HWEF: what toroid(s) to use?

I often get the question “What is/are the best of toroid(s) / ferrite core(s) for the HWEF?”. Even though some people claim to have the answer, the simply truth is it can’t be answered, it depends. Again, I’m no technical expert, but I will try to share what I learned from my HWEF elmer Egbert (PA0EJH).

Power
The first question is: what power do you want to use the antenna with? In practice, my single FT240-43 seems to handle 100W PEP SSB phone fine, it’s not even getting warm after long QSO’s (I did check that once). I’ve also used two FT240-43 cores (3:21 ratio) with 400W PEP SSB phone, no problems even when using it for hours in the PACC contest. I have no experience with higher power, but if you want to use 1 kW (SSB phone that is!), I’d say you need at least three or maybe four 240 sized cores. I’m not familiar with digital modes other than WSPR only using 1W or less.

The knowledgable Mr. Owen Duffy (VK1OD) advises in one of his (two!) reviews of my original English HWEF article from 2012 that a single FT240-43 should be able to handle 40W continuous average power, probably less if enclosed. You do the maths yourself, I’d say around 25W continuous average power for an enclosed core but to be honest, I just don’t know the exact answer.

Band(s)
If you only want to use the aerial on one band, my choice would be not to use an auto transformer but a simple tuned L/C circuit; a coil and a capacitor tuned to the desired frequency. PA1SSB has excellent info on this monoband HWEF, check out the information hosted by PI4VLB (Veron region A22) below. If you want to use the HWEF on multiple bands, a solution using an impedance transformer is the way to go. So what core(s) do you need. My elmer Egbert advised me that the impedance of the primary side of the transformer should be around 200 Ohms for optimal transformation. I have no clue why not to aim for 50 Ohms other than Egbert’s words “it needs to transform energy, not absorb”. I hope somebody (Owen?) can shine a light on this. I did an article about “broadbandity” (bandwidth) of auto transformers and did some very un-scientific measuring. For what it’s worth, my measurements seem to confirm that there seems to be some kind of optimum around 200 – 300 Ohms; that’s where the X is lowest and R closest to the calculated value.

200 Ohms
So let’s assume 200 Ohms is the optimum impedance, what core(s) do you need? I’m a lazy person so I use the online calculators on Kits and Parts a.k.a. The Toroid Kind. Click on “Toroids” in the menu on the left, then pick the one you plan to use e.g. the FT240-43. I’m using the FT240-43 info page for this example. Let’s first investigate what frequency a single FT240-43 2:14 ratio auto transformer has the (assumed optimal) 200 Ohms impedance by typing in 2 turns and 200 Ohms, then hit “Calculate”.

ft240-43 calculator01
ft240-43 calculator02There you go… 2 turns on an FT240-43 will be 4.3 uH inductance and the assumed optimal impedance of 200 Ohms will be at 7.403. Note that this is directly related to the inductance; so any inductor of 4.3 uH will have an impedance of 200 Ohms on 7.403 MHz. This transformer works efficiently on 40m and in practice, works well one band up (20m) and down (80m). Please be aware of the fact that when you connect 20 meters of wire, the system will be a full wave aerial on 14 MHz which, according to some experts, does not have a very good radiation pattern. On the 10m band, 20 meters of wire would be two wavelengths which has the reputation of an an even more odd radiation pattern with many unpredictable lobes (minimums and maximums). In my experience, the HWEF can work relatively efficient on two bands (still making it multiband HI). Sure you can fiddle the system to show 1:1 SWR and remember it’s very, VERY difficult to make a 20m long non radiating wire. That don’t make it a good antenna though, not even a “compromise”. Then again… one antenna is better than none… But TWO (or more) is even better! HI.

Inductance of multiple cores
The example auto transformer will have it’s optimum on 40m, but let’s say I want the optimal performance on 80m, what to do? It’s very difficult if not impossible to put “decimal turns” (e.g. 2.3 turns, 2.8 turns) on a toroid. If you want better formance on lower frequencies, you need more inductance. That can be achieved by stacking two cores instead of using a single core. By doubling the number of course, you double the inductance. In the previous example, the inductance of 2 turns on a single core was 4.3 uH, so 2 turns on two stacked cores will be 8.6 uH. Let’s find out what the optimal frequency is for 8.6 uH by using the calculator again. Enter 8.6 in the uH field and 200 in the ohms field, then hit Calc:
ft240-43 calculator03ft240-43 calculator04
That’s a nice surprise; right in the middle of the (region 1) SSB phone part of the 80m band. So two FT240-43 cores with 2:14 ratio will work efficiently on 80m. Probably not so good on 160m (97 Ohms impedance is too low according to many) and also well on 40m as well. Stacking the two cores will double the power handling, I used two cores with 400+ Watts PEP SSB phone (I’m not allowed the plus but… well… you know).

