# MATHEMATICAL PROOF

## By G3TXQ

**Steve Hunt, G3TXQ** is the creator of the "Broadband HEX BEAM". He has an excellent web site with all kinds of useful information, especially his tips on which type of balun
to use, which ferrite mix, and how many turns to use. See: http://www.karinya.net/g3txq/

**HERE IS STEVE'S MATHEMATICAL PROOF:**

**If you wind a 4:1 Guanella balun as two identical 1:1 chokes on a common core**, you force the CM voltages across the two chokes to be the same because they share the same flux.
If we call the input voltage V, the balun then drives the output terminals to +3V/2 and -V/2 with respect to ground. If you had a perfectly balanced load that would force 3 times the current
into one leg compared to the other. Analysis here:

**Comments by Steve , G3TXQ:**

The voltage on the top output terminal is 3x as great as the voltage on the lower output terminal.

This is not balanced. Indeed it represents a 3:1 imbalance.

No "real world" antenna is fully floating;

fully floating would mean it was impossible for any current to flow between
the antenna and ground.

All "real world" antennas are 3-terminal networks - the 3 terminals being the 2 connections to the antenna, plus ground. This sketch on the right illustrates what I am talking about
è

**Antenna terminals are A &
B**

If the antenna is fully floating, Z_{3} would be infinite and I_{3} would be zero.

If the antenna is balanced, Z_{1}=Z_{2}

**but nothing is implied about Z _{3}**

**Comments by Rick, DJ0IP:**

With Z1 and Z2 being similar (as should be with a balanced antenna), the different voatage levels caused by this type of balun at terminals A and B will cause the current at A and B to be different.

**This is exactly what causes common mode current on the feedline!**

The single-core 4:1 Guanella fails to do its job of keeping the currents balanced in the feedline. Therefore, for all intents and purposes, it is NOT a balun.

Although at this point it might seem logical to use a voltage balun, which forces equal voltages onto each side, it has been shown by W8JI and W7EL that the voltage balun does a very poor job of suppressing common mode currents.

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