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Electronics => RF, Microwave, Ham Radio => Topic started by: A.Z. on October 09, 2021, 03:27:02 pm

Title: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 03:27:02 pm
Hi there, maybe I have too much time in my hands, so my mind is wandering in strange directions, I don't know, but here's something I have been reasoning about lately

Probably you all know about the idea of linear loading an antenna (e g. a doublet) to shorten it w/o using loading coils and, in turn, with pretty good efficience; such antennas are also called "cobra dipoles" (or doublets) due to the "snaking" wire connections for their arms, examples of such an antenna can be found here

https://www.hamuniverse.com/cobraantenna.html (https://www.hamuniverse.com/cobraantenna.html)

http://www.m0pzt.com/80m-cobra-doublet/ (http://www.m0pzt.com/80m-cobra-doublet/)

now, while linear loading offers quite some advantages over other methods of loading/shortening an antenna, it also presents a main (imHo) disadvantage, that is, the radiation resistance of a linear loaded antenna (let's deal with a linear loaded dipole and call it LLD)... was I saying ? Oh yes, the radiation resistance of an LLD will be low, and, as you know, this isn't a good thing

So, I started reasoning about the LLD and had an idea, that is, adding a pair of capacitive hats at the ends of an LLD; see, one of the effects of capacitive hats is to RAISE radiation resistance. so, since linear loading lowers it, the cap hats may compensate and possibly give a more efficient, yet shortened antenna

Now, I didn't run out and build something, also since weather isn't exactly nice, instead I tried modeling an LLD in NEC and then adding it a pair of capacitive hats at the ends of the dipole arms, and the results seemed encouraging

So, and I'll conclude, did anyone here experiment with linear loading and capacitive hats ? And, if so, do they offer a real improvement or mine is just a brain fart :) ?

Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 05:02:01 pm
Quote from: A.Z. on October 09, 2021, 03:27:02 pm
Oh yes, the radiation resistance of an LLD will be low, and, as you know, this isn't a good thing

The reason why radiation resistance is small is a small physical dimensions of antenna.
If antenna dimension is small in comparison to half-wavelength, it will have low radiation resistance.
Just because small antenna occupies too small volume of a space.

If you're needs higher radiation resistance, then you're needs to increase size of your antenna
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 05:57:06 pm
You are right, but I think you missed my point; we shorten a dipole (doublet) by using linear loading, so, in turn, we decrease its radiation resistance; now, adding capacitive hats to a dipole increases its radiation resistance, so the question is:

could it be possible to mix linear loading and capacitive hats so that we can, at least to some extent, recover radiation resistance and, in turn, increase the (shortened) antenna efficiency ?

From my very raw NEC simulations, it seems so, but a simulation is... a simulation, so I asked if someone tried it on a real antenna
Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 06:50:23 pm
you can't cheat physics, if you want a good radiation efficiency, just use full size antenna.

All these things which you name "linear loading" and "capacitive hats" is just intended to change resonant frequency and bandwidth for a small radiator. You can do the same with LC matching circuit. But you're still using a small radiator, so it has low radiation resistance and by adding matching elements you will get just a higher heat loss on these elements.

Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 07:06:13 pm
and I'm not trying to, I know that such an antenna won't have the same efficience as a full size one, what I wonder, and I'll refrain it again is IF using capacitive hats on a linear loaded doublet, it may be possible, to some extent, to recover PART of the radiation resistance lost due to the linear loading shortening of the antenna; I'd go out and try it myself, but given that it's raining dogs and cats and that I'm not exactly in my best shape, I'm trying to understand if, theoretically it could be possible; hope to have been clear now :)
Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 07:14:11 pm
Quote from: A.Z. on October 09, 2021, 07:06:13 pm
is IF using capacitive hats on a linear loaded doublet, it may be possible, to some extent, to recover PART of the radiation resistance lost due to the linear loading shortening of the antenna

Since "hats" increase dimension of your antenna for a little, you will get a little increased radiation resistance because physical dimension of your antenna is increased. But that increase will be small, the same small as antenna dimension change.

