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I erected a 44′ doublet. The ends of the doublet were tied to low branches at the edge of the clearing.
I took along two antenna options, 1) a 44′ doublet and 2) the antenna recommended in the KXAT1 manual - 26 feet of wire with quarter-wave counterpoises. The doublet fit perfectly in the clearing, the ends reaching to the edges of the clearing where they were tied off to low tree branches, and the center held aloft my 20ft Shakespeare TSP-20 wonderpole® fishing pole. I used the doublet and didn't try the Elecraft antenna.

Antenna View
The doublet was constructed using two 22′ lengths of #24-AWG teflon® coated, silver plated wire. The feed point was a small piece of drilled light plastic with holes to allow tensioning. The antenna was secured to the fishing pole using a velcro® strip. The ends of the antenna were simply tied off to branches at the edge of the clearing at about 6ft above the ground. The feed-line for 20m was 22′ 4″ of Radio Shack 300Ω TV twinlead. The feed-line was connected directly to the KX1 using a Pomona 1296 BNC-to-binding post adapter. For 40m, the KXAT1 could not match the doublet, so I connected an additional 6′ of TV twinlead and I was able to get a match - sort of.
In an inverted-vee configuration, with the apex only a quarter-wave above the gound, the 44′doublet is almost omnidirectional, ie. there is only a small gain improvement in the far field between energy broadside to the antenna compared to off the ends of the doublet.

20m Elevation Plot
This antenna, mounted so low to the ground, is something of a compromise on 20m. 20m propagation tends to support fairly long distance communication, for example from Ottawa to California, therefore we should choose an antenna which optimizes gain for signals entering the antenna and leaving the antenna at a relatively low angle of radiation (between about 10° and 20°). Communication is also possible on 20m to the mid-states (for example between Ottawa and South Dakota). For these states an angle between 20° and 30° would be better.
The elevation plot (above) indicates that the antenna was a poor choice for 20m. The gain figures for useful elevations on 20m are very poor (-3dBi for 15°, 0.5dBi for 25°). In fact the antenna only has useful gain above 30° which is not great for 20m signals.
20m 22′ Feedline (Click for larger image)
The feed-line for 20m was 22′ 4″ of 300Ω TV twinlead. This transforms the feedpoint impedance from 180R+660j (Z=680Ω) to 40R+150j (Z=155Ω). The KXAT1 completed the transformation to Z=50Ω.
On 40m, the antenna has less gain all around. The pattern is more omnidirectional, and the useful gain is at higher elevations. 40m propagation supports shorter distance communication (such as Ottawa to Pennsylvania). Distances such as those common for 40m propagation require radiation to enter and leave the antenna at angles from 20° to 30°. Unfortunately, this antenna only has useful radiation above 60° on 40m, which is really only good for NVIS (<600km).

40m Elevation Plot
The feedline needs to be lengthened to enable the KXAT1 to find a match. The feed-point impedance of 21R-640j (Z=640Ω) is transformed to 7R+27j (Z=28&Omega), but this falls outside the matching range of the tuner. I added 6 feet of twinlead, giving a feed-line length of 28′ 4″. This longer feed-line length transforms the feed-point impedance to 9R+134j (Z=134Ω), which the tuner is capable of transforming of Z=50Ω.
40m 22′ Feedline (Click for larger image)
40m 28′ Feedline (Click for larger image)