ELEG3301 2015-2016 Second Term Assignment 2

ELEG3301 2015-2016 Second Term
Assignment 2
1155047511
Li Man Hin
3 × 108
= 0.1224 m
2.45 × 109
Prad = 1 W = 30 dBm
5
θ = arctan
= 26.565◦
10
2
π

sin θ
cos
2
 = 2.3884
GT = 2 × 1.64 × 
cos θ
1. λ =
PR = Prad GT GR
λ
4πr
2
= 1.8142 × 10−6 W = −27.4 dBm
2. r = 3 × 108 × 60 × 60 = 1.08 × 1012 m
3 × 108
= 0.1 m
λ=
3 × 109
PT = 20 W
GT = 10 dB = 10
2
πd
GR =
λ
Pr,min = −160 dBm = 1 × 10−19 W
2
2
πd
λ
⇒ GR =
= 9.21 × 106 ⇒ d = 96.5 m
Pr,min = PT GT GR
4πr
λ
3. d = 0.75λ
d
∴ Dn (θ) = sin 2π cos θ = sin2 (1.5π cos θ)
λ
2
When Dn (θ) = 0,
1.5π cos θ = −π, 0, π
2
cos θ = 0, ±
3
◦
θ = ±90 , ±48.19◦
For peaks, Dn0 (θ) = −1.5π sin(1.5π cos θ) cos(1.5π cos θ) sin θ = 0
sin(3π cos θ) = 0 or sin θ = 0
3π cos θ = −π, 0, π or θ = 0
1
θ = 0, ± ⇒ θ = ±90◦ (rej), 70.529◦
3
1
θ
−90◦
Dn (θ)
0
−70.529◦
1
−48.19◦
0
0◦
1
48.19◦
0
4. (a) f = 2.45 GHz ⇒ λ0 = 0.1224 m
λ0
λ0
λg = √ =
r
2
λ0
0.1224
L = √ = √ = 0.0306 m = 3.06 cm
2 r
2 4
0.4λg ≤ W ≤ 0.8λg ⇒ 2.45 cm ≤ W ≤ 4.90 cm
2
70.529◦
1
90◦
0
(b) Patch Antenna Dimensions
6dB Bandwidth = 2.465 − 2.420 = 0.045 GHz = 450 MHz
3