Transmission Lines and Antennas

Course Objectives:

The course introduces concepts of applied electromagnetism and radiation theory that are fundamental to the field of communications engineering. Building on the theoretical foundations provided by classical electrodynamics and Maxwell’s equations, the course aims to provide students with the concepts required to model some of electrodynamic phenomena of greatest interest in telecommunications. The main topics focus on antennas, the interaction of electromagnetic fields with piecewise-homogeneous or inhomogeneous structures, and the propagation of electromagnetic waves in free space.

Knowledge and understanding:

The course aims at providing conceptual tools and techniques for the description of classical electromagnetic phenomena, with particular attention to most relevant applications in communications engineering. Moving from Maxwell equations and their simplest solutions, students are guided to understand the basics of radiation mechanisms and the propagation of electromagnetic waves in different environments.

Applying knowledge and understanding:

The course of Transmission Lines and Antennas provides students basic design tools for the analysis of guiding structures, transmission lines, antennas and simple radio-links. Moreover, the course allows students to analytically evaluate the interaction of electromagnetic waves with several electromagnetic environments (i.e., multi-layer structures, conductors, dielectrics, cold plasma etc.), according to relevant applications in communication engineering.

Making judgements:

Students will master all analyzed tools and design techniques to solve problems on electromagnetic field propagation and interaction, by considering which theoretical model is the most suitable to achieve accurate solutions.

Communication skills:

Students will be required to properly describe all fundamental concepts introduced throughout the course. Moreover, student ability to technically discuss specific course topics will be carefully evaluated.

Learning skills:

Students will be able to improve their knowledge on the theory of electromagnetic fields, both through the deepening of reference textbooks and also through papers in specialized scientific journals, as well as through new ideas offered by seminars.

The course consists of 79 hours (9 ECTS credits), comprising 49 hours (7 ECTS credits) of classroom-based teaching and 30 hours (2 ECTS credits) of exercises/numerical simulations, and laboratory activities. Should lectures be given in mixed or remote modes, some variations may be introduced in compliance with learning objectives and purposes stated in the course syllabus.

Essential Prerequisites:

• Fundamentals of electrostatics and magnetostatics.
• Fundamentals of Signal Theory and Fourier transform.
• Vector calculus.

Important Prerequisites:

• Differential and integral calculus in one and several variables.
• Phasors and circuit analysis techniques for lumped-parameter circuits.
• Second-order linear ODEs with constant coefficients.

Useful Prerequisites:

• Concept of operator in functional spaces for field representation (reviewed during the course) .
• Basic concepts of differential operators in several variables (reviewed during the course).

0) Overview of orthogonal curvilinear coordinates and differential operators (7 hours)

[Lectures: 5 hours; Exercises/Laboratory: 2 hours]

First and second order differential operators: gradient, divergence, curl, directional derivative, Laplacian (scalar and vector). ● Overview of orthogonal curvilinear coordinates, metric coefficients, differential operators in special cases of interest (Cartesian, cylindrical, spherical). ● Gradient, divergence and curl theorems. ● Green's identities. ● Frequently used vector identities.

1) Maxwell's equations, general principles and plane waves (18 hours)
[Lectures: 11 hours; Exercises/Laboratory: 7 hours]

Introduction to electromagnetics and applications. ● Time-domain Maxwell's equations. ● Lorentz force and continuity equation. ● Interdependence of Maxwell's equations. ● Boundary conditions for electromagnetic fields. ● Frequency-domain Maxwell's equations and complex notation. ● Polarization of electromagnetic fields. ● Constitutive relations. ● Electromagnetic media: non-polar and polar dielectrics, conductors, and cold, collisionless plasma. ● Poynting and uniqueness theorems. ● Solutions of Maxwell's equations in Cartesian coordinates: plane waves. ● Homogeneous and inhomogeneous plane waves: classification. ● Plane wave spectrum and wavenumber domain. ● Dispersion of a 1-D wave-packet and Brillouin diagram. ● Phase and group velocities.

