QST publishes a design by W0SJ for a nominal 50:450Ω EFLW matching device from 160-10m using the following circuit.

The article is ‘in-brief’ as technical stuff that will not interest most hams is published privately on a members-only page. This article is based on the information in the QST article alone (ie not on the private members only supplementary information).

The core has a modest price in North America, but shipping to other parts of the world may make it very expensive… IOW unobtainium to most parts of the world.

Above is the published InsertionLoss. The article states that they were half the value obtained in a back to back measurement, and it should be noted that is a compromised measurement, and secondly that InsertionLoss comprises two components, (dissipative) Loss and MismatchLoss.

The fact that InsertionLoss increases markedly at the lower frequencies is a hint that it has too few turns for those frequencies, and that InsertionVSWR and efficiency may suffer.

The transformer is intended to be used with a load such that the input impedance Zin is approximately 50+j0Ω, Gin=0.02S.

Analysis of a simple model of the transformer with a load such that input impedance is 50+j0Ω gives insight into likely core losses in that matched condition.

Let us calculate the magnetising admittance of the 4t primary at 1.8MHz. The core is a Laird 28B1540-000 ferrite toroid.

Above is a table of complex permeability for Laird 28 material. (I have seen online experts advise that this information is not available… but here it is.) The Laird #28 material is a medium μ NiZn ferrite, somewhat similar to Fair-rite #43 but different enough to not be equivalent.

Now lets model the 4t primary at 1.8MHz.

Gcore is the real part of Y, 0.000826S.

If Yin of the loaded transformer is 0.02S, we can calculate the core efficiency as 1-Gcore/Gin=1-0.000826/0.02=95.8%, core loss is 0.18dB. Note that this efficiency is in the matched condition, and could be higher or lower at other input impedances (η=1-Gcore/Gin). Ferrite materials have fairly wide tolerance, so measurements of actual cores may have some variation.

The balance of the measured InsertionLoss is likely to be MismatchLoss, but that information is not disclosed in the main article. MismatchLoss will include contributions from the shunt magnetising admittance (moderately low in this case) and effects of flux leakage.

## References

- 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).