If you want to get 3 times increase, then you're needs 3 times longer antenna.
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 08:19:19 pm
sorry, now I'm at loss; I never wrote about three times size reduction, just about linear loading and capacitive hats, and linear loading doesn't imply reducing size to one third !
Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 08:33:39 pm
Quote from: A.Z. on October 09, 2021, 08:19:19 pm
and linear loading doesn't imply reducing size to one third !

What antenna type you're talking about when you wrote "linear loading"?

In your first post you're provided a link to 80m Cobra Doublet antenna which has 12 meters length (3.3 times shorter than a full size)
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 09:35:58 pm
those were just examples showing (to whoever not familiar with it) the linear loading, that said, that short one could still be effective, as usual it all depends from "lambda" :) but, aside from antenna size, my point is (maybe I was unclear); is it possible to reduce a doublet by using linear loading and, at the same time restore (to some extent) its efficiency by using capacitive loading ?
Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 10:00:37 pm
in order to restore efficiency for shortened antenna, you're needs to restore it's full size.

But on the other hand, you can put more power into shortened antenna (increase power of your power amplifier) to compensate heat losses and get almost the same radiation power as with full size antenna  :)


I think "linear loading" or "capacitive hat" should not affect radiation resistance much if you don't change antenna dimensions. The main effect should be for resonant frequency and bandwidth.
Title: Re: Linear loaded antennas and capacitive hats
Post by: hendorog on October 09, 2021, 10:45:22 pm
Sounds like an interesting idea to me. I wonder if any of the old school hams have tried it?

What did the radiation pattern look like on NEC?

Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 09, 2021, 11:14:45 pm
that "linear loading dipole" looks very like Nadenenko dipole:
(https://i.imgur.com/7R4lroK.jpg)

The idea is to use thick arms. Such dipole has lower Q, so it's bandwidth is more wide.

Similar dipoles are used on radar "Duga" (РЛС "Дуга" [5Н32] (https://en.wikipedia.org/wiki/Duga_radar)):

(https://i.imgur.com/3KEOTru.jpg)


Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 09, 2021, 11:28:17 pm
that's a cage antenna, not a linear loaded one, if I'm not wrong
Title: Re: Linear loaded antennas and capacitive hats
Post by: T3sl4co1l on October 10, 2021, 12:44:29 am
Well, what do you want out of it?  If you don't care about bandwidth (say need >10% relative BW) or directivity (beyond a basic loop/dipole), it very much doesn't matter what combination of inductors, loops, capacitors and hats you use; keep them balanced/shielded against near fields, while open to far fields, and you simply get whatever bandwidth and efficiency you get.  Radiation resistance being low doesn't really mean anything, you can always match that back to 50 ohms or whatever with a network.  It's when it's low in relation to other circuit resistances, gain suffers.  And don't be fooled by electrical parameters, like impedance bandwidth; that can always be loaded down with extra R, trading gain for BW.  Keep circuit resistance low, so radiation resistance is the dominant loss in the system.

So, for capacity hats as the active elements, solve for whatever resistance they have (calculate/measure), use high-Q inductors, match it to 50 ohms and you're done.  For loops as active elements, same thing but with high-Q capacitors.  Either way, you might get it wired directly (antenna elements basically on feedline and you're done), you might have to do some tuning (L-match or pi network?), or use a transformer.  Bonus points when it's as part of the element(s) themselves, like using a smaller feed loop coupled inside a larger resonant inductive loop, as often done for LF/MF.

Where you put those elements, doesn't matter.  L can be distributed up the element as a helix, anything from a little wiggle to a compact Tesla coil; C can be a lump capacitor, or broad elements or hats.  Obviously you need at least one large element, or both in which case you get pretty much a full size electromagnetic antenna. :)

Tim
Title: Re: Linear loaded antennas and capacitive hats
Post by: HB9EVI on October 10, 2021, 11:06:40 am
in matters of bandwidth, a capacitive hat gives a broader bandwidth than an inductor at the feed point, also losses are lower.
Examples are T and inv. L antennas, whereas in inv. L calculations show, that the horizontal part often acts as radiator too 

otherwise I have to admin, that I'm not familiar with the term of 'linear loading'
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 10, 2021, 11:46:48 am
Quote from: HB9EVI on October 10, 2021, 11:06:40 am
in matters of bandwidth, a capacitive hat gives a broader bandwidth than an inductor at the feed point, also losses are lower.
Examples are T and inv. L antennas, whereas in inv. L calculations show, that the horizontal part often acts as radiator too 

