Page 208 - Maxwell House

188 Chapter 4

= −2 ∆ [(m/m) ⋅ Ω ⋅ A = V]
0
� (4.83)
∆ = �
Formally, the equivalent magnetic current magnitude is frequency dependable, but it does not
change the main result: at each frequency the structure of electric and magnetic fields created
by the electrically small loop antenna and magnetic dipole are identical.

The following from this statement the near-field structure around the loop is displayed in Figure
4.3.5c. These drawings are the replica of the plot in Figure 4.3.1a adjusted through the
replacement ⟹ , ⟹ −. When the currents and dimensions are chosen according to
(4.83), the infinitesimal electric dipole and a small loop antenna are defined as dual sources
since the magnetic field of one is identical to the electric field of the other and vice versa. More
conclusions can be made from this analogy:

1. The total near-field structure consists of
two components of magnetic field , , and

single azimuthal component of electric
field (see Figure 4.3.6 and compare to

Figure 4.3.1b).
2. In far-field area only two orthogonal
components of EM fields are left as Figure
4.3.4b demonstrates, one magnetic and one

electric (compare to 4.3.5c). The radial

component becomes so insignificant that it

can be neglected in far-field area.
Figure 4.3.6 Loop field components in 3. Both non-zero components are
spherical coordinates
tangential to the radiation spherical phase and
magnitude waveform and thus represent the
transverse wave propagating in the radial direction.
4. There is no radiation at all along the z-axis, which would correspond to the radiation
directly overhead the magnetic dipole and loop. The radiation is maximum in XY-plane that
is the horizontal / azimuthal plane. Now any reference plane parallel to XY-plane contains
the electric component only. Therefore, the magnetic dipole and loop is omnidirectional

in the E-plane.
5. The patterns in XZ- or YZ-plane are bi-directional (see (4.82) and Figure 4.3.5) and have a
shape reminiscing the infinity symbol ∞ or lying figure 8. Now any reference plane parallel
to XZ- or YZ-plane and passing through the z-axis contains the magnetic component
only. Therefore, for the magnetic dipole and loop antenna vertical / elevation planes are H-
planes.
6. As expected and according to (4.82) Poynting’s vector of the harmonic wave radiated by
the loop antenna points out the radial direction, satisfies the radiation condition (3.72) and
equals to

2
) (4.84)
1 ∗ ∗ 2 sin 2
= �− � × ( ) = ⁄ = � � 0 (
2

0

0

0
0
2 2 2 2