EFHW-2843009902-43-2020-3-6kThis article applies the Simsmith model described at A simple Simsmith model for exploration of a common EFHW transformer design – 2t:14t to a ferrite cored 50Ω:200Ω transformer.

This article models the transformer on a nominal load, being \(Z_l=n^ 2 50 \;Ω\). Keep in mind that common applications of a 50Ω:200Ω transformer are not to 200Ω transformer loads, often antennas where the feed point impedance might vary quite widely, and performance of the transformer is quite sensitive to load impedance. The transformer is discussed here in a 50Ω:200Ω context.

Above is the prototype transformer using a 2843009902 (BN43-7051) binocular #43 ferrite core, the output terminals are shorted here, and total leakage inductance measured from one twisted connection to the other.

The prototype transformer is a 3:6 turns autotransformer with the two windings twisted bifilar.

Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side.

- Secondary side leakage inductance Lls is divided by n^2 to obtain the value primary referred leakage inductance in the circuit diagram.
- Cse is an equivalent shunt capacitance to partially model self resonance effects.
- Bm is the magnetising susceptance (calculated from other parameters).
- Gm is the magnetising conductance (calculated from other parameters).
- Llp is the primary side leakage inductance.
- Ccomp is a compensation capacitance.

A Simsmith model was built to implement the transformer model above.

- Complex core permeability is captured from a permeability data file.
- np is the number of turns on the primary.
- ratio is the turns ratio.
- cores is the number of cores in a stack.
- cse is Cse per the circuit diagram.
- Ll is the value of Llp and Lls' (which are assumed equal).

Having measured the short circuit input inductance to be 43nH, it is distributed equally over Llp and Lls' so Ll is entered as 22nH.

Above is a screenshot of the Simsmith model. Block D1 is used for data entry to supply some values direct and calculated to the following blocks.

Tfmr is the model of the transformer as shown in the diagram earlier.

Above is a plot of the measured total leakage inductance over 1-30MHz.

Above is a plot of calculated 1-k where k is the flux coupling factor. Again the measured leakage inductance and winding inductances show that k is not independent of frequency, and 1-k (which determines leakage inductance in a coupled inductor model) varies over more than 2:1 range in this example. The graph demonstrates that models that are based on an assumption that k and 1-k are independent of frequency are flawed.

Above is the modelled VSWR response of the compensated transformer on a nominal load. It is very good from 3.5-30MHz.

Above, drilling down on more detail, the \(Loss=10 log \frac{PowerIn}{PowerOut}\) curve is very good. Maximum loss is at about 4MHz, and at 0.06dB loss @ 7.0MHz means that 98.6% of the transformer input power power reaches the transformer output terminals, the deficit being lost mostly in heating the ferrite core.

So, in contrast to the FT240-43 2t:14t transformer:

- ΣA/l is nearly nine times that of the FT240 core, so fewer turns are required for similar core loss;
- shorter winding length helps to reduce flux leakage;
- lower leakage flux improves VSWR bandwidth;
- smaller cores can dissipate less heat;
- reducing core loss reduces the need to dissipate as much heat; and
- compensation capacitor assumes Q of silver mica, the appropriate choice for a transmitting application;

The transformer in free air can probably dissipate around 2W continuous, an at 4MHz where transformer loss is 1.35%, continuous power rating would be 148W (200Ω load, free air). Of course an enclosure is likely to reduce power rating.

Note that leakage inductance is sensitive to the diameter of conductors and the spacing relative to other conductors, so changing the wire conductor diameter and insulation diameter, and wire to wire spacing all roll into changes in leakage inductance. For broadband performance, the goal is least leakage inductance.

Try changing model parameters in the sample model (link below), change mix type, measure the leakage inductance for some different winding configurations and use it.

If you have heard online experts advising the #43 mix is not suitable for this type of application, and that you should use something else… try something else in the model… if you can find a binocular of this size in a more suitable material.

The model input value aol is the core geometry ΣA/l (m) and can be calculated from dimensions using Calculate ferrite cored inductor – rectangular cross section. Some datasheets give ΣA/l or ΣA/l in various units which can be inverted / scaled as necessary. Calculate ferrite cored inductor (from Al) can calculate ΣA/l (m) from Al.

The model does not give a definitive design, but it does help to explore the effects of magnetising admittance and leakage inductance on VSWR bandwidth, loss etc.

## References

Sample Simsmith model for download: EFHW-2843009902-43-2020-3-6k.7z . (Compressed with 7zip.)