Lecture 6

EC 15-1702
Antennas and Propagation
Acknowledgement:
• Prof. C. A Balanis, Antenna Theory, Analysis and design, John
Wiley student edition, 3/e, (2012), ISBN:978-81-265-2422-8
• ieeexplore.ieee.org
• PhD Theses/Journals
• Other Sources…

Students are requested to refrain from using the learning resources outside this domain

October 2023 19-203-0702 Antennas and Propagation : Module 2 1

 Lecture 6

This too shall pass

October 2023 19-203-0702 Antennas and Propagation : Module 2 2

 Lecture 6

Module II
Radiation from an infinitesimal dipole
Total power radiated and its radiation resistance.
Radiation from half wave dipole
Radiation fields and its radiation resistance. near field and far field.
Small loop antennas
Ref: Balanis, Chapter 4 “Linear Wire Antennas”
https://nptel.ac.in/courses/117/101/117101056/
Module 7 Antennas/Section 3 Radiation from a Hertz Dipole

Antenna arrays:
Point Sources - arrays of 2 Isotropic Sources and N element point sources, , Principle of
Pattern Multiplication, Uniform Linear Arrays - Broadside Arrays, Endfire Arrays

October 2023 19-203-0702 Antennas and Propagation : Module 2 3

 Lecture 6

Course Outcomes

On successful completion of teaching-learning and valuation activities, a

student would be able :

1. To understand basic terminology, parameters and concepts of

Antennas
2. To analyze the electric and magnetic field of various basic antennas
3. To study the performance of Antenna Arrays
4. To acquire knowledge on antenna types as well as their application
5. To understand the propagation of the waves at different frequencies
through different layers of atmosphere

October 2023 19-203-0702 Antennas and Propagation : Module 2 4

 Lecture 6

The alternating current element

• I dl : A filamentary current I flowing through an elementary length dl

• dl is so short that I is essentially constant along the length

• an unreal concept

• basic building block of an actual antenna

Hertzian Dipole
October 2023 19-203-0702 Antennas and Propagation : Module 2 5
 Lecture 6
The Problem
Iz Er, Eθ, Hφ

October 2023 19-203-0702 Antennas and Propagation : Module 2 6

 Lecture 6

Remember!

October 2023 19-203-0702 Antennas and Propagation : Module 2 7

The magnetic vector potential due to an infinitesimal dipole (l << λ) Lecture 6

October 2023 19-203-0702 Antennas and Propagation : Module 2 8

 Lecture 6
Components of the magnetic vector potential A
The transformation between rectangular and spherical components

For this problem, Ax = Ay = 0

October 2023 19-203-0702 Antennas and Propagation : Module 2 9

 Lecture 6
Find the H fields from A

Using the symmetry of the problem (no φ variations)

Iz

Ar, Aθ

Hφ

October 2023 19-203-0702 Antennas and Propagation : Module 2 10

 Lecture 6
Find the E fields from H fields (or from A)

The electric field E can now be found using (3-15) or (3-10) with J = 0

Remember, we have only Hφ. This results in Er, Eθ

Similarly, we have only Ar, Aθ. This results in Er, Eθ

October 2023 19-203-0702 Antennas and Propagation : Module 2 11
 Lecture 6

The field components from an infinitesimal dipole (l << λ) along the z axis

Er

Eθ

Hφ

October 2023 19-203-0702 Antennas and Propagation : Module 2 12

 Lecture 6

The field components from an infinitesimal dipole (l << λ) along the z axis

October 2023 19-203-0702 Antennas and Propagation : Module 2 13

 Lecture 6
Power Density The complex Poynting vector

Since Wθ is purely imaginary, it will not contribute to any real radiated power.
However, it does contribute to the imaginary (reactive) power
October 2023 19-203-0702 Antennas and Propagation : Module 2 14
 Lecture 6

The Power radiated from an infinitesimal dipole

The transverse component Wθ of the power density does not contribute to the integral

October 2023 19-203-0702 Antennas and Propagation : Module 2 15

 Lecture 6

Reactive Power Density

Wθ (4-12b)along with the second term of (4-14) can be used to determine the total
reactive power of the antenna.