Single core, increase primary turns
Remember we were calculation TWO turns on TWO cores, but while the calculator only takes one core into account in the calculation, you can see that with 2.8 turns on a single FT240-43 you can get the desired 8.6 uH too. Of course 2.8 is very close to 3 so if you’re not going to use the antenna with more than 100W PEP SSB phone (let’s say 25W continuous e.g. cw or digital modes), you could use a single FT240-43 with 3 primary turns (3:21 ratio):
ft240-43 calculator05As you can see the inductance is a little higher so optimal frequency is a little lower. For a single core with 3 turns, we need a little less inductance, let’s try the smaller FT140-43 that has a little lower Al value:
ft240-43 calculator06
Pretty good, this should work pretty well on 80m and 40m. Be aware that this is a smaller core that can handle less power. In my experience (I started out with the FT140-43 with 2:14 ratio), a single FT140-43 can handle 100W PEP SSB phone. My measurements for the “Broadbandity” article seemed to indicate that a single (240-43) core with 2:14 had the best bandwidth of all transformers.

What about my 2xFT240 3:21 transformer based 80/40 HWEF?
I was young(er) and foolish I guess. I didn’t have the knowledge I have know and the more a learn, the more I realise I there’s much more to learn. In practice, this antenna worked best on 80m but it did well on 40m as well. So looking at the picture above, 3 turns on a single FT240-43 results in 9.68 uH inductance. Stacking two cores will double that so my transformer had 19.36 uH primary, the optimum (impedance 200 Ohms) for that is 1.644 MHz. On 3.7 MHz the impedance would be 450 Ohms, on 7.1 MHz 860 Ohms. Considering that it – seriously – worked well on 80m and 40m, I tend to say the “optimum” impedance is a little higher than 200 Ohms and usable primary impedance is between 200 and 1000 Ohms? This is a *very* unscientific range, there are many knowledgable hams who can say something way more sensible about this, I’m just shooting from the hip.

What I’m using now?
A typical Dutch saying is “I have two left hands” meaning I’m not very handy. I’m not a very good DIY’er… I like it, but I’m not good at it. I’m really jealous of people who make those good looking enclosures, the ones a made put the “amateur” in ham radio amateur HI. So I decided to buy a ready built transformer from Hans Dijkerman’s (PA1HD) Communication World store. I bought the 450W PEP model, it turns out to be a single FT240-43 core with a (now this is smart!) single FT140-43 inside. The transformer has a 2:14 ratio. The total inductance will be around 4.3 uH (2 turns on 240-43) + 3.54 uH (2 turns on 140-43) = 7.84 uH. The optimum frequency (based on 200 Ohms) is 4.06 MHz making it a good compromise between 80m and 40m and that’s what I use it for. Note that while I cannot span away 40 meters of wire, I’m using a 20m and 40m L/C trap in my wire. Therefore, my antenna is half a wave on all three bands; the 20m trap disconnects the middle wire, 40m trap and end wire, the 40m trap disconnects the end wire and on 80m all three wire plus inductance of the L/C traps (on lower frequencies, they act like loading coils). The calculated impedance for 14 MHz is around 700 Ohms. According to my earlier statements, it should work reasonably well but… it doesn’t. My 3.7m trap (on 20m coil!) loaded Hy-Gain long 12AVQ outperforms the HWEF on 20m for both local (Europe) as well as dx (Americas, Asia etc.) QSO’s. I have a suspicion the 20m trap is no good, either it’s off frequency, or the cap is blown, not sure. I noticed that changing the end wire’s direction – only supposed to impact 80m – did not have any impact on 40m performace but did have impact on 20m which is just odd. I have a suspicion, the 20m trap “leaks” and while the 40m trap doesn’t trap 14 MHz signals, it’s a strange unpredictable system which – in practice – doesn’t seem to work well on 20m. So, probably because of the “leaky trap”, not because of the transformer.

