chapter 1 antenna principle & basic antenna …

CHAPTER 1

ANTENNA PRINCIPLE &

BASIC ANTENNA

PARAMETERS

2

ANTENNA PRINCIPLE

3

INTRODUCTION

An antenna is defined by Webster’s Dictionary as “ a usually metallic device (as a rod or wire) for radiating or receiving radio waves.”

The IEEE Standard Definitions of Terms for Antennas (IEEE Std 145-1983) defines the antenna or aerial as “a means for the radiating or receiving radio waves.”

The antenna is the transitional structure between free-space and a guiding device.

4

INTRODUCTION

The antenna (aerial, EM radiator) is a device, which radiates or receives electromagnetic waves.

The antenna is the transition between a guiding device (transmission line, waveguide) and free space (or another usually unbounded medium).

Its main purpose is to convert the energy of a guided wave into the energy of a free space wave (or vice versa) as efficiently as possible, while in the same time the radiated power has a certain desired pattern of distribution in space.

5

INTRODUCTION transmission-line Thevenin equivalent circuit of a radiating

(transmitting) system

Vg - voltage-source generator (transmitter);

Zg - impedance of the generator (transmitter);

Rrad - radiation resistance (related to the radiated power as Prad =I2A ⋅Rrad ) RL - loss resistance (related to conduction and dielectric losses);

jXA - antenna reactance.

Antenna impedance: ZA=(Rrad+RL)+jXA

6

INTRODUCTION

transmission-line Thevenin equivalent of transmitting antenna

7

INTRODUCTION

transmission-line Thevenin equivalent of receiving antenna

8

INTRODUCTION

9

INTRODUCTION

10

BRIEF HISTORICAL NOTES

James C. Maxwell develops mathematical model of electromagnetism, “A Treatise on Electricity and Magnetism”, 1873.

Heinrich R. Hertz demonstrates in 1886 the first wireless EM wave system.

Alexander Popov sends a message from a Russian Navy ship 30 miles out in sea, all the way to his lab in St. Petersburg, 1875.

Guglielmo Marconi performs the first transatlantic transmission from Poldhu in Cornwall, England, to Newfoundland, Canada.

11

BRIEF HISTORICAL NOTES

The beginning of 20th century (until WW2):

boom in wire antenna technology and in wireless

communications (up to UHF, over thousands of

kilometers), DeForest triode

WW2 marks a new era in wireless

communications and antenna technology: new

microwave generators (magnetron and klystron).

New antenna types: waveguide apertures,

horns, reflectors, etc.

12

REVIEW OF ANTENNA TYPES

Single elements Wire antenna

13


Single elements aperture antennas — mostly microwave (1 to 20 GHz), high

power

14


Single elements

Single patches

15


Single elements

Printed patches

double-layer printed Yagi antenna with electromagnetically

coupled feed

16


Single elements Printed patch shapes

17


Single elements

printed slot antennas — typical range above 10 GHz

18

REVIEW OF ANTENNA TYPES Single elements

reflector antennas — high directivity, electrically large

19


reflector antennas — radio-astronomy

20


lens antennas — infrared and optical

21


array

•electronic scanning (phased arrays)

•beam shaping (nulls, maxima, beamwidth)

22

RADIATION MECHANISM

Radiation is produced by accelerated or

decelerated charge (time-varying current

element)

Definition: A current element (IΔl), A×m, is a

filament of length Δl and current I.

23

RADIATION MECHANISM

Assume the existence of a piece of a very thin wire where electric currents can be excited.

The current i flowing through the wire cross-section ΔS is defined as the amount of charge passing through ΔS in 1 second:

vSlSi 1

ρ (C/m3) is the electric charge volume density,

v (m/s) is the velocity of the charges normal to the cross-section,

Δl1 (m/s) is the distance traveled by a charge in 1 second.

[1.1] A

24

Where J is the electric current density.

The product ρ1=ρ.ΔS is the charge per unit length

(charge line density) along the wire.

RADIATION MECHANISM

zvJ

lvi

Equation [1.1] can be also written as:

[1.2]

[1.3]

adt

dv

dt

dill [1.4]

So that

A/m2

A

A/s

25

RADIATION MECHANISM

where a (m/s2) is the acceleration of the charge.

The time-derivative of a current source would

then be proportional to the amount of charge q enclosed in the volume of the current element

and to its acceleration:

aqaldt

dil l [1.5] A x m/s

26

RADIATION MECHANISM

To accelerate/decelerate charges, one needs sources of electromotive force and/or discontinuities of the medium in which the charges move.

