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The Antenna Tuner will load an End Fed Long Wire effectively, especially if it is cut to aprox. an Odd Quarter Wave-Length of your target band... 186 ft / 16.5 ft and 186 ft / 33 ft... The entire antenna is #12 stranded insulated copper. The Antenna Tuner is a 1977 HeathKit HFT-9, a small QRP size tuner of the Cap-Coil-Cap double"L" design.
Currently the antenna is resonate at about 7.7 Mhz. You would like it to be resonate at 7.1 Mhz. Take the old resonate frequency divided by the new resonate frequency and multiply by the original length, (7.7/7.1)*65 = 70.5 or so. The result is about 70.5 feet which would have you adding 5.5 feet to the existing antenna.
Some antenna designs use multiple parallel elements like this. For example, fan dipoles. Or, as you can see the Butternet HF9V has a couple parallel wires hanging off it in the upper half: These extra elements add additional resonant modes to the antenna, which is what makes these antennas multi-band.
The fact that the wire length is only 41 foot in length, this means that it is about a 1/4 wavelength at 40 meters. Is this ok? Would it make sense to get one longer at about 66 foot, so that it would be a half wavelength at 40 meters instead.
confirm that the open connector gives a nice small dot on the open circuit side of the Smith chart. connect the balun and short-circuit the connector with a screwdriver or knife. Confirm that you see a small short circuit on the left hand side of the chart. consider a port extension if you need to connect a long cable after calibration.
The CP is however the second element of the EFHW with its total length being the sum of both element lengths. The EFHW can therefore logicaly be viewed as an Off Center Fed Half Wave (OCFD) antenna). As expected, initial attemtps of modeling an EFHW (without a CP) with EZNEC produced feed point impedances tending to infinity.
A voltage-fed antenna, like an EFHW, does not need a ground for radiation purposes, (and neither do other half wave antennas, but that's a different discussion), it needs it for high voltage DC shunting generated by static, or lightening protection; you should ground your coax shield with accepted practices.
I tried to get rid of the capacitor, to change it value with a variable capacitor, to change the 64:1 transformer to the 49:1 one, to change the length of the antenna, etc. Currently I spend three weekends on this project. No matter what I tried I get a single band antenna. It looks like I'm missing something.
$\begingroup$ R Pau is correct, Simon Hefford. but consider that your, description of the antenna is not correct for most bands you list, and the one it is a halfwave for, 40M (7.1MHz), you should be using a much higher ratio transformer for, like 49/64:1; you are in the ballpark and you just need to do a little impedance and reactance tuning with a tuner.
I built a 40m end fed halfwave antenna and unun, and the wire is about 66 ft long. I have some tall trees nearby I can hang it in, semi-permanently. Which of the following would be better? A) hanging the far end nice and high, about 50ft, but then slope down the feed end to about 8ft