2011
Lectures for Antennas I
1. Short dipole antenna
2. Far-field approximation
3. Antenna radiation characteristics: Pattern,
dimensions, directivity, gain, and resistance
An antenna is a device that transducer a guided wave into an
unbounded medium or vice versa. Antennas are made in various
shapes and size and used in radio, V, communication, cell phone,
radar, etc, etc. Here are the summary of some fundament terms and
properties of antenna.
 Reciprocity: Most of linear antenna are reciprocal, meaning that
antennas exhibiting the same radiation pattern for transmission as
for reception.
 Polarization: antenna polarization describes the direction of E- or
H- radiations fields.
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2011
 Antenna impedance: pertains to the transfer of power from a
generator to the antenna when the antenna is used as transmitter
and, conversely, the transfer of power from the antenna to a load.
When the antenna is used as a receiver.
 Radiation sources:
Radiation sources include current source and aperture fields.
1. Short Dipole Antenna
The simplest the antenna will be a short-dipole antenna or Hertzian
dipole antenna. The following figure show a short-dipole antenna
was fed by a T-line.
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The short referred here means the length of dipole (l<< , roughly
l</50) so we can consider the AC current magnitude I0 on dipole is
uniform constant and does not change across the length of the
dipole. If the antenna is oriented to z-axis, and we supply an AC
current to the dipole,
it   I 0 cos t  I 0 e jt
The current density on the line will be:
 I

J  0 e jt a z
s
If we recalled what we learned from EE1259, (notes provided again),
the vector potential A for the EM field is:


Ar ,    0
4

0
J  e  jkr '
dv
'

v' r '
4

Ia z  jkr '
v' sr ' e dsdz
If we observes the EM wave a few wavelength distance away, since
the dipole length is super short, we can say
r  r’
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Now, the vector potential can be analytically evaluated as:

 0  l / 2 I  jkr
 0 I 0 l e  jkr 
Ar ,   
az
e dz 
az
4 l / 2 r
4
r
In spherical coordinate system, the antenna characteristics can be
described (r,, ) referred as the range, zenith angle, and azimuth
angle respectively. The only thing we have to do to convert the
above vector potential is to change unit vector az to unit vectors in
spherical coordinate.



a z  a r cos  a sin 

 0 I 0 l  e  jkr



Ar ,    a r cos  a sin  
4  r




 0 I 0 l  e  jkr 

 cos
Ar 
4  r 
 I l  e  jkr 
 sin 
A   0 0 
4  r 
A  0
Having vector potential, it is straightforward to evaluate E and H
field.


1
H   
 A

E   
Then we obtain
4
0
1
j 0

 H
2011
 j
I 0 lk 2  jkr
1 
H    
e
sin   
2
4
 kr kr  
 1
2 I lk 2
j 
E r    0  0 e  jkr cos 


2
4
kr 3 
 kr 
 j
I 0 lk 2
1
j 
E   
 0 e  jkr sin   


2
4
kr 3 
 kr kr 
Where 0=(0/0)1/2120 ().
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