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8/12/2019 Broad Array
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1. Broad Side Array 1: φ=0
N=2-20 and d=
In this section we are going to analyze the variation of number of elements (N)
while fixing the distance (d) between those elements.
MatLab Code:
lam=1/2;
N=input('Number of elements in array=');
d=lam/2;
theta=0:0.01:2*pi;
Bd=(2*pi/lam)*d*cos(theta);
num=sin(N*Bd/2);
den=sin(Bd/2);
F=abs(num./den);
polar(theta,F);
y=['N = ',num2str(N),'; Wavelength = 1/2'];
title(y);
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0.5
1
1.5
2
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210
60
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90
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120
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180 0
N = 2; Wavelength = 1/2
2
4
6
8
30
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60
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90
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120
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150
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180 0
N = 8; Wavelength = 1/2
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5
10
15
30
210
60
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180 0
N = 14; Wavelength = 1/2
5
10
15
20
30
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60
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180 0
N = 20; Wavelength = 1/2
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Conclusion:
The above figures shows the radiation pattern at N=2, 8, 14 and20. From
the above figures we can conclude that as the number of elements N is
increased, decreases and consequently the Directivity increases.
In addition to that the numbers of side lobes are multiplying at the center
of the radiation pattern.
In order to avoid the appearance of grating side lobes in the radiation
pattern d should be ≤
.
The code below shows that we have modified d to be ≤
.
Matlab Code:
lam=1/2;
N=input('Number of elements in array=');
d=lam/4;
theta=0:0.01:2*pi;
Bd=(2*pi/lam)*d*cos(theta);
num=sin(N*Bd/2);
den=sin(Bd/2);
F=abs(num./den);
polar(theta,F);
y=['N = ',num2str(N),'; Wavelength = 1/4'];
title(y);
The simulation will be at N=8 and the figures below show the results.
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The figure on the left shows that when we take d less than the wave length the sidelobes decrease, so as we decrease d the number of lobes decreases.
2
4
6
8
30
210
60
240
90
270
120
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150
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180 0
N = 8; Wavelength = 1/4
2
4
6
8
30
210
60
240
90
270
120
300
150
330
180 0
N = 8; Wavelength = 1/2
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2. Broad Side Array 2:
In this section we have fixed the number of elements N and we vary
.
N=10 and
: 0.1-1.5
N=10;
d=input('Enter the distance between two elements=');
theta=0:0.01:2*pi;
Bd=(2*pi)*d*cos(theta);
num=sin(N*Bd/2);
den=N*sin(pi*d*cos(theta));
F=abs(num./den);
polar(theta,F);
y=['N = 10; Distance =',num2str(d)];
title(y);
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0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
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180 0
N = 10; Distance =0.6
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
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150
330
180 0
N = 10; Distance =0.1
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0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
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150
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180 0
N = 10; Distance =1.5
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
N = 10; Distance =1
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Conclusion:
We can conclude from the above figures that as
increases, number of lobes will
increase and starts to radiate.
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3. End-Fire Array 1: φ=βd
N=2-20 d=
In this section we are going to analyze the variation of the number of elements (N)while fixing the distance between those elements.
MatLab Code:
lam=1/2;
N=input('Number of elements in array=');
d=lam/4;
theta=0:0.01:2*pi;
f=(2*pi/lam)*d*cos(theta)-(2*pi/lam)*d;
num=sin(N*f/2);
den=sin(f/2);
F=abs(num./den);
polar(theta,F);
y=['N = ',num2str(N),'; d = lam/4'];
title(y);
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2
4
6
8
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60
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120
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150
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180 0
N = 8; d = lam/4
0.5
1
1.5
2
30
210
60
240
90
270
120
300
150
330
180 0
N = 2; d = lam/4
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5
10
15
20
30
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60
240
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180 0
N = 20; d = lam/4
5
10
15
30
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60
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180 0
N = 15; d = lam/4
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Conclusion:
The above figures shows the radiation pattern at N=2, 8, 15 and20. From
the above figures we can conclude that as the number of elements N is
increased, decrease and we observe huge amount of side lobes at thecenter.
4. End-Fire Array 2:
In this section we have fixed the number of elements N and we have varied
.
N=10 and
: 0.1-1.5
N=10;
d=input('Enter the distance between two elements=');
theta=0:0.01:2*pi;
f=pi*d*(cos(theta)-1);
num=sin(N*f);
den=N*sin(f);
F=abs(num./den);
polar(theta,F);
y=['N = ',num2str(N),'; d/lam = ',num2str(d)];
title(y);
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0.2
0.4
0.6
0.8
1
30
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60
240
90
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120
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180 0
N = 10; d/lam = 0.1
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
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180 0
N = 10; d/lam = 0.4
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0.2
0.4
0.6
0.8
1
30
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60
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90
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120
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180 0
N = 10; d/lam = 1
0.2
0.4
0.6
0.8
1
30
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60
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90
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120
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180 0
N = 10; d/lam = 0.8
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Conclusion:
It’s clear that when we vary
: between 0.1 and 1.5 there’s unwanted
radiations resulted from the side lobes in unlike when we varied the
number of elements N.
0.2
0.4
0.6
0.8
1
30
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60
240
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120
300
150
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180 0
N = 10; d/lam = 1.5
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