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T.H.HUang
Chapter 1. Introduction
Learning Objectives
1. Electromagnetic Model
2. Electromagnetic Spectrum
3. Demands from Wireless Communications;
4. SI Units, Universal Constant, and Numeric Precision;
5. Review of Complex Numbers and Phsors
Electromagnetics ()
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We are immersed in Electromagnetic (EM) fields.
Light
Overview
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Historical Events in Electromagnetics
Hans Christian Oersted finds current produces magnetic field.
600B.C.
1785
1819
1820
1831
1873
1887
1901
1st record of electric and magnetic behaviorby Thales of Miletus
Forces between charges measured by Charles Coulomb
Forces between current carrying wires found byAndre Marie Ampere.
Michael Faraday finds that time-varying magnetic fields
create electric field.
James Clerk Maxwell formulates Maxwells Equations
Heinrich Hertz detects electromagnetic waves.
Marconi transmits and receives radio wavesacross the Atlantic Ocean.
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Major Inventors
James Clerk Maxwell (1831-1879) was born in
Edinburgh, Scotland. He served as a professorin London and Cambridge. At the age of 24,Maxwell translated and verified Faradays theoriesin mathematical formulations known today asthe Maxwell equations.He also showed that these equations implicitlyrequire the existence of electromagnetic wavestraveling at the speed of light.
Ref: Radio Frequency Integrated Circuits andTechnologies, by Frank Ellinger, Chapter 1,2007 Springer-Verlag Berlin Heidelberg.
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Major Inventors
Illustration of Marconis experiment1903 MarconiTransmission Station
Guglielmo Marconi (1874-1937) was born in
Italy. Based on the insights of Hertz, Marconisucceed in transmitting radio signal over a fewkilometers at Bologna in 1896.He is a worldwide famous person. When he died,all radio transmitters were shut down for minutesof silence.
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Electromagnetic Model
Electromagnetics : the study of the effects ofelectric charges at restand in motion.
Two approaches to develop a scientific subject:the inductive() and the reductive()approaches.
Inductive
Observations ofexperiments orphenomenon
TheoremsandLaws
ReductiveVerifications,and furtherpredictions
Postulation,Axioms
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This textbooks is based on the reductive approach.
First : to define the basic quantities of electromagnetics;Second : the rules of operations, vector algebra,
vector calculus, and partial differential equations;Third : the fundamental postulates will be presented and
then if possible be verified experimentally.
Reductive * to postulate a few fundamental relations
for a ideal model.
* the postulated relations are axioms, from
which particular law and theorems can be
derived.
* The validity of the model and the axioms is
is verified, by their ability to predict consequences
then check with experimental observations.
Electromagnetic Model
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Electromagnetic Model
A field is a spatial distributionof a some quantity,
which may or may not be a function of time;
A field is defined by the electrical or magnetic action force.
-----
+++++
Ex: explode.jpg
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The source of electric field : charges (electrons / holes);
The source of magnetic field : current
Iq
E
E
E
E
HH
Electric potential
Magnetic potential
Fields & waves is essential in the explanation ofaction at a distance. ()
q
I
Electromagnetic Model
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Action at a distance
Media is not necessary;
A model which states the energy translation
without media.
Example :
light : from the sun and the stars
Gravitational field : between you and earth, moon and earth,
Electric / Magnetic fields : interaction between magnet
Electromagnetic Model
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A time-varying electric field is accompanied bya magnetic field, and vice versa.
The spirit of EM wave. Maxwells Equations
Faradays Law
tt
HB
E
Electromagnetic Model
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Two examples tell the inadequacy of circuit theory
concepts and the needs for electromagnetic fieldconcepts.
open
circuited Not in a straight line.
Electromagnetic Model
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[source]: IE3D simulation of cell phone antenna, provided by Prof. H.-R. Chuang.
E-Field H-FieldExample:
EM Simulator Nowadays
Simulators : Sonet, HFSS, IE3D, ADS Momentum, and so on
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Electromagnetic Wave
An electromagnetic Wave carries Energy;
2003 MIT
Sunlight EM Energy Heat ;
Energy Propagation (direction rule: Ex H)
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Electromagnetic Spectrum
X-ray : causes damage (not use);
Fiber optical communication :
ultraviolet & visible light.
