Msc. Lecture 1_rf&Me

7/28/2019 Msc. Lecture 1_rf&Me

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TE 7005

RF & Microwave Engineering

Semester Spring 2013Engr. Ghulam Shabbir

M.Sc Telecommunication Engineering


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Text Books

1. Microwave Engineering by David Pozar

2. Microwave Devices & Circuits by SamuelY. LIAO


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Grading of Evaluation Components

Sessional:

4 Quizzes (40),

4 Home Assignments (40),

Project/Presentation/Attendance (10),

Total:

20% of Sessional + 20% Mid Semester +

40% Final Exam + 20% Viva


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Microwave Engineering means engineering and design of

communication/navigation systems in the microwavefrequency range.

Microwave Engineering

Applications: Microwave oven, Radar, Satellite communi-

cation, direct broadcast satellite (DBS) television, personal

communication systems (PCSs) etc.


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Microwave Engineering

The field of radio frequency (RF) and microwave

engineering generally covers the behavior of alternating

current signals with frequencies in the range of 100 MHz

(1 MHz = 106 Hz) to 1000 GHz (1 GHz = 109 Hz).

RF frequencies range from very high frequency (VHF)

(30300 MHz) to ultra high frequency (UHF) (3003000

MHz).

The term microwaveis typically used for frequencies

between 3 and 300 GHz, with a corresponding electrical

wavelength between = c/ f= 10 cm and = 1 mm,

respectively.

Signals with wavelengths on the order of millimeters are

often referred to as millimeter waves.


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The Electromagnetic Spectrum


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Introduction to Microwave Engineering

Figure-1 shows the location of the RF and microwavefrequency bands in the electromagnetic spectrum.

Because of the high frequencies (and short wavelengths),

standard circuit theory often cannot be used directly to

solve microwave network problems. In a sense, standard circuit theory is an approximation,

or special case, of the broader theory of electromagnetics

as described by Maxwells equations.

This is due to the fact that, in general, the lumped circuitelement approximations of circuit theory may not be

valid at high RF and microwave frequencies.


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Microwave components often act as distributedelements, where the phase of the voltage or current

changes significantly over the physical extent of the

device because the device dimensions are on the order

of the electrical wavelength. At much lower frequencies the wavelength is large

enough that there is insignificant phase variation across

the dimensions of a component.


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The other extreme of frequency can be identifiedas optical engineering, in which the wavelength is

much shorter than the dimensions of the

component.

In this case Maxwells equations can be simplifiedto the geometrical optics regime, and optical

systems can be designed with the theory of

geometrical optics


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History of Microwave Engineering

J.C. Maxwell (1831-1879) formulated EM theory in 1873.

O. Heaviside (1850-1925) introduced vector notation andprovided an analysis foundation for guided waves andtransmission lines from 1885 to 1887.

H. Hertz (1857-1894) verified the EM propagation along wire

experimentally from 1887 to 1891 G. Marconi (1874-1937) invented the idea of wireless

communication and developed the first practical commercialradio communication system in 1896.

E.H. Armstrong (1890-1954) invented superheterodynearchitecure and frequency modulation (FM) in 1917.

N. Marcuvitz, I.I. Rabi, J.S. Schwinger, H.A. Bethe, E.M. Purcell,C.G. Montgomery, and R.H. Dicke built up radar theory andpractice at MIT in 1940s (World War II).

ps. The names underlined were Nobel Prize winners.


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Brief Microwave History

Maxwell (1864-73)

integrated electricity and magnetism

set of 4 coherent and self-consistent equations

predicted electromagnetic wave propagation

Hertz (1886-88)

experimentally confirmed Maxwells equations

oscillating electric spark to induce similaroscillations in a distant wire loop (=10 cm)


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Marconi (early 20th century) parabolic antenna to demonstrate wireless

telegraphic communications

tried to commercialize radio at low frequency Lord Rayleigh (1897)

showed mathematically that EM wave

propagation possible in waveguides

George Southworth (1930)

showed waveguides capable of small

bandwidth transmission for high powers


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R.H. and S.F. Varian (1937)

development of the klystron

MIT Radiation Laboratory (WWII)

radiation lab series - classic writings

Development of transistor (1950s)

Development of Microwave Integrated

Circuits

microwave circuit on a chip

microstrip lines

Satellites, wireless communications, ...


