Short Notes

In this web page, some notes clarifying certain points of the theory, demonstrating solutions to specific problems and containing formulas useful in exercises, will be gradually uploaded.

SECTION O (Preliminary Section)

Problem Set O Model Solutions: Some exemplary answers for the Problem Set O prepared by Mr. Tommi Rimpliläinen. The previous version had an error and now the correct one has been uploaded. PDF

SECTION A (Electrostatic Fields)

Cylindrical and Spherical Coordinates: The cylindrical and spherical coordinate systems are commonly employed in several problems but the expressions of the elementary area and volume elements are not so trivial as in the Cartesian system. They are presented in a note by Prof. Anvar Shukurov from Newcastle UniversityPDF

Line Charge Potential: A short note evaluating explicitly the electrostatic potential of an infinite line charge with constant density. PDF

Gauss Law: A series of tricky questions to test your comprehension of Gauss Law compiled by Prof. Xiangjun Xing from Syracuse University with copyright from Pearson Education. PDF

SECTION B (Laplace Equation)

Laplace in Cylindrical Polar Coordinates: A note prepared by Prof. Birne Binegar from Oklahoma State University describing the procedure of determining the solution of the Laplace equation in cylindrical polar coordinates. PDF

Image Theory: Some notes containing formulas of image theory for spherical and planar cases. It is written by Mr. James Silva from MIT open courseware. PDF

Vector Operators: The differential vector operator in Cartesian, cylindrical and spherical coordinates from a student portal of MIT. PDF

Cartesian Laplace: A general methodology to be followed for more complicated boundary value  problems of Laplace equation in a two-dimensional Cartesian configuration. The principle of linear superposition is employed. PDF

Matlab Contours: A small tutorial explaining how to produce a contour plot in MATLAB computing environment. PDF

Exercise B4 Model Solution: An exemplary answer for the problem 4 of Problem Set B prepared by Mr. Tommi Rimpliläinen. PDF

SECTION C (Magnetostatic Fields)

Amperes Law: Some fundamental applications of the Amperes Law by Distinguished Prof. Matthew Sadiku from Prairie View A&M University. PDF

Magnetostatic Examples: Several solved examples on magnetostatics for canonical geometries are compiled by Dr. Dipan Kumar Ghosh from Indian Institute of Technology, BombayPDF

Line and Planar Currents: An explicit computation of the magnetic field developed by an infinite straight line current and an infinite planar sheet as done into the classroom. PDF

Loop Current: The computation of the magnetic field along the axis of a metallic ring flown buy constant electric current. It has been performed by Dr. Pat Donohoe from Mississippi State UniversityPDF

Hollow Cylinder Resistance: The electric resistance of a hollow cylinder under constant voltage. A short report from MIT open courseware. PDF

SECTION D (Maxwell’s Equations)

Vector Laplacian Operator: The complexity of the vector laplacian operator (which is incorporated in the Helmholtz equation) when applied to non-Cartesian coordinate system, is demonstrated in the the attached Mathematica file. PDF

Maxwell Laws and Boundary Conditions: The lecture notes of Prof. Keith Whites from the South Dakota School of Mines and Technology concerning the way that change in electric field affects the magnetic field and vice-versa. The physically imposed boundary conditions are also analyzed. PDF

Distortionless Propagation: A short note of mine that elaborates the idea of distortion and attenuation when waves are propagating in a homogeneous unbounded medium. PDF

SECTION E (Plane Waves)

Hertz Dipole: The lecture notes of Prof. Keith Whites from the South Dakota School of Mines and Technology related to the evaluation of the field of a Hertzian dipole. PDF

Uniform Plane Waves: The notion of plane waves is analyzed in an exemplary way in the related chapter of Prof. Sophocles Orfanidis‘s book from Rutgers University. PDF

Wave Polarizations: Linearly, circularly and elliptically polarized waves are examined in this presentation by Prof. Simon A. Carn from Michigan Technological UniversityPDF

Reflection and Transmission: An interesting review by Prof. Natalia K. Nikolova from McMaster University elaborating some well-known reflection and transmission problems. PDF

SECTION F (Waves & Impedances in Transmission Lines)

TEM Transmission Lines: An interesting tutorial related to Transmission Lines by Prof. Sophocles Orfanidis from RutgersUniversity. PDF

Phase and Group Velocity: A compact note explaining the concept of Phase and Group Velocity by Prof. Roger Barlow from University of ManchesterPDF

Distortionless Transmission Line: An illustrative presentation related to the idea of Distortionless Propagation through a transmission line offered by Prof. James Stiles from  the University of Kansas. PDF

Impedances at Smith Chart: A note that clarifies the use of Smith Chart when it is used for admittance representation offered by Prof. James Stiles from  the University of KansasPDF

Impedance Matching: A short study explaining why do we need impedance matching in microwave circuits has been performed by Prof. David B. Leeson from University of Stanford. PDF

Smith Chart Formulas: A collection of the most common formulas related to the practical use of Smith Chart (PDF) prepared by myself. PDF

General Transmission Line: The derivation of equations characterizing the unit cell of a general transmission line is include in this note of mine. PDF

Two-Wire Line: As it has been discussed in the course, the capacitance per unit length (p.u.l.) is a significant quantity related to any structure that the TEM-wave assumption holds, admitting it to behave as a transmission line. The derivation of the capacitance p.u.l. of a two-wire transmission line is included my note. PDF

Induction and Conductance P.U.L.: The induction and the conductance per unit length of a general transmission line are expressed in terms of the capacitance per unit length. PDF

Transmission Line Theory: An in-depth analysis elaborating transmission line theory prepared by Prof. Hon Tat Hui from National University of Singapore. PDF

SECTION G (Simple Waveguides)

Parallel-Plate Waveguides: An analysis on Parallel-Plate Waveguides containing the derivation of the Helmholtz equation, the imposition of the boundary conditions prepared by Prof. Jose Schutt-Aine from the University of IllinoisPDF

Rectangular Waveguides: A thorough overview describing the phenomena related to Rectangular Waveguides offered by Prof. Sophocles Orfanidis from Rutgers University. PDF

Sample Solution for Problem Set G: An indicative answer from Prof. Ari Sihvola. Since it has been published, no more returned exercises from this problem set would be accepted. PDF


(c) by Costas Valagiannopoulos

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