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While experimenting with end-fed antennas I've made two 1:49 transformers.

The first one has an air core, as shown in the article by John, M0UKD. This transformer doesn't even work as a transformer until you add a capacitor in parallel to the load. The secondary winding of the transformer and the capacitor should form an LC-circuit resonant on the desired frequency. The transformer works very well, but the bandwidth is narrow.

For the second one, I used FT240-43 ferrite core, as shown in the article by Rudy, N6DOZ. This transformer is wideband and works on 3-30 MHz. Although when loaded to 2450 Ohm non-inductive load (metal-oxide or metal-film resistor) instead of 50 Ohm we see a slightly inductive load:

enter image description here

From what I know this is because the large secondary winding works as an inductance in series with the load. This inductance can be compensated by placing a capacitor in parallel to the primary winding of the transformer. Here is the effect of placing a 57 pF capacitor (47 pF || 10 pF):

enter image description here

The part that I don't quite understand is why the transformers work so differently depending on the core material? Why the one that uses a ferrite core is so wideband while the first one doesn't even work as a transformer without an extra capacitor?

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    $\begingroup$ Just a guess, but I would expect the resonant circuit formed by the air-core coil to have a high Q. It's not loaded much by the high impedance end of the antenna and depending on how it's coupled to the primary, it may have a light load there also. This would(should?) lead to a sharper response. The type 43 material ferrite has a reasonably high permeability and is designed to work as a wideband transformer in the 5 - 400MHz range (info taken from toroids.info/FT240-43.php). $\endgroup$
    – Buck8pe
    Dec 8, 2021 at 9:06
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    $\begingroup$ By the way, here are a couple of interesting references that I found helpful. One is my all time favorite RF book, Bowicks RF Circuit Design (checkout chapter 2, resonant circuits): archive.org/details/BOWICKC.1997.RFCircuitDesign; electronics.stackexchange.com/questions/589947/… $\endgroup$
    – Buck8pe
    Dec 8, 2021 at 9:18

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"Why ferrite-core transformers are wideband while air-core are not?"

Air-core "transformer" is composed of 2 inductors "TUNED" with a magnetic coupling slightly less than 1. The resulting effect is a narrow bandwith "transformer".

Example with coupling coefficient of 0.01 to 0.5

enter image description here

Ferrite-core "transformer" is "same" thing except that magnetic coupling is quasi perfect. So it really has the behavior of a transformer with large bandwith.

I have made a simulation in 2 cases (resistor ad hoc on output, open output, same K ... k1=k2).

I think it would be more clear now. See that "coupling" K is quasi "1".

enter image description here

And here what happen when capacitors are also used.

enter image description here

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