# End Fed Half Wave matching transformer – 80-20m

A prototype broadband transformer for a End Fed Half Wave operated at fundamental and first, second, and third harmonic is presented. The transformer comprises a 32t of 0.65mm enamelled copper winding on a FT240-43 ferrite core, tapped at 4t to be used as an autotransformer to step down a load impedance of around 3300Ω to around 50Ω. The winding layout is unconventional, most articles describing a similar transformer seem to have their root in a single design.

## RLC meter measurement of inductances at 10kHz

Inductance was measured using a RLC meter at 10kHz. The inductances were 15.8, 824 and 1056µH.

From that we can calculate for the two winding parts, M=-(1056-(15.8+824))/2=-108.1µH, and we can calculate flux coupling factor k=108.1*(15.8*824)=0.947 at 10kHz.

The flux leakage is quite low at 10kHz by virtue of the medium core permeability, and the winding concentrated, almost close wound.

But, things change as the frequency is increased. Above is the complex permeability characteristic of the #43 material used.

The real part of permeability decreases and the imaginary part increases (representing core loss). We can estimate the magnetising impedance and admittance from the core dimensions and the permeability characteristic above. At 7.1MHz, rather than look like a nearly pure inductance of 15.8µH as it did at 10kHz, the 4t winding looks like an inductance of 7.3µH in series with 224Ω of resistance (due to core loss).

A first approximation of the transformer behaviour is that it is an ideal transformer shunted with its magnetising admittance 0.00143-j0.00209S.

If the transformer and load are adjusted to input VSWR(50)=1, Zin=50+j0Ω, Yin=1/50+j0S. If a component of the real part 1/50=0.02 is due to the magnetising conductance, then we can calculate the percentage of input power lost in heating the core as 0.00143/0.02*100=7.1%.

For 3.6MHz, the core loss is 0.00166/0.02*100=8.3% of input power, and the case for 14.2MHz is left as an exercise for the reader.

## VNA measurements

The transformer was swept from 1 to 30MHz with a 3250Ω resistor in series with the VNA rx port, so the transformer load is 3300Ω. The resistor was measured with an accurate ohmmeter, and it is assumed that departure from ideal is small. It is beyond the accuracy of the VNA to measure the resistor simply. Above, we can see the uncompensated transformer. Note R falls and X increases below 3MHz, a result of low magnetising impedance (high admittance).

At the high end, X increases above about 7MHz though R is fairly good up to 20MHz, a result of leakage inductance. Although flux leakage is quite small at 10kHz, at RF with reduced permeability we can see signs of significant flux leakage. Above is the sweep with a 100pF capacitor in shunt with the input. It improves the VSWR at 15MHz from 4.0 to 2.5, but things go worse even more quickly at higher frequencies… this is the nature of this form of compensation.

The compensation capacitor should be a good quality RF capacitor, eg a 500V silver mica should suit up to 100W input, or a Class 1 ceramic capacitor should suffice. An alternative is a 1.9m length of RG6 formed into a U shape or a small coil, and BOTH ends connected in parallel with the input winding, this should have a Q of better than 1000 at 15MHz and a very high voltage withstand.

## Summary

The design presented is a low cost broadband transformer for matching an n half waves end fed antenna to 50Ω feed for 80-20m with reasonably low core loss (<10%). It uses readily available materials, and has sufficient core surface area to be good for 100W SSB input.

These type of antennas find use for low power portable operation with transmitters that are tolerant of wide variation in load impedance.

A somewhat lower turns ratio may provide a better match… more when I have tested it on some real antennas.

## Variation to the design

The design depends heavily on the #43 ferrite material characteristic, core size, and winding turns. The winding are arranged as an autotransformer and near close wound to reduce flux leakage. substituting or varying details may result in a significant departure from described behaviour.

The material is probably not a good choice for a 7-30MHz transformer, I would be investigating a different mix.

## Going forward

The next step is to test the transformer at part of a complete antenna system. Above, taps have been added to the transformer for turns ratios of 4:24,28,32. As mentioned, lower taps may better suit the system.