There are at least two different methods of achieving 40/80m operation by just adding
inductors to an antenna: while they look similar they are based on different behavior.
It would seem that the 80m loading coils might have enough inductance to look like a
choke on 40m, but that rarely is the case in practice. (It does work for combinations
with a wider split such as 20m / 80m.) So to make the coil act like a trap you have
to design it to be parallel resonant due to the stray capacitance. That means that the
turns spacing, wire size, and former material are all critical to proper operation. You
can use this inductance calculator to help you get close, because it reports the
self-resonant frequency:
http://hamwaves.com/antennas/inductance.htmlIn that case you choose a coil design that is self-resonant on 40m to act like a trap,
then add however much wire you need to the end to get the 80m resonance where you
want it.
Note that while such antennas are advertised as "no lossy traps", because of the self-
resonance of the coils they can actually have
more loss than a well-designed trap.
In my experience, using an explicit trap is usually easier than trying to get the right
self-resonant property of the coil.
The other approach doesn't rely on the self-resonance of the coil, but rather is carefully
placed and adjusted so that the wire is at 3/4 wave resonance on 40m, while simultaneously
providing an 80m resonance. This approach has a lot more interaction between the resonant
frequencies in the two bands, and tends to have a narrower operating bandwidth on 40m.
The free Demo version of EZNEC should be sufficient to model these, at least as half the
antenna fed against ground, and that may be helpful to understand the differences.
In practice, however, I have found design, construction and adjustment of standard trap
antennas to require less work than either of these two methods. Something like this:
http://www.vk1od.net/antenna/coaxtrap/8040.htmWith real coils, neither of these two methods is likely to work any better than the trap
version, and by adding an explicit capacitor across the coil rather than counting on the
value of stray capacitance to form the trap it makes a more reproducible design.