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MicrowaveNetworks

Microwaves?

S-parameters

Power Dividers

Couplers

Filters

Amplifiers


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Antenna and Wave Propagation

Surface Wave

Direct Wave

Sky Wave

Satellitecommunication

Microwave &Millimeter Wave

Earth

Ionsphere

Transmitting

Antenna

Receiving

Antenna

Repeaters(Terrestrial communication)

50Km@25fts antenna

Troposphere


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Functional Block Diagram of a

Communication System

Input signal

(Audio, Video, Data)InputTransducer Transmitter

Output

TransducerReceiver

Output signal

(Audio, Video, Data)

Channel

Electrical System

Wire

or

Wireless


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Typical Block Diagram of a Microwave

System


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Microwave Applications


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Electromagnetic Spectrum

The microwave spectrum is usually defined as

electromagnetic energy ranging from approximately 1 GHzto 100 GHz in frequency, but older usage includes lower

frequencies.

Radio frequency (RF) engineering is a subset of electrical

engineering that deals with devices that are designed tooperate in the Radio Frequency spectrum.

These devices operate within the range of about 3 kHz up

to 300 GHz.

RF engineering is incorporated into almost everything that

transmits or receives a radio wave, which includes, but is

not limited to, Mobile Phones, Radios, WiFi, and walkie

talkies.


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Microwave transmission refers to the technology

of transmitting information or energy by the use of radiowaves whose wavelengths are conveniently measured in

small numbers of centimeter; these are called microwaves.

This part of the radio spectrum ranges across frequencies of

roughly 1.0 GHz to 30 GHz. These correspond towavelengths from 30 centimeters down to 1.0 cm.

Microwaves are widely used for point-to-point

communications because their small wavelength allows

conveniently-sized antennas to direct them in narrow

beams, which can be pointed directly at the receivingantenna.


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This allows nearby microwave equipment to use the same

frequencies without interfering with each other, as lowerfrequency radio waves do.

Another advantage is that the high frequency of

microwaves gives the microwave band a very large

information-carrying capacity; the microwave band hasa bandwidth 30 times that of all the rest of the radio

spectrum below it.

A disadvantage is that microwaves are limited to line of

sight propagation; they cannot pass around hills or

mountains as lower frequency radio waves can.


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Microwave radio transmission is commonly used in point-

to-point communication systems on the surface of theEarth, in satellite communications, and in deep space radio

communications.

Other parts of the microwave radio band are used for

radars, radio navigation systems, sensor systems, and radioastronomy.


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The next higher part of the radio electromagnetic

spectrum, where the frequencies are above 30 GHz andbelow 100 GHz, are called millimeter waves" because their

wavelengths are conveniently measured in millimeters, and

their wavelengths range from 10 mm down to 3.0 mm.

Radio waves in this band are usually strongly attenuated bythe Earthly atmosphere and particles contained in it,

especially during wet weather.

Also, in wide band of frequencies around 60 GHz, the radio

waves are strongly attenuated by molecular oxygen in the

atmosphere. The electronic technologies needed in the millimeter wave

band are also much more difficult to utilize than those of

the microwave band.
http://en.wikipedia.org/wiki/Millimeter_wavehttp://en.wikipedia.org/wiki/Millimeter_wave


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Mic

rowave

Millimeter

Wave

RF


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Wireline and Fiber Optic Channels

WirelineCoaxial Cable

Waveguide Fiber

1kHz

10kHz

100kHz

1MHz

10MHz

100MHz

1GHz

10GHz

100GHz

1014H

z

1015H

z

MicrowaveMillimeter

wave

RF


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WirelineCoaxial Cable

Waveguide Fiber

1kHz

10kHz

100kHz

1MHz

1

0MHz

10

0MHz

1GHz

1

0GHz

10

0GHz

1

014H

z

1

015H

z

l>

Microwave

EngineeringOptics

Transmission Line

Wireline and Fiber Optic Channels


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Radio-Frequency Bands (1)


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Radio-Frequency Bands (2)


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The term microwave refers to alternating current signals with

frequencies between 300 MHz (3108 Hz) and 30 GHz (31010Hz), with a corresponding electrical wavelength between 1 m

and 1 cm. (Pozar defines the range from 300 MHz to 300 GHz)

The term millimeter wave refers to alternating current signals

with frequencies between 30 GHz (3

1010

Hz) to 300 GHz(31011 Hz), with a corresponding electrical wavelengthbetween 1 cm to 1 mm.

