# 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 program of the Propagation and Radiation curricular unit is divided into two parts, in the first part, the focus is on wave propagation and in the second part radiation is studied. It should be noted that this program is taught using three types of classes: theoretical classes, practical classes and laboratory sessions.

### Evaluation method

- The evaluation has a theoretical component (weight of 80%) and a practical component (weight of 20%).
- Approval is obtained with a grade of 9.5 or higher in each component.
- If a student passes the laboratory component but fails the theoretical component, the mark of the laboratory component will be frozen for three school years.

**Theoretical Component**

- The theoretical component is done through two tests of equal weight taken during the semester or by exam. It is also possible to improve your grade on the final exam date. The only material allowed for consultation in the exams is the official form of the course.
- The tests/exams will be given face-to-face. Online assessments are different from face-to-face assessments. Online assessment grades above 17 have to be defended in an oral.

**Practical Component**

- The practical component evaluation will be based on the execution of two laboratory sessions with a questionnaire (mini-test).
- Anyone who attends the labs (at least 1) but does not have a positive average can take an oral exam on the 2nd assignment to raise the grade up to a maximum of 14 points.

## 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.