AE7PD documented his measurements of a 3.16m perimeter circular transmitting loop, 1.8m centre height above ground, that he made using 16mm copper tube and a split stator tuning capacitor:

- https://www.hamradioandvision.com/measuring-loop-efficiency/
- https://dog-asparagus-b2eb.squarespace.com/100-watt-loop-antenna/

AE7PD gives the radiation efficiency on 20m as 30.5% or -5.2dB.

I present here an alternative analysis of the antenna as measured on 20m.

Assuming the measurements were made with the antenna clear of disturbing conductors etc, and that 5/8″ tube means 16mm OD.

The key measurements were:

- centre frequency 14.165MHz, VSWRmin=1.0;
- VSWR=2.62 bandwidth 22kHz.

A NEC-4.2 model of the antenna at 14MHz was built and calibrated to the measured half power bandwidth (22kHz). Model assumptions include:

- ‘average' ground (σ=0.005, εr=13);
- Q of the tuning capacitor = 2000;
- conductivity of the loop conductor adjusted to calibrate the model half power bandwidth to measurement.

Note that the model may depart from the actual test scenario in other ways.

Above is the VSWR scan of the calibrated model, the load is matched at centre frequency and half power bandwidth is taken as the range between ReturnLoss=6.99dB points.

The NEC model reveals that the loop reactance is 256Ω.

Above is a result screen from the NEC model showing some key quantities that can be used to dissect the feed point resistance into important components. Radiation Efficiency given here as 16.6% can be expressed as -7.8dB.

Above, decomposition of the total feed point resistance into components Rr (radiation resistance), Rg (ground loss resistance). and Rstructure (structure loss resistance).

Also of interest is the gain calculated by the model.

Above is the radiation pattern. As expected for an STL near ground, the maximum gain is towards the zenith and in this case it is -2.24dB. The Directivity show in an earlier screenshot (as RDF) is 5.59dB.

## Comparison of NEC model with (Duffy 2014)

(Duffy 2014) is an online calculator for finding STL gain from bandwidth. The basic calculator assumes free space conditions, but provision is made to tweak Rr and Directivity for ground effects.

Above is the uncalibrated model, uncalibrated to mean using the bandwidth measured near ground, but Rr and Directivity for free space conditions.

Note that the perimeter is 0.149λ, well above the stated accurate range of the underlying free space model, as will be seen by comparison with the NEC model which for instance gives Rrfs=0.093Ω, the classic formula gives Rrfs=0.098Ω.

Note that the loop is large enough that current is not sufficiently uniform for the classic formula to be accurate, so little surprise that there is a discrepancy.

More importantly, NEC's calculation of Rr of the loop in the presence of ground being 0.0058Ω is substantially less than predicted by traditional formulas and the main contribution to the NEC's efficiency being near half of AE7PD's estimate.

Adjusting Rr to the model (Rr/Rrfs=0.594), and Directivity to the model (5.59dB) we obtain an efficiency of -8.0dB and gain of -2.4dB which are both within tenths of a dB of the model results.

## Conclusions

The model applies to the scenarios described, and extension to other scenarios may not be valid.

Calculate small transmitting loop gain from bandwidth reconciles well with the NEC-4.2 model.

AE7PD's estimate of efficiency is almost 3dB higher than indicated by the calibrated NEC-4.2 model, a result of its being based on some traditional formulas that have issues that I have discussed elsewhere.

NEC-4.2 is a more complete model of the scenario and when calibrated to the measured half power bandwidth, it probably our best analytical estimator of radiation efficiency.

## References

- Duffy, O. 2014. Calculate small transmitting loop gain from bandwidth https://www.owenduffy.net/calc/SmallTransmittingLoopBw2Gain.htm.