[Antennas] Re: gain and directivity

[Barry L. Ornitz]

Ed Yeary, W4TEY, in nearby Harrogate, TN (I live in 
Kingsport), asked about gain and directivity of vertical 
base station antennas:

> I recently got into a discussion over the local 2 meter 
> repeater. Some older hams and some brand new ones were 
> talking about j-poles and gain and directivity as well as 
> directivity in vertical base station antennas. The 
> nearest I can figure is that no one agrees. 

Forgive my laughter here as this is one of the most concise 
and accurate statements I have read about hams and 
antennas!    :-)     I have learned that age or on-the-air 
activity has no relationship to understanding antennas.  
Fortunately you have come to a good place to learn.

> My take was that the j-pole supposedly exhibits about 2.5 
> to 3.0 gain and may be somewhat directional. I have 
> personally experienced quite a bit of directivity in my 
> vertical antennas at home.  They are, of course, 
> advertised as being omni-directional. Apparently a lot of 
> factors such as nearby objects and grounding affect 
> this. I know a lot of this stuff is based on theoretical 
> antennas in free space  but it sure makes for good 
> repeater fodder to listen to. 

To start, gain is a meaningless concept unless you have a 
reference to compare to.  Antenna gain is always expressed 
as a ratio such as the gain with respect to a dipole, or 
gain with respect to an isotropic radiator (a convenient 
mathematical concept that does not exist in reality - an 
isotropic radiator radiates equally well in all 
directions).  Antenna manufacturers are especially good at 
hiding the information about what reference is used so they 
can inflate the gain.  For example the brand-X antenna 
claims 30 dB gain, but the fine print says the reference 
antenna is a spaghetti noodle soaked in salty water!

A J-pole is a dipole with a unique impedance matching 
system.  But as an antenna it is a simple half-wave 
dipole.  It has no gain over a dipole as it is a dipole.  
But all dipoles, in their favored direction, have a little 
over 2 dB gain over an isotropic antenna.  Likewise a 
ground plane antenna, which is a quarter wave vertical 
antenna over a ground plane, has a 3 dB loss with respect 
to a dipole.  In a real ground plane antenna, the radials 
are an imperfect ground plane; likewise drooping radials 
produce some vertical component of radiation below the feed 
point.  These combine to reduce the loss slightly and to 
distort their pattern from a theoretical one.  The result 
is that your J-pole may present anywhere from approximately 
1.5 to 2.5 dB gain over a real ground plane antenna.

Directivity is another concept that requires additional 
knowledge.  It can be expressed in many ways.  Again you 
have to provide some additional information.  Typically you 
might define directivity in terms of beamwidth and some 
relationship of radiated power.  For example, a good Yagi-
Uda antenna might have a beamwidth of 15 degrees in the 
horizontal plane as defined to where the radiated power has 
dropped 3 dB.  Thus if you pointed this antenna directly at 
a distant station, and then turned the antenna 7.5 degrees 
away from the station in either direction, the distant 
observer would see your signal level drop 3 dB.

But note that I said "in the horizontal plane" above.  
Antenna patterns are three dimensional so directivity must 
be expressed always noting in which direction the 
measurement is made.  

As you are probably aware, a dipole antenna has a radiation 
pattern in free space that is toroidal (doughnut shaped).  
Assuming the dipole is horizontal, the radiation pattern 
measured in the horizontal direction is shaped like a 
figure-8 normal to the dipole itself.  This means that the 
dipole radiates little off its ends, and that most of the 
signal is radiated perpendicular to the physical dipole.

Now turn the dipole to the vertical direction.  Measured in 
the horizontal plane the pattern shows the same radiation 
in all directions.  So you can describe the horizontal 
pattern as omni-directional.  But wait, what about the 
vertical pattern?  It is the figure-8 pattern again.  Most 
of the energy is radiated horizontally with little or none 
straight above or below (again this is free space).

The antenna patterns become more complex when the antenna 
is located over ground rather than free space.  Essentially 
a perfect ground acts as a reflector or mirror.  Any signal 
from the antenna hitting the ground is reflected (angle of 
incidence is the angle of reflection).  So at any given 
distant point, you will receive signals both directly from 
the antenna and signals reflected from the ground.  Since 
the paths of these signals are of different lengths, the 
signals arriving at a distant point may have different 
phases from each other.  The result is that the signals 
add either constructively or destructively to produce the 
signal at the receiving point.  If you do the calculations 
for a large number of points, you will generate the actual 
radiation pattern of the antenna.  What was once a nice 
simple pattern suddenly becomes one with multiple lobes.

Of course, real ground is different than an ideal ground; 
it has losses and it may be far from flat.  Nearby objects 
to the antenna create their own absorption and reflections 
distorting the antenna patterns too.  So you are exactly 
right in your statement above.  The pattern of a real 
antenna can be quite different from that of a theoretical 
antenna.

I believe the horizontal directivity aberrations you note 
are due to such things as nearby objects and how the 
antenna is mounted (*).  Even how the feedline attaches to 
the antenna can distort that pattern if radiation occurs 
from the feedline (this effect is common in J-poles).  In 
the real ground planes I mentioned earlier, the horizontal 
pattern is distorted by the radials with more radiation 
along the directions of the radials.  To improve the omni-
directional characteristics, you need LOTS of radials.

A different issue comes up, however, when talking about the 
vertical radiation pattern of a vertical antenna.  Even if 
the antenna produces an omni-directional pattern in the 
horizontal plane, the vertical pattern is important.  Note 
that earlier I mentioned both gain and directivity.  They 
are intimately tied into each other.  The only way to 
achieve gain in one direction is to lose gain in another.  
This is an important concept and understanding it will make 
learning about antennas far easier.

To achieve omni-directional horizontal gain from a vertical 
antenna, you must compress the vertical pattern of the 
antenna to make it radiate more of its signal in the 
horizontal direction.  The ideal ground-plane antenna or 
vertical dipole radiates a considerable portion of its 
energy above the horizon.  If you can direct more of this 
energy toward the horizon, you effectively have more gain.  
To do this, various methods are used.  For a simple ground 
plane, you can lengthen the vertical radiator to 5/8 
wavelength.  In a dipole the analogy would be a double-
extended Zepp which is 5/4 wavelength long.  Similarly you 
can stack a number vertical dipoles above each other, and 
with proper feed excitation they radiate in phase.  This is 
the Franklin antenna.  Getting the phasing correct is a 
little tricky.  Sometimes stubs are used, perpendicular  
to the antenna (like the stub on a Ringo where the stub is 
just wrapped into a circle), and sometimes special coaxial 
sections are used (like in commercial Stationmaster 
antennas).

I hope this has helped explain things a little.  Discussing 
antennas on the local repeater is certainly fun, but buying 
a copy of the ARRL Antenna Book and carefully reading it 
will teach you that many of the things you hear on the air 
are myths and misconceptions.  If you wish to dig even 
deeper into antenna theory, I would suggest "Antennas" by 
John Kraus (W8JK); this is a college text but it is 
extremely well written with clear explanations.  [The 
professor who taught my graduate school class on antennas 
studied under Kraus.  My actual degrees are in chemical 
engineering, and I am probably one of a very few chemical 
engineers to have ever taken antenna courses!]

        73,  Barry L. Ornitz     WA4VZQ     ornitz@tricon.net

(*)  Living in Harrogate, down in the valley, Cumberland 
Mountain likely prevents you from contacting many Kentucky 
repeaters.  I live atop one of the highest ridges in town.  
If I am not careful, I sometimes bring up several repeaters 
at the same time.