagnetic field vectors. Reflection and refraction of electromagnetic waves at a flat interface. Snell's laws and Fresnel's formulas. Concepts of Brewster angles, total internal reflection, surface effect Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators. Guided electromagnetic waves and guiding systems. Waveguides (16 hours) [ 1 ], s General information about guiding systems and guided waves. Hollow metal waveguides: rectangular, round. The structure of the electromagnetic field, the main types of waves, phase and group velocities, wavelength in the waveguide, characteristic impedance, attenuation of electromagnetic 8

9 thread waves, excitation and coupling of waveguides, selection of waveguide sizes for operation on a given type of waves. Coaxial and two-wire transmission lines (4 hours) [3], p. 4-9 Features of T waves and the main parameters of T waves in a coaxial and two-wire transmission line. Phase constant, phase velocity, group velocity, line wavelength, characteristic impedance. Range of single-mode operation of a coaxial line. Volumetric resonators (8 hours) [ 3 ], with a section of the guide structure as a resonator. General theory of cavity resonators based on rectangular, cylindrical and coaxial waveguides. Natural frequency and quality factor of resonators. Excitation of resonators. Part of radio wave propagation.1.4. Section 4. Electromagnetic waves propagation near the Earth's surface. The influence of obstacles. Basic concepts and definitions (4 hours), p. 4-7 Basic concepts and definitions in the theory of RRP. The role and place of radio wave propagation issues in the training of radio engineers. History of the development of the theory of RRR. Classification of radio waves by frequency ranges and methods of propagation along natural paths. Propagation of radio waves in free space (10 hours), with the Electromagnetic field of isotropic and directional emitters in free space. Equations of ideal radio communication for emitters 9

10 different types. Huygens-Fresnel principle. Fresnel zones in free space. Essential and minimal areas of space during the propagation of radio waves. Transmission losses when radio waves propagate in free space. The influence of the Earth's surface on the propagation of radio waves (18 hours), with Electrical parameters earth's surface. Statement and general solution of the problem of radio wave diffraction around a homogeneous spherical Earth's surface. Analysis of the general solution to the problem: the influence of the electrical parameters of the Earth's surface and the distance between corresponding points on the value and behavior of the attenuation factor in space. Line-of-sight distance and line-of-sight attenuation factor calculation. Interference formulas. Limits of applicability of interference formulas. Calculation of attenuation multiplier in shadow and penumbra zones. Reflection of radio waves from the Earth's surface, significant and minimal areas of the reflecting surface. Taking into account the influence of the curvature of the Earth's surface when reflecting radio waves. The influence of the heterogeneity of the electrical parameters of the Earth's surface on the propagation of radio waves along it. The influence of irregularities of the Earth's surface on the propagation of radio waves. Rayleigh criterion. General information about the propagation of radio waves near statistically uneven surfaces Section 5. The influence of the Earth's atmosphere on the propagation of radio waves. The influence of the Earth's troposphere on the propagation of radio waves (10 hours), with the Composition and structure of the Earth's atmosphere. Electromagnetic parameters of the troposphere, stratosphere and ionosphere. Refraction of radio waves in the troposphere and ionosphere. Wave trajectory equation and beam radius of curvature. Types of refraction of radio waves in the troposphere. Equivalent radius of the Earth. The formation process and parameters of tropospheric waveguides. 10

11 The influence of the Earth’s ionosphere on the propagation of radio waves (8 hours), with the Trajectory of radio waves in the ionosphere. Reflection of radio waves from the ionosphere. Critical and maximum frequencies. Phase and group velocities of radio wave propagation in the ionosphere. The influence of the Earth's magnetic field on the propagation of radio waves in the ionosphere. Scattering and absorption of radio waves in the troposphere and ionosphere. Methods experimental research troposphere and ionosphere Section 6. Models and methods for calculating radio paths. Radio lines for various purposes. Ranges of applied frequencies (8 hours), with lines of radio broadcasting, television, radio communications, radar, radio navigation, radio control and telemetry. The purpose of radio links, the frequency ranges used and the characteristics of the propagation of radio waves in these ranges along the radio link route. Methods for calculating various radio lines, with Methods for calculating radio lines for various purposes and various ranges of radio waves. eleven

12.. Thematic plan of the discipline..1. Thematic plan of the discipline for full-time students Name of sections and topics Number of hours for full-time study Types of classes (hours) lectures PZ (C) LR audit. DOT audit. DOT audit. DOT Independent work Tests Types of control Examinations Abstracts LR Course work TOTAL Section 1. Integral and differential equations of electromagnetism 1.1 Basic concepts and definitions 3 1. Maxwell's equations fundamental equations of electrodynamics Energy characteristics of the electromagnetic field (EMF) Electromagnetic waves form of existence of EMF Particular types of EMF equations 7 Section. Boundary-value problems of electrodynamics 8.1 Basic methods for solving problems of electrodynamics 9. Plane electromagnetic waves (EMW) in a homogeneous medium 10.3 Spherical EMW in infinite media. Emission of electromagnetic waves Flat electromagnetic waves in an inhomogeneous medium 1 Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators Guided electromagnetic waves and guiding systems. Waveguides Coaxial and two-wire transmission lines Volume resonators Section 4. Propagation of 4 electromagnetic waves near the Earth's surface. Influence of obstacles Basic concepts and definitions

13 18 4. Propagation of radio waves in free space The influence of the Earth's surface on the propagation of radio waves 0 Section 5. The influence of the Earth's atmosphere on the propagation of radio waves The influence of the Earth's troposphere on the propagation of radio waves 5. The influence of the Earth's ionosphere on the propagation of radio waves 3 Section 6. Models and methods for calculating radio paths Radio links of various appointments. Ranges of frequencies used 5 6. Methods for calculating various radio links Thematic plan of the discipline for full-time and part-time students Name of sections and topics Number of full-time hours Types of classes (hours) Lectures PZ LR Auditorium. Pillbox Audithorn. Pillbox Audithorn. Pillbox Samost. work Tests Types of control Control. work PZ LR Course. works Total Section 1. Integral and differential equations of electromagnetism 1 Basic concepts and definitions Maxwell's equations - fundamental equations of electrodynamics Energy characteristics of the electromagnetic field (EMF) Electromagnetic waves - the form of existence of EMF Particular types of EMF equations 4 7 Section. Boundary-value problems of electrodynamics Basic methods for solving problems of electrodynamics Plane electromagnetic waves (EMW) in a homogeneous medium Spherical EMW in boundless homogeneous media. Emission of electromagnetic waves Flat electromagnetic waves in an inhomogeneous medium

14 1 Section 3. Electromagnetic waves in guide systems. Electromagnetic oscillations in volumetric resonators Guided electromagnetic waves and guiding systems. Waveguides Coaxial and two-wire transmission lines Volume resonators Section 4. Propagation of electromagnetic waves near the Earth's surface. Influence of obstacles Basic concepts and definitions Propagation of radio waves in free space Influence of the Earth's surface on the propagation of radio waves Section 5. Influence of the Earth's atmosphere on the propagation of radio waves Influence of the Earth's troposphere on the propagation of radio waves Influence of the Earth's ionosphere on the propagation of radio waves Section 6. Models and methods for calculating radio paths Radio links for various purposes. Ranges of frequencies used Methods for calculating various radio links Thematic plan of the discipline for students of part-time study p/p Name of sections and topics Number of hours for full-time study Types of classes (hours) lectures PZ (C) LR audit. DOT audit. DOT audit. DOT Independent work Tests Types of control Test papers Abstracts LR Coursework TOTAL Section 1. Integral and differential equations of electromagnetism 1.1 Basic concepts and definitions 3 1. Maxwell's equations fundamental equations of electrodynamics Energy characteristics of the electromagnetic field (EMF)