The reactive power density, which is most dominant for small values of kr, has both radial
and transverse components.

It merely changes between outward and inward directions to form a standing wave at a
rate of twice per cycle.
October 2023 19-203-0702 Antennas and Propagation : Module 2 16
 Lecture 6

Power radiated and the Radiation Resistance of an infinitesimal dipole

(η = 120π )

October 2023 19-203-0702 Antennas and Propagation : Module 2 17

 Lecture 6

True or False?

The reactance of an infinitesimal dipole is capacitive.

Ref:
Balanis
October 2023 19-203-0702 Antennas and Propagation : Module 2 18
 Lecture 6

Wherever there is forward movement there is

bound to be a turbulence

October 2023 19-203-0702 Antennas and Propagation : Module 2 19

 Lecture 6

So far…
Io – A – H - E Er,Eθ,Hφ
Infinitesimal dipole

• Fields
• Power Density
• Radiated Power
• Radiation Resistance

October 2023 19-203-0702 Antennas and Propagation : Module 2 20

 Lecture 6

Field regions around an infinitesimal dipole

K r=1;
(2π/λ).r=1 4.8b
Radian Distance
r= λ/ 2π
K r<1;
(2π/λ).r<1 Near Field
r=<λ/ 2π 4.10a

K r>1;
(2π/λ).r>1 Intermediate Field
r> λ/ 2π
K r>>1; Far Field
(2π/λ).r>>1
r>> λ/ 2π
4.10b
October 2023 19-203-0702 Antennas and Propagation : Module 2 21
 Lecture 6

Field Regions surrounding an antenna

October 2023 19-203-0702 Antennas and Propagation : Module 2 22

 Lecture 6

Field regions around an infinitesimal dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 23

The field terms Lecture 6

1/r 1/r2
1/r Radiation Term Inverse Distance Term
(contributes to the flow 4.8b
of energy away from the Predominant far away
source) from the antenna

1/r2 1/r3
1/r2 Induction Field Term Predominant very close to
(contributes to the the antenna 4.10a
energy that is stored in
the field during one
quarter of a cycle and
returned to the circuit 1/r 1/r2 1/r3
during the next)

1/r3 Electrostatic Field Term Similar to an electrostatic

dipole 4.10b
Ref:Jordan and Balmein
Electromagnetic Waves and Radiating Systems
October 2023 19-203-0702 Antennas and Propagation : Module 2 24
 Lecture 6

Near Field Region The Last term within bracket dominates

K r<<1; (2π/λ).r<<1; r<<λ/ 2π

4.8b

4.10a

4.10b
October 2023 19-203-0702 Antennas and Propagation : Module 2 25
 Er and Eθ , are in time-phase Lecture 6
Near Field Region
K r<<1 but they are in time-phase quadrature with Hφ;

there is no time-average power flow associated with them

October 2023 19-203-0702 Antennas and Propagation : Module 2 26

 Lecture 6

Properties of the Near Field Region (K r<<1)

Electric Fields are similar to that of a

static electric dipole(1/r3) terms

Magnetic Field is similar to that of a

static current element

quasi-stationary fields

the energy in this region is basically imaginary

(stored)

October 2023 19-203-0702 Antennas and Propagation : Module 2 27

 Lecture 6

Intermediate Field Region The first term within bracket dominates

K r>1; (2π/λ).r>1; r> λ/ 2π

4.8b
4.23d

4.10a
4.23a

4.23b

4.10b
October 2023 19-203-0702 Antennas and Propagation : Module 2 28
Properties of the Intermediate Field Region Lecture 6

4.23d Er and Eθ lose their in phase nature and

approach time quadrature

But, Eθ and Hφ components approach time-

4.23a
phase

This is an indication of the formation of time-

4.23b average power flow in the outward (radial)
direction (radiation phenomenon)

October 2023 19-203-0702 Antennas and Propagation : Module 2 29

 Lecture 6
Far Field Region
The first term within bracket of Eθ,Hφ dominates
K r>>1; (2π/λ).r>>1; r>> λ/ 2π Er approximated to 0
1/r 1/r2

4.8b

1/r2 1/r3

X 4.10a

1/r 1/r2 1/r3

4.10b
October 2023 19-203-0702 Antennas and Propagation : Module 2 30
 Lecture 6

Kr
For Kr>>1, the terms
containing 1/(kr)2 and 1/(kr)3
decay much faster than 1/(kr)

Therefore at large distances

from the Hertzian Dipole only
the terms containing 1/r are
retained

October 2023 19-203-0702 Antennas and Propagation : Module 2 31

 Lecture 6

Properties of the Far Field Region (K r>>1)

The E- and H-field components are
perpendicular to each other and
transverse to the radial direction of
propagation

the r variations are separable from those

of θ and φ.

