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Some dedicated hams have spent a lot of effort gathering empirical data on various constructions for common-mode chokes. For example, G3TXQ's work is commonly referenced, and K9YC's is pretty well-known as well.

However, I'd like to build a 4:1 current balun. Several sources (like this one) describe why two cores are necessary. They are wired in parallel on the 50Ω (transceiver) side and in series on the 200Ω (antenna) side.

The question is, what ferrites and windings should I use in this case? Is it sufficient to construct two 1:1 common mode chokes according to G3TXQ's or K9YC's instructions for the bands of interest, then wire them together as described in the previous paragraph? Or is it not that simple?

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Is it sufficient to construct two 1:1 common mode chokes ... then wire them together as described in the previous paragraph?

It is nearly as simple as that. Here's a wiring diagram:

enter image description here

In a perfect world, the transmission line wound around each core would have a characteristic impedance of $\sqrt{200*50}$=100-$\Omega$. Books on this subject by Sevick and the ARRL Antenna Book describe means for achieving the required impedance using insulated copper wire and teflon tubing. In his Speaker Wire Balun Test, KN5L demonstrates the efficacy of a readily-available household item in this application.

For use at the 100-W power level, I constructed a balun of this type with 18-ga speaker wire wound on FT140-43 ferrite toroid cores:

enter image description here

I did not perform any loss measurements on this balun. It's possible -61 material would deliver lower loss, as long as the wound turns deliver sufficient choking reactance for your application.

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