EELE 5333

Antenna & Radio

Propagation

Part II:

Antenna families

Winter 2020

Re-Prepared by

Dr. Mohammed Taha El Astal

Chapter 4:

Linear Wire Antennas

Session 2

Acknowledgment

This PPT is prepared based mainly on Dr.Talal Skaik’s PPT, Balanis

Antenna Book, and Dr. Ashok Kumar

Contents:

• Introduction

Calculation of Radiation Fields by an Infinitesimal Dipole

Determining of Infinitesimal Dipole Parameters

The time-average complex Poynting vector (time average

complex power density) is written as:

4

Infinitesimal Dipole, Power Density & Radiation Resistance

𝐸𝑟 and 𝐸𝜃 exists 𝐸∅ exists only

The complex power moving in the radial direction is obtained

by integrating W over sphere of radius r.

The transverse component Wθ of the power density does not contribute

to the last integral. Thus P does not represent the total complex power

radiated by the antenna.

Since Wθ is purely imaginary, it will not contribute to any real radiated

power. However, it does contribute to the imaginary (reactive) power

which along with the second term of P can be used to determine the total

reactive power of the antenna.5

3

4)(sin

0

3

d

Infinitesimal Dipole, Power Density & Radiation Resistance

Total reactive power of the

antenna

6

2

0

3

2

0

3)(3

lI

kr

jlIP

3

2

0

)(1

3 kr

jlIP

Time-average power radiated is the real part of P.

2

0

3

lIPrad

The imaginary part of P is the time-average imaginary (reactive) power in radial direction which is:

3

2

0

)(

1

3-

kr

lIj

For large values of kr (kr >>1 or r >> λ), the reactive power

diminishes and vanishes when kr = ∞.

Infinitesimal Dipole, Power Density & Radiation Resistance

You can see now, why it called reactive only when it is very close to antenna

Since the antenna radiates its real power through the radiation resistance, it is

found by:

where Rr is the radiation resistance, and it is found by:

Example: Find the radiation resistance of an infinitesimal dipole whose overall length is l = λ/50.

Solution:

Since the radiation resistance of an infinitesimal dipole is about 0.3 ohms, it will present a very

large mismatch when connected to practical transmission lines, many of which have characteristic

impedances of 50 or 75 ohms. The reflection efficiency (er ) and hence the overall efficiency

(e0) will be very small.7

rrad RIlI

P2

0

2

0

2

1

3

2

2

2

803

2

llRr

2

0

3

2

0

3)(3

lI

kr

jlIP

Infinitesimal Dipole, Power Density & Radiation Resistance

Reactive Near Field (kr

Reactive Near Field

(kr

Radiating Near Field (kr>1) (Fresnel) Region

This is intermediate field region

rEkr

Ekrkr

krkr

kr

krkrrr

in 1

neglect

in 1

,)(

1neglect

1)(

1 1

1

in 1

neglect

11

122

2

2

H

10

Infinitesimal Dipole, Field Regions

Far Field (kr>>1) Region

Er will be smaller than Eθ because Er is inversely

proportional to r2 , where Eθ is inversely proportional

to r → Er ≈ 0.

11

Ean smaller th be willE

in )(

1,

1 and,Ein

1neglect

1)(

1 1

1

in 1

neglect 11

122

r

2

2

E

H

krkrkr

krkr

krkr

krrr

r

Infinitesimal Dipole, Field Regions

Far Field (kr>>1) Region

The ratio of Eθ to Hφ is equal to

where

Zw = wave impedance

η = intrinsic impedance (377 ≈120π ohms for free-space)

The E and H field components are perpendicular to each other, transverse to the radial direction of propagation (TEM).

12

H

EZw

Infinitesimal Dipole, Field Regions

The average power density is given by:

The radiation intensity U is given by:

The maximum value occurs at θ = π/2 and it is equal to

The directivity is given by

, 13

2

0

3

lIPrad

Infinitesimal Dipole, Radiation Intensity & Directivity

Three-dimensional radiation pattern of infinitesimal dipole

14

Infinitesimal Dipole

Dr. Mohammed Taha El Astalmtastal@iugaza.edu.psDr.mastal@gmail.com

10/2020