Graphics Programs Reference
In-Depth Information
Rectangular Grid Arrays
C
on
sider the re
ct
angular grid as shown in Fig. 8.20. The dot produ
c
t
, where the vector is the vector to the element in the array and
is the unit vector to the far field observation point, can be broken linearly into
its
x-
and
y-
components. It follows that the electric field components due to the
elements distributed along the x- and y-directions are respectively, given by
NM
×
r
i
•
r
0
r
i
ith
r
0
z
far field
point
θ
φ
y
d
x
d
y
x
Figure 8.20. Rectangular array geometry.
N
∑
I
x
n
e
jn
1
(
)
kd
x
θφ
sin
cos
E
x
θφ
(
,
)
=
(8.54)
n
=
1
N
∑
I
y
m
e
jm
1
(
)
kd
y
θφ
sin
sin
E
y
θφ
(
,
)
=
(8.55)
m
=
1
The total electric field at the far field observation point is then given by
E
θφ
(
,
)
=
E
x
θφ
(
,
)
E
y
θφ
(
,
)
=
(8.56)
N
∑
N
∑
I
y
m
e
jm
1
(
)
kd
y
θφ
sin
sin
I
x
n
e
jn
1
(
)
kd
x
θφ
sin
cos
m
=
1
n
=
1
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