otherwise I have to admin, that I'm not familiar with the term of 'linear loading'

as for linear loading, a good primer may be the one found here

http://www.antentop.org/w4rnl.001/amod15.html (http://www.antentop.org/w4rnl.001/amod15.html)

the idea was explored by several hams as a way to shorten an antenna (usually a doublet) so allowing to use it in restricted spaces and still obtain multiband operation, an example of such an antenna can be found here

https://www.hamuniverse.com/cobraantenna.html (https://www.hamuniverse.com/cobraantenna.html)

and a commercial version, here

https://www.k1jek.com/ (https://www.k1jek.com/)

now, while linear loading offers some advantage over other loading methods (e.g. inductive loading) its main drawback is that it lowers the radiation resistance, and the impedance at the feedpoint may become pretty low (say 30 or even 12 ohm or less)

Now, to get back to my initial question, since adding capacitive hats to an antenna (let's use a multiband linear loaded doublet for this discussion) increases its radiation resistance... would be possible to add capacitive hats to the ends of our linear  loaded doublet to somewhat "recover" (to some extent by the way) the radiation resistance lost due to linear loading ?




Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 11, 2021, 02:12:07 am
As I read, these "linear loaded" antenna has a bad efficiency and suffers from common mode currents and other issues. So, it's better to avoid it. This is a bad choice for antenna.

If you're needs more wide bandwidth then just use classic Nadenenko dipole (also called "cage dipole").

If you're needs shortened antenna then just use shortened dipole with matching circuit at feending point.
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 11, 2021, 01:54:07 pm
Quote from: hendorog on October 09, 2021, 10:45:22 pm
Sounds like an interesting idea to me. I wonder if any of the old school hams have tried it?

What did the radiation pattern look like on NEC?

That's one of the think I'd like to discover, but apparently folks which replied (thanks you all btw !) seem to be focuse on stuff like bandwidth and so on, and are missing my main question; anyhow, the (VERY PRIMITIVE !!) NEC model I used is below, it can be loaded in the free 4NEC2 or in other NEC sw and will allow to play with the idea; the radiation pattern is somewhat similar (depending on frequency, this is a "multiband" antenna) to the one from a doublet

Code: [Select]

CM .
CM linear loaded doublet with capacitive hats
CM .
CE

' symbols
SY freq=3.000       
SY fspc=0.15        
SY wire=0.00075     
SY vspc=0.05        
SY leng=10.3        
SY ends=(leng+0.20) 
SY rads=0.25        
SY hgt1=10          
SY hgt2=hgt1-vspc   
SY hgt3=hgt2-vspc   
SY hgt4=(hgt3+rads) 
SY hgt5=(hgt3-rads) 
SY segl=11          
SY segm=3           
SY segs=1           

' feedpoint spacer wires
GW  1 segm   0     0    hgt1      0  fspc  hgt1 wire
GW  2 segm   0     0    hgt1      0 -fspc  hgt1 wire

' arms wires
GW 10 segl   0  fspc    hgt1      0  leng  hgt1 wire
GW 11 segl   0 -fspc    hgt1      0 -leng  hgt1 wire
GW 12 segl   0  fspc    hgt2      0  leng  hgt2 wire
GW 13 segl   0 -fspc    hgt2      0 -leng  hgt2 wire
GW 14 segl   0  fspc    hgt3      0  leng  hgt3 wire
GW 15 segl   0 -fspc    hgt3      0 -leng  hgt3 wire

' arms junctions
GW 20 segs   0  leng    hgt1      0  leng  hgt2 wire
GW 21 segs   0 -leng    hgt1      0 -leng  hgt2 wire 
GW 22 segs   0  fspc    hgt2      0  fspc  hgt3 wire
GW 23 segs   0 -fspc    hgt2      0 -fspc  hgt3 wire 

' arm ends stubs
GW 30 segs   0  leng    hgt3      0  ends  hgt3 wire
GW 31 segs   0 -leng    hgt3      0 -ends  hgt3 wire