The term RF is an abbreviation for the Radio Frequency. It

refers to alternating current signals that are generally appliedto radio applications, with a wide electromagnetic spectrum

covering from several hundreds of kHz to millimeter waves.

What are Microwaves?


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= 30 cm: f = 3 x 108/ 30 x 10-2 = 1 GHz

= 1 cm: f = 3 x 108/ 1x 10-2 = 30 GHz

Microwaves: 30 cm1 cm

Millimeter waves: 10 mm1 mm

(centimeter waves)

= 10 mm: f = 3 x 108/ 10 x 10-3 = 30 GHz

= 1 mm: f = 3 x 108/ 1x 10-3 = 300 GHz

m

smHz

/103

wavelength

clightofvelocityffrequency8

Note: 1 Giga = 109


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f =10 kHz, = c/f = 3 x 108/ 10 x 103 = 3000 m

Phase delay = (2 or 360) x Physical length/Wavelength

f =10 GHz, = 3 x 108/ 10 x 109 = 3 cm

Electrical length =1 cm/3000 m = 3.3 x 10-6, Phase delay = 0.0012

RF

Microwave

Electrical length = 0.33 , Phase delay = 118.8 !!!Electrically long - The phase of a voltage or current changes significantly

over the physical extent of the device

Electrical length = Physical length/Wavelength (expressed in )


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US Military Microwave Bands


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US New Military Microwave Bands


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IEEE Microwave Frequency Bands

G id d S i


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Guided Structures at RF Frequencies

Planar Transmission Lines and

Waveguides

Good for Microwave Integrated

Circuit (MIC) ApplicationsGood for Long Distance

Communication

Conventional Transmission Lines

and Waveguides


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How to account for the phase delay?

A

B

A B A B

Low Frequency

Microwave

A B A B

Propagation delaynegligible

Transmission linesection!

l

Printed Circuit Trace

Zo: characteristic impedance

(=+j): Propagation constant

Zo

,

Propagation delay

considered


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Electromagnetic Theory


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Maxwells Equations

Electric and magnetic phenomena at the macroscopic

level are described by Maxwells equations, aspublished by Maxwell in 1873.

This work summarized the state of electromagnetic

science at that time and hypothesized from theoretical

considerations the existence of the electricaldisplacement current, which led to the experimental

discovery by Hertz of electromagnetic wave

propagation.

Maxwells work was based on a large body of empiricaland theoretical knowledge developed by Gauss,

Ampere, Faraday, and others


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Maxwells Equations

With an awareness of the historical perspective, it is

usually advantageous from a pedagogical point of viewto present electromagnetic theory from the inductive,

or axiomatic, approach by beginning with Maxwells

equations.

The general form of time-varying Maxwell equations,then, can be written in point, or differential, form as

0

,

,

,

B

D

Jt

DH

Mt

BE

Eis the electric field, in volts

per meter (V/m)

His the magnetic field, in

amperes per meter (

A/m).

M ll E ti


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Maxwells Equations Equations in point (differential) form of time-varying

0

,

,

,

B

D

Jt

DH

Mt

B

E

EquationContinuity,0

t

J

( 0, 0)E M

Generally, EM fields and sources vary with space (x, y, z) and time (t) coordinates.

Equations in integral form

, Faraday's Law

,Ampere's Law

, Gauss's Law

0, No free magnetic charge

C S

C S

S

S

BE dl ds

t

DH dl ds I

t

Dds Q

Bds

,

Divergence theorem

,

Stokes' theorem

v s

s c

A A ds

A A dl

Time-Harmonic Fields


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Where MKS system of units is used, and

E: electric field intensity, in V/m.

H : magnetic field intensity, in A/m.

D : electric flux density, in Coul/m2.

B : magnetic flux density, in Wb/m2.

M : (fictitious) magnetic current density, in V/m2.

J : electric current density, in A/m2

.: electric charge density, in Coul/m3.

ultimate source of the electromagnetic field.

