>its been around for at least 20 yrs,
Collinear antenna design have been around in many versions since long, much longer then 20 years.
It was patented 1924 by C. S. Franklin, almost 100 years ago. and this antenna type is also known as a Franklin antenna.
>and it has a respectable 5 or 6 db of gain
No it haven't. dB
i maybe. dB is relative to something you not did specify.
What gain you achieve is roughly calculated as it is a number of stacked halfwave dipoles.
Antenna type is mostly either centerfeed or endfeed.
>It is usually embedded in a black plastic radome
What enclosure an antenna is placed within is not an antenna property. Neither color, but yes many plastic tubers contains an antenna of some kind.
An alternative and sometimes better describing name of this antenna type could be co-phasing antenna.
>The coil is not a loading coil,
If it is a coil, it is a coil even if it is placed within an antenna structure and load? No it does not load anything, it adds serial reactance.
The phasing element can be designed in many ways, open or short stub, two coils winded in opposite directions close to each other is common, and the phasing pattern can in many cases be performed at PCB as well as using heavy metal designs.
> its to introduce a time delay.
At antenna-language do we call section between the halfwave elements for phasing element, not timedelay as that is something else.
>You dont get much more gain from more than three sections.
I have no such problems with my antennas and there are a lot of other designs that not have your limitation.
This antenna structure is nothing else then a kind of antenna array and stacking a rather high number of element is possible.
As best is gain increased with 3 dB for each doubling of number of sections as for any similar array, but poor design can of course reduce that number.
In most cases is antenna efficiency reduced for each added section but that is something else then gain.
This is a (Franklin) collinear antenna in 14 sections. Measured gain above 15 dBi. It is top-terminated with a resistor.Your link to Martybugs antenna, is not a working antenna array and whatever it is is it a real poor working co-phased antenna.
You can find descriptions of co-phasing in Balanis ANTENNA THEORY ANALYSIS AND DESIGN but collinear antenna as a defined structure, its theory is described relative simple at page 134 and forward in
Transmission Lines Antennas and Waveguides. The book is first printed 1945 but still relevant and where following design is explained in more detail.