Such discontinuities can be bends or open ends of wires, change in the electrical properties of the region, etc.

In summary:

If charge is not moving, current is zero → no radiation.

If charge is moving with a uniform velocity → no radiation.

If charge is accelerated due to electromotive force or due to discontinuities, such as termination, bend, curvature → radiation occurs.

27

RADIATION MECHANISM

28

RADIATION MECHANISM

29

FUTURES CHALLENGES

Integration problem Monolithic MIC technology

Meta-materials, etc.

Innovative antenna designs Smart antenna

Reconfigurable antenna, etc.

New applications WLAN, UWB, GPS, etc.

Complicated design Higher frequencies

Low profile

Higher gain, etc.

30

BASIC ANTENNA

PARAMETERS

31

INTRODUCTION

To describe the performance of an

antenna, definitions of various parameters

are necessary.

Some of the parameters are interrelated

and not all of them need be specified for

complete description of the antenna

performance.

IEEE Standard Definitions of Terms for

Antennas (IEEE Std 145 – 1983)

32

RADIATION PATTERN

An antenna radiation pattern or antenna pattern is defined as “a mathematical function or a graphical representation of the radiation properties of the antenna as a function of space coordinates.

In most cases, the radiation pattern is determined in the far-field region and is represented as a function of the directional coordinates.

Radiation properties include power flux density, radiation intensity, field strength, directivity phase or polarization.”

33

RADIATION PATTERN Representation of the radiation properties of the antenna

as a function of angular position

Power pattern: the trace of the angular variation of the received/radiated power at a constant radius from the antenna

Amplitude field pattern: the trace of the spatial variation of the magnitude of electric (magnetic) field at a constant radius from the antenna.

Often the field and power pattern are normalized with respect to their maximum value, yielding normalized field and power patterns.

The power pattern is usually plotted on a logarithmic scale or more commonly in decibels (dB)

34

RADIATION PATTERN

Figure 1.1: coordinate system for antenna analysis

35

RADIATION PATTERN

36

RADIATION PATTERN

For an antenna, the Field pattern (in linear scale) typically represents a

plot of the magnitude of the electric or magnetic field as a function of the angular space.

Power pattern (in linear scale) typically represents a plot of the square of the magnitude of the electric or magnetic field as a function of the angular space.

Power pattern (in dB) represents the magnitude of the electric or magnetic field, in decibels, as a function of the angular space.

Note: the power pattern and the amplitude field pattern are the same when computed and plotted in dB.

37

RADIATION PATTERN

Figure 1.2: 3-D and 2-D patterns

38

RADIATION PATTERN

,r

,

,E

Plotting the pattern: The trace of the pattern is obtained by setting the length of the radius-

vector

[1.6]

Corresponding to the [1.7]

Point of the radiation pattern proportional to the strength of the field

[1.8]

(in the case of an amplitude field pattern) or proportional to the power

density

2

,E

[1.9]

(in the case of a power pattern).

39

RADIATION PATTERN

Figure 1.3: plotting the pattern

40

RADIATION PATTERN

In Fig. 1.4, the plus (+) and the minus (-) signs in the lobes indicate the relative polarization of the amplitude between the various lobes, which changes (alternates) as the nulls are crossed.

To find the points where the pattern achieves its half-power (-3 dB points), relative to the maximum value of the pattern: Field pattern at 0.707 value of its maximum.

Power pattern (in linear scale) at its 0.5 value of its maximum.

Power pattern (in dB) at -3 dB value of its maximum.

The angular separation between the two half-power points is referred to as HPBW.

41

RADIATION PATTERN

Figure 1.4: two-dimensional normalized field pattern of a 10-element

linear array with a spacing of d = 0.25λ

42

RADIATION PATTERN

Figure 1.4: two-dimensional normalized field pattern of a 10-element

linear array with a spacing of d = 0.25λ

43

RADIATION PATTERN

All three patterns yield the same angular separation between the two half-power points, which referred as HPBW (as illustrate in Figure 1.4)

Practical: the three dimensional pattern is measured and recorded in a series of two-dimensional-patterns.

44

RADIATION PATTERN LOBES

Various parts of radiation pattern are referred to as lobes.

Various lobes can be sub-classified in major or main, minor, side and back lobes. (see Fig. 1.5)

Radiation lobes is a “portion of the radiation pattern bounded by regions of relatively weak radiation intensity.”

