Practical_Antenna_Handbook_0071639586

C h a p t e r 2 : r a d i o - W a v e P r o p a g a t i o n 17
distributed over an area (B) that is four times as large as area A. Thus, the power density
falls off according to 1/d 2 , where d is the distance from the source. This is called the inverse
square law.
An advancing wave can experience additional reductions in amplitude when it
passes through matter. In this case, true dissipative attenuation may indeed occur. For
instance, at some very high microwave frequencies there is additional path loss as a
result of the oxygen and water vapor content of the air surrounding our globe. At other
frequencies, losses originating in other materials can be found. These effects are highly
dependent on the relationship of molecular distances to the wavelength of the incident
wave. For many frequencies of interest, the effect is extremely small, and we can pretend
radio waves in our own atmosphere behave almost as though they were in the
vacuum of free space. Many materials, such as wood, that are opaque throughout the
spectrum of visible light are fundamentally transparent at most, if not all, radio frequencies.
Isotropic Sources
In dealing with both antenna theory and radio-wave propagation, a totally fictitious
device called an isotropic source (or isotropic radiator) is sometimes used for the sake of
comparison, and for simpler arithmetic. You will see the isotropic model mentioned several
places in this book. An isotropic source is a very tiny spherical source that radiates
energy equally well in all directions. The radiation pattern is thus a perfect sphere with
the isotropic antenna at the center. Because such a spherical source generates uniform
output in all directions, and its geometry is easily determined mathematically, the signal
intensities at all points can be calculated from basic geometric principles. Just don’t forget:
Despite all its advantages, there is no such thing in real life as an isotropic source!
For the isotropic case, the average power in the extended sphere is
Pt = (2.6)
4π d
P av 2
where P av = average power per unit area on surface of spherical wavefront
P t = total power radiated by source
d = radius of sphere in meters (i.e., distance from radiator to point in
question)
The effective aperture (A e ) of a receiving antenna is a measure of its ability to collect
power from the EM wave and deliver it to the load. Although typically smaller than the
surface area of a real antenna, for the theoretical isotropic case, A e = l 2 /4π. The power
delivered to the load is then the incident power density times the effective collecting
area of the receiving isotropic antenna, or
P = P A
(2.7)
L
By combining Eqs. (2.6) and (2.7), the power delivered to a load at distance d is
given by
av
e
Pl
2
t
L
=
(4π)
2 2
d
P
(2.8)