> Sure, a parallel LC circuit (trap) will do it but not a coil alone
An EZNEC model shows that a 110ft dipole 30 feet above ground* resonates at
3.64MHz and 7.13MHz when 39uH coils are added 11 feet from each end. The
2:1 SWR bandwidths are narrow (100kHz on 80 and 150kHz on 40) even with
realistic inductors (Q=100). There is no possibility of stray capacitance
because in the simulation they're mathematically idealized objects.
This is just one example. I did not try to optimize it, just tried to get
it to resonate on two bands.
Now, real antennas do not use pure inductors, and probably stray capacitance
is not negligible for most coils that would make this technique work. But
this is an example that, in principle, it is possible to get dual resonance
on a "second harmonic" band using ONLY inductors and wire.
*ground in this case is Norton Sommerfeld (Real/High Accuracy) with 0.005S/m
and dielectric constant 13
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