Page 209 - Maxwell House

SOLUTION OF BASIC EQUATIONS OF ELECTRODYNAMICS 189

7. Pulling (4.84) inside the integral in (4.71) we obtain the power radiated by the loop

2 2 2
4
) (4.85)
= � � ( 2 4 � ( 2 � ( 2
) ≅ 15 585 �
) ≅ 160 �
Σ 2 0 2 2
3
2
For electrically small loop of ≅ 0.0001 (∆ = 0.01 in (4.83)) the numerical factor in
(4.85) is around 1.6 ⋅ 10 only. Therefore, the small loop antenna is not a very good transmit
−4
or receiving antenna.
According to (4.96), there
are two ways to fix this
problem. We can increase
the loop circumference up
a) b)
to 2 = when /
Figure 4.3.7 a) Coil antenna, b) Ferrite rod antenna = 1/4 or connect the
2
multiple electrically small
loops in series (i.e. coil) as shown in Figure 4.3.7a. Besides, the magnetic field concentration
can be reached by winding the coil around the ferrite rod of high permeability. It is possible to
show that the power in (4.85) is roughly proportional to ( ) where N is a number of turns
2

in the coil and is the ferrite road relative permeability. The ferrite rod antennas are almost

universally used in portable receivers on the long, medium and short wave bands because of
their compactness. Another application is a miniature antenna in Radio Frequency
Identification (RFID) tags attached to all items that are to be tracked. Unfortunately, the ferrite
rods become practically useless at the frequencies above 20 – 30 MHz since their magnetic
permeability drops very fast beyond this frequency band.

4.3.4 Huygens' Principle and Huygens’ Radiator

In 1678 Dutch physicist Christian Huygens stated that the new wavefront of a propagating wave
at the instant + ∆ conforms to the envelope of spherical wavelets spreading from every point
(see the set of black points in Figure 4.3.8a on the original wavefront (with the understanding
that the wavelets have the same speed as the overall wave). An illustration of this idea, known
as Huygens' Principle, is shown schematically in Figure 4.3.8a.

a) b)
Figure 4.3.8 a) Huygens’ Principle illustration, b) Orthogonal electric and magnetic dipole as
equivalent of wavelet source

Assuming that the original and new wavefront belongs to far-field area each of the secondary
wavelet source can be considered as an infinitesimal patch 1 shown in Figure 4.3.8b. The