Single-Turn Transmitting Loop Antennas of Various Regular ShapesAuthor: R.J.Edwards G4FGQ © 1st November 2000
Magnetic loop antennas are so named because most of the energy in the near field is contained in the magnetic component and very little in the electric component. This applies to all loops with perimeters less than 1/2-wavelength, including those with a tuning capacitor connected between nearly-touching ends.
To obtain a usable radiating efficiency the loop conductor is formed from self-supporting copper or aluminum tube, or a broad flat strip, because of the large RF current flowing in the loop and the small radiation resistance.
Useable efficiency can be obtained if a loop's diameter is as small as two-percent of a wavelength or less. Because of that, magloops are popular for their space-saving qualities. They also are popular because of their unobtrusiveness and efficiency without need for a ground-radial system. Furthermore, depending on the maximum and minimum range of the tuning capacitor, the operating frequencies of a particular loop antenna can cover a 5 to 1 range. These merits are particularly attractive in the 160-meter through 30-meter ham bands.
However, a high-voltage high-value variable capacitor is needed for multi-band operation. For operating convenience this can be a remote-controlled motor-driven vacuum capacitor. In most cases an additional impedance-matching network is not required.
This program models a loop as a twin curved-conductor transmission line with one end connected to a source of RF energy and a tuning capacitor across the other end. The inductance, capacitance and impedance (Zo) depend on the loop dimensions. The phase velocity is as for any air-spaced line. The line resistance is the sum of conductor, induced ground loss, and radiation resistance. These have both distributed and equivalent lumped values.
Ground loss has two components:- that due to the current induced in a mirror image of the loop below the surface with the resistance of the image loop being proportional to the soil resistance, plus that due to current flowing in the soil via capacitance between the loop and the soil surface. The total loss varies in a complex manner with antenna height, soil resistance, soil permittivity, the RF skin depth of the soil, and the operating frequency.
At very low heights, close coupling to the ground detunes the antenna and the program automatically re-computes the tuning capacitance needed to maintain resonance. That effect is greatest at lower frequencies and lower soil resistance. However, a loop antenna would not normally be operated so low as to cause significant detuning, because excessive ground-loss would result. A height greater than 1/2 the loop diameter is advised for good performance.
The computed efficiency at very low heights is approximate, but illustrates the general behaviour when a loop antenna is in close proximity to other conducting materials. Even if a more precise efficiency calculation method was used, soil characteristics are rarely known accurately, so the end-result still would be approximate.
A loop spaced two or more diameters away from other conducting materials is effectively isolated except for capacitance to its small coupling loop. The sometimes recommended Faraday screen actually increases stray capacitance.
Where a loop is not circular, its effective diameter is similar to a circular loop having the same loop area.
Tuning motor control cables should be run symmetrically with respect to the two halves of a loop and be choked with RF chokes immediately outside the loop area.
The S-meter readings of radio receivers at distances of 800 and 8000 km (500 and 5000 miles) via the ionosphere F-layer are predicted as a practical indication of loop antenna performance. The calculated 800 km path is one hop, in darkness, with a 34-degree angle of elevation, with the frequency above 1.8 MHz. The 8000 km path is three hops, in sunlight, with an elevation of 10-degrees, and a frequency above 7 MHz. The operating frequency should be within 25% of the maximum usuable frequency (MUF) depending on the solar angle, the solar flux, etc.
The transmitting loop is assumed to be in the same plane as the radio path direction. The receiving antenna is assumed to be an efficient, full-size, quarter-wave vertical with ground-radials.
The assumed S-meter calibration is S9 = 50 uV into a matched receiver input resistance of 50 ohms with one S-unit equaling 6dB. The predicted S-meter readings are those most likely when unspecified propagation variables have typical mean values.
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