At PD7MAA’s BN43-202 matching transformer for an EFHW I gave an estimate of the core loss in PD7MAA’s transformer.

An online expert questioned the analysis and later measurements, and proposed his own transformer design as evidence.

Notably, his transformer uses #61 material and a larger binocular core, a Fair-rite 2861006802 with 2t for a nominal 50Ω primary, giving loss measurements at 7MHz of 0.08dB. Note that the confidence limits of that loss measurement because of the way in which it was obtained (eg a 1% error in the 1120Ω load resistor contributes 0.043dB error to the result), but the measurements do suggest that the loss is probably very low.

Though the loss is low and Return Loss is high at 7MHz, the limits for ReturnLoss>14dB (VSWR<1.5) is 5-18MHz. With compensation, that range may be changed.

## Prediction

Lets apply the method laid out at PD7MAA’s BN43-202 matching transformer for an EFHW.

The best Fair-rite data I can find quickly is a chart of the impedance of a one turn winding.

Scaling from this graph, Xs is close of 35Ω at 7MHz, so lets used that to derive some basic parameters for the core.

Firstly, lets find the permeability of #61 at 7MHz.

Freq (MHz) |
µ’ |
µ” |

7.000e+0 |
1.214e+2 | 1.159e+0 |

Using that in a calculator to iteratively find the value of ΣA/l that gives Xs=35Ω at 7MHz, we obtain ΣA/l=0.0054m, this captures the magnetic path geometry of the binocular core.

Let us now use that core characteristic to calculate the magnetising admittance of the 2t primary winding.

Gcore is the real part of Y, 0.0000421S.

If Yin of the loaded transformer is 0.02S, we can calculate the core efficiency as 1-Gcore/Gin=1-0.0000421/0.02=99.8%, core loss is 0.009dB.

The total loss of this type of transformer will be dominated by the core loss.

## Conclusions

The posted measured results, though having wide confidence limits, fall quite in line with a theoretical prediction using the method laid out at PD7MAA’s BN43-202 matching transformer for an EFHW. The measurements are evidence that the design method works.

The superior efficiency of the tested transformer is due to a better magnetic design, better than the PD7MAA design.

## References

- PD7MAA EFHW antenna for 40-10m qrp
- 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).