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Lecture

Guided Propagation: Vector Components and Boundary Conditions

In course

EE-445: Microwaves, the basics of wireless communications

This course is an introduction to microwaves and microwave passive circuits. A special attention is given to the introduction of the notion of distributed circuits and to the scattering matrix ...

Description

This lecture covers guided propagation modes, vector components, and boundary conditions in electromagnetic fields. It discusses the separation of variables, Helmholtz equation, longitudinal and transverse components, dispersion diagrams, and electromagnetic field reconstruction. The instructor explains the propagation constant, eigenvalues, and eigenmodes of the guide, as well as the TEM, TE, TM, and hybrid modes in different structures.

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Instructor

Anja Skrivervik

Anja Skrivervik obtained her electrical engineering degree from Ecole Polytechnique Fédérale de Lausanne in 1986, and her PhD from the same institution in 1992, for which she received the Latsis award. After a stay at the University of Rennes as an invited Research Fellow and two years in the industry, she returned part time to EPFL as an Assistant Professor in 1996, and is now a Professeur Titulaire at this institution, where she is the head of the Microwave and Antenna Group. Her research activities include electrically small antennas, antennas in biological media, periodic structures, reflect- and tranmitarrays, and numerical techniques for electromagnetics. She is author or co-author of more than 200 peer reviewed scientific publications. Her teaching activities include courses on microwaves and antennas, and she has course at Bachelor, Master and PhD levels. She was director of the EE section form 1996-2000, and is currently the director of the EE doctoral school at EPFL. She is very active in European collaboration and European projects. She was the chairperson of the Swiss URSI until 2012, is a Board member of the European School on Antennas and is frequently requested to review research programs and centers in Europe. She is a member of the board of directors of the European Association on Antennas and Propagation (EurAAP) since 2017.

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Related concepts (32)

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Robin boundary condition

In mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.

Transverse mode

A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an optical fiber and in a laser's optical resonator. Transverse modes occur because of boundary conditions imposed on the wave by the waveguide.

Neumann boundary condition

In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.

Boundary value problem

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

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