Unit ELECTROMAGNETIC FIELDS
- Course
- Computer science and electronic engineering
- Study-unit Code
- 70A00066
- Curriculum
- Ingegneria elettronica
- Teacher
- Cristiano Tomassoni
- Teachers
-
- Cristiano Tomassoni
- Hours
- 81 ore - Cristiano Tomassoni
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2023/24
- Learning activities
- Caratterizzante
- Area
- Ingegneria elettronica
- Academic discipline
- ING-INF/02
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Transmission lines
Resolution of transmission line equations. Progressive waves and stationary waves. Line characteristic parameters. Smith's Chart: Applications.
Basic Equations and Theorems of Electromagnetism
Call: scalar and vector fields; Vector operators; Phasor method
Fundamental equations: electromagnetic field; Maxwell equations; Constituent relations; Principle of duality; Boundary conditions; Problem classification e.m .; Electrostatic and magnetostatic.
Electrodynamics: Poynting theorem, physical interpretation; Complex vectors, polarization; e.m. Field and power in complex notation; Maxwell equations and Poynting theorem in the frequency domain; Wave equation, electrodynamic potentials, waves, amplitude and phase functions.
Plane Waves
Propagation Vector and Phase Speed. plane waves as a solution to Maxwell's equations. Uniform plane waves in non-dissipative media: TEM, TE and TM waves. Reflection and transmission with normal incidence; Oblique incidence: laws of reflection; coefficients of reflection; Total reflection; Reflection from the surface of a good conductor. Dielectric polarizability.
Radiation e.m.
Green function for free space; Potential vector for any source. Hertz Dipole. Radiation conditions. Reciprocity and equivalence theorems; Their applications. Antennas: radiation diagram; Directivity and equivalent area. Friis formula, radar equation.
guided wave propagation
Cylindrical symmetry structures. Expression of fields e.m .: TE, TM and TEM waves; Equivalent transmission lines. Cutting frequency.
Wave guides, Dielectric guides. - Reference texts
- David M. Pozar,
Microwave Engineering
(Fourth Edition),
Wiley, 2011 - Educational objectives
- To understand the physical phenomena related to the propagation of the electromagnetic waves. To develop a unitary vision of problems related to the high frequency use of the electromagnetic spectrum in electronics and communications.
- Prerequisites
- To the end of realizing the theoretical and technical part are necessary the following courses:
Analysis 2, geometry 1, Physics B, Network theory. - Teaching methods
- The course is organized as follows:
Classroom lessons on all subjects of the course;
Classroom exercises with the use of software suitable for solving electromagnetic problems;
Laboratory exercises. - Other information
- The teacher provides teaching material to illustrate the lecture topics in detail
- Learning verification modality
- The exam provides for an oral examination, a written test, and possibly the presentation of a technical report.
The oral test consists of a discussion lasting about 30 minutes. Aimed at ensuring the level of knowledge and understanding acquired by the student on the theoretical and methodological content developed in the program. The oral test will also allow student communication skills with language ownership and autonomous display organization.
The written test consists in solving theoretical and computational problems. - Extended program
- Nature of light: historical overview of the dispute between light as a wave or light as a particle. Description of the two-slit experiment: behavior of light as a wave. Quantum two-slit experiment with single photons: quantum nature of light. Electromagnetic spectrum.
Divergence theorem and Stokes' theorem. Derivation of general formulas for gradient, divergence, and curl calculations (independent of the coordinate system used). Maxwell's equations. Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday-Neumann law, and Ampere-Maxwell law derived from Maxwell's equations.
Constitutive relations: electric polarization vector and relationship between electric field and electric displacement. Contribution of losses to the dielectric constant. Relative dielectric constant. Electrical loss tangent.
Isotropic materials, electrically anisotropic materials, and magnetically anisotropic materials. Birefringence. Time-dispersive media, Debye model, and Cole-Cole model. Space-dispersive media. Interface conditions between two media: condition for electric displacement vector D, condition for magnetic induction vector B, condition for electric field vector E, and condition for magnetic field vector H. Concept of electric wall and magnetic wall.
Transmission lines, solutions of telegrapher's equations in the time domain. Calculation of transmission line parameters: propagation coefficient, characteristic impedance, attenuation, and phase velocity. Solutions for lossless lines. Reflection coefficient in transmission lines. Power transmitted on a lossless line. Variation of reflection coefficient with distance from the load, calculation of input impedance of a terminated line. Voltage Standing Wave Ratio (VSWR). Variation of voltages, currents, and impedances along transmission lines. Line terminated with a closed circuit. Line terminated with an open circuit, lambda/2 line, and lambda/4 line. Impedance jump between two transmission lines.
