On the Antenna Gain Formula - International Journal of Applied ...

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3. Derivation of the new formulas
Method 1: Array antenna gain
Consider a standard array of two rectangular folded antenna side by side as shown in the figure 1. Each element of
circumference C is carrying current I. The far-field electric and magnetic strength of one element of the array in
the horizontal plane are respectively given by (Kraus, 1988; Kraus et al, 2002; Balanis, 2005):
60C
I
-1
E(
)
J1(
C
sin ) , Vm (16)
2r
C
I
-1
H(
)
J1(
C
sin ) , Am (17)
2r
Where,
Circumference of theloop antenna, C
C
,
Wavelength, of the radio wave radiated
is the azimuth angle in the horizontal plane about the vertical plane, and J 1 is the first-order Bessel function
given as:
2
4
C sin C sin C sin
1
1!2!
J
1(
C
sin )
1
.......... , (19)
2
2 2
Here, the Bessel function is approximated to 3 rd term because the dimensions (length and breadth) of the
rectangular loop in this work is less than the wavelength o the radio frequency signal (100 – 650MHz) considered.
As the power exponents increase the corresponding finite term become insignificant.
Let us concentrate on the electric field only. The field intensity E 1 due to the single element 1 of the array can be
expressed as:
E1 E( )
E1
E(
) , (20)
Where, is a dimensionless constant of proportionality.
Based on the principle of pattern multiplication, the total field intensity E T due to the 2 elements in the array can
be expressed as:
1
2!3!
(18)
E T
ET
E1
E2
2E1
, (21)
3
5
60C
sin 1 sin 1 sin
I C
C
C
E T
( )
, (22)
r
2 1!2! 2 2!3! 2
60C
I C
sin 1 3 3sin sin 3
1 5 sin 5
5sin 3
10sin
( )
C
C
,
r 2 16 4 384
16
2 4
6
4 6
6
60I
C 3 10 5
C
C
C
C
C
E T
( )
sin
sin 3 sin 5 ,
2 64 5824
64 5824
r
5824
2 4
6
C 3 10 0.5832 0.063773 0.002725
C
C
a
2
4
6
2 64 5824
4 6
C 5 0.021258 0.001362
C
Let b
, (25)
4
6
64 5824
6
C 0.000272
c
6
5824
(24)
(23)
46