1~100GHz : wireless communication.Atmosphere attenuation windows:
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Frequency Band Naming :
Ex. DTV-B : 48 MHz ~ 860 MHz, 6 MHz / channel
Electromagnetic Spectrum
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Frequency Band Naming :
Electromagnetic Spectrum
Automotive Speed Detector Type Operation Frequency
X-band
K-band
Ka-band
10.525 GHz
24.150 GHz
34.300 GHz
[]
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Spectrum in KHz
Ex. Sangean SG-62212
AM : 535 1605 KHzFM : 88 108 MHz
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Spectrum in MHz
* Wireless Mouse
(AMPS)(GSM/PCS)
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Spectrum in GHz (I)
(WLAN)
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(ISM band)
Spectrum in GHz (II)
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GSM Spectrum
FrequencyRange (in MHz)
(RX)(TX)
GSM 400
GSM 850
GSM 900
GSM 1800
GSM 1900
450.4 457.6
478.8 486.0
460.4 467.6
488.8 496.0
824 849 869 894
880 915 925 960
1710 1785 1805 1880
1850 1910 1930 1990
GSM Spectrum
Silicon-based technology IC operated up to ~6GHz (Ex. WLAN 802.11a)
Silicon-based technology IC operated up to ~60GHz (WPAN)
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Electromagnetic Spectrum
In vacuum, the speed of light , c (m/sec),
f c
Where is the wavelength, and f is the frequency.
c = 2.998x108 m/sec, (in vacuum)
Question: the wavelengths of 900MHz / 1800MHz / 2.45GHz / 5.25GHzsignals in the free space?
Ans: for reference :1 GHz
= 30 cm;
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Electromagnetic Spectrum
From the communication viewpoint,
the higher frequency operation, the larger amountof information (data) can be translated.
From the viewpoint of antenna size,
the higher frequency used, the smaller size of
antenna size could be. (efficiency issue)
From the viewpoint of circuitry,
the higher frequency used, the higher power
consumption could be.
P = cV2/2 * f (logic circuitry)
U = h f, U is the energy of a photon,h is Plancks constant (= 6.63x10-34 J-sec)
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Electromagnetic Model
Circuit Theory vs. EM Theory
1. As a sine wave with 900MHz,= 33.3 cm;
2. As a sine wave with 5GHz, = 6.0 cm
PCB Level IC Level
scale = mm ~ cm scale = um ~ mm
Other issues: bond wire inductance (1 mm 1 nH);
Chip applications: correct microstrip line /interconnect line models; parasitic capacitances.
Free Space:
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Wave Propagation on the PCB:
EM wave propagation speed slows down on PCB the wave length is reduced.
= f
Glass Epoxy substrate (FR-4,r ~ 4.8);Wave speed reduction 1/(4.8)0.5 = 0.45;Wave length reduction 1/(4.8)0.5 = 0.45;
1 GHz eff = 30 cm x 1/(4.8)0.5 = 13.7 cm
Question : in Silicon,r ~ 11.8, eff @ 10 GHz = ?
Electromagnetic Model
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Circuit theory deals with lumped-parameter systems
using the components of resistors (R), inductors (L),and capacitors (C).
Wavelength the dimension of the circuitry;
In lumped-circuit model: circuit transient behavior
is independent of space coordinates.
Hints: transmission line equations are both time- and distance-dependent.
The solutions V( ) and I( ) of transmission line equations
are:
V(z;t) = Re[V(z) ejt]andI(z;t) = Re[I(z) ejt]
As V(z),I(z) =constant,independent of z,Circuit theory
Electromagnetic Model
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Demands of Wireless Communications
Modern Cellular Phone: Phone service + GPS + PDA + Games
Hexagonal Cells for Base Stations : smaller amount ofcarrier frequencies (7 foscs); no overlap among thecells using the same carriers.
1
23
4
5
6
7
1
Cells noted as 1 could use the same frequency.
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Electromagnetics plays in
(RF IC)(PCBs)
(Wave in Air)
(Antenna)
(Fiber)
Demands of Wireless Communications
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Electromagnetics plays in
1. Waves propagate in space and through material
media;
2. Waves are radiated and received by antennas;
3. Waves propagate in transmission lines such as
coaxial cables;
4. Efficient signal handling requires impedance matchingof transmission lines;
5. RF components, such as those in the RF front-end
and in the towers box, are typically designed and
understood via electromagnetics;
6. Communications between towers may employ fiber
optics and optical components;7. Noise and interference between electronic components
impact system performance;
Demands of Wireless Communications
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Electromagnetics plays in the phone unit :
PCB : microstrip line effect (scale: mm~cm)Packages : parasitics (cap. & res.)
