Antenna

An Antenna is used for transmitting and receiving radio waves.

They are especially designed to transform guided waves into

free-space waves, or vice versa.

This transformation should be done as efficiently as possible

Examples of Antennas
 Antenna Basics
Radiation Pattern: Relative distribution of radiated power as a
function of direction in space

Antennas and wave propagation th edition,

McGraw-Hill.
 Antenna Basics
Main lobe maximum direction

Main lobe

1.0

Half-power point (left) Half-power point (right)

0.5
Half-power beamwidth (HP)

Beamwidth between first nulls (BWFN)

Minor
lobes
 Antenna Basics
Principal E and H plane patterns: It is common practice to show
planar sections of radiation patterns instead of full 3D pattern

E-plane pattern is view of the radiation pattern obtain from a

section containing maximum value of the radiated field and in
which the E field lies in the chosen sectional view

H-plane pattern is the sectional view in which H field lies in the

plane of the section and section is chosen to contain maximum
direction of radiation
 Directivity and Gain
The variation of intensity of radiation with direction in space is described by the directivity
function

The gain function of an antenna is defined in terms of the input power

Pr Pin
dPr d
G , 4 D ,
Pin
Directivity and Gain are the maximum values of the
respective functions
 Radiation Resistance
Equivalent resistance which would dissipate the same power
as radiated by the antenna, when the current through the
resistance is same as that of the antenna terminals.

For a Hertzian dipole

 Effective Height and Aperture
Effective height is particularly useful in determining the open circuit voltage for a receiving antenna

For a recovering antenna, received power is related to incident power density as

G
 Equivalent circuit of TX/RX Antenna

Voltage
source

Antenna equivalent circuit RF front-end

Equivalent circuit

-
Transmitter
Antenna
 Antenna Field Zones

To
infinity
The dividing line of
Far field
is Boundary sphere Or
of antenna region Fraunhofer
R = 2L2/ region

The near field or Fresnel zone is

r<R L
Near field
The far field or Fraunhofer zone Or
is Antenna
Fresnel region

r>R region
 Antenna Basics

E j B
H j D J

E j 0 H k02 E j 0 J
E k02 E j 0 J
The above equation need to be solved to find E for a given J
 Antenna Basics

Alternatively, since =0 we can write

=
Therefore,
=0
Hence we can write, =
= =
2
A k02 A 0 J A j 0 0
 Antenna Basics
Lorentz condition

A j 0 0 0

2
A k 02 A 0 J
1
H A
0

A
E j A
j 0 0
Radiation from a short filamentary current element

2
k02 Az 0 Jz Z

In the source free region

r
1 2 Az
r k02 Az 0
r2 r r
Y
jk0 r
e
Az C
r
X

jk0 r
e
A 0 Idl az
r
 Radiation from a short filamentary current element

0Idl jk0 r
A e ar cos a sin
4 r

1
Solving for E and H , and retaining the terms varying as
r
the radiated field components can be written as:
e jk0 r
E j 0 Idlk0 sin a
4 r
e jk0 r
H jIdlk0 sin a
4 r
 Radiation Pattern: Dipole

0 0
E-plane 30 330 30 330
H-plane

Z 60 300 60 300

Z
1 1 0.8
0.8 0.6 0.6
0.4 0.2 0.4 0.2
90 270 90 270

Y
120 240 120 240

X
150 210 150 210
180 180

(a) Dipole antenna model (b) Dipole 3D radiation pattern (c)E-plane (d) H-plane
 Radiation from a short filamentary current element
Complex Poyinting vector
1 * * 2 2 2 ar
E H II 0 dl k0 sin
2 32 2 r 2
2
dPr 1 2 * * 2 2 sin
r Re E H ar II 0 dl k0
d 2 32 2
* 2 2 * 2
II 0 dl k 0
2
2 II 0 k0 dl
Pr sin sin d d
32 2 0 0 12
D , 1.5sin 2
2
1 2 2 dl
I Rr Pr Rr 80
2 0
 The Equivalence Principle

Zero
Sources field
S
S

Zero
Zero
field
Sources field
Electric Magnetic
S conductor conductor
S S
(a) (b) (c)

(a) Original problem (b) magnetic current backed by an electric conductor; (c)
electric current backed by a magnetic conductor.
Radiation Field Computation from Current sources
To distant
Field point
Z
Source

Geometry for evaluation of radiated field

In the radiation zone
and

Partial H-field due to J

Partial E-field due to M

The total Held is the sum of these partial fields,