Chapter 1: Waves and Phasors

ripples on oceans and lakes, sound waves traveling through air, electromagnetic waves that constitute light, earthquake waves...  Sinusoidal waves in a lossless medium:.[r]

Luong Vinh Quoc Danh 1

Bài giảng: TRƯỜNG ĐIỆN TỪ (CT361)

(ELECTROMAGNETICS)

Chapter 1: Waves and Phasors

(Sóng và Phức vector)

Giảng viên: GVC.TS Lương Vinh Quốc Danh

Bộ môn Điện tử Viễn thông, Khoa Công Nghệ

E-mail: lvqdanh@ctu.edu.vn

Electromagnetic waves

• Produced by the movement of electrically charged

particles

• Can travel in a “vacuum” (they do NOT need a medium)

• Travel at the speed of light

• Also known as EM waves

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Electric field

 The Nature of Electromagnetism

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Electric fields – Coulomb’s Law

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Electric field intensity:

Electrical force acting on charge q 2

due to charge q 1 :

0 : Electrical permittivity of free space, equal to 8.854 x 10-12 F/m

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Magnetic fields – Biot-Savart Law

µ 0 : Electrical permeability of free space,

equal to 4 x 10 -7 H/m

- Discovered as early as 800 B.C by the Greeks.

- A certain stone attracts pieces of iron, called magnetite (Fe3O4).

Magnetic flux density B:

Magnetic field intensity H:

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Velocity of Light

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 Velocity of light in free space:

µ = µ r µ 0 ; µ r : Relative magnetic permeability of the material

 =  r 0 ;  r : Relative electric permittivity of the material



1



v

 Velocity of light in non-vacuum:

Example: speed of light

in glass: ~ 2 x 108 (m/s)

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Usain Bolt : world record holder at the

2009 Berlin World Championships His top speed is 12.27 m/s!

Source: http://www.planet-science.com

Static and Dynamic Fields

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 A static distribution of charges produces an electric field

Charges in motion (an electrical current) produce a magnetic field.

A time-varying electric field will generate a time-varying magnetic field, and

vice versa

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Traveling Waves

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 Waves are a natural consequence of many physical processes: waves and

ripples on oceans and lakes, sound waves traveling through air, electromagnetic waves that constitute light, earthquake waves

 Sinusoidal waves in a lossless medium:

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Traveling Waves (cont.)

 Phase velocity (propagation velocity):

: angular velocity of wave

: phase constant



 Sinusoidal waves in a lossy medium:

Traveling Waves (cont.)

Attenuation factor

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Energy Decay of the 2004 Sumatra Tsunami in the World Oceans

Electromagnetic Spectrum

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Radio waves

• Longest wavelength EM waves

• Uses:

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Review of Complex Numbers

 Complex number z is written in the form:

Properties of Complex Algebra

Properties of Complex Algebra (cont.)

Phasor analysis is a useful mathematical tool for solving problems

involving time-periodic sources

Phasor Vs, contains amplitude and phase information but is independent

of the time variable t.