Free-Space Propagation Loss - Understanding GPS: Principles and Applications - page 670

PG
PG

PGG
P

Λ=

TT

=

TTR

(C.1)

( )

RR R

Since (C.1) is merely a definition, it could also be defined as the reciprocal of
what is shown. The particular definition was selected so that the numerator is typi-
cally greater than the denominator, making the propagation loss usually a quantity
greater than unity, or positive when expressed in decibels. This corresponds with
common usage (e.g., “a 180-dB propagation loss”).
It is often convenient to perform calculations for a receive antenna having unit
gain ( G R =

1), calculating the received isotropic power (RIP).
The free-space propagation loss model described in this appendix applies when
the transmitting antenna and receiving antenna are located in free space (ideally, a
vacuum) where there are no other nearby conductive objects and no obstructions. In
practice at L-band at least, it is sufficient that the LOS path between transmitter and
receiver is not obstructed, that there are no obstructions even near the LOS path,
and that the transmitter to receiver LOS path is far from conducting surfaces, even
the Earth's surface. If one of these conditions do occur, actual propagation loss may
be much greater than predicted using the free-space model.
Furthermore, the transmitting antenna and receiving antennas must be sepa-
rated by many wavelengths so that they are not within each other's near fields. At
L-band, several meters of separation are adequate for antennas having modest gain.
Detailed criteria for quantifying the conditions under which free-space propaga-
tion applies and ways to predict propagation losses under conditions other than free
space can be found in [1] and are beyond the scope of this appendix. In many cases,
free-space propagation is a good first-order model for L-band propagation from
space to a terrestrial or airborne receiver, from an airborne transmitter to an air-
borne receiver, or from an airborne transmitter to the ground (or for these same
paths with transmitter and receiver exchanged). These situations are clearly of
interest to GNSS.
Consider a transmitter radiating an EIRP of P T G T . As the electromagnetic wave
propagates, its power spreads out in a spherical pattern, so that the same amount of
power remains in a given solid angle measured from the transmit antenna. The PFD,
however, which is the power per unit area in the surface of the sphere, diminishes as
the radius of the sphere increases with increasing distance from the transmitter.
Now assume that the solid angle is small and the radius of the sphere is large
enough that the solid angle can be approximated by a flat patch tangent to the
sphere and thus normal to the LOS between transmit antenna and receiver.
The effective area of an antenna, A , is given by

λ

2

G

A = (C.2)

4 π

c / f is the wavelength, with c the speed of propagation, f is the frequency,
and G is the antenna gain. When the receive antenna gain is G R , the effective area of
the receive antenna is

where λ =