Peter Wotherspoon, VE3GYY, suggested an array consisting of 9 vertical wire dipoles spaced 1/4 wavelength apart, fed in phase to produce a broadside pattern. His original idea was for a feed network consisting of equal lengths of 300 ohm twinlead, grouped in threes:
Peter didn't propose any particular length of feeders, and, as is discussed elswhere, this scheme won't necessarily accomplish the goal of feeding all the elements in phase, mostly because of the mutual impedances between the elements. It seemed a good exercise to figure out what those impedances actually are. NEC can make short work of this sort of problem, or, one could use an approximation for the mutual impedance between halfwave resonant dipoles, values for which are tabulated in a variety of places.
I started by building a NEC model of the dipoles. I made them all 5 meters long, and running the model at 30 MHz. In actuality, these dipoles would be a bit "long", but, since I was interested in finding out the mutual effects, and more importantly, whether the earth had any signficant effect. I did this by running the model in free space, with perfect earth, and with real earth (but not the Sommerfield Norton ground model, which I really should do, because these really are near field effects...). I ran it 3 times, with the center of the array 3 meters, 4 meters, and 5 meters off the ground (since the "arm" of the dipole is only 2.5 m long, this corresponds to the lower end of the dipole being 0.5, 1.5, and 2.5 meters off the ground). The elements were spaced an eighth wavelength (i.e. 1.25 meters) apart.
The mutual impedances were measured by exciting one of the elements, and connecting a 10K resistor across the feeds of the other 8 elements. A bit of complex math in a spreadsheet results in the mutul Z numbers.
The NEC input files and the Excel analyses are here:
This was interesting...
Now, I tried a feed network using 1/4 wave lines of 300 ohm twinlead, all tied to the same point. NEC Model file
The feed impedance isn't all that strange: 83.3+j26.9, 90.2+j25.6 (perfect ground), 86.1+j26.5(real ground, approx), and a quick check on the magnitudes and phases shows them all being about the same.
/radio/antenna/ve3gyy.htm - October 2000 - Jim Lux
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