' cap hat spokes
GW 40 segs  0  ends  hgt3      rads  ends  hgt3 wire
GW 41 segs  0  ends  hgt3     -rads  ends  hgt3 wire
GW 42 segs  0 -ends  hgt3      rads -ends  hgt3 wire
GW 43 segs  0 -ends  hgt3     -rads -ends  hgt3 wire
GW 44 segs  0  ends  hgt3         0  ends  hgt4 wire
GW 45 segs  0  ends  hgt3         0  ends  hgt5 wire
GW 46 segs  0 -ends  hgt3         0 -ends  hgt4 wire
GW 47 segs  0 -ends  hgt3         0 -ends  hgt5 wire

' cap hat spokes outer junctions
GW 50 segs  rads  ends  hgt3  0  ends  hgt4 wire
GW 51 segs  rads  ends  hgt3  0  ends  hgt5 wire
GW 52 segs -rads  ends  hgt3  0  ends  hgt4 wire
GW 54 segs -rads  ends  hgt3  0  ends  hgt5 wire
GW 55 segs  rads -ends  hgt3  0 -ends  hgt4 wire
GW 56 segs  rads -ends  hgt3  0 -ends  hgt5 wire
GW 57 segs -rads -ends  hgt3  0 -ends  hgt4 wire
GW 58 segs -rads -ends  hgt3  0 -ends  hgt5 wire


' ground parameters
GE  -1
GN  2  0  0  0  13  0.005

' wires loading (copper)
LD  5   0  0  0  58000000

' feedpoint placement
EK
EX  0 1 1 0 1 0 0

' initial test frequency
FR  0  1  0  0  freq  0

' end of model
EN


just in case, the resulting antenna topology is show in the attached image; in the image I've increased various spacing values to allow understanding how the wires are connected

Title: Re: Linear loaded antennas and capacitive hats
Post by: T3sl4co1l on October 11, 2021, 02:39:34 pm
You mean this question?

Quote from: A.Z. on October 09, 2021, 05:57:06 pm
could it be possible to mix linear loading and capacitive hats so that we can, at least to some extent, recover radiation resistance and, in turn, increase the (shortened) antenna efficiency ?

The key is basically this,

Quote from: T3sl4co1l on October 10, 2021, 12:44:29 am
Radiation resistance being low doesn't really mean anything, you can always match that back to 50 ohms or whatever with a network.  It's when it's low in relation to other circuit resistances, gain suffers.

[Depending on arrangement,] you might get it wired directly (antenna elements basically on feedline and you're done), you might have to do some tuning (L-match or pi network?), or use a transformer. (...)

Where you put those elements, doesn't matter.  L can be distributed up the element as a helix, anything from a little wiggle to a compact Tesla coil; C can be a lump capacitor, or broad elements or hats.  Obviously you need at least one large element, or both in which case you get pretty much a full size electromagnetic antenna.

And yeah, add zig-zags in whatever direction to the list, nothing wrong with that.  Note that your arrangement has something of a folded dipole geometry, so it'll probably have a regular (full resonant) mode corresponding to the length of that fold; there will be some end/loading/proximity effect due to the fold not being actually correct (forming a shorted loop as a folded dipole proper), but folding again on to the capacity hats, so you'll want to build a model (sim or IRL) to see exactly where that lands, and at what impedance.  Then trim accordingly.

Also, to clarify: since these are electrically small, your pattern is essentially going to be a short dipole or loop, with corresponding maximum gain of 0dB to an ideal short dipole.  Gain being lower, is saying the efficiency suffers by so-and-so much insertion loss or whatever.  Power going into element/network resistance rather than radiation resistance.

Efficiency is defined by resistance.  Want high efficiency?  Use low resistance materials.  Don't make it out of bailing wire, use copper.  Preferably thick wire, stranded, especially as Litz, or cage elements.  The bigger the elements are, the less critical the material is; aluminum is great, steel is even acceptable in large structures.  Want radiation resistance near feedline impedance?  Add a matching network, no one needs to know that it's got extra lumped elements in there.  (Of course, doing that for multiple bands at once, may be a nontrivial exercise. :P )  Or cut it cleverly so that the structure serves the same purpose (matching).  Take a gamma match for example, that's an entirely mechanical method.