The shape of the pattern is not a function

of the radial distance r

The fields form a TEM wave whose wave

impedance is equal to the intrinsic
Eθ Hφ impedance of the medium.

October 2023 19-203-0702 Antennas and Propagation : Module 2 32

 Lecture 6
Radian Sphere
The radian distance: r = λ/2π (or kr = 1)

The radian sphere: The sphere whose radius is r = λ/2π

Defines the region where the reactive power density > radiated power density

Represents the volume occupied mainly by the stored energy of the Electric and
Magnetic Fields

A reference

Defines the transition between the stored energy pulsating in the θ direction (Wθ)
and energy radiating in the r direction (Wr)
October 2023 19-203-0702 Antennas and Propagation : Module 2 33
 Lecture 6

Problem 4.2 Balanis Homework

October 2023 19-203-0702 Antennas and Propagation : Module 2 34

 Lecture 6

Radiation Intensity (U) of an infinitesimal dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 35

 Lecture 6
Directivity of an infinitesimal
dipole
Θ=0

Maximum Effective Aperture

Θ=90

October 2023 19-203-0702 Antennas and Propagation : Module 2 36

 Lecture 6

Infinitesimal Dipole Home work: Complete the table

?
Far Field
Components
W
P
Rr
U
W
D

October 2023 19-203-0702 Antennas and Propagation : Module 2 37

 Lecture 6

Small Dipole

(λ/50 < l ≤ λ/10)

October 2023 19-203-0702 Antennas and Propagation : Module 2 38

 Lecture 6

Current distribution along a dipole

Infinitesimal Dipole Small Dipole Finite Length Dipole

l <λ/50 λ/50 < l ≤ λ/10 l > λ/10

Constant Current Triangular Current Sinusoidal Current

Distribution Distribution

October 2023 19-203-0702 Antennas and Propagation : Module 2 39

 Lecture 6

Current distribution along a dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 40

 Lecture 6
Current distribution along a dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 41

 Lecture 6

Remember!!!

I– A – H - E Radiation Properties

October 2023 19-203-0702 Antennas and Propagation : Module 2 42

Small Dipole (λ/50 < l ≤ λ/10) Lecture 6

October 2023 19-203-0702 Antennas and Propagation : Module 2 43

 Lecture 6

Vector Potential A for a Small Dipole

Since the potential
function for the
triangular
distribution is one-
half of the
corresponding one
for the constant
(uniform) current
distribution, the
corresponding
fields of the former
are one-half of the
October 2023 19-203-0702 Antennas and Propagation : Module 2
latter. 44
 Lecture 6

Fields from a Small Dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 45

 Lecture 6

Radiation Resistance of a Small Dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 46

 Lecture 6

Directivity of a Small Dipole

Since the directivity of an antenna is

controlled by the relative shape of the

field or power pattern, the directivity,

and maximum effective area of this

antenna are the same as that of an

infinitesimal dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 47

 Lecture 6

To Conclude..

Field regions around an infinitesimal dipole

Radiation Intensity

Directivity

Current Distributions of dipoles of varying lengths

Small Dipole

Fields, Rr, D, Ae

October 2023 19-203-0702 Antennas and Propagation : Module 2 48

 Lecture 6

Next …

Finite Length Dipole ( l >λ/10)

Half Wave Dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 49

 Lecture 7

EC 15-1702
Antennas and Propagation
Acknowledgement:
• Prof. C. A Balanis, Antenna Theory, Analysis and design, John
Wiley student edition, 3/e, (2012), ISBN:978-81-265-2422-8
• ieeexplore.ieee.org
• PhD Theses/Journals
• Other Sources…

