2011
Lectures for Antennas I
1. Far-field approximation
2. Antenna radiation characteristics: Pattern,
dimensions, directivity, gain, and resistance
1. Far-field approximation:
Since we are always interested in E and H fields in great distance
while r>>, we can simply the E and H fields by considering:
kr=2r/>>1
so 1/kr>>1/(kr)2, and
jI 0 lk 0  e  jkr

E   
4  r
E  
H  
0

 sin 

V / m
 A / m
2. Antenna radiation characteristics: Pattern, dimensions,
directivity, gain, and resistance
Power Density:
The power density can be expressed by the time-average Poynting
vector.
1
2011



 
1
S ave  Re E  H *
2
  0 k 2 I 02 l 2
S r ,    
2 2
 32 r
S max
 2
 sin   S max sin 2 

15I 02

r2
F  ,   
1
 

2
S r ,  
S max
Total Radiation Power:
2

S r , ,  sin dd  r
 0  0
Prad  r 2 
d  sin dd
2
2
S max  F  ,  d
4
2011
Beam dimensions:
For an antenna with a single main lobe, the pattern solid angle
describes the equivalent width of the main lobe.
 p   F  ,  d
4
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2011
 For an isotropic antenna with F(,)=1, p=4 (sr)
 In practical, the beam width can be also described using halfpower beam width (3-dB width) or null beam width.
Antenna Directivity:
Directivity characterizes the ratio of the antenna’s maximum
radiation intensity to its average intensity.
D
S max Fmax


1
S ave
Fave
4
1
 F  ,  d

4
p
4
Radiation efficiency:
If the total power supplied to the antenna is Pt, a part, Prad, is
radiated out into space, and the remainder, Ploss, is dissipated as heat.
The radiation efficiency  is defined as:

Radiation gain:
4
Prad
Pt
2011
The gain of an antenna has similar definition as the directivity D, but
also account for Ohmic loss.
G
S max
Pt
4r 2
Radiation gain:
The total power supplied to the antenna is Pt and the radiated power
Prad, can also be characterized using impedance concepts as loss
resistance and radiation resistance:
Prad 
1 2
I 0 Rrad
2

5
Prad 
1 2
I 0 Rrad  Rloss 
2
Rrad
Rrad  Rloss