I ran the same model in 4Nec2 as below but changed the hat from the traditional 
two wires to four, spaced 90 degs.  Complex base Z is near 16+j0.  Even though 
two symmetrical top-hat wires produce little radiation, four wires result in 
wires that are only 24 ft long to achieve resonance -- versus 41 ft with only 
two wires.  Getting to six would result in a smaller top hat but may not be 
worth the mechanical hassle.    

>"4Nec2 shows that with a 68 ft. thin radiator, resonance can be achieved with 
>wires roughly 41 ft. per side.  With a ground field of 60 radials, 90 ft long 
>on sandy ground, 4Nec2 reports a base impedance of 15.4+j2.5."  

Paul, W9AC

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