# An NEC-4.2 model of VK5BR’s 1m square loop for 20m

(Butler 1991) gives a design for a Small Transmitting Loop (STL) for 14MHz and some other bands.

He gives key design data:

```Tube Diameter d   0.75 inch
Circumference S  12.7 feet
Area A =   10 square feet
Frequency f =  14.2MHz
Power P   100 watts
Radiation Resistance Rr =   0.137 ohm
Loss Resistance RL =   0.064 ohm
Efficiency n =  68%
Inductance L =   3.27 micro-henry
Q factor =   723
Inductive reactance XL =   291 ohms
Bandwidth B =   19.6kHz
Distributed capacity Cd =   10.4pF
Capacitor potential Vc =   4587V
Tuning capacitor Ct =   28pF
```

The data above appear to ignore some important factors, and estimate some others based on an assumption of uniform current.

## NEC model

A comparison NEC-4.2 model was constructed.

Key assumptions for the NEC model:

• Qcap = 1000;
• antenna centre height = 1.5m;
• average ground (0.005/13);
• matching system assumed lossless;
• fed at the top of the loop, cap down;
• impedances are referred to the nominal feed point of the main loop.

Note that the loop is sufficiently large that the current is not uniform around the loop, and that acts to transform some values to the feed point equivalent. For example, the conductor resistance at the feed point is not simply the RF resistance of the equivalent length. Above is a breakup of the input impedance Rtotal into three components:

• Rgnd – a resistance to represent the loss by heating of the soil;
• Rstr – the total structure loss resistance (conductor and capacitor).

Butler ignored Rgnd (ie Rgnd=0) and capacitor loss, and his estimate for conductor loss seems to assume uniform current. The values for Rrad and Rstr from the NEC model are different because they capture the capacitor loss, and effects of current distribution. Rgnd is significant, and including it makes a large difference.

So, the antenna with claimed efficiency of 68% is, dependent on ground and actual capacitor and matching, probably more like 20%, almost 6dB lower.

The additional losses reduce the capacitor voltage to around 3240VRMS (4600Vpk).

## Conclusions

Butler’s efficiency claim would seem unrealistically high.