ANTENNAS and MICROWAVES ENGINEERING (650427) · ANTENNAS and MICROWAVES ENGINEERING (650427) 2/26/2018 Dr. Omar R Daoud 2 Introduction ... I UZ I U I a a L u dt d dt d moving loop

Philadelphia University

Faculty of Engineering Communication and Electronics Engineering

Part 1 Dr. Omar R Daoud 1

ANTENNAS and MICROWAVES

ENGINEERING

(650427)

2/26/2018 Dr. Omar R Daoud 2

Introduction

Electromagnetic Waves (EM)

Static EM (Electrostatic/ Magnetostatic) Fields Electric (stationary charges) and magnetic (steady current)

fields are independent each other

Dynamic/Time varying EM Fields (Waves) Electric and magnetic fields are interdependent

The current is time varying (moving/accelerated charges)

They can be represented as

E(x,y,z,t)

H(x,y,z,t)

Introduction

Faraday’s Law

A static magnetic field produces no

current flow,

In a closed loop, a time varying field

will produce an electromotive force

(emf) which leads to a flow current.

An increasing magnetic field out of the

page induces the current or an emf.

The continuous-conductive-loop

distributed resistance is modeled as a

series resistor Rdist


Introduction

Transformer and motional emf

Stationary Loop in Time Varying B

Field

A stationary conducting loop is in a

time varying magnetic B field.

Applying Stokes theorem

Thus,


S

BSE d

tdVemf

t

BE

Introduction


Stationary Loop in Time Varying B

Field

Thus,

The time varying electric field is not

conservative, or not equal to zero.

The work done in taking a charge about

a closed path in a time varying electric

field, for example, is due to the energy

from the time varying magnetic field.


Introduction


Moving Loop in static B Field

Due to the conducting loop movement

with u velocity, an emf is induced (the

force on a charge moving with uniform

velocity in magnetic field)


Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth

Copyright © 2005 by John Wiley & Sons. All rights reserved.

Figure 4-12 (p. 185)Conductive bar moving along a pair of parallel conductive rails.

L

memf ddV LBuLE

Introduction


Moving Loop in Time Varying Field


LS

memf ddt

dV LBuSB

LE

Introduction


Example

The loop shown is inside a uniform

magnetic field B = 50 ax mWb/m2 . If

side DC of the loop cuts the flux lines

at the frequency of 50Hz and the loop

lies in the yz plane at time t = 0, find

the induced emf at t = 1 ms.


Introduction


Example

Since the B field is time invariant, the

induced emf is motional, that is:


L

memf ddV LBuLE

zDC dzdd aLL

aaL

u

dt

d

dt

d loopmoving

1002,4 fcm

Introduction


Example

Transforming the B field into

cylindrical coordinate, since u and dL

is in cylindrical coordinates:

B0 = 0.05


a-aaB sincos00 BB x

z

z

B

BB

a

aaa

Bu

cos

0sincos

00 0

00

dz

dzdzBd

cos2.0

cos05.010004.0cos0

LBu

Introduction


Example

To determine recall that,

To calculate C, since the loop is in

the yz plane, then at


mVdzV

z

emf cos6cos2.0

03.0

0

Ctdt

d

2,0 t

Introduction


Example

Therefore,

At t = 1 ms,


mVt

tVemf

100sin6

2cos6cos6

mV.Vemf 8255)001.0(100sin6

Introduction

Displacement Current

At Static field

A conduction current density (related

to electric field Ohm’s Law) could be

defined

The divergence of curl of a vector is

identically zero, thus it is clearly

invalid for time varying fields since it

violates the law of current continuity,

Maxwell resolved this issue by

introducing the displacement current density.


dc JJH

Introduction


At low frequencies, Jd (rate of change of the electric flux density)

is usually neglected compared with

Jc. But at radio frequencies, the two

terms are comparable.


tc

DJH

dcc iidt

dd

SDSJLH

Introduction


The generated i(t) according to

apply the sinusoidal voltage source

v(t) in the circuit is the conduction

current.

Consider the loop surrounding the

plane surface S1.

By static form: the circulation of H

must be equal to the current that cuts

through the surface. But, the same

current must pass through S2 that

passes between the plates of

capacitor.