15 5 1.4 Electromagnetic waves form of existence of EMF Particular types of EMF equations Section. Boundary-value problems of electrodynamics Basic methods for solving problems of electrodynamics 9. Plane electromagnetic waves (EMW) in a homogeneous medium Spherical EMW in infinite media. Emission of electromagnetic waves Flat electromagnetic waves in an inhomogeneous medium Section 3. Electromagnetic waves in guide 3 systems. Electromagnetic oscillations in volumetric resonators Guided electromagnetic waves and guiding systems. Waveguides Coaxial and two-wire transmission lines Volume resonators Section 4. Propagation 4 of electromagnetic waves near the Earth's surface. Influence of obstacles Basic concepts and definitions Propagation of radio waves in free space Influence of the Earth's surface on the propagation of radio waves Section 5. Influence of the Earth's atmosphere 5 on the propagation of radio waves Influence of the Earth's troposphere on the propagation of radio waves 5. Influence of the Earth's ionosphere on the propagation of radio waves 3 Section 6. Models and methods for calculating radio paths Radio lines for various purposes. Frequency ranges used 5 6. Methods for calculating various radio links

16.3. Structural and logical diagram of the discipline Electrodynamics and propagation of radio waves Section 1 Integral and differential equations Section Boundary problems of electro- Section 3 Electromagnetic waves in guides Section 4 Propagation of electromagnetic waves near Section 5 Influence of the Earth’s atmosphere on propagation Section 6 Models and methods for calculating the propagation Basic concepts and definition - Maxwell's equations - fundamental Basic methods for solving problems of electromagnetic waves and Guided electromagnetic waves and Basic concepts and definition - Influence of the Earth's troposphere on the propagation of Radio links for various purposes. Range - Energy characteristics of electric plane - Plane electromagnetic waves Spherical electromagnetic waves in a boundaryless Coaxial and two-wire transmission lines Propagation of radio waves in free pro- Influence of the Earth’s ionosphere on propagation Methods for calculating various ra- Electromagnetic wave form sup- Plane electromagnetic waves Volume resonators Influence of the Earth's surface on propagation Propagation of radio waves in space Particular types of electromagnetic equations

17.4. Time schedule for studying the discipline (for students studying using DOT) Title of the section (topic) Duration of studying the section (topic) 1 Section 1. Integral and differential 7 days. equations of electrodynamics Section. Boundary value problems of electrodynamics 9 days. 3 Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators 7 days. 4 Section 4. Electromagnetic propagation 7 days. waves near the Earth's surface 5 Section 5. The influence of the Earth's atmosphere on the propagation 4 days. radio waves 6 Section 6. Models and methods for calculating radio paths 4 days. 7 Test 1 day. 8 Test day. TOTAL.5. Practical block 5.1. Practical classes Practical classes (full-time study) 4 days. Number and name of the topic Topic.3 Spherical electromagnetic waves in boundless media. EMW radiation Topic 3.1 Guided EMW and guiding systems. Waveguides Topic 4. Propagation of radio waves in free space Solving problems on the emission of electromagnetic waves by elementary electric and magnetic dipoles Determining the dimensions of waveguides and the characteristics of electromagnetic fields in rectangular and round waveguides Determining the parameters of radio communication lines in free (outer) space Name of topics for practical classes Number of hours Topic 4.3 Influence on - Calculation of EMF voltage at the

18 surface of the Earth on the propagation of radio waves on radio lines passing near the surface of the Earth Practical classes (correspondence and part-time forms of study). Practical classes for students of the specified forms of study are not provided for in the educational work plans..5.. Laboratory work Laboratory work (full-time study) Number and name of the section (topic) Section. Boundary value problems of electrodynamics Topic.. Plane electromagnetic waves Topic.4. Flat electromagnetic waves in an inhomogeneous medium Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators Topic 3.1. Guided electromagnetic waves and guiding systems Topic 3.3. Volumetric resonators Name of laboratory work Study of the polarization of the electromagnetic field Study of the reflection and refraction of plane electromagnetic waves at a flat interface between two homogeneous dielectric media Study of the fundamental wave in a hollow rectangular metal waveguide Study of the electromagnetic field in a cylindrical volumetric resonator Number of hours

19 Section 4. Propagation of electromagnetic waves near the Earth's surface Topic 4. Propagation of radio waves in free space Topic 4.3. The influence of the Earth's surface on the propagation of radio waves Study of a region of space that has a significant influence on the propagation of radio waves in a homogeneous medium Study of the influence of the Earth's surface on the propagation of radio waves 4 4 Laboratory work (part-time and part-time courses) Number and title of section (topic) Section. Boundary value problems of electrodynamics Topic.. Plane electromagnetic waves Topic.4. Flat electromagnetic waves in an inhomogeneous medium Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators Topic 3.1. Guided electromagnetic waves and guiding systems Topic 3.3. Volumetric resonators Name of laboratory work Study of the polarization of the electromagnetic field Study of the reflection and refraction of plane electromagnetic waves at a flat interface between two homogeneous dielectric media Study of the fundamental wave in a hollow rectangular metal waveguide Study of the electromagnetic field in a cylindrical volumetric resonator Number of hours

20 Section 4. Propagation of electromagnetic waves near the surface of the Earth Topic 4. Propagation of radio waves in free space Topic 4.3. The influence of the Earth's surface on the propagation of radio waves Study of a region of space that has a significant influence on the propagation of radio waves in a homogeneous medium Study of the influence of the Earth's surface on the propagation of radio waves 4 4 Laboratory work (correspondence course) Number and name of the section (topic) Section. Boundary value problems of electrodynamics Topic.. Plane electromagnetic waves Topic.4. Flat electromagnetic waves in an inhomogeneous medium Section 3. Electromagnetic waves in guiding systems. Electromagnetic oscillations in volumetric resonators Topic 3.1. Guided electromagnetic waves and guiding systems Topic 3.3. Volumetric resonators Name of laboratory work Study of the polarization of the electromagnetic field Study of the reflection and refraction of plane electromagnetic waves at a flat interface between two homogeneous dielectric media Study of the fundamental wave in a hollow rectangular metal waveguide Study of the electromagnetic field in a cylindrical volumetric resonator Number of hours 4

21 Section 4. Propagation of electromagnetic waves near the Earth's surface Topic 4.. Propagation of radio waves in free space Topic 4.3. Influence of the Earth's surface on the propagation of radio waves Study of the region of space that has a significant influence on the propagation of radio waves in a homogeneous medium Study of the influence of the Earth's surface on the propagation of radio waves.6. The point-rating system for assessing knowledge when using DOT The discipline Electrodynamics and radio wave propagation, 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 ends with passing an exam. The first part of the course contains three sections (twelve topics), when studying which you must complete the first test, consisting of two tasks. Each topic in the reference note ends with a list of self-test questions that should be considered open-ended practice tests. After studying each topic, you must answer the questions of the training tests of the current (intermediate) control, which contains five questions. The study of each section ends with an answer to the questions of the midterm control test, which contains ten questions. The numbers of the corresponding tests are given in the thematic plan. Rating points are determined as follows: - for the correct answer to a midterm control test question - a point; - for a correctly solved problem - 0 points. If you successfully work with the materials of the first part of the course, the student can receive x10x3 +0x =100 points. Overcoming the threshold of 70 points, as well as completing a cycle of laboratory work in sections and 3 during the examination session and receiving a 5

