Richard, G3CWI, measured the impedance and bandwidth of a Alexloop Walkham, a popular small transmitting loop (STL). The antenna was situated in the clear at 1.65m centre height above natural ground.

The key measurements were:

- centre frequency 7.014MHz, |Z|=51Ω, VSWR=1.1;
- VSWR=3 bandwidth 16.2kHz.

The step size of the analyser prevented measurement exactly at resonance, but R changes very closely with frequency near resonance so we can estimate it quite well. The above figures can be used to find R close to resonance.

Within the limits of measurement error, we can say that R at resonance should be very close to 51Ω, and VSWRmin close to 1.02.

We can infer the half power bandwidth from the quantities above, it is 14.2kHz.

A NEC-4.2 model of the antenna at 7MHz was built and calibrated to the implied half power bandwidth (14.2kHz). 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.

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 1.402% can be expressed as -18.5dB.

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 -13dB. The Directivity show in an earlier screenshot (as RDF) is 5.84dB.

## 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=0.875), and Directivity to the model (5.84dB) we obtain an efficiency of -18.5dB and gain of -12.6dB 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.

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.