Introduction





current.


plane surface S1.

But, there is no conduction current

passes through an ideal capacitor,

(where J=0, due to σ=0 for an ideal

dielectric ) flows through S2. This is

contradictory in view of the fact that

the same closed path as S1 is used.


Introduction





current.


plane surface S1.

But to resolve this conflict, the

current passing through S2 must be

entirely a displacement current,

where it needs to be included in

Ampere’s Circuital Law.


Introduction





current.


plane surface S1.

So we obtain the same current for

either surface though it is conduction

current in S1 and displacement

current in S2.


122SSS

d dIt

Qd

tdd SJSDSJLH

Introduction

Maxwell Equations

Gauss’s Law

Gauss’s Law for Magnetic Field

Faraday’s Law

Ampere’s Circuital Law


v D encQd SD

0 B 0 SB d

t

BE

tc

DJH

SDSJLH d

tdd c

SBLE d

td

Introduction

Lossless TEM waves

A Transverse Electromagnetic wave

mode (TEM) means:

Both fields magnetic and electric are

always normal or perpendicular to each

other.

TEM Waves has no E field or H field

components along the direction of

propagation.

Consider an x-polarized wave

propagating in the +z direction in some

ideal medium characterized by µ and ε, with σ = 0 (medium lossless).




A plot of the equation E(z,0) = E0cos(z)ax at 10

MHz in free space with E0 = 1 V/m.

xztEtz aE cos, 0

1pu

pu

Introduction

Lossless TEM waves

By applying Faraday’s Law




A plot of the equation E(z,0) = E0cos(z)ax at 10

MHz in free space with E0 = 1 V/m.

tt

HBE

yy

zyx

ztEztEz

ztE

zyx

aa

aaa

E

sincos

00cos

00

0

dtztE

d

ztEt

y

y

aH

aH

sin

sin

0

0

CztE

y aH

cos0



If no conduction current, C must be zero.

Introduction

Lossless TEM waves

Example

Suppose in free space that:

E(z,t) = 5.0 e-2zt ax V/m.

Is the wave lossless?

Find H(z,t).


Introduction

Lossless TEM waves

Example

Since the wave has an attenuation term (e-2zt) it

is clearly not lossless.

To find H


2 2

2

5 10

5 0 0

x y z

zt zt

o y y

zt

e tex y z zt

e

a a a

HE a a

2 210 10, =zt zt

y y

o o

td e dt te dt

H a H a

2 2

2

10 10

2 4

zt zt

y

o o

t Ae e

z z m

H a

udv uv vdu 2 and .ztu t dv e dt

Introduction

EM waves: Fundamental and Equations

For the source point in a space of time

varying E field, a H field is induced in the

surrounding region.

For a changing H field with time, an induced

E field will be found.

Energy is pass back and forth between E and

H fields as they radiate away from the source

at the speed of light.

In a free space, the constitutive parameters

are σ = 0, µr = 1, εr = 1, so the Ampere’s Law

and Faraday’s Law equations become :


ttc

EH

DJH 0

tt

HE

BE 0

Introduction


The EM waves radiates spherically, but at a

remote distance away from the source they

resemble uniform plane wave.

In a uniform plane wave, the E and H fields

are orthogonal, or transverse to the direction

of propagation ( to propagate in TEM mode ).

Consider


xz zteEtz aE cos, 0

zeE

E

0

0Initial amplitude at z = 0

exponential terms attenuation

Angular frequency

Phase constant

Phase shift

f 2f

T12

2 f

dt

dzu p

Introduction


Using Maxwell’s equation, the Helmholtz

wave equation can be derived as

where is the propagation constant (consists of

attenuation and phase constants) and defined as


2

22

tt

EEE

ss jj EE 2

022 ss EE

jjj )(

112

112

2

2

Introduction


The general solution for the Helmholtz wave

equation can be expressed as

The magnetic field can be found by applying

Faraday’s Law :

The intrinsic impedance can be defined as


zzxs eEeEzE 00)(

xz

xz zteEzteEtz aaE coscos, 00

yzz

s ej

Ee

j

EaH

00

j

H

E

0

0

nj

n ej

j

0

0

H

E

2tan

Introduction


The loss tangent is the ratio of magnitude of

conduction current density to displacement

current density in a lossy medium and can be

expressed as:

tan δ is used to determine how lossy a

medium is

Good (lossless or perfect) dielectric if

Good conductor if


tan

jj s

s

d

c

E

E

J

J

,1tan

, 1tan

Introduction


To determine the E, H and propagation

direction, the Fleming’s Left Hand Rule is

used.

