Page 210 - Maxwell House

190 Chapter 4

electrical and magnetic vectors are orthogonal and located on the pitch surface. The
electromagnetic wave propagates outward in the direction of Poynting’s vector S. Can we
imitate such secondary wavelet source combining an electric and magnetic radiator? As it
follows from Figure 4.3.8b, the answer is yes. To illustrate it, let us put on the patch 1 surface
. The magnetic field loops around the dipole and
the vertical electric dipole with current
is directed in the opposite on the dotted surfaces 2 and 3. Now, let us replace the electric dipole

with horizontal magnetic dipole with the current as shown in Figure 4.3.8b and look again
at the magnetic field structure. Evidently, the magnetic dipole creates on the surfaces 2 and 3
in-phase magnetic fields. Therefore, the combination of these two collocated dipoles on the
same patch 1 generates on the surface 3 two magnetic fields in-phase while the same fields
compensate each other on the surface 2. Proceeding the same steps, we can come to conclusion
that the electric fields are in-phase on the surface 3 and deduct on the surface 2. Due to this
effect, the forward radiation ( = 90°) from the surface 3 much exceeds the back radiation ( =
−90°) from the surface 2. If so, the composition of the orthogonal electric and magnetic dipole,
called Huygens’ radiator, radiates the maximal energy in the same direction as the wavelet

Y
Magnetic Dipole

X

Direction of Direction of Z
Minimum Maximum
Received Received
Signal
Signal
a) b)

Figure 4.3.9 Radiation pattern of collocated dipoles a) in E-plane, b) 3D pattern

patch shown in Figure 4.3.8. The far-field electric field created in E-plane by a collocated
electrical and magnetic dipole according to (4.82) is equal to

∆ (−)
( ) = sin
0

2 ∆

� ⇒ = ( ) + ( ) = (1 +
0

∆ (−) 2
( ) = −

2
(−) (4.86)
sin)

Here we assume that = − to suppress entirely the back radiation. We also took into
0
consideration that the electric dipole is be-directional in E-plane (black line in Figure 4.3.9a)
while the orthogonal magnetic dipole is omnidirectional (green line in Figure 4.3.9a) in the
same plane. Evidently, the expression in (4.86) stays unchanged in H-plane since in this plane
the electric dipole is omnidirectional while the orthogonal magnetic dipole is be-directional.
Figure 4.3.9b displays the 3D radiation pattern of these two dipoles that shows the magnitude
of -component (or as you wish) as a function of the spherical coordinates and

according to (4.86).