Antennas & Wave Propagation

(ELC 521)

Spring Semester 2019/2020

By

Dr. Hazem El-Banna

elbanna30000@gmail.com

Electronics and Communication Eng. Dept.

 Chapter:3

Wire Antennas

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 Wire Antennas Lecture 3

Suggested Readings
Most of the material in this lecture are based on:
 Chapter 4, Simon Saunders & Alejandro A. Zavala“ Antennas and
propagation for wireless communication systems,” John Willy, 2nd
ed., 2007.

 Chapter 4 and 5, Constantin Balanis“ Antenna Theory Analysis and

Design,” John Wiley, 3rd ed., 2005.

 For more mathematical details

Chapter 3, Constantin Balanis“ Antenna Theory Analysis and

Design,” John Wiley, 3rd ed., 2005.

4/8/2020 3
 Contents Lecture 3

Today we are going to talk about:

Wire Antennas
 Infinitesimal dipole
 Small dipole
 Finite length dipole
 Travelling wave antenna
 Loop antennas
 Antennas over ground

4
How to Compute fields
Remember that: General form of Grad., Div. and Curl for all coordinates:

U1 U2 U3 h1 h2 h3

Cartesian Coord. x y z 1 1 1

Cylindrical Coord.   z 1  1

Spherical Coord. r   1 r r sin

1  1  h1â U1 h 2â U 2 h 3â U3

  â U1  â U 2
h1 U1 h 2 U 2  1
A   U1  U 2  U 3
1  h1h 2 h 3
 â U3 h1A U1 h 2 A U 2 h 3A U3
h 3 U 3
1  
    


  
. A   h 2 h 3 A U1  h1h 3 A U 2  h1h 2 A U3 
h1h 2 h 3  U1 U 2 U 3 
1    h 2 h 3     h 1 h 3     h 1 h 2  
 
2
  
 h U   U      
h 1h 2 h 3   U 1  1 1  2  h 2 U 2  U 3  h 3 U 3 
Wire Antennas

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 Wire Antennas Lecture 3

1-Elementry ( Infinitesimal ) dipole

•Geometry •Vector potential A
l ≤ λ /50

R~ r

z
•Current

Io Iz

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 Wire Antennas Lecture 3

•Field components

4/8/2020 LECTURES 9
 Wire Antennas Lecture 3

•Far field (kr >> 1)

Hence: •Rdiation density

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 Wire Antennas Lecture 3

•Radiated power

•Radiation resistance

•Input resistance
Rin= Rr / sin2(kl/2)
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 Wire Antennas Lecture 3

•Directivity

•Effective area

LECTURES 12
 Wire Antennas Lecture 3

•Field pattern

Radiation pattern of the infinitesimal dipole is on the form of a Doughnut

shape

H plane E plane

4/8/2020 LECTURES 13
 Wire Antennas Lecture 3

2-Small ( short ) dipole

•Geometry •Current
 Wire Antennas Lecture 3

•Vector potential A •Directivity

•Radiation resistance

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•Field components
•Effective area
 Wire Antennas Lecture 3

•Field pattern

Radiation pattern of the infinitesimal dipole is on the form of a Doughnut

shape

H plane E plane
Note: Its clear that the small dipole have the same pattern, directivity and
effective area as elementary dipole

4/8/2020 LECTURES 16
 Wire Antennas Lecture 3

3-Finte length (symmetrical) dipole

•Geometry •Current
 Wire Antennas Lecture 3

•Field components

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 Wire Antennas Lecture 3

•Radiation density •Field pattern

•Radiation
intensity

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 Wire Antennas Lecture 3

Half wave dipole (l=λ/2)

Field components Power radiated

Directivity and radiation resistance

Power density and intensity

Ω
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 Wire Antennas Lecture 3

4-Travelling wave dipole antenna

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 Wire Antennas Lecture 3

Example: L=λ/2 and ν=(1- 0.6)c Example: L=5λ

ν=c ν =0.8c

ν =0.6c

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 Wire Antennas Lecture 3

Examples: V - antenna

Rhombic antenna

4/8/2020 LECTURES 23
Wire Antennas Lecture 3

Remember that:
 Wire Antennas Lecture 3

5-Cicular loop with constant current

•Geometry

Finding R

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 Wire Antennas Lecture 3

4/8/2020 LECTURES 26
Wire Antennas Lecture 3

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 Wire Antennas Lecture 3

•Current and magnetic vector potential A

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 Wire Antennas Lecture 3

•Radiated field

•Field pattern

J1 =

LECTURES 29
Wire Antennas Lecture 3

2a=0.1λ 2a=1λ

2a=1.5λ 2a=5λ

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 Wire Antennas Lecture 3

•Radiated power and radiation resistance

Wav Pav

Wav

Pav

Pav

For large loop (a   2)

/x

Pav

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 Wire Antennas Lecture 3

4/8/2020 LECTURES 32
 Wire Antennas Lecture 3

•Directivity

 a   a 
2 2 2 2
I0 I0
 J1  ka sin   ka sin  1.84   0.584
2 2
U max
8 8

ka  0.584 
2
U max C
D0  4  4  2ka  0.584   0.682  
2

Prad 2 

4/8/2020 LECTURES 33
 Wire Antennas Lecture 3

6-Small loop (a<  6 )

•Radiated field

1 1
J1  ka sin     ka sin     ka sin    ...
3

2 16
 Wire Antennas Lecture 3

•Radiation resistance

Pav 2 k k

Pav k
 Wire Antennas Lecture 3

•Directivity
2
  k 2a2  r2
 
2
U  r Wr      
2 2 2
 0
I sin E r , ,
2 4  2
The maximum value of U occurs at   /2
2
  k 2a2 
U max  U 
2
  2   I0
2 4 
 
Prad      ka  I 0
4 2

 12 
U max 3
D0  4 
Prad 2
•Effective area

4/8/2020 LECTURES 36
 Wire Antennas Lecture 3

7-Antennas over ground

Direct and reflected rays

Actual and equivalent problems

 Wire Antennas Lecture 3

Vertical dipole( monopole)

•Field components

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 Wire Antennas Lecture 3

Number of lobes

for
n=
 Wire Antennas Lecture 3

•Radiation intensity •Radiation resistance

•Power Radiated

Optimum directivity at:

•Directivity
 Wire Antennas Lecture 3

•Monopole applications

4/8/2020 LECTURES 41
 Wire Antennas Lecture 3

Horizontal dipole
•Field components

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 Wire Antennas Lecture 3

Number of lobes

for n=
 Wire Antennas Lecture 3

•Radiation intensity •Directivity

•Power Radiated

•Radiation resistance
Wire Antennas Lecture 3

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