2) Transmission lines (14 hours)
[Lectures: 8 hours; Exercises/Laboratory: 6 hours]

Guiding structures with cylindrical symmetry and metallic contour. ● TEM modes. ● Voltage and current on a transmission line. ● Telegraphers' equations in time and frequency domains. ● Solution of Telegraphers' equations. ● Reflection coefficient and VSWR. ● Impedance transformer formula. ● Termination on matched, short-circuited, open-circuited, and generic loads. ● Lossy transmission lines. ● Coaxial cable and bifilar line impedance calculation. ● Matching techniques by quarter-wavelength transformer and by stubs. ● Overview of codes to solve related electromagnetic problems.

3) Reflection and transmission of plane waves (18 hours)
[Lectures: 10 hours; Exercises/Laboratory: 8 hours]

Normal incidence. ● Snell-Cartesio laws. ● Fresnel coefficients for parallel (TM) and orthogonal (TE) polarizations. ● TE/TM equivalent transmission lines and formalism for planar multilayer structure analysis. ● Transmission in lossless media. ● Total transmission and total reflection. ● Transmission in lossy media: interface air-good conductor. ● Leontovich boundary condition. ● Brief overview of high-frequency approximation of EM field and elements of radiopropagation. ● Experimental verification of Snell's laws at optical frequencies. ● Overview of codes to solve related electromagnetic problems.

4) Radiation and antennas (15 hours)
[Lectures: 10 hours; Exercises/Laboratory: 5 hours]

Electrodynamic potentials. ● Field radiated by an elementary electric dipole. ● Duality theorem. ● Field radiated by an elementary loop. ● Reactive and radiative near-field conditions. ● Far-field conditions. ● Field radiated by linear antennas. ● Image theorem and application to monopole antennas. ● Overview of simple codes to solve related electromagnetic problems.

5) Transmitting and receiving antennas (7 hours)
[Lectures: 5 hours; Exercises/Laboratory: 2 hours]

Fundamental parameters to characterize transmitting antennas. ● Calculation of parameters for dipole and loop antennas. ● Characterization of receiving antennas. ● Friis formula for link budget. ● Brief overview of RADAR equation and RCS.

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Contribution of the course to the Goals of the 2030 Agenda for Sustainable Development

The topics covered by the course are directly or indirectly aimed at the development of sustainable technological solutions, as well as at contributing to high-quality education, according to Goals 4, 7, 9, 11, and 12 of the 2030 Agenda for Sustainable Development.

Applied Electromagnetics:

[1] J. Kong, "Electromagnetic Wave Theory", EMW Publishing, Cambridge, Massachusetts.

[2] C. A. Balanis, "Advanced Engineering Electromagnetics", Wiley.

[3] G. Franceschetti, "Campi Elettromagnetici", Bollati Boringhieri.

[4] C. G. Someda, "Electromagnetic Waves", CRC Press.

Fundamentals of Antennas:

[5] C. A. Balanis, "Antenna Theory: Analysis and Design", Wiley.

[6] F. S. Marzano, N. Pierdicca, "Fondamenti di Antenne", Carocci.

[7] S. J. Orfanidis, "Electromagnetic Waves and Antennas", vol. II (Antennas).

The oral exam consists of 3-4 main questions on course topics (see Syllabus), and possible exercises. Students have to demonstrate adequate understanding and mastery of the topics discussed, together with clarity of topic explanation. 

Learning assessment may also be carried out online, should the conditions require it.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview to plan any compensatory and/or dispensatory actions based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l'integrazione Attiva e Partecipata) - Servizi per le Disabilità e/o i DSA referring teachers at the Department.

Moreover, students are asked to solve simple exercises on course main topics.

Some possible examples: 

• Discuss constitutive relations in time and frequency domains. 
• Definition of antenna directivity and calculation for an elementary dipole antenna.
• Boundary conditions for the electromagnetic field.
• Discuss the theory of electrodynamic potentials and their application to the radiation theory.
• Prove and discuss applications of the Poynting theorem in the time/phasor domains.
• Derive the telegrapher’s equations and their solutions in terms of traveling and standing waves.
• Derive the Smith Chart and illustrate some of its applications.
• Design an impedance-matching network using a quarter-wave transformer to match a given load.
• Design an impedance-matching network using series/shunt stubs to match a given load.
• Calculate the Fresnel coefficients for a system of planar dielectric interfaces.