45


Figure 1.5: Radiation lobes and beamwidths of an antenna pattern

46

RADIATION PATTERN LOBES A major lobe (also called main beam) is defined as “the

radiation lobe containing the direction of maximum radiation”.

A minor lobe is any lobe except major lobe.

A side lobe is “a radiation lobe in any direction other than intended lobe”. Usually a side lobe is adjacent to the main lobe and occupies the hemisphere in the direction of the main beam.

A back lobe is “a radiation lobe whose axis makes an angle of approximately 180º with respect to the beam of the antenna”.

Minor lobes usually represent radiation in undesired directions, and they should be minimized.

Side lobes are normally the largest of minor lobes.

47


Figure 1.6: Linear plot of power pattern and its associated lobes and

beamwidths.

48


Figure 1.7: Normalized three-dimensional amplitude field pattern (in linear

scale) of a 10-element linear array antenna with a uniform spacing of 0.25λ

and progressive phase shift (β = -0.6π) between the elements.

49

ISOTROPIC, DIRECTIONAL &

OMNIDIRECTIONAL PATTERN

Isotropic pattern is the pattern of an antenna having equal radiation in all directions. This is an ideal (not physically achievable) concept. However, it is used to define other antenna parameters. It is represented simply by a sphere whose center coincides with the location of the isotropic radiator.

Directional antenna is an antenna, which radiates (receives) much more efficiently in some directions than in others. Usually, this term is applied to antennas whose directivity is much higher than that of a half wavelength dipole.

Omnidirectional antenna is an antenna, which has a non-directional pattern in a given plane, and a directional pattern in any orthogonal plane (e.g. single-wire antennas).

50 Figure 1.8: Omnidirectional Antenna Pattern.



51



Figure 1.9: Principle E- and H-plane patterns for a pyramidal horn antenna.

52

PRINCIPAL PATTERNS

Principal patterns are the 2-D patterns of

linearly polarized antennas, measured in the E-plane (a plane parallel to the |Ē| vector and

containing the direction of maximum radiation)

the H-plane (a plane parallel to the vector,

orthogonal to the E-plane, and containing the

direction of maximum radiation).

H

53

PATTERN BEAMWIDTH

Figure 1.10: Pattern beamwidth.

54

PATTERN BEAMWIDTH

Half-power beamwidth (HPBW) is the angle

between two vectors, originating at the pattern’s

origin and passing through these points of the

major lobe where the radiation intensity is half its

maximum.

First-null beamwidth (FNBW) is the angle

between two vectors, originating at the pattern’s

origin and tangent to the main beam at its base.

Often, it is true that FNBW≈2⋅HPBW

Example The normalized radiation intensity of an antenna is represented by

Find

a. half-power beamwidth HPBW (in radians and degrees)

b. first-null beamwidth FNBW (in radians and degrees)

Solution

Since the U(θ) represents the power pattern, to find the half-power

beamwidth you set the function equal to half of its maximum, or

Since this is an equation with transcendental functions, it can be solved

iteratively . After a few iterations, it is found that

57

58

So θh = 14.32

Since the function U(θ) is symmetrical about the maximum at θ = 0, then the HPBW

is HPBW = 2θh = 28.65. b) To find the first-null beamwidth (FNBW), you set the U(θ) equal to zero, or This leads to two solutions for θn.

The one with the smallest value leads to the FNBW. Again,

because of the symmetry of the pattern, the FNBW is

H.W

1-Find the half-power beamwidth (HPBW) and first-null

beamwidth (FNBW), in radians and degrees, for the

following normalized radiation intensities:

59

2-Find the half-power beamwidth (HPBW) and first-null

beamwidth (FNBW), in radians and degrees, for the

following normalized radiation intensities:

60 Figure 1.11: Field regions of an antenna.

FIELD REGIONS

61

FIELD REGIONS Reactive near-field region is defined as “that portion of

the near-field region immediately surrounding the antenna wherein the reactive field predominates”.

λ is the wavelength

D is the largest dimension of the antenna

For a very short dipole, or equivalent radiator the outer

boundary is commonly taken to exist at a distance

λ/2π from the antenna surface.

3

62.0 DR [1.10]

62

FIELD REGIONS Radiating near-field region (Fresnel) is defined as “that

region of the field of an antenna between the reactive near-field region and the far-field region wherein radiation fields predominate and wherein the angular field distribution is dependent upon the distance from the antenna”.



