Review of Boswell et al paper “Performance of a small loop antenna in the 3-10 MHz band”

(Boswell et al 2005) discussed a small transmitting loop (STL) and offered predictions and measurements of performance.

This article is a review of the discussion at 7MHz.

The STL is a 1m diameter circular loop of 22mm diameter copper conductor at 1,5m height over ground with parameters δ=0.005 and ε=10.

Performance is assessed by prediction and measurement of near-field strength.


Above, Figure 6 from (Boswell et al 2005) shows their predictions and measurements of field strength in the near-field at a range of distances at ground level.

Boswell's approach

The far field gain of an antenna system at 0° elevation is zero (-∞dB), but in the near-field zone, the field strength is significant, predictable and measurable.

Boswell predicts the near-field strength at 1.5m height using Norton's ground model, and calculates radiation efficiency from the reduction in measured field strength.

For 7MHz, from the curves in his Fig 6 he comes to an efficiency of 2.3%.

Boswell measured the input resistance of the loop to be 0.260Ω, and calculates radiation resistance (Rr) to be 6.0mΩ (2.3% of 0.260Ω). It is interesting that the calculated value of Rr is quite close to the calculated Rr of the loop in free space, 5.7mΩ, that does not necessarily follow. Essentially this is accounting for the 16dB gap between lossless prediction and measurement, and attributing it to dissipative losses in the loop structure.

NEC-4 model

In this review, an NEC-4 model was constructed of the main loop.

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Above shows Boswell's predicted and measured curves, and the NEC-4 model predictions with and without losses in the main loop. In the lossy case, the loop was built out with loss to calibrate the feed point impedance to Boswell's measurements. Note that the lossless loop model does include the effects of loss in the ground and radiation efficiency was calculated at 19.8% or -7.0dB.

It is interesting to note that the NEC-4 lossless model is similar to Boswell's Norton model, but about 3.5dB lower.

If a trend line is drawn though Boswell's measurement series to ‘de-noise' it, the NEC-4 lossy prediction is 3.8dB higher.

Note that Boswell did not actually measure ground parameters at the test site, and error in ground type may explain some of the measurement gap.

The NEC-4 model predicts radiation efficiency of 2.2% (-16.7dB), again quite close to Boswell's calculation but applying Boswell's measurements to the lossy NEC model at 40m distance would suggest actual efficiency is 3.8dB lower or 0.9%.


  • The technique of reconciling near-field measurements with a good model may provide a practical means of assessing as-built performance of an STL.
  • Models of lossless loop performance vary.
  • The method depends on soil parameters which should be measured at the test site at the same time for best accuracy.


  • A Boswell, A Tyler, and A White. Apr 2005.  Performance of a small loop antenna in the 3-10 MHz band In IEEE Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005.