I see in chap. 19 of my 19th ed. ARRL Antenna Handbook a description
of a quadrifilar balun transformer with taps at 16:1, 9:1, 6:1 and
4:1.

Is such a balun sold commercially?

If I homebrew it, how do I know where to put the three lower-ratio
taps? Inasmuch as the taps are usually made by putting a small loop in
the magnet wire, this can't be done after the winding is done.

Ken KC2JDY


Ken
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Because impedance is the square of the turns, take the square root of each impedance and tap at that point. ex. 16:1 tap at 4 turns back from the end of the winding, 9:1 at 3 Turns, 6:1 at 6^.5 turns, and 4:1 at 2 turns. Remember to use the correct balun material so that at the lowest frequency of use, the reactance of the windings is at least 4x the reactance (XL) for that frequency. The frequency formula XL = 2*pi*F(Mhz) * L (uH) helps here.
Finally test your balun using a resistor of value 800 ohm across the 16:1 tap and confirm the 50 ohm reading is steady across the frequency range you intend to use.