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Had to comment on this earlier post.  Resonance has nothing to do with impedance. Consider a half-wave, Mark I Mod 0 dipole for 40 meters, cut for somewhere around 66 feet overall.  It will be resonant (meaning that inductive and capacitive reactances are equal and opposite, cancelling each other out at that particular frequency and leaving only radiation resistance to represent impedance. This radiation resistance probably won't be exactly 50 ohms; it depends on antenna height, proximity to trees, buildings, power poles and a dozen or more other unknowns.

 

Now then, if we try to use this same antenna and feedline to work on 20 meters, guess what?  The antenna is still resonant (meaning zero net reactance) at twice the frequency, but the radiation resistance is through the roof - likely in the thousands of ohms.  A quick check of things with an antenna analyzer will show this.

 

BUT, the same antenna will work quite well on 15 meters (three times the frequency the dipole was actually cut for).  It will show a low value of net reactance (theoreticaly zero), and an impedance will within most equipments' ability to work with.