Q : total charge contained in closed surface S.

I : total electric current flow through surface S.

Time Harmonic Fields

0

,,

,

B

DJDjH

MBjE

When steady-state condition is considered, phasor representations of

Maxwells equations can be written as : (time dependence by multiply e -jt)

2: Displacement current density, in A/m EM wave propagatiomD

In free space In istropic materials


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Constitutive Relations

Question:2(6) equations are not enough to solve 4(12) unknownfield components

In free space

HB

ED

0

0,

where 0 = 8.85410-12 farad/m is the permittivity of free space.0 = 410

-7 Henry/m is the permeability of free space.

In istropic materials

(e.g. Crystal structure and ionized gases)

3 3 3 3,

x x x x

y y y y

z z z z

D E B H

D E B HD E B H

)1(,)(

);1(,

0"'

0

0"'

0

mm

ee

jHPHB

jEPED

wherePe is electric polarization,Pm is magnetic polarization,

e is electric susceptibility, and m is magnetic susceptibility.

Complexand

The negative imaginary part ofand account for loss in medium (heat).


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, Ohm's law from an EM field point of view

=

= ' ( " )

= ( ' " )

"tan , Loss tangent

'

J E

H j D J

j E E

j E E

j j j E

where is conductivity (conductor loss),

is loss due to dielectric damping,(+ ) can be seen as the total effective conductivity,

is loss angle.

In a lossless medium, and are real numbers.Microwave materials are usually characterized by specifying the real

permittivity, =r0,and the loss tangent at a certain frequency.

It is useful to note that, after a problem has been solved assuming a

lossless dielectric, loss can easily be introduced by replaced the real with

a complex .

Example1.1 : In a source-free region, the electric field intensity is given as


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follow. Find the signal frequency?

V/m4 )3( yxjezE Solution :

)3(

0)3(

0

0

412

400

1

yxj

yxj

eyx

e

zyx

zyx

jHHjE

)3(

002

)3(

0

)3(

0

0

0

16

0412

1 yxj

yxjyxj

ez

ee

zyx

zyx

jE

EjH

Boundary Conditions


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Boundary Conditions

2121

2121

,

,,

HnHnEnEn

BnBnDnDn

Fields at a dielectric interface

Fields at the interface with a perfect conductor (Electric Wall)

S

S

JHnEn

BnDn

,0

,0,

Magnetic Wallboundary condition (not really exist)

0

,

,0

,0

Hn

MEn

Bn

Dn

S

tyconductiviAssumed

It is analogous to the relations between voltage and current at the end ofa short-circuited transmission line.

It is analogous to the relations between voltage and current at the end ofa o en-circuited transmission line.

H l h lt (V t ) W E ti


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Helmholtz (Vector) Wave Equation

In a source-free, linear, isotropic, and homogeneous

medium

0

,022

22

HH

EE

is defined the wavenumber, or propagation constant

, of the medium; its unit are 1/m.

Plane wave in a lossless medium

( ) ,

1( ) [ ],

jkz jkzx

jkz jkzy

E z E e E e

H z E e E e

k

Solutions of above wave equations

H

E

k

is wave impedance, intrinsic impedance of medium.

In free space, 0=377.

Transverse Electromagnetic Wave

(TEM)

x yE H z

,

EjH

HjE

is phase velocity defined as a fixed phase point on 1dz


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)tan1()(1'"'

jjjjjjj

is phase velocity, defined as a fixed phase point on

the wave travels.

In free space, vp=c=2.998108 m/s.

kdtvp

f

vv

k

pp

22

is wavelength, defined as the distance between twosuccessive maximum (or minima) on the wave.

Plane wave in a general lossy medium

In wave equations, jk for following conditions.

-1: Complex propagation constant (m )

: Attenuation constant(Np/m;1Np/m=8.69dB/m), : Phase constant(rad/m)

21s

is skin depth or penetration depth, defined as the

amplitude of fields in the conductor decay by an amount

1/e or 36.8%, after traveling a distance of one skin depth.

Good conductor

Condition: (1) >> or (2) >>

Scattering Parameters (S Parameters)


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Scattering Parameters (S-Parameters)

Consider a circuit or device inserted

into a T-Line as shown in the Figure.

