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Antenna Fundamentals
[ ]
[ ]
[ ] [ ] D D ˆ ˆ
4 R
e e 1 - 1 - P
P
- A e 1 - D
14. A D
SWR- 1
SWR 1
and ˆ 1 ˆ
13 SWR
Z Z
Z -Z
- e e 1 -
e D P
4 U
- G e
- P e P
P
4 U ,
8. G
4 A
and D P
4 U
7. D
P
4 U ,
6.D
5.PLF ˆ ˆ
4.P U( , )sin d d
E E
3.U , r W
E E
2.W aˆ
E
aˆ
E
Hˆ(r, , ) -aˆ
1.E(r, , ) aˆ E aˆ E
2 0t 0r t r
2 2 r
2 cdt cdr t t
r
2 t r
2
0
2 em cd
2
em 0
L 0
L 0
2 t cd
t 0 rad
max 0 t
rad t in
in
g
2
em 0 rad
max 0
rad
g
2 t r
0
2
0
rad
2 2 av
2
2 2 av r
ρ • ρ
π
λ = Γ Γ
ρ • ρ
π
λ = Γ
π
λ
π
π θφ
λ
π
π
π θφ
= ρ • ρ
=∫ ∫ θφ θ θ φ
η
θφ = =
η
η
η
θφ =
θφ = +
ππ
θ φ
θ φ
θ φ
φ θ
θ θ φ φ
Array Theory
[ ( ) ]
[ (^ ) ]
kd sin cos and kd sin sin
sin
N
sin
N
sin
M
sin
M
- PlanarArray:AF
kdcos 2
u
AF a cos 2 n- 1 u
AF a cos 2 n- 1 u
5.NonuniformLinearArray:
(Hansen Woodyardendfirearray)
2 Nkd D 1.
(ordinaryendfirearray)
2 Nkd D
(broadsidearray)
Nkd
- D
N
- Hansen Woodyardendfirearray: - kd
aˆ aˆ sin cos aˆ sin sin aˆ cos
aˆ -aˆ sin aˆ cos
- aˆ aˆ cos aˆ sin
where kdcos and cos aˆ aˆ
sin
N
sin
N
1.AF
x x x y y y
y
y
x
x
M 1
n 1
2M 1 n
M
n 1
2M n
0
0
0
r x y z
x y
x y
N array r
Ψ = θ φ +β Ψ = θ φ + β
= θ
π
π
π
π β= +
= θ φ+ θ φ + θ
= φ + φ
= φ+ φ
Ψ= γ+β γ= •
∑
∑
=
=
φ
ρ
Antenna Synthesis
1. Schelkunoff’s Polynomial
z,z ,z ,........arenull locations
where z e and Ψ kdcosθ β
AF a e a z-z z-z .............. z-z
1 2 3
j Ψ
N
n 1
n 1 2 N- 1
j Ψ n
= (^) ∑ =
2. Fourier Transform Method
SF( ) I (z)e dz
SF e d 2
I(z )
(i) LineSource
j z a
2
2
1
θ = ′ ′
ξ ξ π
ξ′
′
′
′ξ
ζ
ζ
∫
∫
AF( ) a e
whereΨ kdcosθ β
AF e d 2
a
ii) LinearArray
M
m-M
jm m
jm m d
2
1
∑
∫
=
ψ
ψ
ζ
ζ
θ =
Ψ ψ π
3. Woodward Lawson Method
( cos -cos )
Nkd
cos -cos 2
Nkd sin
TotalarrayfactorAF f b
cos -cos 2
Nkd
cos -cos 2
Nkd sin
Foreachsamplef b
(ii)LinearArray
cos -cos 2
k
cos -cos 2
k sin
TotalspacefactorSF s b
cos -cos 2
k
cos -cos 2
k sin
Foreachsamples b
(i)LineSource:
b AF forlineararray
b SF forlinesource
Sampleexcitationco-efficientforeachsample:
NumberofsamplesN 2 M 1
Samplelocation cos m m 0, 1, 2,...............
Sampleseparation
m
m M
m -M
m
M
m -M
m
m
m
m m
m
m M
m -M
m
M
m -M
m
m
m
m m
m d m
m d m
θ θ
θ θ
θ = ∑ = ∑
θ θ
θ θ
θ θ
θ θ
θ = ∑ = ∑
θ θ
θ θ
= θ=θ
= θ=θ
θ = ∆ = ± ±
λ ∆=
= =
Horns
4 .Foroptimumdirectivity a 3 and b 2
a
and p (a a) 4
b
3.p (b b)
- cos and cos
where 0 x - 2
x
- x
- H-sectoralhorn:Phasevariation k x
where 0 y - 2
y
- y
- E-sectoralhorn:Phasevariation k y
1 2 1 1
2
1
h H 1
2
1
e E 1
1 e e 2 h h
h 2 2
2
e 1 1
2
= λρ = λ ρ
ρ = −
ρ = −
ρ =ρ ψ ρ =ρ ψ
⇒ ≤δ ′ ≤ ρ ρ ρ
δ ′ =
= δ ′
⇒ ≤δ ′ ≤ ρ ρ ρ
δ ′ =
= δ ′
Some Standard Integrals
3 c x dx c
- cos
c 2
c 2
sin
c 2
c x e dx c
- cos
c 2
c 2
sin
- e dx c
- sin d
c/ 2
4
2 2
2 jx
c/ 2
2
jx
c/ 2
0
3
^ =
π ∫
α
α
α π
π =
π ∫
α
α
∫ θ θ =
α
α
π
Corner Reflector
- aˆρ =aˆx cosφ+ aˆy sinφ
