A correspondent wrote suggesting that he had seen online NEC patterns showing a 30″ square small untuned loop to have a gain of around 10dBi, more than 30dB better than given by Calculate small loop Antenna Factor.

Firstly, lets describe a loop for study, a square diamond with sides of 760mm (30″) of 2mm diameter copper fed in one corner at 7.1MHz.

## Calculate small loop Antenna Factor

Calculate small loop Antenna Factor models a small loop in free space (therefore does not include ground losses).

Above is the calculator result, the key figures are Antenna Factor 31.75dB and Gain -44.5dBi.

## NEC-4.2 model

An NEC-4.2 model was constructed with external excitation (1V/m) incident on the loop which has a 50+j0Ω load inserted at the feed point to represent the receiver load.

Here is the model source.

CM Small square untuned loop CM NEC-4.2 CM CM 1. Plane wave excitation CM CM Owen Duffy CM Note: rotations might not work properly in various NEC-2 versions, beware of segment size issues in NEC-2. CE GW 1 5 -0.38 0 -0.38 0.38 0 -0.38 0.001 GM 1 3 0 90 0 0 0 0 1 GM 0 0 0 90 0 0 0 2 1 GE 0 LD 5 0 0 0 58000000 LD 4 1 1 1 50 0 GN -1 EK EX 1 1 1 0 45 0 0 0 0 0 FR 0 0 0 0 7.1 0 EN

The key result to be extracted from the model run is the current in the 50Ω resistor in segment 1 of wire 1. The magnitude of the current is 5.1204E-04, so the voltage developed in the resistor V=5.1074-04*50=0.02554V. Antenna Factor is the ratio of the E field excitation to the terminal voltage of the receiver, so in dB it is 20*log(1/0.02554) =31.83 dB/m.

The NEC model’s 31.83 dB/m is close to the calculator prediction of 31.75dB/m, but includes the benefit of the lossy ground reflection .

Likewise, Gain calculated from the NEC Antenna Factor of 31.83 dB/m is -44.6 dB, about a tenth of a dB of the original calculator prediction.

Of course, transmission line loss to receiver needs to be factored in separately.

## Conclusions

Within the stated limits of the models, valid models should provide consistent results, and they do in this case.

Results should be validated by measurement, and whilst I have not measured this particular loop, I have validated a slightly smaller loop (600mm square) that I use regularly for field strength measurement and so have confidence in the modelling tools for this application.

My correspondent’s report of a 30″ square untuned loop with gain of -10dBi on 7MHz suggests a misunderstanding or the online expert’s model is seriously flawed.

It is common that extravagant claims are made of small loops by would be aficionados, be wary.