By knowing the EM wave’s direction of

propagation, given as unit vector ap, is the

same as the cross product of Es with unit

vector, aE and Hs with unit vector aH :


SS

SSP

HE

HEa

SPS

SPS

HaE

EaH

1

HE

EH

HE

aaa

aaa

aaa

P

P

P

Introduction


Example


H(x,t) = 100 cos(2π x 107t – βx + π/4) az mA/m.

Find E(x,t).


Introduction


Example

Since

H(x,t) = 100 cos(2π x 107t – βx + π/4) az mA/m.

So then,

Since free space is stated,


0.100 , , 4

120 0.100 12

j x j

s z P x

j x j j x j

s P s x z y

e e

e e e e

H a a a

E a H a a a

12 cos yt x E a2 2

2 30 rad mc f

7 212 cos 2 10

30 4y

Vx t x

m

E a

Introduction


Example


E (x,y,t) = 5 cos(π x 106t – 3.0x + 2.0y) az V/m.

Find

H(x,y,t)

The direction of propagation, ap


Introduction


Example

Since

E (x,y,t) = 5 cos(π x 106t – 3.0x + 2.0y) az V/m.


3 25 j x j y

s ze eE a3 2 3 210 15j x j y j x j y

s s x yj j e e j e e E H a a

3 2 3 2 3 2 3 210 152.53 3.8j x j y j x j y j x j y j x j y

s x y x y

o

j je e e e e e e e

j j

H a a a a

6 6 A( , , ) 2.53cos 10 3 2 3.80cos 10 3 2

mx yx y t x t x y x t x y H a a

So that,

Introduction


Example

Since

where

and then,


s sP

s s

E Ha

E H

6 4 6 419 12.65j x j y j x j y

s s x ye e e e E H a a

y

yjxj

x

yjxj

p aeeaeea 4646 55.083.0

Introduction

EM waves: Propagations in different media

Lossless, Charge – Free

Charge free, ρv=0, medium has zero conductivity,

σ=0.

This is the case where waves traveling in vacuum

or free space (free of any charges).

Perfect dielectric is also considered as lossless

media.


, 0

1pu

jjj )(

jjjjj 22)0(

j

j

0 1200

Introduction


Example (Lossless, Charge – Free) In a lossless, nonmagnetic material with :

εr = 16, and H = 100 cos(ωt – 10y) az mA/m.

Determine :

The propagation velocity

The angular frequency

The instantaneous expression for the electric field intensity.


Introduction EM waves: Propagations in different media

Example (Lossless, Charge – Free)


883 10

0.75 1016

p

r

c x mu x

s

The propagation velocity:

The angular frequency:

8 80.75 10 10 7.5 10p

radu x x

s

From given H field :

8( , ) 100cos 7.5 10 10 z

mAy t x t y

m H a

So, the time harmonic H field is:

0.100 ,

1200.100 3

j y

s z

j y j y

s P s y z x

r

e

e e

H a

E a H a a a

8( , ) 9.4cos 7.5 10 10 x

Vy t x t y

m E a

Finally, the instantaneous expression for E field is:

Introduction


Dielectric

It is treated as a lossless approximation,

It has a complex permittivity, complex

propagation constant with attenuation constant

greater than zero.

The intrinsic impedance is also complex,

resulting a phase difference between E and H

fields.


Introduction


Conductor

In any decent conductor, the loss tangent,

σ/ωε>>1 or σ>>ωε so that σ ≈ ∞, so that:


j

j

j

045)1(2

jej

2pu

f2

Introduction

EM waves: Normal Incidence

Consider a plane wave that are normally

incident which means the planar boundary

separating the two media is perpendicular to

the wave’s propagation direction.

