EMT ch1 cheng

8/8/2019 EMT ch1 cheng

1/45

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.



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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



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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



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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



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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.



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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



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Frequency Band Naming :


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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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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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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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 = ?



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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



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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)



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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;



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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



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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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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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smcoo

1


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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



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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 :



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Complex Conjugate :

]Im[2

zz

],Re[2

zz

imples,

zzz

iszofmagnitudetheand

ezyjxz

**

*

j*

zz

Also



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)21(21

12212121

221121

212121

21212121

2222211111

)()(

))((

:

)()(:

,,,

:

j

jj

ezz

yxyxjyyxx

yjxyjxzz

tionMultiplica

yyjxxzzAddition

andzzyyxx

ezyjxzandezyjxz

Equality



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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



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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[ ])



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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



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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]



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For a fun!

http://www.falstad.com/vector/

Pre-understand what is divergence and curl

Documents

EMT ch1 cheng