# Small untuned loop for receiving – NEC model

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.