If the antenna has a dimension that is not large compared to wavelength, this region may not exist.

23 262.0 DRD [1.11]

63

FIELD REGIONS Far-field region (Fraunhofer) is defined as “that region

of the field of an antenna where the angular field distribution is essentially independent of the distance from the antenna”.



The far-field patterns of certain antennas, such as multibeam reflector antennas are sensitive to variations in phase over their apertures.

22DR [1.12]

64

FIELD REGIONS

Figure 1.12: Typical changes of antenna amplitude pattern shape from

reactive near field toward the far field.

65

RADIAN & STERADIAN

The measure of a plane angle is a radian.

One radian is defined as the plane angle with its vertex at

the center of a circle of radius r that is subtended by an

arc whose length is r.

rC 2 [1.13]

There are 2π rad (2πr/r) in a full circle.

66

RADIAN & STERADIAN

The measure of a solid angle is a steradian.

One steradian is defined as the solid angle with its vertex

at the center of a circle of a sphere radius r that is

subtended by a spherical surface area equal to that of

square which each side of a length r.

24 rA [1.14]

There are 4π sr (4πr2/r2) in a closed sphere.

67

Therefore, the element of solid angle dΩ of a sphere can

be written as:

RADIAN & STERADIAN

ddrdA sin2

The infinitesimal area dA on the surface of a sphere of

radius r, is shown in Fig. 1.22 is given by:

[1.15]

ddr

dAd sin

2

(m2)

[1.16] (sr)

69

= solid angle in a sphere

70

RADIAN & STERADIAN

Figure 1.14: Geometrical arrangements for defining a radian and a steradian

Beam Area

71

The beam area or beam solid angle or A of an antenna is given by the integral of the normalized power pattern P( over a

(sphere (4π sr

where dΩ= sin θ dθ dφ, sr

The beam area of an antenna can often be described approximately in terms of the angles subtended by the half-power points of the main lobe in the two principal planes.

where θHP and φHP are the half-power beamwidths (HPBW) in the two principal planes, minor lobes being neglected.

72

Example(BOOK)

Find the number of square degrees in the solid angle on a spherical surface that is between θ = 20 and θ = 40 (or 70 and 50 north latitude) and between φ = 30 and φ = 70 (30 and 70 east longitude).

73

RADIATION POWER DENSITY

Electromagnetic waves are used to transport information

through a wireless medium or a guiding structure, from one

point to other. It is then natural to assume that power and

energy are associated with electromagnetic fields. The quantity used to describe the power associated with an electromagnetic wave is the instantaneous Poynting vector defined as:

P= E x H

P = instantaneous Poynting vector (W/m2)

E = instantaneous electric-field intensity (V/m)

H = instantaneous magnetic-field intensity (A/m)

[1.17]

74


The total power crossing a closed surface can be obtained

by integrating the normal component of Poynting vector

over the entire surface. In equation form:

P = ∫∫S W.ds = ∫∫S W.ñ da w

P = instantaneous total power (W)

ñ = unit vector normal to the surface

da = infinitesimal area of the closed surface (m2)

[1.18]

75


For applications of time varying fields, it is often more

desirable to find the average power density which is

obtained by integrating the instantaneous Poynting vector

over one period. For time-harmonic variations of the form

ejωt. So, the complex fields E and H which are related to

their instantaneous counterparts E and H.

[1.19] tj

tj

ezyxtzyx

ezyxtzyx

,,Re;,,

,,Re;,,

H

E

H

E

[1.20]

76


By using the equation [1.19] and [1.20] and the identity (as

shown in page 39), The time average Poynting vector

(average power density) can be written as:

[1.21] (W/m2) HERe2

1;,,,,

avav tzyxzyxp p

The ½ factor appears in equation [1.21] because E and H

fields represent peak values and it should omitted for RMS

values.

77


The imaginary part of equation [1.21] represent the reactive

(stored) power density associated with the electromagnetic

fields. So, The power density associated with the

electromagnetic fields of an antenna in its far-field region is

predominately real and will be referred to as radiation density. The average power radiated by an antenna:

[1.22]

ds

danWdsWPP

S

S

av

S

radavrad

HERe2

1

ˆ

78


0

2

2

0 0

2

00

4

sinˆˆ

Wr

ddrarWadsWP rr

S

rad

An isotropic radiator is an ideal source that radiates equally

in all directions. Isotropic radiator have the symmetric

radiation, which there is no function of the spherical

coordinate angles θ and Φ. Thus the total power radiated is

given by:

[1.23]

2004

ˆˆr

PaWaW rad

rr

[1.24]

The power density:

(W/m2)

79

U = radiation intensity (W/unit solid angle)

RADIATION INTENSITY

radPrU 2

Radiation intensity in a given direction is defined as “the

power radiated from an antenna per unit solid angle.” The

radiation intensity is a far-field parameter.

