# Thoughts on the ARRL EFHW antenna kit transformer

I have not built and measured the thing, but have done the first step in a feasibility study.

The transformer design is not novel, it is widely copied and this may be one of the copies. The design is usually published without any meaningful performance data or measurements.

The article Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – comparison of measured and predicted laid out a method for approximating the core loss of a EFHW where the load is adjusted to that input VSWR50=1, ie input Z=50+j0Ω.

That method will be applied here for a good initial estimate of core loss.

I will present calcs for 80m and 40m since there are lots of articles and videos encouraging people to extend the antenna to 80m (with and without a loading coil).

It is quite practical to build an EFHW transformer with less than 0.5dB (11%) core loss.

## Amidon FT240-43 toroid with 2t primary

The first point to note is that Amidon's 43 product of recent years is sourced from National Magnetics Group, and is their H material. It is not a good equivalent to Fair-rite's 43 mix.

Let's make a first estimate of core loss at 3.5MHz.

We can estimate the complex permeability which is needed for the next calculation.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

We can calculate core magnetising loss as $$Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00950}{0.02}\right)=1.7 \; dB$$.

Let's make a first estimate of core loss at 7MHz.

We can estimate the complex permeability which is needed for the next calculation.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

We can calculate core magnetising loss as $$Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00778}{0.02}\right)=1.4 \; dB$$.

## Fair-rite FT240-43 toroid with 2t primary

Let's make a first estimate of core loss at 3.5MHz.

We can estimate the complex permeability which is needed for the next calculation.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

We can calculate core magnetising loss as $$Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00522}{0.02}\right)=1.1 \; dB$$.

Let's make a first estimate of core loss at 7MHz.

We can estimate the complex permeability which is needed for the next calculation.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

We can calculate core magnetising loss as $$Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00521}{0.02}\right)=1.0 \; dB$$.

## Conclusions

The first estimate of core loss of 1.7dB at 3.5MHz of the specified Amidon FT240-43 is quite high and causes me to not even think of building one. Core loss is a little better at 7MHz at 1.4dB, but still unacceptable for me.

A genuine Fair-rite core is better at 1.1dB at 3.5MHz, but again, I think it also unacceptable just on the basis of core loss alone. Core loss is a little better at 7MHz at 1.0dB, but still unacceptable for me.

At the lowest published design frequency of 7MHz using the specified Amidon FT240-43 core, under the assumptions stated above, 28% of input power is lost in heating the core. That equates to 70W of the rated 250W converted to heat in the core.

This issue is not the only one with the design and implementation.