Students are requested to refrain from using the learning resources outside this domain

October 2023 19-203-0702 Antennas and Propagation : Module 2 1

 Lecture 7

Module II
Radiation from an infinitesimal dipole
Total power radiated and its radiation resistance.
Radiation from half wave dipole
Radiation fields and its radiation resistance. near field and far field.
Small loop antennas
Ref: Balanis, Chapter 4 “Linear Wire Antennas”
https://nptel.ac.in/courses/117/101/117101056/
Module 7 Antennas/Section 3 Radiation from a Hertz Dipole

Antenna arrays:
Point Sources - arrays of 2 Isotropic Sources and N element point sources, , Principle of
Pattern Multiplication, Uniform Linear Arrays - Broadside Arrays, End fire Arrays

October 2023 19-203-0702 Antennas and Propagation : Module 2 2

 Lecture 7

Course Outcomes

On successful completion of teaching-learning and valuation activities, a

student would be able :

1. To understand basic terminology, parameters and concepts of

Antennas
2. To analyze the electric and magnetic field of various basic antennas
3. To study the performance of Antenna Arrays
4. To acquire knowledge on antenna types as well as their application
5. To understand the propagation of the waves at different frequencies
through different layers of atmosphere

October 2023 19-203-0702 Antennas and Propagation : Module 2 3

Whether You Think You Can,
or
Think You Can't ...
You're Right
-Henry Ford

October 2023 19-203-0702 Antennas and Propagation : Module 2 4

 Infinitesimal Dipole Small Dipole Finite Length Dipole
l ≤ λ/50 (λ/50 < l ≤ λ/10) l > λ/10
Current Distribution Constant Current Triangular Current Sinusoidal
Field Components

Eθ Hφ
Power Density (W)

Radiation Intensity (U)

Directivity (D) Half Wave Dipole

l = λ/2

Radiation Resistance
(Rr)
October 2023 19-203-0702 Antennas and Propagation : Module 2 5
 Lecture 7

Current Distribution and Radiation Patterns

October 2023 19-203-0702 Antennas and Propagation : Module 2 6

 Lecture 7

Finite Length Dipole ( l >λ/10)

The finite dipole antenna is

subdivided into a number of

infinitesimal dipoles of length dz’

October 2023 19-203-0702 Antennas and Propagation : Module 2 7

 Lecture 7

October 2023 19-203-0702 Antennas and Propagation : Module 2 8

 Lecture 7

Finite Length Dipole ( l >λ/10)

October 2023 19-203-0702 Antennas and Propagation : Module 2 9

 Lecture 7

A due to a finite length dipole

October 2023 19-203-0702 Antennas and Propagation : Module 2 10

 Lecture 7

For an infinitesimal dipole of length dz positioned along the z-axis at z’ , the

electric and magnetic field components in the far field are given as

October 2023 19-203-0702 Antennas and Propagation : Module 2 11

 Lecture 7

Array of infinitesimal Dipoles

October 2023 19-203-0702 Antennas and Propagation : Module 2 12

 Lecture 7

Array of infinitesimal Dipoles – Pattern Multiplication

For this antenna, the element factor is equal to the

field of a unit length infinitesimal dipole located at a
reference point (the origin)

In general, the element factor depends on the type of

current and its direction of flow

While the space factor is a function of the current

distribution along the source.

October 2023 19-203-0702 Antennas and Propagation : Module 2 13

 Lecture 7

Summing the total Electric Field due to all the elements

October 2023 19-203-0702 Antennas and Propagation : Module 2 14

 Lecture 7

Eθ

October 2023 19-203-0702 Antennas and Propagation : Module 2 15

 Lecture 7

Hφ

October 2023 19-203-0702 Antennas and Propagation : Module 2 16

 Lecture 7

Power Density (W)

October 2023 19-203-0702 Antennas and Propagation : Module 2 17

 Lecture 7
Radiation Intensity (U)

October 2023 19-203-0702 Antennas and Propagation : Module 2 18

 Lecture 7
Elevation plane amplitude patterns for a thin dipole with sinusoidal current distribution
(l = λ/50, λ/4, λ/2, 3λ/4, λ).

