Antenna Radiation Patterns Directivity and Gain.
No physical antenna radiates uniformly in all directions. Rather,
antennas radiate EM waves better in certain directions than
others. In fact, many antennas will not radiate in some directions
at all. A radiation pattern is a plot that shows the relative far field strength of `E (or `H ) versus angular direction (q,Æ) at a fixed distance from the antenna (again, in the far field). It is often a polar plot. We’ll take the Hertzian dipole antenna as an example. From equation (12) in the previous lecture we found in the far field that
The magnitude of this phasor electric field is
What is of interest in an antenna radiation pattern is the variation
of |`E| in q and Æ at a fixed r, which is in the far field of the
antenna. In the case of the Hertzian dipole antenna in (2), this
variation is simply | sinq| :
This radiation pattern indicates a number of characteristics of
this Hertzian dipole antenna:
1. Maximum radiation is at q = 90° . This is called broadside radiation.
2. There is no variation in Æ, as expected.
3. There is no radiation in directions along the ends of the
antenna (q = 0, 180°). Radiation Patterns of Longer Dipole Antennas
The radiation patterns of dipole antennas get far more interesting
as their electrical length increases. We’re only considering the
electrically short Hertzian dipole antenna in this course, but
we’ll show a couple of radiation patterns for two other dipole
antenna lengths without proof.
Dipole antenna radiation patterns stay roughly the same shape
up to lengths ? 0.5 l . The main beam then sharpens for lengths
from ? 0.5 l to 1 l . There is only one beam of radiation for
these lengths. There are no so-called side lobes. (You can
experiment with this yourself by adjusting the dipole antenna
length L in the VisualEM worksheet “Radiation Pattern of a
Dipole Antenna.”)
For lengths longer than 1 l , the radiation patterns change
considerably with the addition of multiple main beams and the
appearance of side lobes:
Beamwidth? E plane, H plane? Directivity and Gain
An important characteristic of an antenna is its ability to focus
radiated power in a given direction in the far field. The directivity D(q ,Æ ) of an antenna is the ratio of the power
density radiated in the (q,Æ) direction at some distance in the far field of the antenna to the power density at this same point if the total power were radiated “isotropically” (i.e., equally in all
directions. Mathematically, directivity is defined as
While there is no such thing as a physical antenna that radiates
equally well in all directions (i.e., isotropically), we use this
artifice as a normalization quantity in the denominator of (3) to
assess the focusing ability of a given antenna. If a total power Prad is radiated isotropically by an antenna, then
the time average power density anywhere on a sphere of radius r
Is
Using (4) in (3) along with the definition of SAV, then (3) Becomes
The gain of an antenna is defined similarly as directivity. In
particular, the gain G(q ,Æ ) of antenna is the ratio of the power density radiated to some point in the far field of an antenna to the total power accepted by the antenna, Pin, when radiated isotropically. Mathematically, antenna gain is defined as
The radiation efficiency er of an antenna is defined as
Using this in (6) and comparing to (5) we find that
G(q,Æ) = er D (q,Æ)
In short, the gain G(q ,Æ ) of antenna includes the effects of losses in the antenna (and other surrounding structures), if
present. The directivity of an antenna is determined solely by the
pattern shape of the antenna.
Example N33.1. Calculate the directivity of a Hertzian dipole
antenna of length ÑL with current az I A. If the antenna is made of steel, is 62” long and 1/8” in diameter, and is operating at 1 MHz, calculate the antenna gain. In the far field of this antenna
Substituting (1) into (9)
The total power radiated by this antenna is found by integrating
this power density over a closed surface, the simplest of which is
an imaginary sphere centered on the dipole antenna:
There fore
Substituting (10) and (11) into the definition of directivity in (3),
and using (4) gives
Consequently,
The maximum directivity, D, occurs for this antenna when
q = 90º at which
To calculate the gain of the antenna, we first must compute its
radiation efficiency. The efficiency of this antenna was
computed previously in Example N32.1. As we saw in that
example, the equivalent input circuit at the terminals of the
Hertzian dipole antenna is
The total time average power delivered to the input terminals of
this antenna is
while the total radiated time average power is
Substituting (12) and (13) into the definition of radiation
efficiency (7) gives
It was this last equation for er that was used previously in Example N32.1. There it was found that er = 8.95% for this steel antenna.
Using we find that
G(q , Æ) = 0.0895.1.5. sin 2 q = 0.134 sin 2 q
And the maximum gain G occurs for this antenna at q = 90°
Where
G = 0.134 or GdB = 10log10 G = -8.72 dB Conclusion
To conclude, it is important to realize that there is no real “gain”
associate with such antennas. These are made of metal and are
completely passive devices. There is no signal amplification.
The “gain” that has been defined in this lecture refers to the
focusing properties of the antenna beyond that of an isotropic
radiator.
