N6THN’s novel balun – flux leakage

N6THN’s novel balun presented measurement of the Insertion VSWR of the subject balun, and N6THN’s novel balun – an explanation gave explanation that included mention of flux leakage as a contributor to the quite high inductance per unit length of the transmission line formed by the two windings.

A correspondent suggested that with a ferrite core, flux leakage is insignificant. This article calculates the coupled coils scenario.

The balun as described

Above is the ‘schematic’ of the balun. Note the entire path from rig to dipole.

Flux coupling factor

Let’s use the impedance measurement with short circuit termination to find the inductance of the two coupled windings in series opposed.

Above is a plot of the impedance, R+jX. X at 1MHz implies L=8.6µH. Remember that this is the inductance of two series opposed coils, so it includes the effect of mutual inductance.

We can estimate reasonably by calculation that the inductance of one coil L1 @ 1MHz is 114µH.

Measurement of a SC termination gave \(L=(L1-M)+(L2-M)=8.6µH \) and since L1=L2 we can calculate \(M=114e-6-\frac{8.6e-6}{2}=109.7\;µH\) and from that the flux coupling factor \(k=\frac{M}{\sqrt {L1L2}}=\frac{109.7}{114}=0.9623\).

So, k is very high, there is very little flux leakage, but not enough to ignore… it has a huge bearing on the outcome.