Power delivered by a generator on a transmission line. Power delivered by the generator as a function of available power. Formula for calculating input impedance in the case of lossy lines. Power dissipated on the lossy line and on the load.
Smith chart. Reflection coefficient and VSWR on the Smith chart. Analytical derivation of constant resistance and constant reactance circles. Transformation from reflection coefficient to impedance. Calculation of input impedance of a line using the Smith chart. Smith chart for admittance. Additional information on the chart: Maximum Voltage, Minimum Voltage, and VSWR. Concept of matching.
Use of the Smith chart for matching with lumped elements: series-parallel adapter and parallel-series adapter. Quarter-wavelength adapter, single stub adapter.
Introduction to uniform plane waves, wave equation (Helmholtz equation) in the frequency domain, plane waves in the frequency domain in lossless media. Relationship between electric field and magnetic field in plane waves. Impedance of free space. Comparison between plane waves and transmission lines.
Helmholtz equation in the time domain. Solution of Helmholtz equations for the electric field in the time domain and calculation of the corresponding magnetic field. Plane waves in dissipative media and solution of Helmholtz equations in dissipative media.
Calculation of main parameters in dissipative media (impedance, attenuation, wavelength, etc.). Approximations for low-loss media.
Plane waves in plasma: plasma frequency, attenuation, wave number, and wave impedance in plasma. Plane waves in good conductors, skin effect, and skin depth in good conductors.
Calculation of skin depth for copper at different frequencies. Calculation of admittance in good conductors.
Plane wave solution in the general case: solution of the Helmholtz equation for the electric field using the method of variable separation and calculation of the corresponding magnetic field. Dispersion equation and wave vector. Orthogonality between the electric field, magnetic field, and wave vector.
Plane waves in media with losses, equiphase and equiamplitude surfaces. Phase velocity. Polarization: decomposition of the field vector into real and imaginary parts. Linear polarization, right-handed circular polarization (RHCP), left-handed circular polarization (LHCP), elliptical polarization.
Poynting's theorem in the frequency domain and energy balance. Energy stored in the electric and magnetic fields. Active and reactive power balance. Poynting's theorem in the time domain and energy balance. Relationship between the Poynting vector in the time domain and the frequency domain. Time-averaged power as the real part of the Poynting vector in the frequency domain. Calculation of the Poynting vector of plane waves from the electric field alone or the magnetic field alone.
Attenuation constant between two equiphase planes of a plane wave. Plane wave incident normally on a dielectric. Poynting vector in the case of normal incidence. Continuity of the pointing vector at the interface between two dielectrics. Energy balances between incident, reflected, and transmitted waves. Media with losses: Normal incidence at the interface between low-loss dielectrics, Normal incidence at the interface between dielectric and plasma.
Plane wave in a dielectric incident orthogonally on a conductor. Surface current induced by the incident wave on the metal as a function of the electric field. Leontovich's condition. Average power dissipated by the wave on the metal. Normal incidence on an ideal metal. Standing wave.
Oblique incidence. Snell's laws for reflected and transmitted waves.
Fresnel's formulas: transmission and reflection coefficients for waves with orthogonal and parallel polarization. Derivation of Fresnel's formulas considering orthogonal waves as TE waves and parallel waves as TM waves.
Brewster's angle. Reflected and transmitted power density in oblique incidence. Concept of critical angle. Attenuation of the transmitted wave in case of incidence above the critical angle.
Examples of the application of the critical angle: optical fiber and dielectric guides. Scalar potential and vector potential: derivation of the Helmholtz equations for the scalar potential and vector potential. Examples of application of the vector potential: waveguide (TE and TM modes).
Use of the vector potential for calculating radiation from an elementary dipole: Calculation of the vector potential as a solution of the homogeneous Helmholtz equation. Calculation of the vector potential generated by an infinitesimal current at the origin of the coordinate system. Calculation of the magnetic field and electric field relative to the vector potential of an infinitesimal current. Variation of magnetic fields with distance: behavior of the EM field near the infinitesimal current source. Behavior of the EM field in the far field. Concept of local plane wave in the far field of an infinitesimal current.
Calculation of the vector potential generated by a generic current density distributed over a finite volume: approximation of the vector potential in the far field and separation of the radial and angular dependencies. Calculation of the far-field EM field relative to the vector potential of a current source distributed over a volume. Demonstration that the far field of an antenna can be locally seen as a plane wave.
During the lectures, exercises on the topics covered will also be performed. Electromagnetic simulators will be used to visualize the behavior of fields in some simple components.
Finally, experiments will be conducted: (non-quantum) double-slit experiment using a laser pen. Experiments with varying magnetic induction flux to generate currents in copper coils. Use of currents in coils to generate magnetic fields. Electric motor. Calculation of the Earth's magnetic field using a compass and a wire carrying current.