Antenna Characteristics
The directivity D of an antenna may be defined as the ratio
of the antenna's maximum radiation density to the radiation density of the same
radiated power Prad radiated
isotropically.[1]
Expressed mathematically,
where
-
D = antenna directivity, numeric,
-
Pd, max = maximum radiation
density, in any direction, W/m2
-
r = radial distance from the antenna
to the observation point, m
-
Prad = total power radiated
by the antenna, W
Because of the scattering of radio waves that occurs due to their
interaction with the environment, the direction in which maximum radiation
density occurs is usually not of great interest in wireless sensor network
design, especially if the network is to be used indoors. Exceptions to this are
some outdoor applications that more closely approximate free-space propagation
conditions (i.e., those with little or no scattering of the incoming wave),
which can choose to take advantage of this fact by employing antenna directivity
to increase range. Instead of directivity, often the parameter of most interest
to the network node designer is antenna efficiency.
The efficiency of an antenna may be defined as
where
-
η = antenna efficiency (a numeric
fraction)
-
Paccept = power accepted by
the antenna from the source, W
The antenna efficiency η considers only
power accepted by the antenna from the source. For maximum power transfer from
transmitter to antenna, however, the impedance of the antenna must be
correct.[2] The result of
any impedance mismatch may be characterized by[3]
where
-
M = mismatch factor (a numeric
fraction)
-
Pavail = power available
from the source
-
s11 = s-parameter associated with the input reflection coefficient
at the antenna port
Neglecting any polarization
concerns, the gain G of an antenna then can be defined as
the product of the antenna directivity, its efficiency, and any mismatch
effects:
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