Practical_Antenna_Handbook_0071639586

C h a p t e r 3 : A n t e n n a B a s i c s 95
spherical coordinates; that is, it is a circular field whose axis is the same as that
of the rods that form the source antenna.
For a given receiving antenna at a fixed, distant point we can combine all the geometrical
and numerical factors of Eq. (3.19) into a single constant, k, that is valid for that
particular spacing and orientation of the transmit and receive antennas. The resulting
equation is
E
RX
= kITX t−r c
( ) (3.21)
where I TX(t-r/c) is the drive current to the transmit antenna t = r/c seconds prior to the time
at which we measured E RX .
As is true of our globe, a small surface area on a large sphere appears flat. So it is
with radio waves: Although the waves break away from the source and propagate outward
in space, forming an ever-expanding sphere, at any distant receiving site, the
wave appears to be a plane wave.
If we divide Eq. (3.19) by Eq. (3.20), we find that all the terms cancel except for
As it turns out,
E
H
θ
φ
60π = = 120 π
(3.22)
1 2
−7
µ
0
4 10 H/m
2 2
144 10 120 377
ε = π •
= π • = π = Ω
1
0
−9
• 10 F/m
36π
(3.23)
m 0 and e 0 are, of course, the permeability and permittivity of a vacuum—free space, in
other words. The square root of their ratio, or 377 W, is called the impedance of free space.
Interestingly, the vacuum of free space has at least two characteristics (e 0 and m 0 ) and an
impedance (measured in ohms). So the “nothing” of free space isn’t exactly nothing, is
it? Perhaps we should call it the æther . . . .
In the more general case, the E- and H-fields associated with a spherical or plane
TEM wave propagating through an arbitrary medium characterized by m and e are related
by
E
H
θ
φ
= µ ε
(3.24)
The antenna we have just described is known as a hertzian dipole because it is very
short compared to the wavelength of the signal applied to it—exactly the situation with
Heinrich Hertz’s laboratory setup of 1887. The shape of this antenna’s E-field pattern is
totally described by the sinq term; it is doughnut-shaped in a three-dimensional view,
and a figure eight when viewed in two dimensions with the axis of the dipole lying in
the plane of observation. Compared to an isotropic radiator, which is totally fictitious
but which—if it did exist—would radiate equally in all directions, the directivity of this