[1.25]

The total power obtained by the radiation intensity:

2

0 0

sin ddUUdPrad[1.26]

80

DIRECTIVITY The directivity of an antenna is defined as “the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. The average radiation intensity is equal to the total power radiated by the antenna divided by 4π. If the direction is not specified, the direction of maximum radiation intensity is implied.”

The directivity of a non-isotropic source is equal to the ratio

of its radiation intensity in a given direction over that of an

isotropic source.

radP

U

U

UD

4

0

[1.27]

81

DIRECTIVITY If the direction is not specified, it implies the direction of

maximum radiation intensity (maximum directivity)

expressed as:

radP

U

U

U

U

UDD max

0

max

0

max0max

4 [1.28]

D = directivity (dimensionless)

D0 = maximum directivity (dimensionless)

U = radiation intensity (W / unit solid angle)

Umax = maximum radiation intensity (W / unit solid angle)

U0 = radiation intensity of isotropic source (W / unit

solid angle)

Prad = total radiated power (W)

82

Approximate Directivity

0

83

ANTENNA EFFICIENCY The total efficiency of the antenna et is used to estimate the total loss of

energy at the input terminals of the antenna and within the antenna structure. It includes all mismatch losses and the dielectric/conduction losses (described by the radiation efficiency e as defined by the IEEE Standards)

The overall efficiency:

dcdr eeeet [1.29]

et = total efficiency (dimensionless)

er = reflection = (mismatch) efficiency (dimensionless)

ecd = conduction efficiency (dimensionless)

ed = dielectric efficiency (dimensionless)

Γ = voltage reflection coefficient at the input terminals of the antenna.

radcd

radcd

RR

Re

22

ocd

b

lR

84

ANTENNA EFFICIENCY

Figure 1.16: Reference terminals and losses of an antenna

85

ANTENNA GAIN

The gain G of an antenna is the ratio of the radiation

intensity U in a given direction and the radiation intensity

that would be obtained, if the power fed to the antenna

were radiated isotropically.

inP

UG

,4, [1.30]

in most cases, we deal with relative gain which defined as “the

ratio of the power gain in a given direction to the power gain of a

reference antenna in its referenced direction”. The power input

must be same for both antennas. The reference antenna usually

a dipole, horn, or any other antenna whose gain can be

calculated or it is known.

86

ANTENNA GAIN

In most cases, the reference antenna is a

lossless isotropic source.

When the direction is not stated, the power gain is usually taken in the direction of maximum radiation.

A half-wavelength dipole antenna, with an input impedance of 73 is to be

connected to a generator and transmission line with an output impedance of

50. Assume the antenna is made of copper wire 2.0 mm in diameter and the

operating frequency is 10.0 GHz. Assume the radiation pattern of the antenna is

Find the overall gain of this antenna

87

)(sin),( 3 oBU

SOLUTION

First determine the directivity of the antenna

)(

),(4),(

totradP

UD

697.13

16

)(sin3

16

4

3

)(sin4),(

max0

3

2

0

3

DD

B

BD o

Next step is to determine the efficiencies

88

965.0)5073

50731()1(

22

r

cdrt

e

eee

radcd

radcd

RR

Re

964.09991.0965.0

9991.00628.073

73

0628.0107.52

10410102

)001.0(2

015.0

22 7

79

cdrt

cd

ocd

eee

e

b

lR

Next step is to determine the gain

dBdBG

GG

G

DeeG cdr

14.2)636.1(log10)(

636.13

16964.0

)(sin3

16964.0),(

),(),(

100

max0

3

89

BEAM EFFICIENCY

The beam efficiency is the ratio of the power radiated in a cone of angle 2θ1 and the total radiated power. The angle 2θ1 can be generally any angle, but usually this is the first-null beam width.

[1.31]

90

FREQUENCY BANWIDTH

This is the range of frequencies, within which the antenna characteristics (input impedance, pattern) conform to certain specifications.

