Small efficient matching transformer for an EFHW – NEC model at 3.6MHz

The article Small efficient matching transformer for an EFHW laid out a design for a small EFHW transformer.

This article builds an NEC model for an EFHW antenna at 3.6MHz incorporating a realistic model of the above transformer.

NEC provides for a NT card characterising a two port network using Y parameters.

Y parameter model for the transformer

The Y parameter model is based on measured input impedance with port 2 open circuit, and short circuit, and the observed turns ratio.

Impedance was measured with the uncompensated transformer at 3.6MHz using an AA-600, the compensation in the reference article has little effect at 3.6MHz.

Above, the calculated Y parameter model including a prototype NT card. This model captures the various loss components of the transformer, mainly magnetising loss, at 3.6MHz.

Note that the Y parameter model is frequency specific.

NEC model

Above is a graphic showing the geometry of the NEC model. Essentially the feed point has about λ/10 ‘counterpoise’ at a height of 0.3m to the left of the feed point, and a wire slopping upwards at about 45° for the main antenna conductor.

Although the NT card is frequency specific to 3.6MHz, we get a fair idea of the VSWR response over a narrow frequency range. The minimum VSWR of 1.095 at 3.6MHz is correct.

Above is a summary of the NEC model. Network loss captures the loss in the transformer, and at 100W input the transformer loss is just under 10W. This is much better transformer efficiency than almost all of the published designs that I have reviewed.

Radiation efficiency is 38%, a combination of conductor loss, transformer loss and ground loss, mostly ground loss.

Above is the pattern, highest gain is at towards the zenith as can be expected of a low antenna. Maximum gain is about 1dBi.

Above, at lower elevation (30°) the pattern shows a little skew due to the sloping radiator.

Conductor loss is calculated at 1.6% for 2mm diameter copper. This is quite low but could easily exceed 10W for thin ‘stealth’ copper wire, and worse for steel or stainless steel conductors.

If this looks like an improvised antenna that performs well, keep in mind that the top of the sloping wire is at 28m height.