22 laboratory tests provide access to the exam. The second part of the course is studied in the sixth semester and ends with an exam. The second part of the course consists of three sections (seven topics), during the study of which you must complete a second test consisting of two tasks. Each topic in the reference notes ends with self-test questions that should be treated as open-ended practice tests. After studying each topic, you must answer the questions of the training test of the current (intermediate) control, consisting of five questions. The study of each section ends with an answer to the questions of the midterm control test, which contains ten questions. The numbers of the corresponding tests are given in the thematic plan. The determination of rating points when studying the second part of the course is carried out in the same way as the first part. With successful work with the materials of the second part of the course, the student can receive x10x3 + 0x = 100 points. Overcoming the threshold of 75 points and completing a series of laboratory works during the examination session ensures admission to the exam. 3. Information resources of the discipline 3.1. Bibliographic list Main: 1. Kalashnikov, V.S. Electrodynamics and propagation of radio waves (electrodynamics): letters. lectures / V.S. Kalashnikov, L.Ya. Rhodes. SPb.: Publishing House of North-West Technical University, Rhodes, L.Ya. Electrodynamics and radio wave propagation (radio wave propagation): textbook.-method. complex: textbook / L.Ya. Rhodes. - St. Petersburg: Publishing house of North-West Technical University, Krasyuk, N.P. Electrodynamics and propagation of radio waves: textbook. manual for universities / N.P. Krasyuk, N.D. Dymovich.- M.: Higher. school, additional: 6

23 4. Petrov, B.M. Electrodynamics and propagation of radio waves: textbook. for universities / B.M. Petrov. - ed., rev. M.: Hotline Telecom, Krasyuk, N.P. Propagation of VHF in the inhomogeneous troposphere: textbook. allowance / N.P. Krasyuk, L.Ya. Rhodes. L.: SZPI, Chistyakov, D.A. Laws and equations of electrodynamics as consequences of Maxwell’s equations: lecture notes / D.A. Chistyakov. SPb.: SZPI, Chistyakov, D.A. Fundamentals of electrodynamics in problems with solutions: writing. lectures/ D.A. Chistyakov. SPb.: SZPI, Chistyakov, D.A. Maxwell's equations, physical axioms of electrodynamics: letters. lectures / D.A. Chistyakov. SPb.: SZPI, V electronic library NWTU at the address there are sources from bibliography under numbers: 1;; Background summary (script educational process) The discipline Electrodynamics and radio wave propagation, as mentioned above, is a fundamental discipline and is entirely based on courses in physics and higher mathematics. In this regard, when starting to study it, it is necessary to recall in memory the basic information from the second part of the course in general physics (electricity and magnetism) and the following sections of higher mathematics: equations of mathematical physics, vector analysis, field theory. The main goal of the discipline is to study Maxwell's equations, their physical meaning and the application of these equations to solve applied problems in radiophysics and radio engineering. The methodology and sequence of studying the discipline correspond to the list of thematic topics. The material of each topic is rich in mathematical relationships, the physical interpretation of which is often quite complex, so studying the material requires serious, thoughtful work. 7

24 3..1. Basic concepts and definitions in electrodynamics Basic concepts and definitions are presented in the following pages. When studying this section, it is necessary to understand the purpose of the discipline in the training of radio engineers, its place and tasks in the system of modern ideas of natural science, paying special attention to the materiality of the electromagnetic field. It is necessary to understand that the electromagnetic field in all its manifestations is completely characterized by two main and four additional vectors. The electromagnetic field exists and is considered in various environments, which are classified according to the nature of the dependence of their electromagnetic parameters on time, spatial coordinates, magnitude and direction of the vectors of the electromagnetic field existing in a given environment. All mathematical relationships in this course are written in SI units. Questions for self-test 1. What are the main features of the electromagnetic field that confirm its materiality? What is the physical meaning of the vectors characterizing the electromagnetic field? 3. What form do the material equations for the electromagnetic field vectors have? 4. What classifications of media are used in electrodynamics? 3... Maxwell's equations - fundamental equations of electrodynamics The content of this section is presented in on pages It is necessary to pay attention to the fact that Maxwell's equations are the result of a generalization of a large number of physical laws, they represent the fundamental dependencies of macroscopic electrodynamics, allowing one to obtain all the basic relations of the theory of electromagnetic 8

25th field. It should be understood that the sources of the electromagnetic field are electrically charged particles, either moving or at rest. In practical applications, the harmonic time dependence of the quantities included in Maxwell's equations is often used, so it is convenient to use the symbolic method to represent them. Questions for self-test 1. What experimental laws underlie Maxwell’s equations? What is the physical meaning of displacement current? 3. What is the physical meaning of Maxwell’s equations in integral and differential forms? 4. What is the difference between the symmetric and asymmetric forms of writing Maxwell’s equations? Energy characteristics of EMF The content of this section is presented in the following pages. The electromagnetic field as a type of matter has a certain energy. The law of conservation is valid for him. The analytical representation of this law is the electromagnetic energy balance equation - the Umov-Poynting theorem. Questions for self-test 1. What energy components can be included in the electromagnetic field energy balance equation? Write down the expression for the Poynting vector in the case of time-harmonic fields. Electromagnetic waves are the form of existence of EMF. The content of this section is given in the pages. From Maxwell’s equations it follows that the electromagnetic field can

26 exist in the form of electromagnetic waves. Adequate relations describing the wave nature of the electromagnetic field are wave equations - second-order partial differential equations, which can be obtained directly from Maxwell's equations - first-order partial differential equations. To solve various kinds of applied problems, wave equations for field vectors and wave equations for electrodynamic potentials are usually used. With the harmonic dependence of electrodynamic processes on time, the recording form and solution of wave equations are significantly simplified. Questions for self-test 1. What types of wave equations are used to solve electrodynamics problems? What is the meaning of the calibration ratio? 3. What is the difference between the d'Alembert and Helmholtz equations and the generalized wave equation? 4. Is there a difference between the vector potential and the Hertz vector in the case of a harmonic electromagnetic field? Particular types of EMF equations The content of this section is given on the pages Equations of stationary and static fields are obtained as special cases from the equations of electrodynamics - Maxwell's equations, provided that the sources of the electromagnetic field are either stationary (independent of time), or, in addition, also motionless (static). Stationary and static fields are material; for them the law of conservation and transformation of energy is satisfied, but they are not of a wave nature and the equations describing their behavior do not contain a time dependence (for example, the Poisson and Laplace equations). Self-test questions 10

27 1. Under what conditions does Maxwell’s system of equations break up into systems of electro- and magnetostatic equations? What is the difference between stationary and static fields? 3. How is the energy value of the electrostatic field determined? 4. Write second-order partial differential equations for static and stationary fields. 5. What methods are used to solve electrostatics problems? Basic methods for solving problems of electrodynamics The content of this section is presented on pages 1 7. When mastering this section, it is necessary to study the features of the formulation and solution of internal and external problems of electrodynamics, paying special attention to the formulation of conditions for the uniqueness of the solution of electrodynamic problems for limited and unlimited volumes of space, the basic principles and theorems used in constructing solutions to practical problems. Study rigorous and approximate solution methods, taking into account that the solution results by any rigorous methods are the same, while the results of solving the problem obtained by various approximate methods differ from each other. Questions for self-test 1. How are internal and external problems of electrodynamics formulated? What is the role of the radiation condition in solving external problems? 3. How is the uniqueness theorem for solving problems of electrodynamics formulated? 4. Under what conditions is the principle of superposition of solutions valid? 5. For what media does the reciprocity theorem hold and what is its essence? 6. What is the role of the equivalence theorem for external problems of electrodynamics? 7. What is the basis for solving problems using the retarded potential method? 11

