(Findling, A & Siwiak 2012) documented measurements they made of a popular small transmitting loop (STL), an Alexloop Walkham.

Now Alexloops seem to have undergone some evolution, and there does not seem to be a clear list of model names or numbers with features or specifications, so to some extent the antenna is a little non descript.

The article did not document the environment of the test antenna, but Findling explained in correspondence that it was relatively clear of conducting structures and about 1.2m above natural ground.

A NEC-4.2 model of the antenna at 7MHz was built and calibrated to their measured half power bandwidth (19kHz). Model assumptions include:

- ‘average’ ground (σ=0.005, εr=13);
- Q of the tuning capacitor = 1000;
- 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, it is challenging to glean all the data that one would like from the article.

Above is an extract from (Findling, A & Siwiak 2012).

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 124Ω.

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 1.073% can be expressed as -19.69dB.

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 at the zenith and in this case it is -14dB. The Directivity show in an earlier screenshot (as RDF) is 5.84dB.

## Comparison of NEC model with experimental results

The key experimental result was radiation efficiency of -15.77dB (2.65%) which is almost 4dB better than the model results.

There may be two main contributions to this, the use of term 2*Rrad in the efficiency calculation, and the value of radiation resistance Rr (Rrad) may not account for the effect of ground reflection on Rr.

(Findling, A & Siwiak 2012) mention “ideal loaded Q” in calculating Qrad which hints that they may be disciples of (Hart 1986) . They calculated Qtotal from the loop antenna alone, and for their given efficiency calculation, Qrad should be calculated for exactly the same scenario but with all of the dissipative losses extracted. Qrad should be of the order of 28,447 for their antenna, and their efficiency on that basis should be 10*log(376.29/28447)=-18.79dB (1.32%).

## 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.

Adjusting Rr to the model (Rr/Rrfs=0.89), and Directivity to the model (5.84dB) we obtain an efficiency of -19.7dB and gain of -13.9dB which are both within 0.1dB of the model results.

## Conclusions

The model applies to the scenarios described, and extension to other scenarios may not be valid. Note that different models of Alexloop may have significantly different behavior.

The radiation efficiency calculated by (Findling, A & Siwiak 2012) of their test antenna does not reconcile well with an NEC-4.2 model and appears to be optimistic, possibly due to a flawed concept of Qrad.

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

## References

- Duffy, O. 2014. Calculate small transmitting loop gain from bandwidth https://www.owenduffy.net/calc/SmallTransmittingLoopBw2Gain.htm.
- Hart, Ted (W5QJR). 1986. Small, high efficiency loop antennas In QST June 1986.
- Findling, A & Siwiak, K. Summer 2012. How efficient is your QRP small loop antenna? In The QRP quarterly Summer 2012.