We can refer to this circuit or deviceas a two-port network.

The behavior of the network can be

completely characterized by its

scattering parameters (S-parameters),or its scattering matrix, [S].

Scattering matrices are frequently

used to characterize multiport

networks, especially at high

frequencies.

They are used to represent microwave

devices, such as amplifiers and

circulators, and are easily related to

concepts of gain, loss and reflection.

11 12

21 22

S SS

S S

Scattering matrix

Scattering Parameters (S Parameters)


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The scattering parameters represent

ratios of voltage waves entering and

leaving the ports (If the samecharacteristic impedance, Zo, at all ports

in the network are the same).

1 11 1 12 2.V S V S V

2 21 1 22 2

.V S V S V

11 121 1

21 222 2

,S SV V

S SV V

In matrix form this is written

.V S V

2

1

11

1 0V

VS

V

1

1

12

2 0V

VS

V

1

2

22

2 0V

VS

V

2

2

21

1 0V

VS

V

S tt i P t (S P t )


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Properties:

The two-port network is reciprocal

if the transmission characteristics

are the same in both directions

(i.e. S21

= S12

).

It is a property of passive circuits

(circuits with no active devices or

ferrites) that they form reciprocal

networks.

A network is reciprocal if it is equal

to its transpose. Stated

mathematically, for a reciprocal

network

,t

S S

11 12 11 21

21 22 12 22

.

tS S S S

S S S S

12 21S SCondition for Reciprocity:

1) Reciprocity

l


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Microwave Applications

Wireless Applications TV and Radio broadcast

Optical Communications

Radar

Navigation

Remote Sensing

Domestic and Industrial Applications

Medical Applications

Surveillance

Astronomy and Space Exploration


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Radar System Comparison

Radar Characteristic wave mmwave optical

tracking accuracy poor fair good

identification poor fair good

volume search good fair poor

adverse weather perf. good fair poor

perf. in smoke, dust, ... good good fair

i i i i


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Microwave Engr. Distinctions 1 - Circuit Lengths:

Low frequency ac or rf circuits

time delay, t, of a signal through a device

t = L/v T = 1/f where T=period of ac signal

but f =v so 1/f= /v

so L , I.e. size of circuit is generally much

smaller than the wavelength (or propagation

times or phase shift 0) Microwaves: L

propagation times not negligible

Optics: L

Mi Di ti ti


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Microwave Distinctions

2 - Skin Depth:

degree to which electromagnetic field

penetrates a conducting material

microwave currents tend to flow along the

surface of conductors so resistive effect is increased, i.e.

R RDC a / 2 , where

= skin depth = 1/ ( fo

cond

)1/2

where, RDC = 1/ ( a2cond)

a = radius of the wire

R waves in Cu >R low freq. in Cu


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Microwave Engr. Distinctions

3 - Measurement Technique

At low frequencies circuit properties

measured by voltage and current

But at microwaves frequencies, voltages

and currents are not uniquely defined; so

impedance and power are measured rather

than voltage and current

Ci it Li it ti


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Circuit Limitations

Simple circuit: 10V, ac driven, copper wire,

#18 guage, 1 inch long and 1 mm indiameter: dc resistance is 0.4 m,L=0.027H

f = 0; XL = 2 f L 0.18 f10-6 =0

f = 60 Hz; XL 10-5 = 0.01 m f = 6 MHz; XL 1

f = 6 GHz; XL 103 = 1 k

So, wires and printed circuit boards cannot beused to connect microwave devices; we needtransmission lines, waveguides, striplines, andmicrostrip


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High-Frequency Resistors Inductance and resistance of wire resistors

under high-frequency conditions (f 500MHz):

L/RDC a / (2 )

R /RDC a / (2 ) where, RDC = /( a

2cond)

a = radius of the wire

= skin depth = 1/ ( focond)-1/2


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Reference: Ludwig & Bretchko, RF Circuit Design


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High Frequency Capacitor

Equivalent circuit consists of parasitic lead

conductance L, series resistance Rs describing

the losses in the the lead conductors and

dielectric loss resistance Re = 1/Ge (in parallel)with the Capacitor.