The magic 52 material
In a certain Facebook group, specific design using three FT240-52 cores with 2:21 ratio is very popular. I made this transformer and measured it with a 2k5 carbon composite dummy. I’m not sure if my measurements cut any meat but I noticed that this tranformer has a smaller bandwidth looking at the R (50 Ohms) and X (close to 0). Therefore my conclusion was (actually still is) that this is not an optimal solution if you don’t need it to be able to handle QRO power. If you do want to use 1 kW PEP, you probably need at least three cores and 43 material will have way too high inductance so yes, for QRO applications, the 3xFT240-52 is a good solution. Inductance is 3 x 1.32 uH = 3.96 uH, the optimal frequency where impedance is 200 Ohms is 8.04 MHz, I reckon it will work OK on 80m, efficiently on 40m and pretty good on 20 and 10. Owen Duffy has reviewed the Ellington 3 x FT240-52 matching transformer for an EFHW design (Steve Ellington, N4LQ) and calculated a core loss of 0.23dB which is much better than the calculated loss of a single FT240-43 core loss of 1.5 dB. Then again, a single S-unit is 6 dB, the question is whether this is noticable but I can imagine the idea of losing power in the core is not attractive. Note that Owen calculates 2 dB loss for a transformer using 2 turns on the smaller FT240-43. I’ve used Owen’s ferrite cored inductor calculator on 3 turns on a single FT240-43. I took the u’ and u” values from the table from his calculator.

Toroid info Owen Duffy
ft240-43 owen duffy calculator 02
According to Duffy, for a 50Ω match, the total conductance G is 1/50=0.02, and the percentage power lost in the magnetising admittance is Gcore / Gtotal * 100 = 0.00255 / 0.02 * 100=12,8%. That gives a core efficiency of 87.2% or core loss of 0.6 dB, much better. I’m not sure I used the Duffy’s calculator correctly, I’m still studying all the information on the page and trying to grasp the theory behind it. Hopefully Mr. Duffy finds the time to write a review of this unscientific article HI. Note that the 3:21 ratio transformer on the smaller FT140-43 toroid results in (G+jB) of 0.00318-j0.00462 which results in a core loss of 15,9% so efficiency of 84.1% or loss of 0,8 dB.

My 20/10 single FT240-52 HWEF
I’ve come to the conclusion that for efficient multiband operation, I need multiple HWEF’s (and if not, it’s keeps me off the streets). I don’t need a QRO system, mostly SSB phone with 100W PEP, very very seldomly CW or digital and I guess 25W will be sufficient. 3 turns on a single FT240-52 will result in 3 uH which has 200 Ohm impedance around 11 MHz. A little too low, but better than the 2:14 transformer on a single smaller FT140-43 (3.54 uH, 9 MHz). Now let’s use Duffy’s calculator to calculate the (G+jB).

I’m not sure whether I used the correct parameters; I copied all from Owen Duffy’s article on the Ellington design accept for the Al value (330 instead of 1000+), the number of turns and the frequency. The Al value of the FT240-52 is 330, Duffy used 1000+. The formula to calculate inductance is uH=(AL*Turns2)/1000 so tripling the number of cores indeed equals tripling the Al value of a single core. The parameters I used for the calculations are:Duffy calculatie 20mThe results for 20m, 15m and 10m:
14.2 MHz: 0.00278-j0.0031, loss 14%, efficiency 86%, core loss  0.6 dB
21.2 MHz: 0.00239-j0.00249, loss 12%, efficiency 88%, core loss 0.6 dB
28.5 MHz: 0.00219-j0.00215, loss 11%, efficiency 89%, core loss 0.5 dB

Wow!
Still not a good as the big 3 x FT240-52 transformer with 2:14 ratio, but it looks promising. One downside I found in Duffy articles: while the losses of the 52 material are lower, the Q of the 52 core is higher so bandwidth will suffer. How much? I don’t have a clue, let’s try it out, hopefully this week.

The moral of this story
If you want optimal performance on multiple bands, make two HWEF’s. Tune it to your requirements and optimal lowest favorite frequency and get at least one extra band (up). Then… make another one for the higher frequencies you like. I’m going for a 80/40 version and a 20/10 version. The 20/10 probably won’t work on 15m, therefore I really need a third monoband HWEF for 15, maybe a fourth one for the WARC bands and a fifth coil loaded HWEF dedicated to 160m HI.

If you’re willing to sacrifice some performance and don’t use high power, I would personally still go for the 2:14 on a single FT240-43. Loss of 1.5 dB on 40m is acceptable and will be less on higher frequencies, it will easily handle 100W PEP SSB phone (probably more), it’s cheap and simple to make and seems to have the best bandwidth (see “broadbandity” article measurements. Especially if you’re licensed for 40 – 10 like the Dutch PD novice radio amateurs, it seems like a no brainer.

Keep building those HWEF’s and keep safe! Share what you know, learn what you don’t.

73 de PA3HHO (Pleun)

Links / References:
Owen Duffy (VK1OD): End fed matching – PA3HHO design review
Owen Duffy (VK1OD): Ellington 3 x FT240-52 matching transformer for an EFHW
Owen Duffy (VK1OD): Calculate ferrite cored inductor – rectangular cross section
Owen Duffy (VK1OD): Calculate ferrite cored inductor (from Al)
PA1SSB Info voor het maken van een Monoband en multiband end fed antenne