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5.2.1.4 Loop Antenna Far Field Radiation Pattern … Loop Antenna Far Field Radiation Pattern...
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5.2.1.4 Loop Antenna Far Field Radiation Pattern Canonical Validation Problem The far field pattern for a loop antenna can be useful to validate the ability of a simulation code to correctly find far fields. From [5], the fields for a loop antenna are given in equations 5.2.1.4.1 and 5.2.1.4.2. 0 1 0 1 0 ( sin ) 2 0 ( sin ) 2 r jkr r jkr E E ak I e E J ka r H H akI e H J ka r θ φ φ θ η θ θ − − = = ≈ ≈ = ≈− (5.2.1.4.1) So, 0 1 0 1 ( sin ) 2 ( sin ) 2 ak I J ka r akI J ka r η θ θ ≈ ≈ E H (5.2.1.4.2) Where, k = wave number a = the loop diameter η = free space intrinsic impedance r = distance to observer 1 J = Bessel function of first order 0 I = Current through the loop For these calculations, λ π 2 = k , λ × = Constant a (in terms of wavelength) and r = 1. The radiation intensity is given by ( ) ) sin ( 8 2 1 2 2 2 θ η ωµ ka J a W r U o Ι = = (5.2.1.4.3)
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Transcript of 5.2.1.4 Loop Antenna Far Field Radiation Pattern … Loop Antenna Far Field Radiation Pattern...
5.2.1.4 Loop Antenna Far Field Radiation Pattern Canonical Validation Problem
The far field pattern for a loop antenna can be useful to validate the ability of a simulation code to correctly find far fields. From [5], the fields for a loop antenna are given in equations 5.2.1.4.1 and 5.2.1.4.2.
01
01
0
( sin )2
0
( sin )2
rjkr
r
jkr
E Eak I eE J ka
rH H
akI eH J kar
θ
φ
φ
θ
η θ
θ
−
−
= =
≈
≈ =
≈ −
(5.2.1.4.1)
So,
01
01
( sin )2
( sin )2
ak I J kar
akI J kar
η θ
θ
≈
≈
E
H (5.2.1.4.2)
Where,
k = wave number a = the loop diameter η = free space intrinsic impedance r = distance to observer
1J = Bessel function of first order
0I = Current through the loop
For these calculations,
λπ2=k , λ×= Constant a (in terms of wavelength) and r = 1.
The radiation intensity is given by
( ))sin(
82
1
222 θ
ηωµ
kaJa
WrU oΙ== (5.2.1.4.3)
The loop antenna radiated field pattern is calculated using the above mentioned formulas. An example plot is shown above.
The results are grouped in an excel file “Loop Antenna_Farfield.xls” (consists of five sheets). The first sheet includes some notes about the problem taken from “Antenna Theory” by Balanis. The next three sheets have the calculated data for loop antennas whose radius are 0.1 Lambda, 0.2 Lambda and 0.3 Lambda respectively. The final sheet contains the comparison of the three mentioned cases and plots for radiated field pattern and radiated field intensity. All the data presented are normalized to the peak value.
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180 0
Normalized Radiated field pattern
0.1 Lambda0.2 Lambda0.3 Lambda
