This article offers a simple Simsmith model for the Small efficient matching transformer for an EFHW.

Above is the model topology. D1 is a daemon block which essentially, calculates key values for the other blocks based on exposed parameters and the named ferrite material complex permeability data file. The prototype used a Fair-rite 2643625002 (#43) core.

D1 code:

//Misc //Updates Tfmr, CoreLoss, and Cse. $data=file[]; // core mu aol; np; ratio; cse; cores; k; $u1=$data.R; $u2=$data.X; //u1=$u1; //u2=$u2; $ns=np*ratio; Ym=(2*Pi*G.MHz*1e6*(4*Pi*1e-7*$u1*aol*cores*1e9)*np^2*1e-9*(1j+$u2/$u1))^-1; Cse.F=cse; CoreLoss.ohms=1/Ym.R; $l1=1/(2*Pi*G.MHz*1e6*-Ym.I); $l2=$l1*(($ns-np)/np)^2; $lm=k*($l1*$l2)^0.5; Tfmr.L1_=$l1+$lm; Tfmr.L2_=$l2+$lm; Tfmr.L3_=-$lm;

L is the load block.

Cse models the self resonance of the transformer at lowish frequencies, Cse is an equivalent shunt capacitance.

Tfmr is a coupled coils model (above) of a (nearly) lossless autotransformer (core loss will come later). Wire loss is usually insignificant in these type of transformers and is ignored. (It seems that Simsmith will not simulate a pure inductance, in this cases the loss of the ‘lossless transformer is of the order of 5e-6dB, so satisfactory.) It is possible to simplify declaration of this component by using Simsmith’s coupled coils in a RUSE block, I have chosen to take full control and solve the mutual inductance effects explicitly.

(The model assumes that k is independent of frequency which is not strictly correct, but for medium to high µ cores, measurement suggests it is a fairly good assumption.)

Coreloss brings the ferrite core loss to book.

Ccomp models a compensation capacitor used to improve broadband InsertionVSWR.

The G block provides the source and plot definitions.

Plots code:

//Plots //check lossless Tfmr behavior //tfmrloss_dB=10*Log10(Tfmr.P/(Tfmr.P-Tfmr.p)); //Plot("TfmrLoss",tfmrloss_dB,"LossdB",y1); coreloss_dB=10*Log10(CoreLoss.P/(CoreLoss.P-CoreLoss.p)); loss_dB=10*Log10(G.P/L.P); mismatchloss_dB=10*Log10(1/G.P); Plot("CoreLoss",coreloss_dB,"LossdB",y1); Plot("Loss",loss_dB,"LossdB",y1);;

## Results

The model was calibrated to measurement of the prototype, and the fit is quite good given tolerances on components.

The model allows convenient interactive sensitivity analysis where parameters can be dialed up and down with the mouse wheel and the response changes observed.

## 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).