October 2023 19-203-0702 Antennas and Propagation : Module 2 19

 Lecture 7

October 2023 19-203-0702 Antennas and Propagation : Module 2 20

 Lecture 7

Note:
The maximum current for some lengths (l = λ/4, 3λ/4, λ, etc.) does not occur at the input terminals of the antenna

October 2023 19-203-0702 Antennas and Propagation : Module 2 21

 Lecture 7
Radiated Power (P)

October 2023 19-203-0702 Antennas and Propagation : Module 2 22

 Lecture 7
Radiated Power (P)

October 2023 19-203-0702 Antennas and Propagation : Module 2 23

 Lecture 7

Radiation Resistance (Rr)

Rr is a function of l (in wavelengths) when the antenna is radiating

into free-space (η = 120π )
October 2023 19-203-0702 Antennas and Propagation : Module 2 24
 Lecture 7
Directivity (D)

The radiation pattern of a dipole becomes more directional as its

length increases

When the overall length is greater than one wavelength, the

number of lobes increases and the antenna loses its directional
properties.

The directivity is a parameter that is used as a “figure of merit” for

the directional properties of the antenna

October 2023 19-203-0702 Antennas and Propagation : Module 2 25

 Lecture 7
Because the pattern is not a function of φ,
Directivity (D) and Aem

October 2023 19-203-0702 Antennas and Propagation : Module 2 26

 Lecture 7

Input Resistance (Rin)

The input impedance is defined as “the The radiation resistance is referred to
ratio of the voltage to current at a pair the maximum current, which for
of terminals or the ratio of the some lengths (l = λ/4, 3λ/4, λ, etc.)
appropriate components of the does not occur at the input terminals
electric to magnetic fields at a point.” of the antenna (see Figure 4.8).

The real part of the input impedance is To refer the radiation resistance to
defined as the input resistance, which the input terminals of the antenna,
for a lossless antenna reduces to the
radiation resistance, a result of the • First the antenna itself is assumed
radiation of real power to be lossless (RL = 0).

• Then the power at the input

terminals is equated to the power
at the current maximum.
October 2023 19-203-0702 Antennas and Propagation : Module 2 27
 Lecture 7

Input Resistance (Rin)

Where
Rin = radiation resistance at input (feed) terminals
Rr = radiation resistance at current maximum
I0 = current maximum
Iin = current at input terminals

October 2023 19-203-0702 Antennas and Propagation : Module 2 28

 Lecture 7

Dependence of D, Rr and Rin on the dipole length

October 2023 19-203-0702 Antennas and Propagation : Module 2 29

 Lecture 7

Remember!

• Infinitesimal Dipole Constant Current

• Small Dipole Triangular Current

• Finite Length Dipole Sinusoidal Current

October 2023 19-203-0702 Antennas and Propagation : Module 2 30

 Lecture 7
Infinitesimal Dipole Small Dipole Finite Length Dipole
l ≤ λ/50 (λ/50 < l ≤ λ/10) l > λ/10
Current Distribution Constant Current Triangular Current Sinusoidal
Field Components

Eθ Hφ
Power Density (W)

Radiation Intensity (U)

Directivity (D)

Radiation Resistance
(Rr)
October 2023 19-203-0702 Antennas and Propagation : Module 2 31
 Lecture 7

Half Wave Dipole (l =λ/2)

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 Lecture 7

Finite length Dipole (l >λ/10) Half Wave Dipole (l =λ/2)

October 2023 19-203-0702 Antennas and Propagation : Module 2 33

 Lecture 7

Radiated Power (P)

The total power radiated can be obtained as a special case of (4-67), where l=λ/2

Prad = 36.54 I02

So,

Rr = ?

October 2023 19-203-0702 Antennas and Propagation : Module 2 34

 Lecture 7

Directivity (D) and Radiation Resistance (Rr)

D0 = 2.15 dB

In a direction
perpendicular to the
dipole axis, the half
wave dipole will have
an Electric Field
Intensity 2.15 dB
higher than an
isotropic antenna

October 2023 19-203-0702 Antennas and Propagation : Module 2 35

 Lecture 7
Input impedance

The radiation resistance of (4-93) is also the radiation resistance at the input
terminals (input resistance), since the current maximum for a dipole of l = λ/2 occurs
at the input terminals

The imaginary part (reactance) associated with the input impedance of a dipole is a
function of its length; (for l = λ/2, it is equal to j42.5).

