The.MAJOR diminishing returns on more/longer radials. One example from This ARRL doc, on 40m over average soil for a .25 wave length vertical antenna, gong from 9 radials using 125' of wire to 14 radials using 250' of wire gains .42 db, going from 14 radials with 250' of radials to 63 radials with 4000' of radials gains you 1.97 db. Going from 4000' of radials to 8000' gains you another .5 db. On this same example, . From the top to the bottom of this particular chart, 9 radials with 125' of wire to 104 radials with 8000' of wire gains 2.89 db.

The above doc makes some really good reading if your planning to put in an antenna with radials.

Another interesting thing I found is the need to increase radial length as the number of radials is increased. This from a SteppIR vertical instructions sums it pretty well "if more radials are used it is very important to make them longer or you are wasting your efforts."

Your linked article is a little divergent from other research I have seen published and which I have posted here before:

http://www.antennasbyn6lf.com/page/2/

His research showed an optimum length for smaller number of radials at about 20 feet for 40 meters, extending out to a near free space 1/4 wavelength with a large number of radials. His research was done experimentally where the OP's article is a result of simulation.

My own experience is that there does seem to be a resonance at the lengths from N6LF's research, and they have worked very well for me.

I had read some of his before, but I went to your link and read more, most of which I don't understand but to me he seems to be saying for 40m that radials for a 1/4 wave vertical, once you get over 16 at about 5 meters each of so, your getting into a lot of diminishing returns, too. This is from Download QEX sept-oct 2015, Figures 15 and 16 especially.

Tnx for the ARRL link - interesting.

Have also read Rudy N6LF's work.  They do both say rougly the same thing, but with the ARRL article showing lengths about 30 % shorter.

The good news is that this is really easy to measure for one's self using the method that Rudy explains in one of the articles - using an antenna analyzer, simply adjust lengths until the minimum real part of the feedpoint Z is found, as a function of radial number and length.

I'm fond of inverted-L's, and think I will duplicate some of the work in the articles above,  to see if anything changes for inverted-L configuration.

Is an BMU required when running radials? Looking for plans and ideas to put up my own inverted L is why I ask.

What is a "BMU"?

I read up on most of that when I did my vertical install, and ended up with 32 shortish radials and pretty decent antenna.

What's really impressive is when you look at the efficiency (and radiation pattern) of elevated radials. The crib notes
on that is you only need two tuned radials for a 360 pattern, and they only need to be elevated 4-5 feet off the
ground to get better efficiency than pretty much any number of on-the-ground radials. But on-ground radials are
inherently broadband and elevated radials aren't.

This is the basis behind the buddiestick, which is a loaded, single-radial elevated vertical.

Base matching Unit. I got the antenna threads mixed up and realized it was the other thread knowfear was talking about them.

Base Matching Unit. This is the one I think I'm going with on the vertical I'm planning. http://vtenn.com/Blog/?p=1570 If I do it, I'll substitute a relay at the antenna base for the switch so it can be remote switched.

If you are using an antenna that has a serious mismatch to 50 ohms or is non resonant, then yes you'll need to tune it to something reasonable.

Many of those setups "match" the antenna by just being very lossy.

Adding radials/counterpoise may change the antenna tuning and/or reduce bandwidth by reducing what would otherwise go into loss.

Exactly so!

That's one of the beefs I have with the Alpha's and Chameleon's - the undisclosed use of high loss to mask SWR  :(

FWIW here's an example of what reasonable low-loss Unun / Loading coil loss should be: "80 Meters and Up – Portable Base Matching Unit for 42 to 48 Foot Verticals and Inverted-Ls – Medium Power Version" ===> http://vtenn.com/Blog/?p=1570  

This is the measured loss into the impedances presented by a 45 ft-ish antenna against a decent radial field.  This is for a physically small medium power BMU.

80 M / 75 M: Loading coil used, 0.14 dB
60 M:  -1.10 dB
40 M:  -0.31 dB
30 M:  -0.63 dB
20 M:  -1.10 dB
17 M:  -0.69 dB
15 M:  -0.61 dB
12 M:  -0.69 dB
10 M:  -0.84 dB
8 M:  -1.3 dB
6 M:  -1.0 dB






(btw = how does one scale these giant freekin pix on this forum???)

Read the article. Is there a set of more detailed build plans or can I buy this somewhere?

The UNUN half looks like it's just a 9:1 UNUN with 8 turns of wire that the plans are available in numerous places on the net, the other is just turns of wire on the core.

Sorry Texas neighbor - nothing more detailed than what's in the article. As David said, there are other sites showing "tri-filar" in more detail.  As long as you use a 43 ferrite core of that size or a bit larger, and put 8 or 9 turns of any decent wire, then performance will be about the same.  Nothing super critical.

The one in the picture was made to be as small as possible for portable.

Resist the urge to go with plans of the inadequate-on-the-low-bands powdered iron core for the Unun that are often found on web plans.