I put up my 6m mast out in the garden and plugged the antenna, and this is what I get with 3 / 22 ratio (I got +/- the same with 3 / 21)
A good SWR on 14.250 but the 10m band … Not only SWR is bad but the resonant frequency is 29.5 MHz (as predicted by mmana gal simulation).
Edit : Same results on the radio itself, a very satisfying 1.0 (!) SWR on 14.2MHz but 2.6 SWR on 28.2 MHz.
What exactly is meant by the antenna?
Multiband EFHW Antennas
If it is a multi-band EFHW, which is 2 or 4 half-waves long on 28 MHz and has a VSWR of 1 on 14 MHz, this antenna is inevitably too short on 28 MHz, i.e. the resonance will be around 150-200 kHz higher than expected.
This arises because the mechanical antenna length for harmonic frequency bands is not an exact multiple of the antenna length of the fundamental frequency.
The solution would be to choose a compromise antenna length, which, however, does not exactly produce a satisfactory result (SWR) on the lower and upper bands of a 40-10 m EFHW for use without an ATU.
For this reason, for my small radios without an ATU, I only used monoband, linked and later trapped and hybrid EFHW antennas.
EFHW Transformer design verification
The main purpose of a reflection measurement with a non-inductive resistor of the nominal value on the workbench is for the designer to check his design (e.g. to favor the low or high frequency bands or for broadband applications). For information only, the photo below shows the VSWR curve of one of my 1:49 EFHW broadband transformers.
Due to the significant increase in the VSWR at approx. 20 MHz of your EFHW transformer, it must be expected that this also applies to the transmission losses (s21) and that this transformer is therefore not sufficient above approx. 20 MHz for efficiency reasons.
What else could you try? If you want to stick to this toroidal core size, all 21 turns could be pushed together completely so that the turns on the inside lie against each other without any gaps.
What does this change in the course of the VSWR?
Indeed is not looking normal.
Try a longer wire like 20m (19,xxm) build up as sloper. I used only ~20m and only 2 turns primary and 14 secondary.
But the SWR should go much deeper.
In my case on 14 MHz its always deeper then at 28MHz.
My Antenna is resonant on 40m, 20m, 15m, 12m and 10m. No tuner is needed.
HB9BCB Thank you for those explainations. I apreciate. I will give it a try and let you know.
IN3JIB I do not want a 20m slopper. Originally I thought about EFHW because of limited footprint (5 to 10m is acceptable to me) and resonance on desired frequency (I save the 200g of the tuner in my bag). But now, here is the trade :
EFHW 10m : + 6m footprint only (sloper) + no tuner on 20m / - work only 1 band so far
Random wire 16m : + work 40 to 10m easily / - wider 11m footprint (inv V) - 200g tuner to carry
Since I already own the tuner, I’m considering changing my plan towards the random wire solution to be honest. But first I will try the modifcation of the transformer.
Well, I think it’s a succes. I modified the toroid : pushed all turns together + 3 - 21 turns and it’s a big change :
It removed completely the big slope after 25 MHz !!!
I will try on the field now, together with a little adjustment of the antenna wire lenght. Thank you 
This! It should also improve efficiency.
Other things that have an influence:
About your second question:
Good question and I don’t know the correct answer (the calculation for shortened dipoles or quarter waves doesn’t apply). But it doesn’t has to be exact. If the inductance is a bit higher, the remaining wire will be a bit shorter with a narrower bandwidth, and vice versa.
Some time ago I published a document describing a portable 7-band EFHW antenna, about 20m long, with a bypassable coil. How did I find the perfect coil inductance? First I estimated it, and then empirically removed some of the winding until it fit 
.
73 Stephan
It did for sure. After adjusting a bit the wire antenna lenght, I have now a nice SWR < 1.5 on both 14 MHz and 28 MHz (I had to make a little compromise to fit the two band as explained by HB9BCB ).
Now that the base of my antenna is working as intended, I will try to add the shortened 40m section. But enough for today 
Excellent document !
If I’m measuring my transformator with 3.2k it looks like that.
Should be 50 ohm but isn’t lmao. But my antenna is working great and if I’m measuring directly in the field its almost 50 ohms.
