At my old QTH I used an 80m untuned doublet: 125 feet fed with open wire using a remote balun. I put it up my at current QTH, shortening it to about 115 feet to fit my lot.
It worked OK for a low dipole, but it was a bit troublesome. Even with a Murch UT-2000A tuner, I had trouble using it with my amplifier. It also took time to retune when switching bands.
I decided what I needed was a trap dipole. I'd had some success building a trap dipole for the WARC bands using coaxial traps. After reading the analysis by W8JI, I still wanted to use coaxial traps, but I decided to use traps resonant off the operating frequency.
You can see the result above, about half the antenna is visible, with the feedpoint on the left, and one of the traps just to the right of center.
The traps are designed to be resonant about 6.6 MHz. They are made of 76 inches of RG-59A/U, wound in 6 and 1/3 turns around a four inch long piece of 3" schedule 20 PVC. The actual frequency of resonance isn't critical, so long as both traps are identical.
The traps are wired in series, as shown below, the inner wire (black) attaches to the center conductor of the coax, and the outer wire (red) attaches to the shield of the opposite end.
The shield of the inner end is connected to the center conductor of the outer end, as diagrammed by VE6YP.
The center section is made of two 33 foot pieces of wire. In retrospect, another foot might have been better. The outer sections started at 26 feet each. I cut off 10 feet 8 inches to bring the antenna into the band, resulting in 15 feet 4 inches. If you were to duplicate this antenna, I would start with 35 feet and 20 feet, respectively, and trim from there.
Fed with RG-8x to a height of 35-42 feet, the antenna resonates at 7.22 MHz with a VSWR of 1.5:1, and 3.76 MHz with 1:1. With the typical automatic antenna tuner in modern rigs, or the pi network of older amplifiers, this antenna easily covers both 40 and 80m. Being so low, this antenna doesn't have much of a pattern on 80m, and only a gentle broadside pattern on 40m.
I've been pretty happy with the dipole. It works well on 80m early in the evening when the propagation is short. Not bad for an antenna that's less than 100 feet long.
I hope to add a couple more traps to add 30 and 20m this summer. I'll let you know how that works out.