Antenna characteristics, which should conform to certain requirements, might be: input impedance, radiation pattern, beamwidth, polarization, side-lobe level, gain, beam direction and width, radiation efficiency. Usually, separate bandwidths are introduced: impedance bandwidth, pattern bandwidth, etc.

91

FREQUENCY BANWIDTH The FBW of broadband antennas is expressed as the

ratio of the upper to the lower frequencies, where the antenna performance is acceptable:

min

max

f

fFBW

%1000

minmax

f

ffFBW

2minmax0 fff minmax0 fff

[1.32]

For narrowband antennas, the FBW is expressed as a

percentage of the frequency difference over the center

frequency:

[1.33]

92

POLARIZATION Polarization of an antenna in a given direction is defined

as “the polarization of the wave transmitted (radiated) by the antenna. When the direction is not stated, the polarization is taken to be the polarization in the direction of maximum gain”.

Polarization of a radiated wave is defined as “that property of an electromagnetic wave describing the time varying direction and relative magnitude of the electric field vector; specifically, the figure traced as a function of time by the extremity of the vector at a fixed location in space and the sense in which it is traces, as observed along the direction of propagation”.

Polarization is the curve traced by the end point of the arrow (vector) representing the instantaneous electric field. The field must be observed along the direction of propagation.

93

POLARIZATION

Figure 1.17: Rotation of a plane electromagnetic wave and its polarization

94

POLARIZATION

Figure 1.18: type of polarization

95

POLARIZATION

The polarization of the wave can be defined in terms of a wave radiated (transmitted) or received by an antenna in a given direction.

The polarization of the wave radiated by an antenna in a specified direction at a point in the far-field is defined as “the polarization of the (locally) plane wave which is used to represent the radiated wave at that point. At any point in the far-field of an antenna radiated wave can be represented by a plane wave whose electrical-field strength is the same as that of the wave and whose direction of propagation is in the radial direction from the antenna”.

Polarization may be classified as linear, circular or elliptical. If the vector that describes the electric field at a point in space as a

function of time is always directed along a line, the field is said to be linearly polarized.

If the figure that the electric field traces is an ellipse, the field is said to be elliptically polarized.

Linear and circular polarizations are special cases of elliptical, and they can be obtained when the ellipse become a straight line or a circle, respectively.

96

POLARIZATION

At each point on the radiation sphere the polarization is usually resolved into a pair of orthogonal polarizations, the co-polarization and cross-polarization.

The co-polarization must be specified at each point on the radiation sphere.

Co-polarization represents the polarization the antenna is intended to radiate (receive) while cross-polarization represents the polarization orthogonal to a specified polarization, which is usually the co-polarization.

Polarization Loss Factor PLF It happened when receiving antenna not at the

same as the polarization of the incoming

(incident) wave.

Where and Polarization unit vectors of incident wave

and antenna respectively .

Where is the angle between the two unit vectors. The

relative alignment of the polarization of the incoming wave

and of the antenna is shown in Figure

97

99

1 Example

100

Example 2 :

A right-hand (clockwise) circularly polarized wave radiated by an antenna,

placed at some distance away from the origin of a spherical coordinate system,

is traveling in the inward radial direction at an angle (θ, φ( and it is impinging

upon a right-hand circularly polarized receiving antenna . Determine the

polarization loss factor (PLF).

Solution: The polarization of the incident right-hand circularly polarized wave traveling along the −r radial direction is described by the unit vector

while that of the receiving antenna, in the transmitting mode, is represented

by the unit vector

Therefore the polarization loss factor is

Since the polarization of the incoming wave matches (including the sense of rotation)

the polarization of the receiving antenna, there should not be any losses.

A linearly polarized wave traveling in the negative z-direction has a tilt angle (τ ) of 45. It is incident upon an antenna whose polarization characteristics are given by

Find the polarization loss factor PLF (dimensionless and db).

101

Solution

102

Effective Aperture

plane wave

incident A physical

Pload

103

Antenna Effective Area Ae

Measure of the effective absorption area

presented by an antenna to an incident

plane wave.

Depends on the antenna gain and

wavelength

Aperture efficiency: ap = Ae / Ap Ap: physical area of antenna’s aperture, square meters

][m ),(4

22

GAe

104

THE RADIO COMMUNICATION LINK

The power received over a radio communication link “ as showing in the figure

below” by assuming lossless, matched antennas, “PLF=1” let the transmitter

feed a power Pt to a transmitting antenna of effective aperture Aet.

At a distance r a receiving antenna of effective aperture Aer Intercepts some of the power radiated by the transmitting antenna and delivers it to the receiver R.