It's essentially orthogonal to topology -- most any design has some freedom of material choice or thickness, at least for the kind of thing we're talking about here, I think.  That's why you're getting answers that seem at angles to the question! ;D

Tim
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 11, 2021, 06:17:12 pm
Tim, fine with me, mine wasn't some kind of attempt to revolutionize physics or invent some gravity defying device, LOL !

I was reading some  notes about shortening dipoles/doublets using linear loading (I was thinking at an antenna idea, but that's outside the topic for this thread); anyhow, the notes stated that, one of the disadvantages of linear loading, is the decrease in radiation resistance, now, from previous experience and literature, I knew that, adding capacitive hats allows to better distribute currents AND (and that's what hit me) raise the radiation resistance, so (having too much time in my hands, probably, SWMBO and daughter were away :D) I started thinking that, maybe, one could pair linear loading and capacitive hats to obtain a multiband doublet which could be a Godsend for space restricted people

nothing else :)
Title: Re: Linear loaded antennas and capacitive hats
Post by: radiolistener on October 11, 2021, 09:58:51 pm
Quote from: A.Z. on October 11, 2021, 06:17:12 pm
I was reading some  notes about shortening dipoles/doublets using linear loading

So, your goal is to get shortened antenna with better efficiency than "linear loaded dipole" with the same size. Is it right?
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 12, 2021, 03:07:10 pm
Quote from: radiolistener on October 11, 2021, 09:58:51 pm
Quote from: A.Z. on October 11, 2021, 06:17:12 pm
I was reading some  notes about shortening dipoles/doublets using linear loading
So, your goal is to get shortened antenna with better efficiency than "linear loaded dipole" with the same size. Is it right?

Well, it isn't a "goal", just an idea I'm exploring; a (say) 73ft (total width) linear loaded doublet will work pretty well on all bands between 80 and 10 meters and can fit where other multiband antennas can't, now, starting from that, my idea is to explore a possible way to improve the antenna radiation efficiency by raising as much as possible its radiation resistance, and, for such a task, I thought to use a couple of capacitive hats placed at the ends of the linear loaded arms, the resulting antenna, while still allowing to cover the same bands, seems to offer somewhat better radiation (at least judging from the NEC models); also, what puzzled me is that, the literature and the various documents found on the web deal with single loading/shortening methods but, apparently, it seems that nobody ever tried to combine two different methods to try overcoming the problems created by the first method using a second one, again probably mine is just a brain fart, but being temporarily locked and with nothing to do, it's some food for my brain :D


Title: Re: Linear loaded antennas and capacitive hats
Post by: T3sl4co1l on October 12, 2021, 03:38:13 pm
Ok, so I guess the question is narrower than I would expect (and, perhaps than you expect as well?).

To be able to compare radiation resistance, or efficiency or whatever, one needs a baseline for an apples-to-apples comparison.

We might start with a given gauge of wire, and say that's what we're going to build it out of.

Which combination gives the best efficiency, and/or closest radiation resistance to feedline impedance (thus saving on additional tuning elements)?

And we can consider distributions from simple (lumped) loading coils, to distributed loading, to zig-zag or folded sections.

Loading coils can be placed anywhere along the element.  We might argue they're part of the antenna tuner instead, when placed right at the feedpoint, but when placed midways, there's a combination of magnetic induction from the feedline-adjacent section, and electric induction from the terminal section.  The inductance required goes up dramatically with distance from feedline, as in the 0% position, the electrically-short elements look like full-size capacity hats; putting them 100% at the end, they do nothing at all and the required value is infinite.

Typically loading coils aren't used further than 50 to 66% along the element, as the capacity of the far section is so small, requiring quite a lot of inductance to make it resonate, and the feedline-adjacent section is already so long (modest fraction of a full dipole) that it starts to dominate.  You do get the bonus that, give or take some added capacitance to make tuned traps, this is a good way to make a multiband antenna -- resonate the L with a C to make a parallel resonant tank (high series impedance = looks like an open circuit) between the element sections, and you've suddenly got a full resonant dipole at a higher band.


