ANTENNAS

Current distribution
ANTENNAS
Source
Transmission line
z=0
z=H
H
4. Dipoles
(
I ( z ') = I m sin k ( H − z ' )
Source
)
I (0) = Im sin ( kH )
H
Radiation vector
Z
(
I ( z ') = I m sin k ( H − z ' )
Radiation fields
)
N z = 2I m
H
r
 cos k z H − cos kH 
N = zˆ ∫ I ( z ') e j kz z'dz ' = zˆ 2kI m 

k 2 − k z2


−H
Az =
cos( kH cos θ ) − cos kH
k sin 2 θ
µe
cos( kH cos θ ) − coskH
2Im
4π r
k sin2 θ
Spherical components
Same expression is valid for dipoles oriented along x & y axes by
simply substituting
z→ x
zˆ → xˆ
kz → kx
or
or
or
Aθ = −Az sin θ
Aφ = 0
y
ˆy
H=λ/4
H=λ/2
r
E = − jω Aθ θˆ = jω Az sin θθˆ
r E
H = θ φˆ
η
ky
Typical
current distributions
Typical
current distributions
H=λ/8
kz = k cos θ
− jkr
H=5λ/8
H=3λ/2
H=λ
1
Parameters
Parameters
Effective length
Radiation resistance (at current maximun)
r
r
N θˆ + Nφφˆ
N
cos(kH cos θ ) − cos kH ˆ
lef = rad = θ
= −2
θ
I ( 0)
I ( 0)
k sin kH sin θ
P (θ , φ ) =
2
Eθ
η I m  cos ( kH cosθ ) − cos kH 
=


η
4π 2r 2 
sinθ

2
π 2π
Wt = ∫ ∫ P(θ )r2 sinθ dθ dφ = Im2
0 0
r
λ  1 − cos kH  ˆ
lef = − 
θ
π  sin kH 
Transversal
direction
367.405
π
η
2π
∫
( cos ( kH cosθ ) − coskH )
Radiation resistance at feed
terminals
R (0 ) =
0
0
0.5
1
0
=
Rr
sin 2 kH
1.5
Resonant dipole
Directivity
I ( z ') = I m cos kz '
H=λ/4
P (q ) 4p r 2E 2 (q )
( cos ( kH cos q ) - cos kH )2
=
= 120
Wt
hI m2 Rr
Rr
2
4pr
4
Rr I m2
I 2 (0)
λ
Parameters
0
( 1 - cos kH )2
p
D ( ) = 120
2
Rr
transversal
direction
=
1.5
H
π
D (q ) =
Wt
I 2 (0)
I (0) = I m sin ( kH )
100
0
dθ = Im2 ⋅ Rrad
400
R ( H) 200
r λ
lef = ˆz
π
2
sin θ
0
300
r
l
lef = ˆz
2
2
e− jkr
r
Eθ = j60 Im
4
Radiation Resistance:
3
π

cos  cosθ 
2

sinθ
current
120
150
60
30
0.5
180
73 Ω
90
1
0
0
210


D H ,
π
2


Directivity:
2
1
0
1.64
240
0.5
0.01
1
H
300
270
θ
Maximum Effective Length :
0
330
E-Plane
λ/π
1.5
1.5
Loaded antennas
COMPARATIVE TABLE
Currents
E-Plane
120
150
H=λ/4
90
1
120
270
9θ0
Rr
78º
1.64
73Ω
62º
1.94
180Ω
47º
2.41
199Ω
31º
3.33
105Ω
32º
2.17
99.5Ω
Capacitive load
300
60
1.5
1
0.5
0
150
180
D
0
330
240
Beam
width
30
0
210
H=3 λ/8
3D pattern
60
0.5
180
30
0
210
330
240
300
29700
120 θ
60
2
150
H=λ/2
30
1
180
0
0
210
150
H=5 λ/8
330
240 90
120 270
1 .θ5
1
0.5
180
300
60
0
210
330
240
120
H=3 λ/4
270
θ90
300
60
1
150
Equivalent network
30
0
Source
30
Z0
Za
Trans. line
Antenna
Zc
0.5
180
0
0
210
330
240
300
270
Load
90
120
60
2
H=λ
150
30
1
180
0
0
210
330
240
27º
2.52
260Ω
300
270
Load
2
Loaded antennas
Inductive load
Equivalent network
Zc
Source
Z0
Za
Trans. linel
Antenna
Za
Load
Load
3