I made a shortened EndFed.
This Pic is from DC4KU
But I’m taking sometime the coil off and I’m using only the 10m wire. If the space isn’t there.
deployed the antenna somehow. It was not looking good but it worked quite well.
Because I deployed the antenna so badly it was resonant on 12m too 
73
Julian
The dimensioning of the coil as a choke for the frequency bands 20 and 10 m could be done according to the rule of thumb, according to which a reactance of around 10 times the system impedance is required, i.e. at least 500 ohms. The maximum required coil inductance of around 6 uH would then be required for the 20 m band.
The dimensioning of the coil to electrically extend the existing antenna length to a 40 m EFHW could be done like a loading coil for a shortened quarter-wave antenna. In this view, the distance between the feed point (end of the existing 20/10 m EFHW antenna) and the loading coil would be 0 m.
With an online calculator (e.g. from M0UKD) you can easily see that the required coil inductance for a short antenna tail on 40 m is much larger than that previously determined for the choke function and that this function is therefore automatically fulfilled.
Well thank you again if I use that method and use a bit less than 2m as a wire length I retrieve exactly the 35uH of the commercial ones.
What is still not super clear to me is how you would chose the length of the wire. It seems like in the range from 0 to lambda/4 , the required inductance varies from infinite to 0. So I guess we want the wire short enough to meet the dimension constraints, knowing that shortening the wire is enlarging the coil, and as a consequence, reducing the efficiency. Am I correct ?
That’s right - I always have the formula in the back of my mind when building antennas…
73 Armin
hahahaha, yes made a tattoo with the formula hahaha.
For vertical antennas I’m using this calc:
Dan @AI6XG did some experiments with EFHWs. Results on his blog: https://www.ai6xg.com/post/efhw-xfrmr-capacitor and https://www.ai6xg.com/post/end-fed-half-wave-antennas-more-about-the-primary-capacitor
Yes I observed the same on mine. Without the cap, my antenna is not usable on 10m. It helps to flatten the curve.
Today I went for sota activation and here is my observation :
Conclusion for 40m :
Silly idea I got :
Create a bypassable coil that I put at the base of my 20m EFHW antenna to transform it into a 40m EFHW without adding any lenght. I asked google, it seems like others did it before (Adding a loading coil to a 40m Vertical for 80m operation | M0MCX - Amateur Radio - Ham Radio), it’s not looking that good but I might give it a try.
From my experience with a 40/20/15/10 m version (20,x m wire) that is extended by a 110µH coil (plus some 1,6m wire) to allow also 80m is that the usable part of the 80m band is very minimal without a tuner. Maybe 50 kHz maximum. Then the SWR is too bad.
So if your tuner adds already enough inductance to also get 40m why mess around with the coil and 2 m extra wire. This will only make things more complicated to deploy and handle. Keep it simple … for SOTA. The chasers have the good antennas to pick you up
73 Joe
Yep. Built an 80/60/40/20 vertical on that principal: what coil do I need to add 2m up a 20m vertical to make it resonant on …
Presuming centre loaded is more effective than base loaded, which is what an ATU is effectively doing.
So I have a 20m 1/4 wave vertical on a sota pole with a coil 2m up: 1 coil, 3 taps and bypassed for 20m.
However, a better solution seems to be winding the coil on spaced former that lets you clip on to any turn in the coil so you can tune for the paricular operating conditions you find yourself in. Details on reflector(below)… yet to try it here.
Oh I see. So yes you are right, I will not bother with it and just keep it like this. I will do some more tests to check if I can tune on the other bands between 20 and 10m.
Because if I have to bring the tuner , maybe a random wire with a non resonant length would be a smarter choice. From the tables, it looks like 16m is an ideal length. It a bit too long for me but if can easily get 1.2 swr on all bands from 40 to 10m … I could consider the trade off.
Why aren’t u using the 20m? For a huge amount of summit’s 20m wire fits perfectly. And you are resonant on 40-20-15-12-10m without an tuner. For peaks with less space you could use a vertical antenna with coils.
I’am using 20m of course. But if can have 40, why not ? I’m not resonant on 40m without a tuner at all though … Neither on 15 nor 12.
