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MAGNETIC MOMENTS, Number 2
(originally printed in Speleonics 2, Summer 1985)
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*By Ian Drummond*

In this article I want to address the problem of design of loop antennas for transmission. How big an antenna is needed for a given field, what gauge wire should be used, and how much power can an antenna handle?

In general a designer starts from one of two points. Either he can decide on the maximum size of antenna that can be physically handled in the cave or on the surface, or he starts knowing he must achieve a certain range. In either case he will want the greatest range for a given power.

The type of antenna considered here is the air-cored loop with a tuned secondary winding. I am assuming the designer is familiar with the concepts of transformers and resonant circuits, if not I would recommend reading an article such as The Amateur Radio Handbook, Chapter 2, on Electrical Laws and Circuits to gain an understanding of inductance, capacitance, and concepts such as "Q" of a resonant circuit.

The problem with using these basic concepts to design loop antennas, is that two effects, the skin effect, and the proximity effect, increase the apparent resistance of the wire to AC current over its DC resistance, and so degrade the performance of the antenna. These effects are treated in a very useful book "VLF Radio Engineering" by A D Watt, Pergamon Press, (1971), pages 90-101. I have incorporated the necessary formula into a Basic computer program which seems to work well for 3 very different sized loops, all working at 115.4 kHz, on which I have electrical measurements.

The AC resistance is calculated from the formula:

R(AC) = R(DC) x (1 + F + G(K + U)) Ohms

where: F = Skin Effect, G.K = Proximity effect due to nearby wires, G.U = Proximity effect due to the magnetic field of the solenoid. These values are part of the output of the program and so allow the designer to estimate their importance in degrading the magnetic moment (NIA) of the loop.

Design of an antenna using this program becomes a question of trying various combinations of antenna size and shape, wire size, # of turns, etc. to find a combination that gives a good value of the magnetic moment (NIA) without exceeding voltage or current capabilities of the capacitors or wire.

In general for my own applications I have found all parameters except the input impedance to match well. The input impedance was too high by a factor of 2 or so. Frank Reid compared calculations with the actual values for some of his 3.5 kHz loops and found results within a factor of two also. So the program is not perfect, but I believe it is helpful in designing efficient antenna.

All these examples are for a square antenna with a spoke length of 0.5 m. operating at a frequency of 115.4 kHz and with a single turn primary.

Turns |
Wire(AWG) |
NIA (10 watts) |
Peak Volts |
Q |

70 | 28 | 11.7 | 7.4 kV | 87 |

This is the calculation for one of our field antennas and matches well. | ||||

140 | 28 | 14.5 | 15 kV | 113 |

(Doubling the turns only increases NIA by 24% but fries the 6 kV capacitors and the bandwidth is too small) | ||||

70 | 22 | 13.9 | 7.5 kV | 115 |

(Same # turns but thicker wire increases NIA by 19% only and the bandwidth is still too narrow) | ||||

35 | 22 | 11.2 | 3.5 kV | 80 |

(Maybe this would have been a better choice than our original one, less work to make, anyway). | ||||

Julian tried an empirical approach to antenna design. A square antenna with 1.1 m spokes, and a one turn primary. | ||||

4 | 16 | 21.1 | 0.48 kV | 39 |

(Not bad, certainly a lot easier to make, but big for handling in the bush). |

Editor’s Note:

The original article now gave the code for a BASIC computer program to calculate the parameters of tuned loop antennas. The program is still available and in use. Several people have changed format, or implemented it in a spreadsheet.Download the code script (in ASCII format) by clicking here.

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