Generally, consider a time harmonic x-

polarized electric field incident from medium 1

(µr1, εr1, σr1) to medium 2 (µr2, εr2, σr2)


xzii zteEtz aE 10 cos),( 1

y

zjzt

t

s

x

zjztt

s

y

zjzr

r

s

x

zjzrr

s

y

zjzi

i

s

x

zjzii

s

eeE

eeE

eeE

eeE

eeE

eeE

aH

aE

aH

aE

aH

aE

22

22

11

11

11

11

2

0

0

1

0

0

1

0

0

tri EEE 000 ,,

The E field intensities

at z=0

i

riir

E

EEEE

0

0

12

1200

12

120 ,

i

tiit

E

EEEE

0

0

12

200

12

20

2,

2

1

Introduction


Consider a plane wave that are normally

incident which means the planar boundary

separating the two media is perpendicular to

the wave’s propagation direction.

Generally, consider a time harmonic x-

polarized electric field incident from medium 1

(µr1, εr1, σr1) to medium 2 (µr2, εr2, σr2)


xzii zteEtz aE 10 cos),( 1

y

zjzt

t

s

x

zjztt

s

y

zjzr

r

s

x

zjzrr

s

y

zjzi

i

s

x

zjzii

s

eeE

eeE

eeE

eeE

eeE

eeE

aH

aE

aH

aE

aH

aE

22

22

11

11

11

11

2

0

0

1

0

0

1

0

0

tri EEE 000 ,,

The E field intensities

at z=0

i

riir

E

EEEE

0

0

12

1200

12

120 ,

i

tiit

E

EEEE

0

0

12

200

12

20

2,

2

1

Introduction


Standing wave pattern for an incident wave in

a lossless medium reflecting off a second

medium at z=0 where = 0.5.

SWR is a measure of mismatch of the load to

the line.

SWR=1 (matched)

SWR →∞ (total mismatch)


1

1

min

max

E

ESWR

Introduction


Example

A uniform planar waves is normally incident from media

1 (z < 0, σ = 0, µr = 1.0, εr = 4.0) to media 2 (z > 0, σ =

0, µr = 8.0, εr = 2.0). Calculate the reflection and

transmission coefficients seen by this wave.


2 11 2

2 1

120 8; 60 , 120 240

24

240 60 30.60

240 60 5

1 1.60

Introduction


Example

Suppose media 1 (z < 0) is air and media 2 (z > 0) has

εr = 16. The transmitted magnetic field intensity is

known to be:

Ht = 12 cos (ωt - β2z) ay mA/m.

Determine the instantaneous value of the incident

electric field.


2 2

2

12t

j z j zt os y y

EmA mAe e

m m

H a a

2t t

2 o s

2

30 , so 12 , E 0.36 , and 1.13t

j zox

E mA V Ve

m m m

E a

Introduction


Example

Since we know the relation between transmitted E field

and incident E field,


2 1

2 1

3 21 ; , 1

5 5

t i i

o o oE E E

12.83, so 2.83t

j zi ioo s x

EE e

E a

1( , ) 2.83cos .x

Vz t t z

m E a

Introduction

EM waves: Oblique Incidence

Plane of incidence plane containing both a normal to the boundary and the incident’s wave propagation.

The propagation direction is ai and the normal is az, so the plane incidence is the x z plane. The angle of incidence, reflection and transmission is the angle that makes the field a normal to the boundary.

When EM Wave in plane wave form obliquely incident on the boundary, it can be decomposed into:

Perpendicular Polarization, or transverse electric (TE) polarization The E Field is perpendicular or transverse to the plane of incidence.

Parallel Polarization, or transverse magnetic (TM) polarization The E Field is parallel to the plane of incidence, but the H Field is transverse.


We need to decompose into its

TE and TM components

separately, and once the reflected

an the transmitted fields for each

polarization determined, it can be

recombined for final answer.

