If you derive the expression for SWR in terms of antenna R and X you can
differentiate with respect to frequency and determine the conditions for
minimum SWR analytically.
You'll find that when dX/df >> dR/df - the case for most HF wire
half-wave dipoles at any height above any type of ground - minimum SWR
occurs very close to X=0 (resonance)
It becomes less true when the wire diameter is an appreciable fraction
of a wavelength, and even less true for something more complex such as a
beam. In the case of my hexbeam, maximum gain, maximum F/B and minimum
SWR all occur at different frequencies than one another, and other than
resonance. Shooting for resonance at a particular frequency would be the
least useful tuning goal.
Steve G3TXQ
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