ECE 107: Electromagnetism

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1 ECE 107: Electromagnetism Notes Set 1 Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA

2 Introduction (1) atom Electromagnetism (1 or 4 interactions) Nuclear (strong) interaction Weak interaction Nuclear and particle physics Gravity Electromagnetic F e = Rˆ 1 qq πε 0 R12 G gravitational constant ε 0 permittivity in free space Coulomb s Law

3 Introduction (2) Gravity Electromagnetic always attractive small no control attractive/repulsive large extensive control For an electron: F e /F g = 4x10 42, i.e. the electric force is much stronger!

4 Introduction (3) Why does gravity matter? Conservation of charge: Charges can t be created or destroyed On average the universe is neutral

5 Electric fields Electric field due to a charge: - ε = ε r ε 0 - permittivity - Characterizes the effect due to a charge - Can exists in space where no charges are present (still excited by a charge) ε 0 = 8.854x10-12 F/m Electric flux density: D = εe 2 ( C m )

6 Electric fields (2) linear superposition electric dipole

Magnetic fields (1) Magnetic interactions between

(although quantum mechanical in nature) If a needle

called magnetic-field lines Magnet has poles, which

which can be isolated) Magnetic field lines have

7 Magnetic fields (1) Magnetic interactions between metallic materials were known for centuries (although quantum mechanical in nature) If a needle is placed near a magnet, it aligns along lines called magnetic-field lines Magnet has poles, which always exist in pairs (unlike electric charges, which can be isolated) Magnetic field lines have neither a start nor an end Magnetic field also can be created by electric currents

8 Magnetic fields (2) Magnetic flux density induced by a steady current in the z direction ( T ), Tesla - permeability Magnetic permeability of free space Magnetic field: H ( Am) such that B = µ H Amazingly - speed of light

9 Static and dynamic fields (1) Electric field is excited by a charge q. Magnetic field is excited by a current I = dq dt. For a constant current I the electric and magnetic fields are independent from each other. Electrostatics and magnetostatics correspond to stationary charges and currents, respectively. Electrostatic and magnetostatic fields are uncoupled Dynamics corresponds to time varying fields. Dynamic magnetic and electric fields depend on each other. A dynamic electric field generates a dynamic magnetic field and vice versa.

10 Static and dynamic fields (2) Time varying electric field Easiest way is to move a charge This leads to a time varying current and a time varying magnetic field.

11 Static and dynamic fields (3) Under static conditions, electric and magnetic fields are independent, but under dynamic conditions, they become coupled.

Maxwell s Equations (1831 1879) B E = t D H = + J t D = ρ B = From a long view of the history of mankind seen from, say, ten thousand years from now, there

12 Maxwell s Equations ( ) B E = t D H = + J t D = ρ B = From a long view of the history of mankind seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. R. P. Feynman 0

13 Material characterization Properties of materials are characterized by permittivity, permeability, and conductivity ε electric permittivity µ magnetic permeability σ ( Sm= 1 ( Ωm)) conductivity of a material characterizes how easy charges can move in a material perfect dielectric σ = perfect conductor These parameters depend on frequency, temperature, direction,

Material characterization (2) Polarization of atoms changes electric field New field can be accounted for by changing the permittivity Permittivity of

14 Material characterization (2) Polarization of atoms changes electric field New field can be accounted for by changing the permittivity Permittivity of the material Another quantity used in EM is the electric flux density D: Similar arguments for permeability (μ) B = μh where μ r >> 1 for magnetic materials

15 λ = c/frequency

16 Electromagnetics is a foundation of electrical engineering Low Frequency Circuit High Frequency Optics Ultra-high Frequency X/Gamma-rays

17 Electromagnetics is new & exciting Wireless communication: o Radio wave propagation o Antenna design High-speed high-density circuits: o EM mutual coupling o EM compatibility Defense: o Stealth technology o EM missiles 17

18 Stealth technology F117 Night Hawk B-2 Spirit F-22 Raptor Joint Strike Fighter 18

19 Remote sensing: o Earth surface remote sensing o Atmospheric remote sensing o Nondestructive testing o Ground penetrating radar Medical application: o o o Magnetic resonance imaging Microwave imaging EM hyperthermia 19

20 MRI System 20

21 Photonics: o Waveguides and fibers o Resonators o Lasers o Filters o Couplers o Etc, etc, etc 21

22 Photonic waveguides and lasers 22

23 Magnetic storage and memory UCT) ATE

24 Traveling waves (1) Waves carry energy from one point in space to another Examples of waves: Ocean waves, sound waves, mechanical waves on strings, electromagnetic waves Waves of completely different physical nature have many common properties Waves have finite velocity needed to travel from a point to a point. For example, sound waves in air have velocity of 330 m/s, velocity of light is 3x10 8 m/s When the strength of the field associated with a wave depends on the source linearly, then two waves travel independently from each other 24

25 Traveling waves (2) Transient waves are caused by a short-duration source Harmonic waves are generated by a continuously oscillating source Some possible traveling wave types: 25

26 Traveling waves (3): Pulsed waves Consider a one-dimensional wave caused by a pulsed source Let y be the vertical wave displacement and x be the direction of the wave propagation. Then, neglecting any possible loss of energy carried by the wave, where y(,) x t = Af ( t x u) f() t A u is the excitation function is the amplitude is the velocity x= tu 0 f( t xu) 0 x= tu 1 f( t xu) 1 y x= tu 2 2 x f( t xu) 26

27 Traveling waves (4): Sinusoidal waves As an example, assume a one-dimensional ocean wave Let y be the vertical wave displacement and x be the direction of the wave propagation. Then, neglecting any possible loss of energy carried by the wave, A amplitude T period (s) λ wavelength (m) - reference phase 27

28 Traveling waves (5): Sinusoidal waves Reference phase 28

29 Traveling waves (6): Sinusoidal waves Phase - phase velocity - frequency - angular frequency - wavenumber 29

30 Traveling waves (7): Lossy medium When loss is present the wave is attenuated α, ( Np m), neper per meter - the attenuation constant 30

31 Review of phasors (1) Consider a function: It can be shown that - phasor Phasors contain the information about the amplitude AND phase, while the time dependence is known as Use of phasors simplify solutions for harmonic fields 31

32 Review of phasors (2) 32

33 Review of phasors (3) Time Domain Frequency Domain Current through resistor Time domain i = I cos t m ( ω +φ) cos( ω φ) υ = ir = RI t + m Phasor Domain V = RI φ m

34 Review of phasors (4) Time Domain Time domain Phasor Domain

35 Review of phasors (5) Time domain Time Domain Phasor Domain

36 Review of phasors (6)

37 Review of phasors (7) Cont.

38 Review of phasors (8)

39 Review of phasors (9) Traveling waves in terms of phasors: +x traveling wave -x traveling wave 39

40 Transmission lines Why 50 Ohms?

ECEN 3741 Electromagnetic Fields 1

ECEN 3741 Electromagnetic Fields 1 Lecture Notes No. 1 Waves & Phasors Dr. Lin Sun Dept. of ECE Youngstown State University Youngstown, Ohio, 44555 Spring 2015 http://people.ysu.edu/~lsun/ecen3741 1 Chapter