28 cialis? 8. Under what conditions can the Kirchhoff method be considered a rigorous solution method? 9. Formulate the conditions for the applicability of geometric and wave optics methods. 10. What is the essence of the edge wave methods and the geometric theory of diffraction? 11. What is the essence of the electrodynamic modeling method? Plane electromagnetic waves (EMW) The contents of the section are presented on pages 7 4. In this section, it is necessary to pay attention to the fact that to characterize any wave process, the concepts of phase and amplitude wave fronts are introduced. In the general case, phase fronts can have any shape, but the main ones are: flat, cylindrical and spherical. To characterize vector wave processes, in addition to the amplitude, phase and frequency of oscillations, the concept of polarization is introduced. It is necessary to study all existing types of polarization of electromagnetic waves. Here we should also consider the solution of the Helmholtz equations for electromagnetic field vectors in the form of plane waves, paying attention to various mathematical forms of writing expressions, the mutual orientation of the electric and magnetic field strength vectors and the Poynting vector, as well as the connection between them and the electromagnetic parameters of the medium. It is necessary to study the features of the propagation of a plane wave in a dielectric, semiconductor and conductor, paying attention to the specifics of the propagation of a plane wave in conductive media (exponential decrease in amplitude, the appearance of a phase shift and dispersion). Questions for self-test 1. What is the difference between wave processes and oscillatory processes in radio circuits? 1

29. What additional characteristic is introduced to describe vector wave processes? 3. What types of polarization are usually considered in problems of electrodynamics? 4. What are the main properties of a plane wave? 5. What is the nature of the wave number in different media? 6. What are the features of plane wave propagation in conductive media? 7. What is the nature of the dispersion phenomenon during the propagation of a plane wave in a semiconducting medium? 8. What does nonlinearity and anisotropy of the medium lead to during the propagation of a plane wave? Spherical electromagnetic waves in boundless homogeneous media. Radiation of electromagnetic waves The content of this section is given in pages When studying this section, it is necessary to understand the formulation of the problem of the radiation of electromagnetic waves, as well as the fact that radiation is created only by electric charges moving with acceleration. It is necessary to understand the purpose of introducing the concept of an elementary emitter, the types of models of elementary emitters and methods for calculating their characteristics. You should pay attention to the features of the distribution of the electromagnetic field of an elementary emitter in space depending on the distance and angular coordinates, and understand the features of the behavior of the Poynting vector. You also need to know the basic specifications emitters, such as radiation pattern, power and radiation resistance, directivity 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 electromagnetic wave radiation formulated? 3. What solution method is used to calculate the radiation of an elementary electric dipole? 4. Name the characteristic zones of space and separation criteria in which the radiation field is usually considered. 5. Characterize the energy properties of the field emitted by an elementary emitter. 6. What characteristics are characteristic of an elementary radiator as an antenna? 7. What models are used to describe an elementary magnetic emitter? 8. Compare the emissivity of elementary electric and magnetic emitters. 9. What is the shape of the directional pattern of the Huygens element? Flat electromagnetic waves in an inhomogeneous medium The content of this section is presented in on pages When studying this section, the student must understand the formulation of the problem of reflection and refraction of a plane electromagnetic wave at a flat interface between media and the physics of the phenomena that take place at the interface. It is necessary to know the methodology for obtaining relations for the electromagnetic field vectors at the interface, paying attention to the areas of use of boundary conditions. You should also study the content and meaning of such concepts as angle of total internal reflection, Brewster angle, surface effect. Questions for self-test 1. What is the physics of reflection and refraction of a plane wave at the interface? How is the electrodynamic problem of reflection and pre- 14

31 breaking of a plane wave at the interface? 3. What is the point of introducing boundary conditions? 4. How is the polarization of an electromagnetic wave incident on the interface determined? 5. What is the physical meaning of the phenomenon of complete polarization? 6. What is meant by skin layer thickness? 7. Draw the behavior of the modulus and the phase of the reflection coefficient when a plane wave is incident on the interface as a function of the angle of incidence. Guided electromagnetic waves and guiding systems. Waveguides The contents of this section are given in the following pages. In this section, you should study the existing types of guiding systems, the types and main features of electromagnetic waves propagating in them, and consider solving the wave equation for rectangular and circular waveguides. It is necessary to understand the main parameters characterizing the operation of the waveguide: critical wavelength, wavelength in the waveguide, phase and group velocities, characteristic impedance of the waveguide. It is necessary to know and be able to graphically depict the structure of the main types of oscillations in a rectangular and circular waveguide, and also to be able to select the dimensions of the waveguide to operate on a given type of oscillation. You should also have an idea of ​​the distribution of currents on the walls of the waveguide and the excitation and coupling systems of the 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 transmission lines? 3. What types of waves can propagate in waveguides, coaxial lines, and wire lines? 4. Formulate a statement of the problem of electromagnetic propagation 15

32 thread waves in a waveguide. 5. What boundary conditions are used when solving the wave equation in a hollow metal waveguide? 6. Within what limits can the phase and group velocities of electromagnetic waves in a waveguide vary? 7. What type of oscillations is usually called the main one? 8. Based on what conditions is the choice of the dimensions of the waveguide cross-section made? 9. Formulate the requirements for devices for excitation of electromagnetic oscillations in a waveguide Coaxial and two-wire transmission lines The contents of the section are presented on pages 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 electromagnetic waves along the transmission line and in its cross sections. You should also be able to write down expressions for the main parameters characterizing the transmission line data: characteristic impedance, linear capacitance and inductance, attenuation coefficient, and the amount of transferred power. Questions for self-test 1. Formulate the basic properties of a transverse wave in transmission lines. Draw a picture of the lines of force of an electromagnetic wave in the cross-sectional plane of coaxial and two-wire transmission lines. 3. Write down expressions for the main parameters of the transmission lines under consideration. Volume resonators. The content of this section is presented on pages. When studying this section, it is necessary to understand the purpose and design of 16

33 manual features various types volumetric resonators. Familiarize yourself with the method for solving the wave equation for a cavity resonator built on the basis of a rectangular waveguide, the types and structure of the simplest types of oscillations in it, as well as methods for calculating the main parameters of the resonator. You should know the main types of vibrations in cylindrical cavity resonators, methods for determining the natural resonant frequency, quality factor and dimensions of the resonator, and methods of excitation. Questions for self-test 1. What types of cavity resonators are used in microwave technology? What types of oscillations can exist in cavity resonators? 3. How is the quality factor of a cavity resonator determined? 4. From what considerations are the dimensions of cavity resonators built on the basis of rectangular and circular waveguides determined? 5. What resonator excitation systems are used in practice? Basic concepts and definitions in the theory of radio broadcasting The content of this section is presented on 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 for broadcasting systems, radio communications, television, and radar. It should be remembered that the decimal system of dividing the frequency range of waves into subbands is currently accepted throughout the world. It is necessary to have an understanding of the characteristics of the propagation of radio waves in these subbands. Questions for self-test 1. What subbands are the entire range of radio waves divided into? What are the features of the propagation of radio waves in different subbands? 17