Ge = C tan s, where

tan s = (/diel) -1 = loss tangent


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Transit Limitations

Consider an FET

Source to drain spacing roughly 2.5 microns

Apply a 10 GHz signal: T = 1/f = 10-10 = 0.10 nsec

transit time across S to D is roughly 0.025 nsec

or 1/4 of a period so the gate voltage is low

and may not permit the S to D current to flow


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Ref: text by Pozar

Wi l C i ti


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Wireless Communications

Options

Sonic or ultrasonic - low data rates, poor

immunity to interference

Infrared - moderate data rates, but easilyblocked by obstructions (use for TV remotes)

Optical - high data rates, but easily

obstructed, requiring line-of-sight RF or Microwave systems - wide bandwidth,

reasonable propagation


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Cellular Telephone Systems (1)

Division of geographical area into non-overlapping hexagonal cells, where each

has a receiving and transmitting station

Adjacent cells assigned different sets ofchannel frequencies, frequencies can be

reused if at least one cell away

Generally use circuit-switched publictelephone networks to transfer calls

between users


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Cellular Telephone Systems (2)

Initially all used analog FM modulation anddivided their allocated frequency bandsinto several hundred channels, AdvancedMobile Phone Service (AMPS)

both transmit and receive bands have 832, 25kHz wide bands. [824-849 MHz and 869-894MHz] using full duplex (with frequencydivision)

2nd generation uses digital or PersonalCommunication Systems (PCS)

Satellite systems


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Satellite systems

Large number of users over wide areas

Geosynchronous orbit (36,000 km aboveearth)

fixed position relative to the earth

TV and data communications Low-earth orbit (500-2000 km)

reduce time-delay of signals

reduce the need for large signal strength

requires more satellites

Very expensive to maintain & often needsline-of sight

Gl b l P iti i S t llit


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Global Positioning Satellite

System (GPS) 24 satellites in a medium earth orbit (20km)

Operates at two bands, L1 at 1575.42 and L2at 1227.60 MHz , transmitting spread

spectrum signals with binary phase shiftkeying.

Accurate to better that 100 ft and withdifferential GPS (with a correcting known basestation), better than 10 cm.


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Frequency choices

availability of spectrum

noise (increases sharply at freq. below 100

MHz and above 10 GHz)

antenna gain (increases with freq.)

bandwidth (max. data rate so higher freq.

gives smaller fractional bandwidth)

transmitter efficiency (decreases with freq.)

propagation effects (higher freq, line-of sight)


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Propagation

Free space power density decreases by 1/R2

Atmospheric Attenuation

Reflections with multiple propagation pathscause fading that reduces effective range, data

rates and reliability and quality of service

Techniques to reduce the effects of fading areexpensive and complex

Antennas


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Antennas

RF to an electromagnetic wave or the inverse

Radiation pattern - signal strength as a function

of position around the antenna

Directivity - measure of directionality

Relationship between frequency, gain, and size

of antenna, = c/f

size decreases with frequency

gain proportional to its cross-sectional area \ 2

phased (or adaptive) array - change direction of

beam electronically

R iM th


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berikutnyacoordinatesystemsUntuk

zx

anmenghasilkx/partialolehndidefisikaygPerubahan

CsinABA

lainnyar terhadapsatu vectoprojeksi

product,dotatauscalar:cosABA

on vectorsinterseksiBdanAMisalkan

Review

zyy

x

B

B

Math


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sungai)dimengalirygdaun(pusaranrotation

(Russian)ROTor;)()A(

flowoutwardnet:Divergence;A

changeofrate:gradient;u

(Space)ruangdalambervariasi

z)y,u(x,uscalarmemilikifieldsebuahjika

z Curl

y

A

x

A

zA

yA

xA

zz

uy

y

ux

x

u

zxy

zyx


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theorem(batu)Stokes;)(

theoremDivergence;)(

0curlofdivor

0)()(;)()(

0gradientofcurlor0;0

s

vs

dsAdA

dVAdsA

CCCBACBA

uAA


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Maxwells Equations

Gauss

No Magnetic Poles Faradays Laws

Amperes Circuit LawtDJH

tBEB

D

/

/0

Characteristics of Medium


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Characteristics of Medium

Constitutive Relationships

npropagatioofdirectionzconstant,phase

constantonattentuati,jwhere

z)-texp(jtoalproportionHE,

plasmaferrites,exceptscalars,,

surfacesonsonotitself,mediumin the0,J

sAssumptionCurrentConvectiveJJJJE,J

tyPermeabiliMagnetic,H,B

yPermitivitDielectric,ED

vv,cc

ro

,or


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Fields in a Dielectric Materials