To reduce the imaginary part of the input impedance to zero, the antenna is matched
or reduced in length until the reactance vanishes. The latter is most commonly used
in practice for half-wavelength dipoles.

l = 0.47λ to 0.48λ
October 2023 19-203-0702 Antennas and Propagation : Module 2 36
 Lecture 7

October 2023 19-203-0702 Antennas and Propagation : Module 2 37

 Lecture 7

October 2023 19-203-0702 Antennas and Propagation : Module 2 38

 Lecture 7

October 2023 19-203-0702 Antennas and Propagation : Module 2 39

 Lecture 7
https://nptel.ac.in/courses/117/101/117101056/
Module 7 Antennas/Section 8 Monopole and Dipole Antenna
30 minutes onwards

Justify the following statements

1. Most electronic equipments are connected with 50 Ohm cables,

while the antenna connections are made with 75 Ohm cables

2. The radiation pattern of an infinitesimal dipole and a half wave

dipole are qualitatively similar, but quantitatively different

3. The radiation pattern of an antenna can be obtained from the

Fourier transform of the current distribution on the antenna

October 2023 19-203-0702 Antennas and Propagation : Module 2 40

 Lecture 8

EC 15-1702
Antennas and Propagation
Acknowledgement:
• Prof. C. A Balanis, Antenna Theory, Analysis and design, John
Wiley student edition, 3/e, (2012), ISBN:978-81-265-2422-8
• ieeexplore.ieee.org
• PhD Theses/Journals
• Other Sources…

Students are requested to refrain from using the learning resources outside this domain

October 2023 19-203-0702 Antennas and Propagation : Module 2 1

 Lecture 8
Module II

Radiation from an infinitesimal dipole

Total power radiated and its radiation resistance.
Radiation from half wave dipole
Radiation fields and its radiation resistance - near field and far field.
Small loop antennas
Antenna arrays:
Point Sources - arrays of 2 Isotropic Sources and N element point sources, , Principle of
Pattern Multiplication, Uniform Linear Arrays - Broadside Arrays, End fire Arrays

Ref: Balanis, Chapter 5 “Loop Antennas”

October 2023 19-203-0702 Antennas and Propagation : Module 2 2

 Lecture 8

Course Outcomes

On successful completion of teaching-learning and valuation activities, a

student would be able :

1. To understand basic terminology, parameters and concepts of

Antennas
2. To analyze the electric and magnetic field of various basic antennas
3. To study the performance of Antenna Arrays
4. To acquire knowledge on antenna types as well as their application
5. To understand the propagation of the waves at different frequencies
through different layers of atmosphere

October 2023 19-203-0702 Antennas and Propagation : Module 2 3

 Lecture 8

Loop Antenna - Geometries

Can be classified as electrically
small or electrically large

Based on circumference/ perimeter:

Small loop: C< λ/10

Large loop: C ∼ λ

(λ - free space wavelength)

October 2023 19-203-0702 Antennas and Propagation : Module 2 4

 Lecture 8

October 2023 19-203-0702 Antennas and Propagation : Module 2 5

Loop antennas
• Loop antennas with electrically small circumferences or perimeters
have small radiation resistances that are usually smaller than their loss
resistances.
• Thus they are very poor radiators, and they are seldom employed for
transmission in radio communication.
• When they are used in any such application, it is usually in the
receiving mode, such as in portable radios and pagers, where antenna
efficiency is not as important as the signal to-noise ratio.
• They are also used as probes for field measurements and as directional
antennas for radio wave navigation.

October 2023 19-203-0702 Antennas and Propagation : Module 2 6

Radiation resistance of Loop Antennas
The radiation resistance of the loop can be increased, by
increasing its perimeter and/or the number of turns.

Or

Ferrite loop:
To insert, within the circumference or perimeter, a ferrite core of
very high permeability which will raise the magnetic field
intensity and hence the radiation resistance.