34 Propagation of radio waves in free space The content of this section is presented in the pages In this section, you should pay attention to the energy relationships during the propagation of radio waves from omnidirectional and directional emitters in free space. It is necessary to be able to derive and analyze the ideal radio communication equation; using the Huygens-Fresnel principle, construct Fresnel zones and determine the essential and minimal areas of space that influence the propagation of radio waves. It is also necessary to pay attention to the fact that even when radio waves propagate in free space, the flow of electromagnetic field energy weakens with distance. You should be able to explain the physics of this phenomenon and write down the mathematical expression for free space transmission loss. Questions for self-test 1. How to determine the energy flux density and field strength of non-directional and directional emitters in free space? How is the Huygens-Fresnel principle formulated? 3. How are Fresnel zones constructed during RRR in free space? 4. What considerations are used to determine the essential and minimal areas affecting the RRR in free space? 5. How to explain the process of weakening the electromagnetic field in free space? The influence of the Earth's surface on the propagation of radio waves The content of this section is presented in the following pages. In this section, it is necessary to understand that the Earth's surface has a significant influence on the RRF. This influence is taken into account by introducing a free space field attenuation factor, which is calculated based on the specific type of radio path. Need to know electromagnetic parameters 18

35 main varieties of the earth's surface. To determine the attenuation 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 problem, even in the most rigorous formulation, does not take into account the unevenness of the Earth's surface and is solved for a smooth spherical surface. The expressions obtained, even with this formulation of the problem, are extremely complex and calculations of the attenuation factor are possible only with the use of a computer, therefore in engineering practice, for some radio paths, approximate solution methods are used, based on interference formulas in the illuminated region and a single-term diffraction formula in the region deep shadow. To take into account the influence of the real distribution of Earth parameters along the radio path and the roughness of its surface, approximate methods are also used. Attention should be paid to the following phenomena: coastal refraction (curvature of electromagnetic wave trajectories); the effect of increasing the magnitude of the electromagnetic field due to obstacles; to an abrupt change in the magnitude of the electromagnetic field when crossing the boundary of sections of the route with different electromagnetic parameters. Irregularities on the Earth's surface are distributed randomly, which leads to the need to use methods of mathematical statistics when studying the processes of radio wave propagation over such uneven surfaces. Questions for self-test 1. How is the influence of the Earth’s surface on RWP taken into account? What electromagnetic parameters characterize the Earth's surface? 3. How is the problem of radio wave diffraction around the Earth’s surface formulated? 4. What characteristic areas of space are usually identified when studying 19

Guidelines for the study of the disciplines “Electrodynamics and radio wave propagation” and “Electromagnetic fields and waves” for students VDBV-6-16 References Basic literature 1. Nikolsky V.V.,

CONTENTS Preface... 8 Chapter 1. Fundamentals of electromagnetism... 9 1.1. Electromagnetic field...9 1.2. Conduction current density...12 1.3. Law of conservation of charge...14 1.4. Gauss's law...15 1.5. Law

1 1. Goals and objectives of the discipline 1.1. Objectives of teaching the discipline The discipline “Fundamentals of electrodynamics and radio wave propagation” provides basic training for radio engineers in the theory of electrodynamics and

List of questions for preparing for the exam in the discipline “Electrodynamics and radio wave propagation” winter session of the 2018/19 academic year, group RRBO-16 * Questions that were not covered in class,

Abbreviations: Definition F-ka F-la - Pr - definition formulation formula example 1. Electric field 1) Fundamental properties of charge (list) 2) Coulomb's law (F-la, figure) 3) Electric intensity vector

FEDERAL AIR TRANSPORT AGENCY FEDERAL STATE BUDGETARY EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION "MOSCOW STATE TECHNICAL UNIVERSITY OF CIVIL

Federal State Budgetary Educational Institution of Higher Professional Education NATIONAL RESEARCH UNIVERSITY "MEI" "APPROVED" Director of the IRE Miroshnikova I.N. signature

Questions for self-control on the topics: Electrostatics, magnetism, vibrations. 1. What electric charge carriers do you know? 2. How does a charged body differ from a neutral one at the atomic level. 3. What

Bachelors of PHYSICS AND NATURAL SCIENCE (for students of the IBM Faculty) SEMESTER 3 Module 1 Table 1 Types of classroom activities and independent work Duration of implementation or implementation, weeks Labor intensity, hours

Electrodynamics 1. Mathematical methods of electrodynamics. Elements of vector and tensor calculus (brief summary of basic formulas and concepts). Special functions of mathematical physics. 2. Basic

8 ELECTROMAGNETIC FIELD AND RADIATION OF MOVING CHARGES Let us consider the electromagnetic field of a point charge moving in an arbitrary manner. It is described by retarded potentials, which we write in the form

2 Section 1. Basic concepts of the theory of the electromagnetic field Basic quantities characterizing the electromagnetic field. Classification of media in relation to the electromagnetic field. System of equations of electrodynamics.

FOUNDATION OF THE FRAMEWORK OF THE USSR the world about the world of the USSR RESPONSIBILITY OF THE RESULTS OF THE RESULTS RESPONSE ELECTRODYNAMICS.

Federal State Budgetary Educational Institution higher education"Saratov State Technical University named after Yu.A. Gagarin" Department of Automated Electrotechnological

Federal State Budgetary Educational Institution of Higher Professional Education "Academy of Civil Defense of the Ministry of the Russian Federation for Civil Defense, Emergency

Goldstein L. D., Zernov N. V. Electromagnetic fields and waves SECOND EDITION, REVISED AND ADDED TO THE SOVIET RADIO PUBLISHING HOUSE MOSCOW - 1971 The fundamentals of the theory of the electromagnetic field are outlined. Main

DRAFT DISCIPLINE PROGRAM MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Budgetary Educational Institution of Higher Professional Education "Novosibirsk National

ELECTROSTATICS 1. Two types of electric charges, their properties. Ways to charge phones. Smallest indivisible electric charge. Unit of electric charge. Law of conservation of electric charges. Electrostatics.

Title page of the working curriculum F SO PSU 7.18.3/30 Ministry of Education and Science of the Republic of Kazakhstan Pavlodar State University named after. S. Toraigyrova Department of Radio Engineering and Telecommunications

3 1 BASIC LAWS OF ELECTROMAGNETIC FIELD THEORY The system of electrodynamics equations (Maxwell’s equations) describes the most general laws electromagnetic field These laws connect electric

Appendix 7 to order 853-1 dated September 27, 2016 MOSCOW AVIATION INSTITUTE (NATIONAL RESEARCH UNIVERSITY) PROGRAM OF ENTRANCE INTERDISCIPLINARY EXAMINATION TO MASTER'S PROGRAM IN THE DIRECTION

GOU HPE RUSSIAN-ARMENIAN (SLAVIC) UNIVERSITY Compiled in accordance with state requirements for the minimum content and level of training of graduates in the specified areas and Regulations

CONTENTS Introduction................................................... ............... 5 List of accepted notations and abbreviations................................. ...... 7 Accepted designations.................................................. ......

