I've been needing a 40m antenna for a place where I don't have room for the total length of a full size 40m dipole (66 ft). I saw a design that MFJ had, and I thought I'd try to duplicate the design. The design is a combo 20m and 40m dipole.
After investigating some pics (see one attached), it looked like they had traps but there weren't any caps used. It must be that they were using the self-resonance of the coil to achieve the desired results. I counted the number of turns they used (34) and since I didn't have any wire that size I used some 30 AWG enameled wire that I had to make a prototype. I guessed at the size of the PVC pipe. I used the tracking generator of my spec-an to verify the dip, and the first pass yielded a nice dip at 13 MHz. I've since adjusted the turns to get the desired dip in the 14 MHz range.
I made up two prototype traps for testing, and hung them at the end of a 20m dipole I already had up. I then tested the effect of adding the traps at the end of the wire on the existing 20m SWR with my antenna analyzer and found no real effect on that band's resonance, which was very good. After adding a little extra wire after the traps (this is done also in the MFJ design) to make it work in the 40m band (7.0 - 7.3 MHz), I found that it indeed worked very well.
The windings took up about 15.5 ft of wire on each coil, and then I needed about a foot more after the trap to make it work in the 40m band. The original 20m dipole still functions as it did.
So looking at one leg-length (1/2) of the dipole:
We have 16.6 ft (original 20m) + 15.5 ft (trap) + 1 ft = 33.1 ft which is pretty close to one leg of a 40m dipole.
Now I will order some nice 16 AWG enameled wire and make a permanent good design and hang it up properly.
Oh yea, as a bonus, a 40m dipole will work on the 3rd harmonic on 15m, so it's really 3 bands in one.