Introduction

EM waves: Oblique Incidence (TE polarization)


ztxtzxj

tts

yzxjtt

s

zrxrzxj

rrs

yzxjrr

s

zixizxj

iis

yzxjii

s

tt

tt

rr

rr

ii

ii

eE

eE

eE

eE

eE

eE

aaH

aE

aaH

aE

aaH

aE

sincos

sincos

sincos

cossin

2

0

cossin0

cossin

1

0

cossin0

cossin

1

0

cossin0

2

2

1

1

1

1

ri

i

t

sin

sin

2

1

iTE

i

ti

tir EEE 0012

120

coscos

coscos

iTE

i

it

it EEE 0021

20

coscos

cos2

TETE 1

By applying Snell’s Law,

Introduction

EM waves: Oblique Incidence (TM polarization)


y

zxjt

ts

ztxtzxjtt

s

yzxj

rrs

zrxrzxjrr

s

yzxj

iis

zixizxjii

s

tt

tt

rr

rr

ii

ii

eE

eE

eE

eE

eE

eE

aH

aaE

aH

aaE

aH

aaE

cossin

2

0

cossin0

cossin

1

0

cossin0

cossin

1

0

cossin0

2

2

1

1

1

1

sincos

sincos

sincos

iTM

i

it

itr EEE 0012

120

coscos

coscos

iTM

i

ti

it EEE 0021

20

coscos

cos2

t

iTMTM

cos

cos1

For TM polarizations, there exists an incidence angle at

which all of the wave is transmitted into the second

medium Brewster Angle, θi = θBA , where:

22

21

21

22

21

22

22 )(

sin

BA

2

11

1sin

r

rBA

When a randomly polarized wave such as light is

incident on a material at the Brewster angle, the TM

polarized portion is totally transmitted but a TE

component is partially reflected.

Introduction


Example A 100 MHz TE polarized wave with amplitude 1.0 V/m

is obliquely incident from air (z < 0) onto a slab of

lossless, nonmagnetic material with εr = 25 (z > 0). The

angle of incidence is 40. Calculate:

the angle of transmission,

the reflection and transmission coefficients,

the incident, reflected and transmitted for E fields.


Introduction


Example the angle of transmission,

the reflection and transmission coefficients


1

2 2

1 1 1; sin sin 40 ; 7.4

5 5t t

r

o o

6

1 28

2 100 102.09 , 10.45 .

3 10

rx rad rad

c x m c m

1 2

120120 ; 24

25

2 1

2 1

cos cos0.732; 1 0.268

cos cos

i tTE TE TE

i t

Introduction


Example the incident, reflected and transmitted for E fields.


2.09 sin 40 cos40 1.34 1.601 1j x zi j x j z

s y y

Ve e e

m

E a ao o

( , ) 1cos 1.34 1.60i

y

Vz t t x z

m E a

0.732r i

o TE oE E

1.34 1.600.732r j x j z

s y

Ve e

m

E a ( , ) 0.732cos 1.34 1.60r

y

Vz t t x z

m E a

0.268t i

o TE oE E

2 sin cos 1.35 10.40.268 0.268t tj x zt j x j z

s y y

Ve e e

m

E a a

m

Vzxttz y

raE 4.1035.1cos268.0),(

Introduction

Microwaves: General Description

Related History 19th century

1846 - earliest talk on EM wave, “Thoughts on ray vibrations,” Michael Faraday (1791-1867)

1864 - “Maxwell’s equations,” James Clark Maxwell (1831-1879)

1887 - first microwave-like experiment, “electric spark at λ~10cminduces at a distant wire loop,” Heinrich Rudolf Hertz (1857-1894)

1895 - wireless telegraphic communication and 1900 trans-Atlantic Ocean telegraph, Guglielmo Marconi (1874-1937)

20th century 1921 - magnetron, A. W. Hull

1930 - wave propagation in waveguide, George C. Southworth

1937 - klystron, Russell Varian, Sigurd Varian and William Hansen World War II – radar, MIT Radiation Laboratory

~1950 - coaxial cables for radio communication

~1960 - satellite communication

~1980 - remote sensing satellite, DBS (direct broadcast satellite)

~1990 - PCN/PCS (personal communications network/personal communication services), GPS (global positioning system), VSAT (very small aperture terminals)

~2000 - Digital DBS, WLL (wireless local loop), GII (global information initiative) using mobile satellite network, fibers, cables and wireless


