|MadSci Network: Engineering|
Reference John D. Kraus, Antennas, McGraw-Hill, NY, 1950
One of the major parameters used in analyzing the performance of radio frequency (RF)
communications links is the amount of transmitter power directed toward an RF receiver(s)
by the antenna subsystems. This power is derived from a combination of transmitter power
and the ability of the antenna(s) to direct that power toward RF receiver(s).
Today, depending on the frequency, the transmitter power is generated by active
electronic devices including transistors, traveling wave tube amplifiers (TWTA) or
klystrons. The directivity of the antenna is determined by
the antenna design. The product of the transmitter power times the antenna directivity is
called the effective isotropic radiated power (EIRP).
To determine the directivtiy of an antenna we need a reference antenna with which
to compare our antennas performance. Over the years there have been several different
reference antennas used; however, today an isotropic radiator is prefered
as the standard antenna for comparison.
An isotropic antenna transmits equal amounts of power in all directions. A light bulb is a good
example of an isotropic radiator. To increase the directivity of a bulbs light, as in a flash
light or automobile head lamp, we add a reflector (antenna) behind the bulb. At a distance,
in the light beam, the light bulb now appears to be much brighter. The amount that the
bulb appears brighter compared to the bulb with out a reflector is the directivity of the
reflector (antenna). When the directivity is converted to decibels we call it the antenna
gain relative too an isotropic source (dBi).
RF antennas come in many shapes and sizes besides parabolic (dish) reflectors and so we
have to develop a process to determine an antenna’s directivity and gain. To determine the
directivity of an antenna we first determine the number of square degrees about an
isotropic antenna (in a sphere), and we find that it is equal to about 41253 square degrees. If
We measure our actual antenna and find that it concentrates the transmitted power into
4125.3 square degrees, the directivity is determined by dividing the square degrees in an
sphere by the number of square degrees in the actual antenna. In our example the
directivity is 10. If the transmitter power was 100 watts and the directivity is 10 then the
EIRP is 100 x 10 = 1000 watts. This means that the power density (watts per square
meter or watts per square foot) at the receiver is equal to that of an isotropic radiator of
1000 watts. Because engineers like to use power ratios in decibels for RF link analysis, we
convert the directivity (D) to dB and call it antenna gain in dBi (relative to isotropic).
Gain (dBi) = 10 * log 10 (D)
In your question you ask about an antenna with a gain of 3 dBi (note the “i” is generally
omitted in most literature). That means that the directivity was equal to 2 which in turn
means that the antenna concentrates the transmitter power into 41253/2 = 20126.5 square
degrees. At the receiver, a 100 watt transmitter with a 3dBi antenna produces the power density equal to
having a 200 watt transmitter.
The shape of the antenna power distribution can be in any type of 3D geometrical pattern that
we want to use. In your hypothetical 3 dBi antenna we could concentrate the energy around
the equator of the sphere (the horizon on the earth). This is what TV and FM radio
transmitters do. They do not want to transmit wasted power into the space, so they shape
the beams to cover the horizon. The radiation distribution (antenna pattern) would look
like a thin donut with the transmitter at the center. You will often hear an FM station say
that they are transmitting with an effective radiated power (they really mean EIRP) of 100,000
watts, which is the Federal Communications Comission’s EIRP limit for commercial FM stations.
This actually means that the FM station probably has a 10,000 watt transmitter and antenna
an antenna system, usually composed of a vertical array of individual antennas,
with a directivity on the horizon of 10 (10dBi gain).
Antennas can also distribute the transmitter power into two or more different directions
etc. The types of geometrical distribution of transmitter power provided by an
antenna is called the antenna's radiation pattern. The different shapes of radiation
patterns are unlimited and is what keeps antenna engineers busy. In my work with
geostationary earth orbiting satellites (GEO), we shape the spacecraft radiation patterns
to conform to the shape of continents or countries or groups of countries. For
example from GEO the continental USA fills about 8 degrees east-west and 4 degrees
north-south equaling 32 square degrees. Thus we can use antennas with a directivity of D
= 41253/32 = 1289 or Gain = 31.1 dBi. to cover the entire USA. This means that each watt
that we transmit on the spacecraft performs like 1289 watts of transmitter power on the
surface of the earth that we cover. Antenna gain is very important on space craft for
gain reduces transmitter power which in turn reduces prime power (less solar cells needed)
and reduces waste heat (smaller thermal radiators) and weight (mass in orbit).
Receiving antennas also have directivity and gain. An antenna with twice the effective area
of an isotropic antenna will collect twice the amount of power from the passing RF wave.
Each doubling of the effective capture area of an antenna (in square wavelengths)doubles the
amount of power delivered to the receiver amplifiers.
Thus a reciever antenna also can have a directivity of 2 and a gain of 3 dBi(or greater).
It turns out that antennas without active devices embedded in them (which is true for most
practical antennas) have reciprocity. This means that the antennas radiation patterns,
the directivity and the gain are the same regardless if the antenna is used for transmitting
or receiving. Reciprocity is difficult for laypersons to understand; however, it is
easily proved to be true in the referenced textbook.
Best regards, Your Mad Scientist
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