heres a post by jack/freecell from his forum at 292 Radio Shop / FireCommunications Network.......The Export Radio Specialists! .
its pretty cool . he worded it so even someone with limited antenna knowledge (like me) can understand it . i find its also easy to visualize the 1/4 wave ground plane growing into a sigma 4 .
i asked if i could post it around and he said yes as long as i give him credit for his info , which i would have done anyway .
thanks again jack 
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"i have posted this some time ago in The Members Portal, i've decided to
release it here first in the Antenna Group. let me know what you think........
Where the story begins........
when the ground wave field strength of vertical antennas is examined, it is found that if a 1/4
wave antenna has 100 mV. field strength at 1 mile, a 1/2 wave vertical will have about 125 mV.,
a 5/8 wave will have about 140 mV., but a 3/4 wave will have only about 80 mV..
the conditions under which these tests were conducted assume a fixed amount of transmitter power
with all antennas tested matched to the feedline so that Z=50 or R=50, X=0 at the target test
frequency and that all antennas are tested at the same exact feedpoint height.
as the antenna design with regard to wavelength^ is extended from 5/8 wave to 3/4 something not
unexpected occurs. additional lobes appear in the upper elevation plane reducing the amount of
field strength in the major lobe at the lower takeoff angle and the measured ground wave signal
strength is reduced.
(^ electrical, not physical)
and so, conventional antenna theory is confirmed and vindicated not only by the test results
above but given further credibility and affirmation by the many college level engineering texts
that have been written on the subject.
whether or not this was the starting place for the engineers at Avanti when they contemplated
the design of the controversial Avanti Sigma IV is not known but it makes sense that this would
be as good a point as any. herein was the challenge presented to not only defy conventional
theory and design but also in the process to come up with a design that eliminated the formation
of these additional and wasteful high angle lobes while increasing the ground wave gain and at
the same time reducing the sensitivity of the design to objects in the near field which tend to
wreak havoc with feedpoint matching and distort the radiation pattern.
first let's re-establish a few facts so that it's easier to follow along with what lies ahead.
beginning with a basic 1/4 wave ground plane with radials at a 90 degree right angle to the
active radiating element, typical input impedance is roughly 36 ohms at a predetermined height
above earth ground. as the radial elements are lowered towards earth ground the input impedance
rises. conversely, as the radial elements are raised the input impedance is lowered.
as the radials are raised towards the radiating element something else interesting occurs. the
radiating element becomes less sensitive to the influence of surrounding objects and terrain
in the near field, allowing the antenna to be mounted in locations and at heights above ground
that would be extremely deleterious not only to the feedpoint match but also to the radiated
pattern emanating from the radiating element.
as the radials are swept upwards towards the radiating element capacitance between the radials
and the radiating element increases, effectively raising the resonant frequency of the system
or causing the electrical length of both the radials and the radiating element to be shortened.
so, the closer the radials come to the radiating element the more the coupling capacitance
increases, the higher the resonant frequency climbs and the lower the feedpoint impedance drops,
approaching single digits and 0 ohms.
also remember that the gamma match is used to match 50 ohm feedline to loads representing less
than 50 ohms. let's assume at this point that we have raised the radials to the point that the
angle represented at the apex (bottom of the antenna) is such that it approximates a value of
15 degrees. at this point we have gross mismatch, (single digit impedance) a 3/4 wave vertical
element that started out resonant in the middle of the cb band (or whatever) and is now resonant
much further up the band (1/4 radials included) but we have eliminated the sensitivity of the
vertical element to surrounding objects and terrain which provides a distinct operational
advantage, mentioned previously. now we have to match the feedpoint to the feedline and provide
some compensating influence to counter the rise in the resonant frequency of the radiating
element.
as we can see from the above the gamma match is the logical choice for impedance matching and we
can re-resonate both the vertical element and the radials by increasing the physical lengths
until resonance is re-established at the intended operating frequency. we can lengthen the
radials and simultaneously improve the frequency vs. bandwidth attributes AND provide additional
physical support for the radials by simply connecting an aluminum loop that will intersect the
radial ends while extending the physical lengths of each from 89.5" to 107".
with that done we can now direct out attention to re-resonating the vertical element for the
intended operating frequency by providing additional tubing length (inductance) beyond what is
dictated by the standard 3/4 wavelength formula. with that accomplished all that is left is to
implement the gamma match and then adjust these last two variables to match the feedline while
maintaining resonance at the target frequency. this can be the tricky part as the gamma strap,
referred to by SigmaIV enthusiasts as the "Dogbone" also comes into play with these other two
adjustments.
after all of the hard work what you end up with is a full-size modified 3/4 wave vertical that
easily produces twice as much signal as a conventional 3/4 wave @ 80 mV..
as to all of the questions posed by the pundits from the J-Pole camp i have only this to say.
you have no clue what you're talking about. even the most uneducated person can look at these
two designs based on nothing but geometry and determine that they can't be the same antenna
design based on the dissimiliar symmetry alone. what seemingly escapes most of you is the way
that the feedline smoothly transitions into the SigmaIV while closely maintaining the same
basic concentricity (inner conductor to outer conductor diameters) as that of the feedline with
no exceptions as to the size and type of feedline used. this efficiency factor coupled with the
full-size 3/4 wave radiator and revolutionary upswept radial design is why the SigmaIV was ahead
of its time when it was first introduced to the market and lends itself to the design of even
longer antennas (in terms of wavelengths) to produce even higher gain figures without the
restrictions presented by the development of multiple lobes as was the case in the conventional
designs that we were previously limited to."
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now , any thought on if this antenna performs better directly connected to metal mast and earth ground vs. insulating/isolating if from conductive mast and earth ground ?