We can consider a loading coil stretched out, its two ends placed anywhere along the element.  It'll probably need a few extra turns to account for the lower inductivity of the high aspect ratio, and maybe more again to account for the low capacity of each part that's further out than the last.  That is to say, with respect to the couple of turns near the feedpoint, it sees the capacitance of the entire rest of the element; the next section up has more inductance below it (including itself), but less capacitance above; and so on.  In the same way that, for (lumped) loading coils placed far out along the elements, their values need to be quite large to tune the capacitance of the short remaining segment; the same effect is in play here, distributed over the inductor itself.

For zig-zag sections, inductance is added, but it's not aligned to any particular direction; indeed the field from each neighboring section cancels out, so you get much less inductance than for a spiral (where the field accumulates from turn to turn).  I would expect this has a lower Q, for this reason.  But who knows.  It's noteworthy that this type is quite popular for planar designs (on PCB -- just check any Wifi or Bluetooth module for examples).

And similarly for foldback sections, with the difference that, because the length can be a substantial fraction of total element length (indeed, you could fold up a full resonant dipole, which acts to reduce its effective length by a modest amount as a result of the folding, but gain multiple bands from the various length elements thus created).


And again, bonus points for multiband designs, where that's a desirable feature -- and, good luck tuning all of them because components here and there affect the impedance of everything else, so...


I suppose the "best" antenna design, is one which meets all its requirements without any additional help.  Like I said, radiation resistance, at any given point, is irrelevant; what matters is, how much of the impedance at the feedline comes from it.  If the antenna is designed in such a way that it provides its own matching, maybe needing a bit of L or C at worst (but not a full L or Pi section) to clean it up, then you have a design which, you can cut the pieces, assemble, and be done, no components needed, maybe a little trimming to get the frequency just right.


So, in that sense, the fact that a distributed inductance might give lower radiation resistance, might mean it's harder to match to the feedline -- and, as you can see, it's a fairly tenuous chain to get from the one fact, to the overall performance figure.  It's a hint, but by no means conclusive overall.

And, by "narrower", I mean, not to compare designs broadly, but to make some very narrow requirements and judgements of them: like, that it's easy to build (few elements / mechanical components?), doesn't need tuning (or much), or that it's using the same materials (say a fixed quantity of wire, insulators, tubing, etc.).  Short of simulating or building them all, I'm not sure there's much to say generally about that -- which is really also to say, I'm afraid that's beyond the scope of my experience.
Title: Re: Linear loaded antennas and capacitive hats
Post by: profdc9 on October 13, 2021, 05:12:50 pm
I designed a dual band attic antenna with a similar idea: using loading coils and capacitive hats to shorten the size.  It worked pretty well and had reasonable radiation efficiency.  It is 20 and 40 m.  Here's how to build it:

https://drive.google.com/file/d/1rdXsgld91BquQ_yEuWkZa68mkDQAQF3O/view?usp=sharing
Title: Re: Linear loaded antennas and capacitive hats
Post by: A.Z. on October 14, 2021, 08:30:58 am
Quote from: profdc9 on October 13, 2021, 05:12:50 pm
I designed a dual band attic antenna with a similar idea: using loading coils and capacitive hats to shorten the size.  It worked pretty well and had reasonable radiation efficiency.  It is 20 and 40 m.  Here's how to build it:

https://drive.google.com/file/d/1rdXsgld91BquQ_yEuWkZa68mkDQAQF3O/view?usp=sharing

That's nice  :) (for a space constrained setup by the way), and seems that it demonstrates that my idea wasn't totally crazy, in your case you used coils loading, while in my case I was experimenting with linear loading but in either case the result is a loaded antenna with capacitive hats, and judging from your paper, while performance can't be compared with a full size antenna (also since, in your case the antenna is indoors), the antenna allows to get on air with decent results, thanks for your reply !

I wonder if you considered linear loading, in such a case the antenna arms would be built using 3 (or more) conductors cables (flat or round) connected in series, such a thing, given the sizes shown in your pdf would mean that, while keeping the physical size the same, the arms would carry about 6m and 12m of wire (if mantaining the off-center setup), being curious I quickly modified my NEC model to turn it into a dipole with two 3m arms and two hats of the same size of yours

The attached image shows some infos about the simulation, including the radiation pattern on the 40 meters band, and the various gain/impedance/swr curves over the 0.5 to 31 MHz range