1. Goals and objectives of development academic discipline 1.1. The purpose of the discipline The course Electrodynamics and propagated radio waves is a course in the direction 10400.6 "Radio Engineering" and introduces students to the physical fundamentals

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous Institution of Higher Professional Education "Kazan (Volga Region) Federal University" Institute

Test Test tasks in the discipline “Fundamentals of electrodynamics and radio wave propagation” (residual knowledge) Rubrication Measure Difficulty rating score 1 2 4 1 2 2 4 1. Plane electromagnetic waves (EMW)

Type of classes Distribution of discipline hours by semester, number of academic weeks in semesters 1 19 2 20 3 19 4 20 5 19 6 18 7 19 8 7 Total UP RPD UP RPD UP RPD UP RPD UP RPD UP RPD UP RPD UP RPD

Program of the discipline "Antennas and radio wave propagation"; 118. Radiophysics; Associate Professor, Ph.D. (Associate Professor) Nasyrov I.A. MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous

CHAPTER 5 Plane waves The emitter of an electromagnetic wave creates a front of these waves around itself. At large distances from the emitter, the wave can be considered spherical. But at very large distances from the emitter

Electromagnetic waves The existence of electromagnetic waves was theoretically predicted by the great English physicist J. Maxwell in 1864. Maxwell analyzed all the laws known at that time

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous Educational Institution of Higher Education "Novosibirsk National Research State

5 Guided waves A guided wave is a wave that propagates along a given direction. The priority of the direction is ensured by the guiding system 5 Basic properties and parameters of the guided wave

Federal Agency for Education State Educational Institution of Higher Professional Education Ural State Technical University - UPI OSCILLATIONS AND WAVES Questions for a programmed theoretical colloquium in physics for students

Non-profit joint-stock company ALMATY UNIVERSITY OF ENERGY AND COMMUNICATIONS FACULTY OF RADIO ENGINEERING AND COMMUNICATIONS DEPARTMENT OF RADIO ENGINEERING Approved by Dean Medeuov U.I. "2" 06 2012 COURSE PROGRAM (Syllabus)

CONTENTS Preface... 6 How to use the book... 9 Methodological instructions for solving problems... 12 Designations of physical quantities... 14 Introduction... 16 1. Electrostatics and direct current... 18 1.1. Electrostatic

Basic work program in the discipline of Antenna and the development of radio broadcasting Introduction 1.1. Object of study Object of study: 1) radiophysical processes arising during the propagation of radio waves in the atmosphere

CONTENTS Introduction...5 List of accepted notations and abbreviations...7 Accepted notations...7 Accepted abbreviations...7 PART ONE METHODS FOR CALCULATING ELECTROMAGNETIC FIELDS Chapter 1 General information about electromagnetic fields

Center for Quality Assurance in Education Institute Group Name MODULE: PHYSICS (ELECTROMAGNETISM + OSCILLATIONS AND WAVES (MODULE 5 AND 6)) 1 Correct statements 1) the magnetic properties of permanent magnets are determined by

Theory of transmission lines Propagation of electromagnetic energy along guide systems A guide system is a line capable of transmitting electromagnetic energy in a given direction. So channeling

Volgograd State University Institute of Physics and Technology Department of Laser Physics APPROVED BY THE ACADEMIC COUNCIL Minutes of 2014 Director of the Institute of Physics and Technology K.M. Firsov 2014 RECOMMENDED

Contents PREFACE... 3 1. BASIC CONCEPTS AND EQUATIONS OF ELECTROMAGNETIC FIELD THEORY... 6 1.1. Characteristics of the electromagnetic field and environment... 6 1.2. Integral equations of electromagnetic

Theory of seismic waves Discipline program The discipline program “Theory of Seismic Waves” is compiled in accordance with the requirements (federal component) Indicate within which specialty (direction)

QUESTIONS FOR TEST WITH ASSESSMENT ON FUNDAMENTALS OF ELECTRODYNAMICS PHYSICAL DEFINITIONS 1. In what units is electric charge measured in SI and SGSE (GS)? How are these charge units related to each other? Proton charge

Ministry of Education of the Republic of Belarus Educational Institution "Belarusian State University of Informatics and Radioelectronics" "Approved" Dean of the Faculty of Computer Design Budnik

1.1 Electromagnetic field

The electromagnetic field consists of an electric field interdependent with a magnetic field. The electric field is represented by the vector of electrical induction, functionally dependent on the vector of the electric field strength . The magnetic field is represented by the magnetic induction vector
, functionally dependent on the magnetic field strength .

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

- electrical induction;

- magnetic induction.

A stationary electromagnetic vector field is a 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 = 3·10 8 m/s.

where λ is wavelength, m;

T - period, s.

Frequency , Hz

c = λf

Circular frequency, s -1

ω = 2πf.

The longer the electromagnetic wavelength, the lower the frequency. Electromagnetic waves begin with a lower frequency, then radio waves of the ultra-long and long wave ranges begin, then medium waves with a higher frequency, short, ultra-short waves with an even higher frequency. Radio waves are followed by infrared radiation, which has a shorter wavelength but higher frequency than radio waves. Visible light begins as red wavelengths. The names of the flowers begin with letters in the order of the saying: “Every hunter wants to know where the pheasant sits.” Visible light ends in violet waves. This is followed by ultraviolet, x-ray, gamma radiation and cosmic radiation.

The theory of the electromagnetic field is based on vector calculus and vector fields, the most important provisions of which will be discussed below.

1.2 Scalar and vector fields

1.2.1 Potential (irrotational) and vortex vector fields

Potential (irrotational) field linesstart at the source and end at the drain. The lines of the vortex (solenoidal) field have no sources, are always closed, continuous( see picture[ 4 ] ) .

R Figure - Potential (irrotational) and vortex fields

Vector circulation potential field along a closed loopL equal to zero

Flow vortex field vector through a closed surface Sequals zero

An electrostatic field can only be potential (irrotational), a magnetic field can only be vortex.

1.2.2 Scalar field gradient, Hamilton operator

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

Conditional vector or Hamilton operator

Scalar field gradient φ, written using the Hamilton operator (nabla operator)

The level surface φ contains the same values ​​φ = const of the scalar field, therefore the gradient of the scalar field φ is perpendicular to the level surface φ and is directed towards increasing φ (see figure [4]).

Figure - Scalar field gradient

1.2.3 Divergence (divergence)

Given a vector field at a point (x; y; z)

Where
- unit vectors (orts) in the directions of the coordinate axes x, y, z, respectively.

For a vector field at point (x; y; z), divergence (divergence) at point P equal to the limit of vector flux through the surface S, limiting the volume V divided by V as V tends to zero

Divergence values ​​at points P vector fields (see figure [4]).

Figure - Divergence values

When the divergence is greater than zero

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

For negative divergence

inside region V are the sinks of the vector field.

With divergence equal to zero

With muddy field lines permeate the area V or closed (vortex field).

1.2.4 Rotor (vortex)

The rotor (vortex) allows you to estimate the degree of rotation at some point ( x ; y; z ) vector field

where are unit vectors (orts) in the directions of the coordinate axes x, y, z, respectively.

For a vector field at point (x; y; z), the projection of the rotor onto the normal direction to the surface, equal to the limit of vector circulation around contour C, divided by areaΔ S surface bounded by contour C, tending Δ S to zero

The direction of the normal is related to the direction of traversal of the contour C by the right screw rule.

Rotor (vortex) of a vector field using the Hamilton operator

Vector projections
on the coordinate axis

If at point P rotor is zero

,

then there is no rotation at this point and the vector field is potential.

1.3 Types of charge distribution

Volume charge density, C/m 3

Charge concentrated in volume V, C

Surface nary charge density, C/m 2

Charge concentrated on the surface S, C

Liney nary charge density, C/m

Filament charge , Cl

The charge of point charges is equal to the sum of N charges of finite magnitude

1.4 Electric field

Electrical displacement vector (electrical induction) equal to the electric constant ε 0 multiplied by a bracket in which the unit is added to the electric susceptibility χ e multiplied by the electric field strength vector

Electrical constant

Vector of electrical displacement (electrical induction) in a substance

Where ε - absolute electrical permittivity.

Vector of electrical induction in a vacuum

.

1.5 Magnetic field

Magnetic induction vector equal to the magnetic constant μ 0 multiplied by a bracket in which the unit is added to the magnetic susceptibility χ m multiplied by the magnetic field strength vector

Magnetic constant

Vector of magnetic induction in matter

Where μ - absolute magnetic permeability.

