
Small loop antenna (magnetic dipole)

Dipole antenna generates high radiation
resistance and efficiency
For far field region,
l
l 

cos(
cos

)

cos(
)
I0 e

2
2 a
H j

2 r 
sin 




F ( )
15I 02
P(r ,  ) 
F ( )a r , Pn ( ) 
2
F ( ) max
r
2
where

l

l


cos(
cos

)

cos(
)


2
2
F ( )  

sin 




 j r

Half-wave dipole

2
cos
( cos  )
F ( )
2
Pn ( ) 

F ( ) max
sin 2 
p = 7.658, Dmax = 1.64, Rrad = 73.2 

Image theory is employed to build a
quarter-wave monopole antenna.
4
5


Monopole antenna is excited by a current source
at its base.
Directivity is doubled and radiation resistance is
half of that of dipole antenna.
6



The best operation: ground is highly conductive (or
use counterpoise in case of remote antenna)
Shorter than /4 antenna arises highly capacitive
input impedances, thus efficiency decreases.
Solution: inductive coil or top-hat capacitor
Inductive coil
Top-hat capacitor
7


A group of several antenna elements in various
configurations (straight lines, circles, triangles, etc.)
with proper amplitude and phase relations, main
beam direction can be controlled.
Improvement of the radiation characteristic can
be done over a single-element antenna (broad
beam, low directivity)
8
To simplify,
1.
All antennas are identical.
2.
Current amplitude is the same.
3.
The radiation pattern lies in x-y
plane
Il0  e  j  r
E0  j
sin  a ,
From
4
r
Il0  e j  r

a .
Consider   , E 0  j
4
r
2
9
E tot
I1l0  e j r1
I 2l0  e j  r2
 j
a  j
a
4
r1
4
r2
Let I1 = I0, I2 = I0ej,
since r1 and r2 >> d/2 for far field,
we can assume 1  2  
and r1  r2  r.
10
But the exponential terms cannot be approximated, then
d
r1  r  cos 
2
d
r2  r  cos 
2
E tot
I 0l  e  j  r
 j0
4 r
0  2 I 02l 2
P( r ,  ) 
32 2 r 2
 j2
d
 
2
e
cos(
cos


)  a

2
2 

 

2 d
4cos ( 2 cos   2 )  a r
11
We can write this as
P(r,

2
,  )  F unit Farray ar
Funit = a unit factor or the maximum time-averaged power

density for an individual
element
at

2
Farray = array factor = 4cos2 ( )
2
where    d cos    .
This depends only on distance d and relative current phase, .
We can conclude that the pattern function of an array of
identical elements is described by the product of the element
factor and the array factor.
12
We will simplify assumptions as follows:
1.
The array is linear, evenly spaced along the line.
2.
The array is uniform, driven by the same
magnitude current source with constant phase
difference between adjacent elements.
I1  I0 , I 2  I0e j , I3  I0e j 2 , I 4  I0e j 3 ,...I N  I 0e j ( N 1)
E tot
I 0l  e  j  r
 j0
(1  e j  e j 2  ...  e j ( N 1) )a
4
r
2 N
sin (
)
2
F

array
2

sin ( )
2
(Farray)max = N2
13

Yagiuda (rooftop antenna)
Parasitic elements are indirectly
driven by current induced in them
from the driven element.
14
Consider power transmission relation between
transmitting and receiving antennas where
particular antennas are aligned with same
polarization.
Let Prad1 be Ptotal radiated by antenna 1 have a directivity Dmax1,

Prad 1
P1 (r ,  ,  ) 
Dmax1
2
4 r
Prec 2
Prad 1
 P1 (r ,  ,  ) A2 
Dmax1 A2 .
2
4 r
Prad 2
Dmax 2 A1.
With reciprocal property, Prec1  P2 (r ,  ,  ) A1 
2
4 r
Dmax1 Dmax 2
Therefore, we have

.
A1
A2
15
Each variable is independent of one another, so each
term has to be constant, we found that
Dmax1 Dmax 2 4

 2.
A1
A2

16

Effective area (Ae) is much larger than the physical
cross section.
Prec 2
Ae 2 
P1 (r ,  ,  )

More general expressions
Prad
Prec 
Dt ( ,  ) Ar ( ,  )
2
4 r
We can also write
Prec
  
 Dt ( ,  ) Dr ( ,  ) 
 .
Prad
4

r


2
17
Finally, consider Prad = etPin, Pout = erPrec, and Gt = etDt,
Gr = erDr
Pout
  
 Gt ( ,  )Gr ( ,  ) 
.

Pin
 4 r 
2
Friis transmission equation
Note: Assume
- matched impedance condition between the
transmitter circuitry/antenna and receiver
- antenna polarizations are the same.
18

Additional impedance matching network improves
receiver performances

Zin  Zant
Voc2
Voc2
Prec 

2( Z ant  Zin ) 4 Rrad
19

Since the receiver is matched, half the received
power is dissipated in the load, therefore
VL2
1
Prec 
2
2 ZL

Without the matching network,
ZL
VL 
V .
Z L  Z ant oc
20


A monostatic radar system
Some of energy is scattered by target so called
‘the echo signal’ received at the radar antenna.
Let Prad be the radiated power transmitted by the
radar antenna, then the radiated power density P1(r,
, ) at the target at the distance r away is
Prad 1
P1 (r , ,  ) 
D( ,  )
2
4 r
The power scattered by the target is then
Prad 2   s P1 (r, ,  )
s = radar cross section (m2)
This scattered power results in a radiated power
density at the radar antenna of
P2 (r , ,  ) 
Then
Prad 2
Prad 1


D( ,  )
s
2
2 2
4 r
(4 r )
Prec1  P2 (r, ,  ) Ae .
By manipulation of these equations, we have
Prec1
 s 2
2

D
(

,

)
Prad 1  4 3 r 4
or
Prec1
s
2

A
e.
4 2
Prad 1 4 r 

Radiation patterns for dipole antenna
http://www.amanogawa.com/archive/DipoleAnt/DipoleAnt-2.html
Ex1 Suppose a 0.5 dipole transmitting antenna’s
power source is 12-V amplitude voltage in series with a
25  source resistance as shown. What is the total
power radiated from the antenna with and without an
insertion of a matching network?
0.5