1 2

105

Assuming the transmitting antenna is isotropic, the power per unit area available

at the receiving antenna is

If the antenna has gain Gt yield

So power collected by the lossless, matched receiving antenna of effective

aperture Aer is

The gain of the transmitting antenna can be expressed as

Substituting this Gt in Pr yields the Friis transmission formula

m2

m2

106

11.1-2راجع مثال الكتاب

Or

Where where r, θ1, φ1 are the local spherical coordinates for antenna 1 And θ2, φ2 are the local spherical coordinates for antenna 2

تستخدم المعادلة في حالة الهوائيان متقابلة ولا يوجد

انحراف او عدم تقابل

بين ) زاوية(تستخدم اذا يوجد انحراف

θ, φالمرسل والمستلم او الهوائي كدالة ل

107

Calculate the receive power P2 at antenna 2 if the transmi power P1 = 1 kW. The transmitter gain is and the receiver gain is

The operating frequency is 2 GHz. Use the Fig. below to solve the problem. The y-z and y-z planes are coplanar

Example

108

Solution

يجب تحويله الى الدسمل حتى تستطيع استخدامه في ) dB 6(مثلا dB معطى الرقم بـ gainملاحظة في حالة ال

Friisمعادلة

109

What is the maximum power received at a distance of 0.5 km over a free-space 1 GHz

circuit consisting of a transmitting antenna with a 25 dB gain and a receiving antenna

with a 20 dB gain? The gain is with respect to a lossless isotropic source. The

transmitting antenna input is 150 W.

2 28 9/ 3 10 /10 0.3 m, ,

4 4

t ret er

D Dc f A A

mW 10.8 W0108.0500)4(

1003.0316150

)4( 22

2

222

22

22

r

DDP

r

AAPP rt

teret

tr

Solution:

2-11-1. Received power and the Friis formula.سوأل من الكتاب

H.W

110

Repeat Problem 1 for two antennas with 30 dB directivities and separated by

100λ. The power at the input terminals is 20 W.

Q1

Q2

Q3

111

Hertzian Dipole

Is an infinitesimal current element (/ dl). Although such a current element

does not exist in real life

Power Radiated and radiation resistance of Hertzian Dipole

116

The time-average power density is obtained as

Substituting yields the time-average radiated power as

117

Where So the power radiated is become

If free space is the medium of propagation

This power is equivalent to the power dissipated in a fictitious resistance Rrad by

Current

I = Io cos wt that is افتراضي

where I rms is the root-mean-square value of I .

118

So تمثل طول الدايبول بالنسبة للطول الموجيL

Hertzain Dipoleتمثل مقاومة الارسال ل

The resistance Rrad is a characteristic property of the Hertzian dipole antenna and

is called its radiation resistance

Note that the Hertzian dipole is assumed to be infinitesimally small

ان يكون طوله اقل واحد الى Hertzian dipoleشرط ال

عشرة من الطول الموجي

The half-wave dipole derives its name from the fact that its

length is half a wavelength

Half wave Dipole

2/l

-It consists of a thin wire fed or

excited at the midpoint by a

voltage source connected to the

antenna via a transmission line

The field due to the dipole can be easily obtained if we consider it as consisting of

a chain of Hertzian dipoles

The magnetic vector potential at P due to a differential length dl(= dz) of the dipole

carrying a phasor current zll os cos

if

cos'

cos'

zrr

or

zrr

lr

So, we may suppose in the denominator where the magnitude of the distance is needed. For the phase term in the numerator the difference between Br and Br' is significant, so we replace r' by (r - z cosθ ) not r. So we maintain the cosine term in the exponent while neglecting it in the denominator

rr '

Since

Notice that the radiation term of and are in time phase and orthogonal

Power Calculation

For free space

So 2x

)1

1

1

1(

2

1

1

12 uuu

Since

sin)90cos(

sin)90cos(

Note the significant increase in the radiation resistance of the half-wave dipole

over that of the Hertzian dipole

The total input impedance Zin of the antenna is the impedance seen at the terminals of

the antenna and is given by

QUARTER-WAVE MONOPOLE ANTENNA 4/l

The quarter-wave monopole antenna consists of one-half of a half-wave dipole

antenna located on a conducting ground plane as in Figure .The monopole

antenna is perpendicular to the plane, which is usually assumed to be infinite and

perfectly conducting. It is fed by a coaxial cable connected to its base

Where

The integration of monopole only over the

hemispherical surface above the ground plane

0 < θ< π/2

Hence, the monopole radiates only half as much power as the dipole with the same

current, so

Where the total input impedance for a λ/4 monopole

SMALL LOOP ANTENNA

1-It is used as a directional finder (or search loop) in radiation detection

and as a TV antenna for ultrahigh frequencies.

