Small untuned loop for receiving – a design walk through #1 arrived at a design concept comprising an untuned small loop loaded with a broadband amp with input Z being a constant resistive value and with frequency independent gain and noise figure.

Small untuned loop for receiving – a design walk through #2 developed a simple spreadsheet model of the loop in free space loaded by the amplifier andperformed some basic SND calculations arriving at a good candidate to take to the next stage, NEC modelling.

The simple models previously used relied upon a simple formula for predicting radiation resistance Rr in free space, and did not capture the effects of proximity of real ground. The NEC model will not be subject to those limitations, and so the model can be run from 0.5-30MHz.

The chosen geometry was:

- loop perimeter: 3.3m;
- conductor diameter: 20mm;
- transformer ratio to 50Ω amplifier: 0.7; and
- height of the loop centre: 2m;
- ground: average (σ=0.005 εr=13).

## NEC-5.0 model results

The effect of interaction with nearby real ground is to modify the free space radiation pattern. The pattern at low frequencies has maximum gain at the zenith, and above about 15MHz the pattern spreads and maximum gain is at progressively lower elevation. For the purposes of a simple comparison, the AntennaFactor was calculated for external plan wave excitation at 45° elevation in the plane of the loop.

Above is a plot of loop Gain and AntennaFactor at 45° elevation along the loop axis. The frequency range is 0.5-30MHz as the NEC model is not limited by the simple Rr formula. Additionally there is some ‘ground gain’ of around 5dB due to lossy reflection of waves from the ground interface.

The SND statistic was the target of optimisation, so let’s look at that. For simplicity, let’s assume that Directivity is 6dB, and calculate average Gain from the gain reported above using Directity.

Though the initial design criteria was that SND<3dB to 9MHz, the NEC model just misses that (3.15dB), but it is close.

The plot shows the wider perspective that although the optimisation pretty much contained SND up to 9MHz, it continues to grow above that reaching 11dB at 30MHz. If that parameter was important above 9MHz, iterative tweaking and running of the NEC models may provide an optimisation.

Above is the result of a NEC model run with a 1.4:1 transformer at the feed point, effectively loading the loop with 100Ω.

## References

ITU-R. Aug 2019. Recommendation ITU-R P.372-14 (8/2019) Radio noise.