0onconservatientergytoduenegative(heat)mediumin thelossforaccounts

magnitude)oforders4or(3dielectricgoodfor,

j)1(

EE)1(D

itysuceptibildielectric,EdensitymomentdipoleP

density)ntdisplacemeorfluxelectric(D0Jand

somagnetic,nonand,PEDAssume

eo

eo

eoe

oo


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Fields in a Conductive Materials

tantangentlosseffective

tyconductivieffectivetheiswhere

E)](j[E)jj(j

E))j(jj(E)j(j

EjEt

EE

t

DJH

easvaryfieldsEwhere,EJJ tjc


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Wave Equation

andbydescribedmediumin

wavesofconstantnpropagatio:

;H-H

;E-E

E))((

)H(E-E)(E)(

EjHH,-jE

jt/Consider

2

22

22

2

kdefine

similarly

jj

j

General Procedure to Find Fields in a


81/89


Guided Structure

1- Use wave equations to find the z

component of Ez and/or Hz note classifications

TEM: Ez =Hz= 0

TE: Ez =0, Hz 0

TM: Hz =0, Ez 0 HE or Hybrid: Ez0, Hz 0



82/89


Guided Structure

2- Use boundary conditions to solve for any

constraints in our general solution for Ez

and/or Hz

conductorofsurfacethetonormalnwhere

conductorperfec tofsurfaceon0Hor,0Hn

JHn

/En

conductorperfectofsurfaceon0Eor0,En

n

s

t

s

Pl W i L l M di


83/89

Plane Waves in Lossless Medium

directionzin themovingconstantkzt

))kzt(cos(E))kzt(cos(E)t,z(E

:domaintimein theor

eEeE)z(E0Ekz

E

0y/x/andEE

mediumlosslessain

realareandsincerealiskwhere0,EkE

x

jkzjkzxx

2

2

x2

x

22

Ph V l i


84/89

Phase Velocity

cfv

fvf

vv

c

kdt

d

dt

dz

p

p

pp

oo

:spacefreein

or2

k

2

k2))k(z-t(-kz)-t(

maximasuccessive2betweendistance:Wavelength

m/sec1031

vspacefreein

1)

k

constant-t(v

a velocityatelspoint travphaseFixed

8

p

p

W I d


85/89

Wave Impedance

E/Hork

where

)eEeE(

k

H

HjejkEejkE

yz

ExEz

zso;0

yx

Hjt

H-E:eqnsMaxwell'By

jkzjkz

y

y

jkzjkz

x

x

Plane Waves in a Lossy Medium


86/89

Plane Waves in a Lossy Medium

kandjand

0,0note)j1(jj

complexnow,numberewav)j1(

0E)j1(E

E)E(E

)EEj(j)H(jEEEjHandHjE

22

22

2

W I d i L M di


87/89

Wave Impedance in Lossy Medium

losseswithimpedancewavej

where

)eEeE(

j

H

)ztcos(edomaintimeeee

eEeE)z(E0Ez

E

0y/x/andxEEbeforeas

zz

y

zzjzz

zz

xx

2

2

x

2

x

Pl W i d C d t


88/89

Plane Waves in a good Conductor

surfaceon theflowcurrentss,frequenciemicrowaveat

Au)Ag,Cu,(Al,metalsmostform1GHz,10at

depthskin/2/1

2/2/)j1(

/jj/jj

casepractical

s

s

2

Energy and Power


89/89

Energy and Power

)WW(j2PP

sourcesbygeneratedpowerP

dvHH4/dvBHRe4/1W

dvEE4/dvDERe4/1W

lossasdissipatedoredtransmittbemaythat

powercarryandenergymagneticandelectricstore

thatfieldsupsetsenergyneticelectromagofsourceA

*

emo

s

v

*

v

*

m

v

*

v

*

e

Documents

Msc. Lecture 1_rf&Me