2-The term "small" implies that the dimensions (such as po) of the loop are much

smaller than λ.

At far field, only the 1/r term (the radiation term) . So, the electrical field and

magnetic field given by

Where the radiation resistance of a small

loop antenna given by :

Helical Antenna

Is a basic, simple, and practical configuration of an electromagnetic radiator

is that of a conducting wire wound in the form of a screw thread forming a

helix.

The geometrical configuration of a helix

consists usually of N turns, diameter “D”

and spacing “S” between each turn.

The total length of the antenna is L = NS

While the total length of the wire is

Where the length of the wire between each turns

And the circumference of the helix given by

Another important parameter is the pitch angle α which is the angle formed by a

line tangent to the helix wire and a plane perpendicular to the helix axis. The pitch

angle is defined by

When α = 0, then the winding is flattened

and the helix reduces to a loop antenna

of N turns.

On the other hand, when α = 90 then the

helix reduces to a linear wire.

When 0 < α < 90 , then a true helix is formed with a circumference greater than zero

but less than the circumference when the helix is reduced to a loop (α = 0)

The helical antenna can operate in many modes; however the two principal

ones are the normal (broadside) and the “axial” (end-fire) modes.

The represent of the normal mode as shown (a), has its maximum in a plane normal

to the axis and is nearly null along the axis. The pattern is similar in shape to that of

a small dipole or circular loop.

The pattern representative of the axial mode, shown in (b),has its maximum along the

axis of the helix.

A. Normal Mode

To achieve the normal mode of operation, the dimensions of the helix are usually

small compared to the wavelength

The geometry of the helix reduces to a loop of diameter D when the pitch angle

approaches “zero” Eφ

And linear wire of length S when it approaches “90” Eθ

So the limiting geometries of the helix are a loop

and a dipole,

In the normal mode, the helix as shown in Figure can be

simulated approximately by N small loops and N short

dipoles connected together in series

The ratio of the magnitudes of the Eθ and Eφ

components is defined here as the axial ratio (AR),

and it is given by

By varying the D and/or S the “axial ratio” attains values of

The value of AR = 0 is a special case and occurs when Eθ = 0 leading to a

linearly polarized wave of horizontal polarization (the helix is a loop). When

AR=∞, Eφ = 0 and the radiated wave is linearly polarized with vertical

polarization (the helix is a vertical dipole).

Another special case is the one when AR is unity (AR = 1) and occurs when

In which

OR

When the dimensional parameters of the helix

satisfy the above relation, the radiated field is

circularly polarized in all directions other than θ = 0

Two achieve which must be very small compared to the wavelength

This mode of operation is very narrow in bandwidth and its radiation

efficiency is very small. Practically this mode of operation is limited, and it is

seldom utilized.

B. Axial Mode

Is more practical mode of operation, which can be generated with great ease, is

the axial or end-fire mode. In this mode of operation, there is only one major lobe

and its maximum radiation intensity is along the axis of the helix

To achieve circular polarization, primarily in the major lobe, the circumference

of the helix must be in the and the spacing about S= λ0/4.

Where The pitch angle is usually

Design Procedure

The input impedance (purely resistive) is obtained by

While the Half Power Beamwidth

Beamwidth between nulls given by

And the directivity given by

Normal Mode

Axial Mode

Design a five-turn helical antenna which at 400 MHz operates in the normal mode. The spacing

between turns is λ0/50. It is desired that the antenna possesses circular polarization. Determine

the (a) circumference of the helix (in λ0 and in meters)

(b) length of a single turn (in λ0 and in meters)

(c) overall length of the entire helix (in λ0 and in meters)

(d) pitch angle (in degrees)

Solution

Design an end fire right-hand circuilarly polarized helix having a half –power beam width of 45

degrees, pitch angle of 13 degrees and the circumference of 60 cm at frequency of 500 MHz.

Calculate

(a)- turns needed

(b)- directivity (in dB)

(c)- axial ratio

(d) lower and upper frequencies of the bandwidth over which the required parameters remain

relatively constant .

Solution

chapter 1 antenna principle & basic antenna …

Documents