October 2023 19-203-0702 Antennas and Propagation : Module 2 7

 Lecture 8

October 2023 19-203-0702 Antennas and Propagation : Module 2 8

 Lecture 8

October 2023 19-203-0702 Antennas and Propagation : Module 2 9

 Lecture 8

A magnetic dipole of magnetic

moment Iml is equivalent to a small
electric loop of radius a and
constant electric current I0
provided that Iml = j ωµI0 S, where S
= πa2 (area of the loop).

Thus, for analysis purposes, the

small electric loop can be replaced
by a small linear magnetic dipole
of constant current

October 2023 19-203-0702 Antennas and Propagation : Module 2 10

 Lecture 8
Duality

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 Lecture 8

Infinitesimal Electric Dipole Duality

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 Lecture 8

Fields – W – P – Rr
W–U-D

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 Lecture 8

Power Density

When (5-22) is integrated over a closed sphere,

only its radial component contributes to the
complex power Pr.

For the small loop it is

inductive

For the infinitesimal dipole the radial

power density in the near field is
capacitive
October 2023 19-203-0702 Antennas and Propagation : Module 2 14
 Lecture 8
Small Loop Infinitesimal Electric Dipole

Even though the radiation resistance of a single-turn loop may be small, the
overall value can be increased by including many turns. This is a very desirable
and practical mechanism that is not available for the infinitesimal dipole.

October 2023 19-203-0702 Antennas and Propagation : Module 2 15

 Lecture 8

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 Lecture 8

Small Loop Near Field Region

(Kr<<1)

Infinitesimal Electric Dipole

The two H-field components are

in time-phase. However, they
are in time quadrature with
those of the electric field.
This indicates that the average
power (real power) is zero, as is
for the infinitesimal electric
dipole
October 2023 19-203-0702 Antennas and Propagation : Module 2 17
 Lecture 8

Small Loop Infinitesimal Electric Dipole

As for the infinitesimal dipole, the E and H-field components of the loop in the far-field
(kr >> 1) region are perpendicular to each other and transverse to the direction of
propagation. They form a Transverse Electro Magnetic (TEM) field whose wave
impedance is equal to the intrinsic impedance of the medium
October 2023 19-203-0702 Antennas and Propagation : Module 2 18
 Lecture 8

Radiation Intensity

The normalized pattern of the

loop is identical to that of the
infinitesimal dipole
October 2023 19-203-0702 Antennas and Propagation : Module 2 19
 Lecture 8

Directivity
It is observed that the directivity,
and as a result, the maximum
effective area, of a small loop is
the same as that of an
infinitesimal electric dipole.

This should be expected since

their patterns are identical.

October 2023 19-203-0702 Antennas and Propagation : Module 2 20

 Lecture 8

October 2023 19-203-0702 Antennas and Propagation : Module 2 21

Summary

• Electric Loop with axis along z axis is equivalent to a .................... dipole oriented along z axis
• Fields of Magnetic Dipole can be obtained from those of an electric dipole by applying ..................
• The dominant field components in an infinitesimal dipole are Eθ and Hφ, whereas in a loop
antenna they are …………………...
• The radial power density in the near field of an infinitesimal dipole is capacitive, while in a loop
antenna it is ……………………….
• Increasing the number of turns of the loop improves Rr, but also increases …………………..
• The patterns are similar to that of an ……………………….placed along the loop axis.
• ………………. Loops have improved Rr.
• Important applications of Loop antennas are in ……………………………………………

October 2023 19-203-0702 Antennas and Propagation : Module 2 22

Summary

• Electric Loop with axis along z axis is equivalent to a Magnetic dipole oriented along z axis
• Fields of Magnetic Dipole can be obtained from those of an electric dipole by applying Duality
• The dominant field components in an infinitesimal dipole are Eθ and Hφ, whereas in a loop
antenna they are Eφ and Hθ.
• The radial power density in the near field of an infinitesimal dipole is capacitive, while in a loop
antenna it is inductive.
• Increasing the number of turns of the loop improves Rr, but also increases Loss Resistance.
• The patterns are similar to that of an electric dipole placed along the loop axis.
• Ferrite Loops have improved Rr.
• Important applications of Loop antennas are in Measurement Probes/Direction Finding…

October 2023 19-203-0702 Antennas and Propagation : Module 2 23