Chapter 1: Waves and Phasors

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<b>Luong Vinh Quoc Danh</b>

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<b>Bài giảng:</b>

<b>TRƯỜNG ĐIỆN TỪ (CT361)</b>

<b> (ELECTROMAGNETICS)</b>

<b>Chapter 1: </b>

<b>Waves and Phasors </b>

<b> (Sóng và Phức vector)</b>

<b>Giảng viên: GVC.TS. Lương Vinh Quốc Danh</b>

Bộ môn Điện tử Viễn thông, Khoa Công Nghệ

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<b>Electromagnetic waves</b>

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Produced by the movement of electrically charged

particles

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

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Travel at the speed of light

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Also known as EM waves

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<b> The Nature of Electromagnetism</b>

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<b>Electric fields – Coulomb’s Law</b>

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<b>Electric field intensity:</b>
<b>Electrical force acting on charge q₂</b>

<b>due to charge q₁:</b>

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<b>Magnetic fields – Biot-Savart Law</b>

<b>µ₀ : </b>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 (Fe

₃

O

₄

).

<b>Magnetic flux density B</b>:

<b>Magnetic field intensity H</b>:

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<b>Velocity of Light</b>

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<b> Velocity of light in free space</b>:

<b> µ = µ_r µ₀ ; µ_r : </b>Relative magnetic permeability of the material

<b> = _r</b> <b>₀ ; _r : </b>Relative electric permittivity of the material



1



<i>v</i>

<b> Velocity of light in non-vacuum</b>:

<i>Example: speed of light </i>

<i>in glass: ~ 2 x 10</i>8 _(m/s)

<i><b>Usain Bolt</b>: world </i>
<i>record holder at the </i>
<i>2009 Berlin World </i>
<i>Championships. His </i>
<i>top speed is </i> <i><b>12.27 </b></i>
<i><b>m/s</b>!</i>

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<b>Static and Dynamic Fields</b>

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 A static distribution of charges produces an electric field.

<i>Charges in motion (an electrical current) produce a magnetic field.</i>

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

vice versa.

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<b>Traveling Waves</b>

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<i><b> Waves are a natural consequence of many physical processes: waves and </b></i>

<i>ripples on oceans and lakes, sound waves traveling through air, electromagnetic </i>
<i>waves that constitute light, earthquake waves...</i>

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<b>Traveling Waves (cont.)</b>

<i><b> Phase velocity (propagation velocity):</b></i>

: angular velocity of wave
: phase constant

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<i><b> Sinusoidal waves in a lossy medium:</b></i>

<b>Traveling Waves (cont.)</b>

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<b>Energy Decay of the 2004 Sumatra Tsunami in the World Oceans</b>

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<b>Electromagnetic Spectrum</b>

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Radio waves

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Longest wavelength EM waves

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_Uses:

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_{TV broadcasting}

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AM and FM broadcast radio

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Heart rate monitors

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Cell phone communication

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Microwaves

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Wavelengths from 1 mm ~ 1 m

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_Uses:

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_{Microwave ovens}

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Bluetooth headsets

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Broadband Wireless Internet

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Radar

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GPS

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Infrared Radiation

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_{Wavelengths in between microwaves and visible light}

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_Uses:

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Night vision goggles

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_{Remote controls}

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_{Heat-seeking missiles}

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X-rays

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Tiny wavelength, high energy waves

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Uses:

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Medical imaging

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Airport security

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Inspecting industrial welds

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<b>Review of Complex Numbers</b>

 Complex number

<i><b>z</b></i>

<i><b> is written in the form:</b></i>
<i><b>z = x +jy (1.35)</b></i>

Where <b>x = Re(z)</b>
<b>y = Im(z)</b>



<i><b>z</b></i>

<i><b> is written in POLAR form:</b></i>

<i><b> Euler’s identity:</b></i>

<i><b> Complex conjugate of z:</b></i>

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<b>Properties of Complex Algebra</b>

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<b>Properties of Complex Algebra (cont.)</b>

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<b>Phasors</b>

<i><b>Phasor analysis is a useful mathematical tool for solving problems </b></i>

involving

<i>time-periodic sources</i>

.

<i><b>Phasor V</b></i>

<i><b>_s</b></i>

<i>, contains amplitude and phase information but is independent </i>

<i><b>of the time variable t.</b></i>

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Mechanisms and Mechanical Devices Sourcebook - Chapter 1

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