# Propagation and Radiation (Electromagnetics)

## Objectives

- Understand the notion of a monochromatic plane electromagnetic wave, the concept of phase and phase velocity, and the temporal and spatial phase constants;

- Understand Maxwell''''s equations in differential and integral formats, and understand how these are particularized for different scenarios with and without radiation sources;

- Understand the boundary conditions at the interfaces between media where monochromatic plane waves propagate, namely in undefined and semi-undefined media: laws of reflection and transmission, total reflection and power transfer;

- Understand the condition of guided propagation, the propagation mode, and cutoff frequency;

- Know the main characteristics of rectangular and circular cross-section waveguides, as well as how to analyze transmission lines both from the point of view of their fundamental parameters and their adaptation conditions and respective methods of maximizing power transfer

- Understand the basic functioning of optical fibers and the operation in multimodal regime;

- Understand the relationship between vector potential and scalar potential and the respective calculation of fields emitted by a source in the far zone

- Know the concept of duality of Maxwell''''s equations and the basic expressions of the fields radiated by elementary structures, namely by the current element and the elementary aperture

- Understand the operation of different types of antennas, namely their operation at transmission and reception and their fundamental parameters, such as the radiation diagram, the antenna impedance, the gain, and the directivity;

- Understand antenna arrays, their potential and limitations, and the existing degrees of freedom in the array configuration that make it possible to change its spatial selectivity.

## General characterization

##### Code

2184

##### Credits

6.0

##### Responsible teacher

João Francisco Martinho Lêdo Guerreiro, Paulo da Costa Luís da Fonseca Pinto

##### Hours

Weekly - 7

Total - 135

##### Teaching language

Português

### Prerequisites

### Bibliography

Maria João Martins, Isabel Ventim Neves, “Propagação e Radiação de Ondas Eletromagnéticas”, 2ª edição, 2018, LIDEL

M. de Abreu Faro, "Propagação Guiada, Técnica AEIST, 1984

M. de Abreu Faro, "Radiação, Técnica AEIST, 1980

R.E. Collin, "Antennas and Radiowave Propagation", MacGraw-Hill, 1999

### Teaching method

The syllabus for the Propagation and Radiation course is divided into two parts: the first part focuses on wave propagation and the second part studies radiation. It should be noted that this program is taught with the support of two types of classes: theoretical classes dedicated mainly to the exposition of the subject and theoretical-practical classes dedicated to solving exercises and laboratory demonstrations.

### Evaluation method

**Continuous assessment**

- Two components are used to calculate the final mark in continuous assessment: the average of the tests (N_tests) with a weight of 80% and the average of the mini-tests associated with the laboratory sessions (N_LAB) with a weight of 20%.
- Neither component has a minimum mark.
- A pass is obtained if the weighted average of the two components is equal to or greater than 9.5 points.
- The only exam consultation material is the official formula sheet of the course printed in physical format.
- Students with a frozen N_LAB grade from the 22/23 academic year can use it this academic year (23/24) and the next academic year (24/25).

**Assessment by Exam**

- The final grade is the same as the exam grade.
- The exam can be used to retake one of the tests, subject to an invitation from the teaching staff.
- Improving one of the tests alone on the exam date is not permitted.
- The only exam consultation material is the official formula sheet of the course printed in physical format.

## Subject matter

**Propagation**

- Concept of phase, phase velocity, and amplitude. Monochromatic plane wave in complex vector notation: meaning of temporal and spatial phase constants.
- Maxwell''''s equations: differential and integral form. Maxwell''''s equations in the vacuum: application to a monochromatic plane wave. Maxwell''''s equations and boundary conditions: general conditions, perfect conductor boundary.
- Propagation in undefined media: perfect dielectric, dispersion equation, wave characteristic impedance, power transmission. General case of propagation: plane wave in lossy media, in good conductors, and in weakly lossy dielectrics.
- Propagation in semi-defined media: Reflection and transmission, laws of reflection and transmission, coefficients of reflection and transmission, TE polarization, TM polarization, total reflection, wave structures in semi-defined media: dielectric/perfect conductor and dielectric/dielectric boundary: power flow, Brewster''''s angle.

**Guided Propagation**

- Metal-walled waveguides: TEM modes, hollow metal guides (non-TEM modes) - fundamental concepts and systematic determination of modes. Rectangular and circular cross-section guidance. Fundamental quantities - cut-off frequency, wave characteristic impedance, phase, and group velocities. Transmitted power. Evaluation of losses in the conductor. Field structure in guides.
- Transmission lines: characteristic impedance, voltage, and current waves. Fundamental concepts: impedance along the line, input impedance, input voltage, transmission factor, transmitted power, voltage, current wave progression, and stationary wave factor. Load conditions: adapted line and full-interference line. Smith''''s chart. Adaptation of radio-frequency lines: short-circuited single e stub transformer.
- Introduction to fiber optics: contrast, communication systems, attenuation, dispersion, intermodal broadening, numerical aperture.

**Radiation**

- Potentials: definition of vector and scalar potentials, Lorentz condition. Calculation of potentials, differential equations, and integral equations. Harmonic time variation. Calculation of fields: far field, current element, and general case.
- Duality and equivalence of Maxwell''''s equations: Elementary aperture and general case.
- Fundamental concepts of radiation: radiation diagrams, field zones, emitted power, radiation intensity, directivity, gain, and effective area. Friis formulas: optimal conditions and correction factors. Polarization: incident wave polarization, polarization ratio, polarization curve, Poincaré sphere. Polarization of the emitted wave and polarization coefficient. Available power and received power. Bandwidth.
- Linear, stationary wave, and slit wave antennas. Fundamental concepts: emission and reception equivalent scheme, radiation resistance, loss resistance, and antenna resistance. The notion of efficiency and effective length. Received power and adaptation. Short antennas: Hertz electric dipole, short electric dipole. Characteristic parameters of short antennas. Free-space and conductive plane aperture with uniform and non-uniform illumination. Electromagnetic horns and parabolic reflectors.
- Linear arrays: array space factor, array radiation diagram, antenna-image array, a vertical monopole. Reciprocity.