## Physical Principles of Electromagnetic Fields and Antenna Systems

Module Number: EI7485

Duration: 1 Semester

Occurence: Winter and summer semester

Language: English

Number of ECTS: 6

## Staff

Professor in charge: Wolfgang Utschick

## Amount of work

Contact hours: 60

Self-study hours: 120

Total: 180

## Description of achievement and assessment methods

In a written exam, the students prove that they can describe qualitatively the principles of classical electrodynamics and quantitatively solve for fields and particle motions in simple scenarios. They calculate all relevant electrodynamic and circuit parameters of wire antennas, arrays made of such antennas, and systems of multiple arrays.

## Recommended requirements

The lecture is self contained. All physical concepts and necessary mathematical toolsare developed in the course of the lecture.

## Contents

1. The principles of the classical electromagnetic field theory- Forces, fields and inertial frames- The magnetic field is a relativistic effect- Explicit field formulation (Feynman)- Differential field equations (Maxwell)- When to use quantum electrodynamics - The great conservation laws: charge, energy, and momentum- Uniqueness theorem for the field solutions- The equivalence of energy and mass (Einstein)- Scalar and vector potential- Gauge transformations- The wave equation- Special relativity (Lorentz-covariance, 4-vector notation)- Field invariants- Relativistic effects- Duality transformations- Solution of the field equations- Sinusoidal time dependence and complex fields

2. Dipole Radiation- Hertzian dipole- Radiated power and radiation resistance- Antenna pattern and directivity- Effective area- The reciprocity theorem- Antenna current distribution- Effective antenna length- Long dipoles- Antenna efficiency- Canonical minimum scattering

3. Antenna Array Theory- Element coupling part I (partial-field analysis)- Radiated power- Antenna pattern- Optimum excitation- Directivity and superdirectivity- Antenna array efficiency- Arrays of dipoles- A theory of the array of isotrops

4. Multi-antenna systems- Multiport model- Element coupling part II (full-field analysis)- Thermal equilibrium antenna noise- Non-equilibrium receiver noise- Matching and decoupling- Near-field MIMO Systems (full interaction)- Far-field MIMO Systems (partial interaction)Mathematical preliminaries (reviewed in lecture):- vectors- general coordinates- differential vector operators- vector integration- integral theorems (Gauss, Stokes, Green)- gradient fields and scalar potential- solenoidal fields and vector potential

## Study goals

The student has obtained a firm understanding of the physical principles of classical electrodynamics (such as forces and fields, moving charges, waves in free-space, Lorentz-covariance, reciprocity, conservation laws, relativistic effects...) and their application to antenna systems. Based on these principles, the student can calculate e.g., radiated power, received voltage, radiation patterns, directivity, efficiency, height, element coupling, excitation, noise and matching of wire antennas and arrays and is able to derive and use multiport circuit models for multi-antenna systems of both near-field and far-field type.

## Teaching and learning methods

Classical lecture with lecturer presenting the lecture material in the lecture hall.The students can participate by asking question during and after the lecture, andcontact the lecturer by email or in person.

## Media formats

Lecture notes (printed, perhaps also ebook)Homework assignments and detailed solutionsWorking on blackboard, projection slides, sometimes beamer slides

## Literature

Main resource for the lecture:M.T. Ivrlac, "Lecture notes on the Physical Principles of Antenna Systems" (Course material, text-book style of writing, self-study possible, all mathematical tools developed. Available from lecturer.)Additional reading (selection):1. L.D. Landau & E.M. Lifshitz, "The Classical Theory of Fields", 4th revised Englishedition, Pergamon Press, Oxford, and Addison-Wesley, Reading, MA, 1987.2. S.A. Schelkunoff & H.T. Friis, "Antennas, Theory and Practice", Wiley, New York, 1952.3. A. Sommerfeld, "Electrodynamics", Academic Press, New York, 1964.4. J.D. Jackson, "Classical Electrodynamics", John Wiley&Sons, 3rd. edition, 1999.5. R.P. Feynman, R. Leighton, M. Sands, "The Feynman Lectures on Physics", Definitive Edition, Volume 2, Pearson Addison Wesley, 2006.6. A. Einstein, H.A. Lorentz, H. Minkowski & H. Weyl, "The Principle of Relativity. Collected Paperswith notes by A. Sommerfeld", Dover, New York, 1952.7. M.T. Ivrlac, "Lecture notes on Circuit Theory and Communication" (Available from Lecturer)