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