/ pin inductance (scale: mm)
ICs : interconnects parasitics* (scale: um~mm)
Example : Silicon Lab.4133T,bondwireinductorsfor VCO.
pad
http://mst.tu-berlin.de
Demands of Wireless Communications
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SI Units and Constants
SI units (MKSA system)
Six Basic Quantities : Length, Mass, Time, Current,Temperature (Kelvin)Luminous intensity (Candela)
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SI Units and Constants
Other Derived Factors:Unit in MKSA system:
E kg
m / A
s3;B kg / As2;C As
Relations in free space:
HB
ED
o
o
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SI Units and Constants
smcoo
1
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SI Units and Constants
Significant digits : 600, 60, 60.0, and 60.000;
Adding (or subtracting) : 60 + 0.001 = 60;60.0000 + 0.001 = 60.001
multiplying (or division) : 60 x 0.5 = 30;60.0 x 0.5 = 30.0
For lengthy calculation, using more significant digitsthan desired until the calculation is completed.
The pure integers or counted quantities are known
to infinite precision.
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Multiple and sub-multiple prefixes:
Prefix
Exa
Peta
Tera
Giga
Mega
Kilo
Symbol
E
P
T
G
M
K
Magnitude
1018
1015
1012
109
106
103
Prefix
milli
micro
nano
pico
fento
atto
Symbol
m
u
n
p
f
a
Magnitude
10-3
10-6
10-9
10-12
10-15
10-18
SI Units and Constants
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Review of Complex Numbers
Review of Complex Numbers
identity)s(Euler'sinjcose
Im[z]yandRe[z],x,1-j
where
form)(polarez
form)ar(rectangulyjxz
z,numbercomplexA
j
j
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Relation between rectangular and polar representations :
Review of Complex Numbers
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Complex Conjugate :
]Im[2
zz
],Re[2
zz
imples,
zzz
iszofmagnitudetheand
ezyjxz
**
*
j*
zz
Also
Review of Complex Numbers
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)21(21
12212121
221121
212121
21212121
2222211111
)()(
))((
:
)()(:
,,,
:
j
jj
ezz
yxyxjyyxx
yjxyjxzz
tionMultiplica
yyjxxzzAddition
andzzyyxx
ezyjxzandezyjxz
Equality
Review of Complex Numbers
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2
j)(1ej,eej
2
j)(1e)(ej,ej
:relationsUseful
)sin(cosz
n,integerpositiveanyfor:
)()(
0zfor:
/4j/2j/2j
/4j1/2/2j/2j
2/2/12/1
n
)21(
2
122
22
21122121
22
11
2
1
2
j
nnjn
j
ezz
nnzez
Powers
ezz
yxyxyxjyyxx
yjxyjx
zz
Division
Review of Complex Numbers
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Review of Phasor Expression
Engineering Problems like R-C, R-L, and L-C network
analyses, Wave Equations (in Magnetism);
The forcing function (excitation source) varies sinusoidally
with time;
Arbitrary function be expanded into a Fourier series of
sinusoidal components.
Adopt either a cosine or sine reference. (Re[ ], Im[ ])
Review of Phasor Expression
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Phasor expression :
.t variableindependen-timeais
which,expressionphasoraasnamedisZ~
function;ousinstantaneaasnamedisz(t)
where
]eZ~
Re[z(t)
asexpressed
becanz(t)functionvarying-ally timecosinusoidAny
tj
Review of Phasor Expression
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)2/0(0
11
)0(0
11
)2/0(
0
/2j-
)0(0
1)xt(sA
~1)(
)]xt(cosA[
~)(
)xt(sA
eAtsinA
)xt(cosA
AtcosA
~)(
xj
xj
xj
xj
eAj
dtin
Zj
dttz
eAjdt
d
Zjtzdt
d
eAin
eA
Ztz
Transformation from the instantaneous expressionto the phasor expression :
[the end]
Review of Phasor Expression
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For a fun!
http://www.falstad.com/vector/
Pre-understand what is divergence and curl
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