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Antenna Lumped Components.
This study started off with a question I posed to Dr Tim Davies GW4ADL at Swansea University around 1998, the question “what is the equivalent inductance of a long length of a piece of wire used for a long wire antenna”. Should and if the wire length inductance could be calculated, would it be possible to substitute an wound coil inductance component for a section of wire in a long wire antenna. If so, then perhaps a wound coil of inductance, say 3uH equal to 10metres of wire length, therefore reduce a 80metre ¼ wave section in physical length by 10 metres, or by 20metres of physical length with a 6uH wound coil inductance.
The inductance of a wire length can be found by the impedance equation used for co-axial cable, Zo = SQR(L/C), if the capacitance per metre is 120pF/m for UR67 cable, then the inductance per metre is 300nH/m. In any type of cable, only the capacitance alters for the intended impedance, as the inductance or a length of wire would otherwise remain the same value, here at 300nH/m.
If I recall correctly, as 1998 is some time ago, this technique was used later in the week by Tim GW4ADL to make a 1 metre overall length 10m dia-pole, by using the would coil inductance to offset the physical length. The same could be used to reduce the overall height of a vertical antenna, the coil inductance would then in any case concentrate some the current lobe to the coil, the current lobe at the wound coil equal to the overall current lobe found in the same physical length of long wire.
An alternative “Panular” inductor is a flat circular spiral inductor, which can be made into a tiny none rotating “NATO AWAC’s antenna” for aircraft, and so also ship use and mobile etc. The single layer coil antenna, would be in place of a long wire used for shortwave. The lower Ham Radio bands of “LF” or perhaps “MF” frequencies would be able to use a lumped component antenna design, which would dramatically reduce the overall size of the actual antenna construction for the lower bands. For further study to lumped component reactance matching, refer to the next web-page “Arduino Uno DDS VFO HF Signal generator” for a RF signal reference for an HF antenna analyser. The attached article would help design lumped component antenna’s .
Do however notice that for BBC Basic for windows, that a value of 1000 = 1E3 in the calculations. An evaluation copy can be downloaded from the URL link shown : http://www.bbcbasic.co.uk/bbcwin/download.html