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CDX-007,

"I don't see why adding a correctly tuned coil would require shortening the radiator, in fact adding inductance should, if anything, require increased capacitance, adding length to the radiator... "  Oops, just backwards. 

If a larger coil is added to the antenna, then more inductance is added.  That means that if you want the thing to be resonant in the same place as before, then some inductance has to be subtracted from some place.  That 'some place' is the 'whip' part of the antenna, so it's shorter, not longer.  Not decreasing the 'whip's length would mean that the resonant frequency would go down.  If you shorten the thingy just right the resonance stays in the same place.

 - 'Doc