Introduction


Frequency Band

Commercial Broadcasting


Introduction


Frequency Band

RF Bands


Introduction


Frequency Band

Microwave Bands


Introduction


Important Factors

Antenna Size

as antenna size ~ λ, it radiates efficiently

f, λ , size , radiation efficiency

Channel Bandwidth

as f available spectrum bandwidth

f for wider information bandwidth transmission, especially digital

video transmission e.g.,

1% BW of AM radio @1MHz gives 1channel of 10kHz audio

bandwidth

0.1% BW of C-band satellite communication @6GHz gives 1

channel of 6MHz video bandwidth


mailto:@1MHz

mailto:@1MHz

mailto:@6GHz

mailto:@6GHz

mailto:@6GHz

mailto:@6GHz

Introduction


Important Factors Propagation through Atmosphere

ground wave (LF band, 30-300KHz) travels over and near the earth surface

ground absorption loss, especially for h-polarization

AM radio uses vertical polarization,

sky wave (HF band, 3-30MHz) performs refraction (signal bending) in ionosphere, plasma frequency ~ 9MHz

short-wave radio

space wave (VHF, UHF and microwave, 30M-300GHz) direct wave (line-of sight, LOS) and reflected wave

interference or multi-path phenomenon

low atmospheric attenuation and unaffected by rain and cloud

wireless, mobile, terrestrial and satellite communication


Introduction


Devices In general, input/output matching is inherently required for microwave

components over the operating band.

passive devices (without DC bias): diplexer, filter, coupler, power

divider/combiner, isolator, circulator, attenuator, adapter, terminator, cable,

transmission line, waveguide, resonator, detector, mixer, phase shifter, lumped

R, L, C, antenna,…

active devices (with DC bias): amplifier, oscillator, switch, mixer, frequency

multiplier, active antenna, ….

vacuum tube devices


Introduction


Devices Solid state devices


HBT: heterojuction bipolar transistor

MESFET: metal-semiconductor field-effect transistor

HEMT: high electron mobility transistor

MOSFET: metal-oxide-semiconductor field-effect transistor CMOS:

complementary metal-oxide-semiconductor transistor IMPATT diode:

impact ionization avalanche transit-time diode

TRAPATT diode: trapped plasma avalanche triggered transit-time diode

BARITT diode: barrier injected transit-time diode

maser: microwave amplification by stimulated emission of radiation

LSA diode: limited space-charge accumulation mode of the Gunn diode

Introduction


Devices

Vacuum tube technology finds its applications in

high power (W-MW) and high frequency

(200MHz-200GHz)

e.g., magnetron: kW CW source in microwave oven,

MW pulsed source in radar, traveling wave tube

amplifier: >10 W power amplifier in satellite, klystron:

local oscillator in receiver.

Microwave solid-state devices are :

low cost, low power supply, low noise, small, light

weight, easy cooling, reliable and long life time

compared with microwave tubes.


Introduction


Applications Growth and expansion of microwave technology move

from military and satellite applications into information

and entertainment applications.


Introduction


Transmission Lines


Introduction

Concept of Radiation

Radiation Mechanism

Vibration of EM waves from radiation source.

Vibration produced from electric time varying

current source, which is in form of scattering

electrical charges.

Mismatch between the characteristic impedance

of transmission line and open circuit at the other

end produces or generates reflected waves (as

static wave)


Introduction


Radiation Source- Single Wire

The current density, Jz over the cross section of

the wire:

If the wire is ideal conductor, the current density

Js resides on the surface as:

Where qs is the surface charge density. If the

wire is very thin (ideally zero radius), the current

in the wire:

Where ql is the charge per unit length.


zvz vqJ

zsS vqJ

zlz vqI

Introduction



The basic relation between current and charge, and

it also serves as the fundamental relation of EM

radiation.

It states that to create radiation, there must be a

time varying current or an acceleration or

deceleration of charge.

To create charge acceleration or deceleration, the

wire must be curved, bent, discontinuous or

terminated.

To create periodic charge acceleration or

deceleration or time varying current, charge must be

oscillating in a time harmonic motion as for a λ/2

dipole.


