Direct Energy, 2018a

4 ANTENNAS 71
In the second case, this surface area is the fraction of the surface
of the sphere of radius 1 km. At most, this antenna can receive
10 −3
10 −3
4π·(10 3 ) 2
P =20· 10 3 ·
4π · (10 3 2
=1.6 μW. (4.5)
)
From this example, we can already see some of the advantages and challenges
in using electromagnetic waves for communication, and we can see
some of the consequences of antenna design. The transmitted power in this
example is orders of magnitude larger than the received power. In such a
situation, the transmitting circuitry and receiving circuitry will look very
dierent due to the amount of power and current expected during operation.
The antennas used will likely also look very dierent. An antenna
transmitting kilowatts of power may need to be mounted on a tower while
a receiving antenna that receives milliwatts of power may be built into a
portable hand held device.
A typical radio station may want to transmit throughout a city, a radius
much larger than 1 km. Furthermore, no energy conversion device is 100%
ecient. The electrical power at the receiver 1 m away is therefore going to
be less than 1.6 W, and the power at the receiver 1 km away is going to be
less than 1.6 μW. Also, all radio receivers are limited by noise. Suppose, for
example, that this transmitter is placed at the center of a city of radius 1
km and the receiver can only successfully receive signals with power above
1 μW due to 1 μW of background noise. A receiver placed 1 km away at
the edge of the city may be able to receive the signal successfully, while
a receiver further away in the suburbs may not. However, many receivers
placed 1 km away with this surface area of 10 cm 2 could simultaneously
detect the radio signal.
If no building in the city is taller than 10 stories, no receivers are likely
to be found at a height over 30 m, for example, above the surface of the
earth. However, the transmitter in this example radiates power uniformly
in all directions including up. We can design antennas which radiate power
in some directions more than others. If we could focus all power from this
antenna at altitudes below 30 m, the power at a particular receiver may
be larger than we calculated above, so a receiver farther away may be able
to detect the signal. The radiation pattern of an antenna is the spatial
distribution of the power from the antenna. Radiation pattern plots are
discussed further in Sec. 4.4.3.
This example also provides some insights on the safety of working with
antennas. The 10 cm 2 surface area in this example is, to an order of
magnitude, the surface area of a human hand. A typical microwave oven
uses less power than the transmitter in this example. Kilowatts of power