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Intro.1
EIE382 Electromagnetics
Applications of Electromagnetics• When wave propagation effects cannot be neglected
• When radiation is involved
l
AV BV
Intro.2
Examples
Propagation effects cannot be neglected when the signal path is not much smaller than the wavelength (e.g. ~0.1 wavelength)
• High speed digital circuits– System Clock ~ 1GHz
• Inside the circuit, velocity of electromagnetic wave ~2x108 m/s– If signal frequency f = 1GHz,
wavelength λ = 2x108 / 1x109 = 0.2m
Intro.3
Examples
• High frequency analog circuits– Frequency ~ 1GHz – 10GHz
• Bluetooth• WLAN
• Optical Communications
Intro.4
Examples
Radiation becomes efficient when the dimension of conductor larger than 0.1 wavelength
• Antennas
• Electromagnetic interference and compatibility
Intro.5
Who am I?
Lecturer: Dr. W.Y.TamRoom no.: DE604Phone no.: 27666265e-mail: enwytam@polyu.edu.hk
Handouts, Tutorials, … are available atwww.en.polyu.edu.hk/~em/hdem06.htm
I am available at (Consultation hour)9am – 10:30am (Tuesday)9am – 11am (Friday)
Intro.6
Assessment & Textbooks
AssessmentExamination 60%Practical 15%
– Mini-project: Microstrip Patch Antennas Test (x3) 20%Assignments 5%
Textbook and Reference– F. T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice
Hall, 2004.– D. K. Cheng, Fundamentals of Engineering Electromagnetics,
Addison Wesley, 1993.
Intro.7
Syllabus
1. Transmission line (6 weeks)– Traveling waves– Transmission line equations– Lossless transmission lines– Terminated transmission lines– VSWR, Input impedance, Smith Chart– Impedance Matching
2. Time varying electromagnetic fields (4 weeks)
3. Radiation engineering (4 weeks)
Intro.8
Transmission Line
Structure– Any pair of wires and conductors carrying currents in
opposite directions form transmission lines.
Examples– coaxial cables, two-wire lines, microstrip lines on
printed-circuit-boards (PCB)• At very high frequencies, any conductor on a PCB
must be considered as transmission linesModel
– can be studied by the electric and magnetic fields propagating along the line
– But in most practical applications, it is easier to study the voltages and currents in the line instead
Intro.9
Examples
dielectric substrate
Microstrip line
conductor
Intro.10
Revision: Traveling waves
Equation:
– represents a wave travelling in the +z direction with constant amplitude A, where ω=2πf, β=2π/λ
• Suppose at t=0,
Distance zo for one period is
)cos( ztAv βω −=
)cos( zAv β=
βπλπβ
/22==∴
=
o
o
zz
oz
Intro.11
Revision: Traveling waves
– Any point of constant phase advances towards the +z direction, i.e.,
– Taking differentiation for both sides
• Called phase velocity
– Similarly, a wave represented by
travels in the -z direction.)cos( ztAv βω +=
βω
βω
βω
=⇒
=−⇒
=−
dtdz
dtdzKzt
0
Intro.12
Demonstration
Propagation in lossless medium (M1.3):
??
? ?
)cos(
==
==
−=
λω
βω
velocityphaseA
ztAv
Intro.13
Attenuated traveling waves
Equation:
– If α is positive, the wave amplitude is attenuated exponentially as it travels in the +ve z direction. If α is negative, the wave amplitude increases exponentially as it travels in the +ve z direction.
Demonstration
– Propagation in lossy medium (M1.4)
– Phase (M1.7)
( )ztAev z βωα −= − cos
Intro.14
Revision: Phasors
Complex number:
Polar form:
Euler’s identity:
Useful relations:
θθ ∠==
−=+=
zezjjyxz
j
1 z
x
y
θ
θθθ sincos je j +=
2/
1π
ππ
j
jj
ejee
=
==− −
Intro.15
Phasors
Phasor analysis is used for solving problems involving linear systems in which the excitation is a periodic time function.
Converting an instantaneous voltage in terms of the phasor1. Adopt a cosine reference
– E.g.
2. Express time-dependent variables as phasors
)2/cos()sin()(πω
ω−=
=tVtVtv
o
os
( )[ ]( )[ ]tj
tjo
os
eV
eVtVtv
ω
πω
πω
~Re
Re
)2/cos()(2/
=
=
−=−
oj
o jVeVV −== − 2/~ where π
Intro.16
Phasors
Phasor of a traveling wave:
Therefore, the phasor is
( )( )[ ]ztjz
z
eAeztAeβωα
α βω−−
−
=
−
Recos
zjzeAe βα −−
zAe α−is the magnitude, and -βz is the phase angle.
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