Magnetic induction vector in vacuum

1.6 Ohm's law in differential form

Ohm's law for a circuit section

U = IR

Current Density

Let's express

Let's integrate over and we obtain the dependence of the current on 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, S/m.

2 Maxwell's equations

Maxwell's system of equations in differential form describes alternating electromagnetic fields

The vectors in Maxwell's equations represent a non-stationary electromagnetic vector field, which is a function of coordinates x, y, z and time t.

2.1 Special cases of electromagnetic phenomena

In special cases, Maxwell's equations can be simplified.

2.1.1 Stationary electromagnetic field

A stationary electromagnetic field is created by direct currents and is described by vector functions of coordinates that do not depend on time:

Electric field strength;

Electrical induction;

Magnetic field strength;

Magnetic induction.

Vector functions do not depend on time, therefore the partial derivatives with respect to time in Maxwell’s equations are equal to zero:

The system of Maxwell's equations in differential form takes the form that describes a stationary electromagnetic field:

2.1.2 Static electric or magnetic fields

Static fields do not change over time and have no moving charges, therefore no currents

.

Maxwell's system of equations is divided into two systems of equations independent from each other. The first system characterizes the electrostatic field and is called the system of differential equations of electrostatics

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

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

2.1.3 Maxwell's equations in complex form

If the electromagnetic field vectors change in time according to harmonic laws, then Maxwell’s system of equations can be represented in a complex form that does not contain time for complex vectors

or complex amplitudes

2.1.4 Wave equations

From Maxwell's equations in complex form, expressing separately the equations for complex vectors And the result is a wave Helmholtz equations for vectors

and complex amplitudes

Where - wave number, for vacuum

.

3 Plane electromagnetic waves

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

The electric and magnetic field strength vectors of a plane wave are in phase and oscillate along mutually perpendicular directions in a plane perpendicular to the direction of wave propagation. Such waves are transverse (see figure).

Figure - Instantaneous picture of the distribution of electric and magnetic field strength along the direction of propagation of a plane wave. In time, the field pattern moves in space with a phase velocity v f along the z axis

The wave front is a geometric location of field points with the same phase: for a plane wave (see figure), one of these surfaces is the plane z = z 0, perpendicular to the direction of wave propagation. The field parameters do not change when moving within the wave front.

The front of a plane wave is a plane perpendicular to the direction of propagation of the wave. The field parameters do not change when moving within this plane, therefore the partial derivatives in the x and y directions are equal to zero:

In waves Helmholtz equationsfor a plane wave become one-dimensional for vectors

and complex amplitudes

Solving differential equations for vectors

Where , - unit vectors in the direction of the electric and magnetic intensity vectors, respectively;

A, B, C, D - coefficients.

Real parts of vectors

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

Figure - Position of electric field maxima

During Δ tthe maximum position has moved toΔ z,we can write the equality

A cos (ωt − kz ) = A cos (ωt + ωΔt − kz − k Δz ),

in which the arguments are equal

ω t − kz = ωt + ωΔt − kz − k Δz

0 = ωΔt - kΔz

ωΔt = kΔz.

From here we obtain the phase velocity v f - wave front propagation speed

For vacuum

therefore the phase velocity in vacuum

Let's substitute the values ​​of the constants

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

Phase velocity in some medium

Phase speed is independent of frequency.

Amplitudes of two points at a wavelength distance λ with phases differing by 2π are equal, so the equality holds

cos(ωt − kz) = cos(ωt − k(z + λ) + 2π),

in which the arguments are equal

ωt − kz = ωt − k(z + λ) + 2π,

ωt − kz = ωt − kz − kλ + 2π.

Let's reduce ω t − kz

0 = − kλ + 2π,

k λ= 2 π.

Hence the wavelength

For any environment

,

so the wavelength

In a vacuum the wavelength

Wavelength in other media

Vacuum impedance

For dry air, the same wave impedance is assumed.

4 Radio propagation

All electromagnetic waves, including radio waves, propagate in vacuum at a speed of 3·10 8 m/s.

4.1 Propagation of radio waves in free space

We will take the propagation of radio waves in the atmosphere, along the earth's surface, in the earth's crust, in the outer space of our galaxy and beyond as the free propagation of radio waves, which we will consider.

4.1.1 Classification of radio waves 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 lower frequency than short waves, which have a higher frequency.

The use of radio waves is possible thanks to the transmitting device, the natural medium of radio wave propagation and the receiving device, all together forming a radio link.

The earth's atmosphere and surface are absorbing media, electrically inhomogeneous, having conductivity and dielectric constant that are not constant in time and space, depending on the frequency of propagating radio waves.

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

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

The power of electromagnetic waves depends on frequency to the 4th power

P ~ ω 4.

Waves with higher frequencies but shorter wavelengths are capable of more power.

Antennas with a narrow radiation pattern have dimensions significantly larger than the wavelength; for high frequencies it is easier to make such highly efficient antennas.

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

4.2 Antenna theory

The space around the antenna is divided into three areas with different field structures and calculation formulas: near, intermediate and far. In real communication lines, there is usually a far region (Fraunhofer zone) at distances from the antenna

Where L- maximum size of the radiating area of ​​the antenna, m;

λ - wavelength, m.

Characteristic (wave) impedance of a free medium

Poynting vector (Umov - Poynting vector), W/m 2

Where P - power, W;

r- distance from the antenna to the observation point, m.

Where D- Directional coefficient (NAF) of the antenna.

Average far-field Poynting vector

From the relation

Let us express the amplitude of the magnetic field strength

Let's substitute

Let us equate the Poynting vectors

Let's cut it down

Amplitude of electric field strength in the far zone of an antenna in free space

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

5 Propagation of radio waves of various ranges

5.1 Propagation of ultra-long and long waves

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

SDV and DV have a long wavelength, so they bend well around the earth's surface. The conduction currents of these radio waves significantly exceed the displacement currents for all types of the earth's surface, so little energy is absorbed during the propagation of the surface wave. Therefore, VSD and DV can propagate over distances of up to 3 thousand km.

SDV and DV are weakly absorbed in the ionosphere. The lower the frequency of the radio wave, the lower the electron density of the ionosphere is required to turn the radio wave towards the Earth. Therefore, the rotation of the LW and LW occurs at the lower boundary of the ionosphere (during the day in layer D and at night in layer E) at an altitude of 80-100 km. The troposphere has virtually no effect on the propagation of SDV and DV. Around the Earth, VHF and LW propagate, reflected from the ionosphere and from the earth's surface in a spherical layer of 80-100 km between the lower boundary of the ionosphere and the earth's surface.

Communication lines on the SDV and DV have high stability of the electric field strength. Over the course of a day and a year, the signal value changes little and is not subject to random changes. Therefore, VFD and DV are widely used in navigation systems.

The limited frequency range (3-300 kHz) of VHF and DV does not allow placement of even one television channel, which requires an 8 MHz band.

The long wavelength of VLF and DV dictates the use of bulky antennas.

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

5.2 Medium wave propagation

Medium waves (MV) have a wavelength from 100 to 1,000 m, a frequency from 300 kHz to 3 MHz (0.3 - 3 MHz). Terrestrial and ionospheric CBs, which are used primarily in radio broadcasting, can propagate.

Terrestrial SW radio links are limited to a length of no more than 1000 km due to the significant absorption of SW by the earth's surface.

Ionospheric SW can be reflected from the E layer ionosphere. Through the lowest layer D ionosphere, which appears only during the day, SWs pass through and are strongly absorbed in it,virtually eliminating communication during the day. Therefore, at night in the ionosphere, the absorption of SW decreases significantlyand at distances greater than 1000 km from the transmitter, communicationis being restored.