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dIl

Introduction



Important Notes:


Introduction



Configurations:


Introduction



Important Notes:

Consider a pulse source attached to an open

ended conducting wire, connected to ground

through a discrete load at its open end:

When the wire energized, free

electron/charges are in motion due to

electrical lines of force created by the source.

The charges accelerate in the source end of

the wire, and decelerated during reflection

from its end

It is suggested that radiated fields are

produced at each end and along the

remaining part of the wire.


Introduction



Important Notes:

Stronger radiation with a more broad frequency

spectrum occurs if the pulses are of shorter or

more compact duration.

Continuous time-harmonic oscillating charge

produces, ideally, radiation of single frequency

determined by f oscillation.

Pulses radiates a broad bandwidth of radiation.

The shorter the pulse width, the broader the

spectrum.

A sinusoidal waveform of current or charge leads

to a narrow spectrum of radiation; ideally zero

bandwidth at the frequency of the sinusoid if it

continues indefinitely.


Introduction


Radiation Source- Two Wires

Consider a voltage source connected to a two

conductor transmission line which connected to an

antenna.

It creates an E field between the conductors.

The E field has associated with it electric lines of force

that tangent to the E field at each point and its strength

is due to its intensity.

Have tendency to act on free electrons (easily

detachable from atoms) and force them to be

displaced.

The movement creates currents and in turn creates H

field intensity.


Introduction


Radiation Source- Two Wires The creation of time varying electric and magnetic fields

between the conductors forms EM waves which travel

along the transmission line.

The EM waves enter the antenna and associated with them

electric charges and corresponding currents. If remove part

of the antenna, free space waves can be formed by

connecting the open ends of the E lines.

The free space waves are also periodic but a constant

phase point P0 moves outwardly with the speed of light and

travels a distance of λ/2 (to P1) in the time of one half of

period.

Close to the antenna the constant phase point P0 moves

faster than the speed of light but approaches the speed of

light at points far away from the antenna.


Introduction



The water waves created by the dropping of pebble in a

calm body of water, where once the disturbance initiated,

water waves are created which begin to travel outwardly.

When the EM waves are within the transmission line and

antenna, their existence is associated with the presence of

the charges inside the conductors.

When the waves are radiated, they form closed loops and

there are no charges to sustain their existence.

This leads us to conclude that electric charges are required

to excite the fields but are not needed to sustain them and

may exist in their absence. This is direct analogy with water

waves.


Introduction




Introduction


Current Distribution- a Thin Wire

For a lossless two wire TLs, movement of charges creates a

traveling wave current, I0/2 along each wires.

At the end, it undergoes a complete reflection (equal

magnitude and 1800 phase reversal).

When it combines with incident traveling wave, forms a pure

standing wave pattern.

Radiation for each wire occurs time varying nature of

current and the termination of the wire.

For two-wire balanced (symmetrical) TL, the current in a half

cycle of one wire is the same magnitude but 1800 out of

phase for corresponding half cycle other wire.

If the spacing between two wires is very small (s<<λ) , the

fields radiated by the current of each wire are cancelled each

other. The net result is an almost ideal non-radiating

transmission line.


Introduction



As the section begins to flare, it can be assumed

that the current distribution is essentially unaltered

in form in each of the wires. But due to the two

wires of the flared section are not close to each

other, the fields radiated by one do not cancel

those of the other. Ideally, there is a net radiation

by the TL system.


Introduction



This is the geometry of widely used

dipole antenna.

If l<λ, the phase of current standing wave

pattern in each arm is the same

throughput its length.

Spatially it is oriented in the same

direction as that of the other arm.

The field radiated by the two arms of the

dipole (vertical parts of a flared TL).


Introduction



The fields radiated will primarily reinforce each

other toward most directions of observation

If the diameter of each wire is very small (d<<λ)

, the ideal standing wave pattern along the

arms of dipole is sinusoidal with a null at the

end. For center-fed dipoles, the current patterns

are:


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ANTENNAS and MICROWAVES ENGINEERING (650427) · ANTENNAS and MICROWAVES ENGINEERING (650427) 2/26/2018 Dr. Omar R Daoud 2 Introduction ... I UZ I U I a a L u dt d dt d moving loop