Page 52 - Integrated Wireless Propagation Models

30 C h a p t e r 0 n e

where the permittivity E is the principal component of the dielectric constant £,, <J is the
,
conductivity of the dielectric medium in Siemens per meter, and ')... is the wavelength.
Some typical values of permittivity and conductivity for various common types of
media are shown in the following table:

Medium Permittivity e, Conductivity cr, sjm
Copper 1 5.8 X 107
Seawater 80 4
Rur l ground (Ohio) 14 1Q- 2
a
U r ban ground 3 10-4
Fresh water 80 1Q-3
Turf with short, dry grass 3 5 X 10- 2
Turf with short, wet grass 6 1 X 1Q-i
e
Bar , dry, sandy loam 2 3 X 10- 2
e
Bar , sandy loam saturated with water 24 6 X 10- 1
For ground reflections in a mobile radio environment, the permittivity £, of the
dielectric constant £, is always large, and the angle 8 is always much less than 1 rad for
1
the incident and reflected waves. When the incident wave is vertically polarized, then
Eq. (1.9 1 . 1 . 2) can be applied, as illustrated in Fig. . 9 . 1 . 1 .2(b), with the result that
1
.
.
(1.9 1 . 1 . 4)
When the incident wave E; is horizontally polarized, then Eq. (1.9 1 . 1 . 1 ) can be
.
applied, as illustrated in Fig. . 9.1.1.2(a), with the result that
1
(1. 9 . 1 . 5)
.
1
In both of these cases, the actual value of the dielectric constant £, does not have
a significant effect on the resultant values of a and a . It should be noted that
v
,
Eqs. 1 . 9 . 1 . 1 . 4) and (1 .9. 1 . 1 . 5) are valid only for smooth terrain conditions, where
(
8 << .
1
1
In the analysis of reflections from highly conductive surfaces of buildings and struc­
tures, the imaginary part of the dielectric constant £, is very large, and the following are
true:
a "' -1 8 very small
v
a "' v 1 8 close to (2n + 1) n/2 (1.9 1 . 1 . 6)
.
and a "' -1 either 8 very small or £, very large (1. 9 . 1 . 7)
1
.
,
Again, as in Eqs. (1.9.1. 1 . 4) and (1.9 1 . 1 . 5), the actual value of the dielectric constant
.
)
9
£, does not affect the resultant values of a and a in Eqs. (1.9.1.1.6) and (1. . 1 . 1 .7 .
v
,
When the incident wave E; s vertically polarized (but horizontally with respect to
i
the building walls) and the reflected wave is from a highly conductive surface, as in
Fig. . 9 . 1 . 1 .2(a), then the reflection coefficient a is always approximately equal to -1, as
1
,
)
.
shown in Eq. (1.9 1 . 1 .7 .