Due to the interference of ionospheric waves with each other or (and at night) with ground waves, random signal fading (fading) occurs. Anti-fading antennas have a maximum radiation pattern pressed to the earth's surface to combat fadingand cross modulation on NE.

5.3 Shortwave propagation

Short waves (SW) have a wavelength from 10 to 100 m (10 times shorter than medium waves), a frequency from 3 to 30 MHz (10 times higher than the SW frequency). HF are used primarily for radio broadcasting.

HFs are strongly absorbed by the earth's surface and do not bend well around the Earth's surface, so terrestrial HFs extend only a few tens of kilometers.

HFs experience absorption and pass through the lowest layers of the ionosphere D and E, but reflected from the layer F.

Calculation of HF communication lines involves drawing up a schedule of operating frequencies depending on the time of day (wave schedule).

5.4 Features of the propagation of ultrashort waves

Ultrashort waves (UHF) have a wavelength of less than 10 m and a frequency of more than 30 MHz. In terms of frequency, VHF borders with HF at the bottom, and with infrared waves at the top. The ionosphere is transparent for VHF, so VHF lines are used mainly within line of sight.

VHF have a large frequency range capable of transmitting significant amounts of information. 297 television channels can be placed on meter and decimeter waves. There will be only 3 television channels in the entire shortwave range, and not a single one in the entire CB range.

The development of mobile and satellite communications, the Internet and other above-mentioned reasons are forcing radio technology to move to higher frequencies, so VHF is becoming increasingly important.

5.4.1 Line-of-sight VHF propagation

VHF communication lines operating within line of sight:

VHF and television broadcasting;

Radar stations (radar);

Radio relay communication lines (RRL);

Communication with space objects;

Mobile connection.

5.4.2 VHF propagation beyond the horizon

Long-range propagation of VHF beyond the horizon occurs in the following ways:

Due to scattering by inhomogeneities in the troposphere;

Superrefraction in the troposphere;

Scattering by ionospheric irregularities;

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

- due to reflection from meteor trails;

Thanks to the reinforcement of the obstacle (see figure)

Figure - Propagation of radio waves when amplified by an obstacle

List of symbols, symbols, units and terms

D,B - vectors of electric and magnetic induction

E, H - vectors of electric and magnetic field strengths

I(r, t) - electric current

j (r,t) – electric current density vector

P – electromagnetic field power

M - magnetization vector

P - electric polarization vector

q - electric charge

ε,μ – absolute dielectric and magnetic permeability

ε 0 ,μ 0 – dielectric and magnetic constants

ε r ,μ r – relative dielectric and magnetic permeability

P - Poynting vector (Umov - Poynting vector)

ρ,ξ,τ - volumetric, surface and linear charge densities

σ – specific conductivity of the medium

ϕ - scalar electrostatic potential

χ e,χ m - electric and magnetic susceptibility

W – electromagnetic field energy

W e, W m - electric and magnetic field energies

w – electromagnetic field energy density

w e,w m - energy densities of electric and magnetic fields

k - wave number

SDV - ultra-long waves

LW - long waves

SV - medium waves

HF - short waves

VHF - ultrashort waves

Radar - radar station

RRL - radio relay line

D - directional coefficient (DC) of the antenna

G - antenna gain

F(θ,α) - antenna radiation pattern

R 0 - radius of the Earth (6371 km)

Z 0 − characteristic impedance of free space

List of sources used

1.Electrodynamics and propagation of radio waves: textbook. allowance / L.A. Bokov, V.A. Zamotrinsky, A.E. Mandel. - Tomsk: Tomsk. state University of Control Systems and radio electronics, 2013. - 410 p.

2.Morozov A.V. Electrodynamics and propagation of radio waves: a textbook for higher education. military training institutions / Morozov A.V., Nyrtsov A.N., Shmakov N.P. - M.: Radiotekhnika, 2007. - 408 p.

3. Yamanov D.N. Fundamentals of electrodynamics and radio wave propagation. Part I. Fundamentals of electrodynamics: Lecture texts. - M.: MSTU GA, 2002. - 80 p.

4. Panko V.S. Lectures on the course “Electrodynamics and radio wave propagation”.

Consultations with Andrey Georgievich Olshevsky via Skype da .irk .ru

Theoretical foundations of electrical engineering (TOE), electronics, circuit design, fundamentals of digital and analog electronics, electrodynamics and radio wave propagation.

A clear explanation of the theory, closing gaps in understanding, teaching methods for solving problems, consulting when writing coursework and diplomas.

Generation and implementation of ideas. Basics scientific research, methods of generation, implementation of scientific, inventive, business ideas. Training in decision techniques scientific problems, inventive problems. Scientific, inventive, writing, engineering creativity. Statement, selection, solution of the most valuable scientific, inventive problems and ideas.

Publication of creative results. How to write and publish a scientific article, apply for an invention, write, publish a book. Theory of writing, defending dissertations. Making money from ideas and inventions. Consulting in the creation of inventions, writing applications for inventions, scientific articles, applications for inventions, books, monographs, dissertations. Co-authorship of inventions, scientific articles, monographs.

Preparation of students and schoolchildren in mathematics, physics, computer science, schoolchildren who want to get a lot of points (Part C) and weak students for the State Exam (GIA) and the Unified State Exam. Simultaneous improvement of current academic performance by developing memory, thinking, and clear explanation of complex, visual presentation of objects. A special approach to each student. Preparation for Olympiads that provide benefits for admission. 15 years of experience improving student achievement.

Higher mathematics, algebra, geometry, probability theory, mathematical statistics, linear programming.

Aviation, rocket and automobile engines. Hypersonic, ramjet, rocket, pulse detonation, pulsating, gas turbine, piston internal combustion engines - theory, design, calculation, strength, design, manufacturing technology. Thermodynamics, heat engineering, gas dynamics, hydraulics.

Aviation, aeromechanics, aerodynamics, flight dynamics, theory, design, aerohydromechanics. Ultralight aircraft, ekranoplanes, airplanes, helicopters, rockets, cruise missiles, hovercraft, airships, propellers - theory, design, calculation, strength, design, manufacturing technology.

Theoretical mechanics (teormekh), strength of materials (strength of materials), machine parts, theory of mechanisms and machines (TMM), mechanical engineering technology, technical disciplines.

Analytical geometry, descriptive geometry, engineering graphics, drawing. Computer graphics, graphics programming, drawings in AutoCAD, NanoCAD, photomontage.

Logic, graphs, trees, discrete mathematics.

OpenOffice and LibreOffice Basic, Visual Basic, VBA, NET, ASP.NET, macros, VBScript, BASIC, C, C++, Delphi, Pascal, Delphi, Pascal, C#, JavaScript, Fortran, html, Matkad. Creation of programs, games for PCs, laptops, mobile devices. Use of free ready-made programs, open source engines.

Creation, placement, promotion, programming of websites, online stores, making money on websites, Web design.

Computer science, PC user: texts, tables, presentations, training in speed typing in 2 hours, databases, 1C, Windows, Word, Excel, Access, Gimp, OpenOffice, AutoCAD, nanoCad, Internet, networks, email.

Installation and repair of stationary computers and laptops.

Video blogger, creating, editing, posting videos, video editing, making money from video blogs.

Choice, achieving goals, planning.

Training in making money on the Internet: blogger, video blogger, programs, websites, online store, articles, books, etc.

Skype: da.irk.ru

Websites: www.da.irk.ru

01/11/18 Olshevsky Andrey Georgieviche-mail:[email protected]

You can support the development of the site using the payment form below.

You can also pay for consulting and other services of Andrey Georgievich Olshevsky