At FT82-43 matching transformer for an EFHW I wrote about the likely losses at 3.6MHz of a common design using a FT82-43 ferrite core with a 3t primary. In that case, expected efficiency (meaning PowerOut/PowerIn) of the transformer was less than 65% at 3.6MHz.

I have been offered input VSWR curves for such a configuration, and they are impressive… but VSWR curves do not address the question of loss / efficiency.

Note that building loss into antenna system components is a legitimate and common method of taming VSWR excursions, eg TTFD, CHA250, many EFHW transformers, but in some applications, users may prioritise radiated power over VSWR.

## Design context / objectives

Objectives are:

- used with a load such that the input impedance Zin is approximately 50+j0Ω, Gin=0.02S;
- broadband operation from 3.5-30MHz;
- VSWR less than 2 with nominal 3200Ω load; and
- transformer efficiency > 90% at 3.6MHz.

The following describes such a transformer using a Fair-rite 2643625002 core (16.25×7.29×14.3mm #43).

I mentioned in the reference article that the metric ΣA/l captures the geometry, the larger it is, the fewer turns for same inductance / impedance. ΣA/l for the chosen core is 3.5 times that of a FT82-43 yet it is only 1.6 times the mass.

The transformer is wound as an autotransformer, 3+21 turns, ie 1:8 turns ratio.

## Uncompensated

Firstly, lets estimate at 3.6MHz minimum number of turns to ensure that magnetising conductance is less than about 0.002S (for better than 90% core efficiency).

Above, 3t on the primary delivers Gcore<0.002S.

Above is a sweep of the uncompensated prototype with a 3220+50Ω load.

Let work through a loss analysis.

Because of the division of power between the 3220Ω resistor and VNA input, there is effectively an attenuator of -10*log(50/(50+3220))=18.16dB, so |S21| has a component due to this division. Lets call this element the LoadAttenuator.

Zin=46.52+j6.72Ω. From that we can find Mismatch Loss.

MismatchLoss is 0.03dB.

Loss (to mean PowerIn/PowerOut) can be calculated in dB as -|S21|-LoadAttenuator-MismatchLoss=–18.64-18.16-0.03=0.450dB, or an efficiency of 10^(-0.45/10)=90.2%.

Note that there is some uncertainty in the measurements, but we can be confident that the loss is no where near the figure estimated for the FT82-43 design.

## Compensation

A 100pF silvered mica was connected in shunt with the transformer primary. This is not an optimal value, benefit may be obtained by exploring small changes to that value.

Above is a sweep of the roughly compensated transformer. The capacitor makes very little difference to the low frequency behavior, but it reduces the input VSWR significantly at the high end. VSWR<1.8 over all of HF.

## Comparative power handling

This transformer has more surface area than a FT82-43 based one, so it has higher capacity to dissipate heat, and it is more efficient, so it will have higher power capacity than the FT82-43 based one.

Above is a thermograph of the transformer at 20W input at 3.6MHz. Ambient temperature is 20°, and the core temperature increased by 5° over 120s @ 20W continuous input. That does not seem inconsistent with the expectation calculated above of about 10% core loss at 3.6MHz.

## Real antennas

The tests here were using a dummy load on the transformer, and that did allow confirmation of the design and expected loss at 3.6MHz.

Real end fed antennas operated harmonically do not present a constant impedance, not even in harmonically related bands. Note that the resonances do not necessarily line up harmonically, there is commonly some enharmonic effect.

Being a more efficient design that some, it might result is a wider VSWR excursion that those others as transformer loss can serve to mask the variations in the radiator itself.

## Does it matter?

Well, in ham radio, everything works. But systems that work better increase the prospects of contacts.

## References

- FT82-43 matching transformer for an EFHW
- Find |Z|,R,|X| from VSWR,|Z|,R,Ro
- A new impedance calculator for RF inductors on ferrite cores
- Calculate ferrite cored inductor (from Al)
- Calculate VSWR and Return Loss from Zload (or Yload) and Zo
- Duffy, O. 2015. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. https://owenduffy.net/files/EstimateZFerriteToroidInductor.pdf.
- ———. 2006. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. VK1OD.net (offline).