What happens to balance when you QSY off the frequency where the loaded side of the antenna element is resonant?
The impedance of the short side will change faster than the impedance of the long side. So, the coaxial cable shield should be connected to the long side to present the lowest impedance over frequency. This will result in more current along the long antenna wire and less along the coaxial cable shield. The feedline choke will have less "work" to do.
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Now for the simulations.
The antenna is modeled as three wires; a 32' wire with the RF source and a loading coil near the RF source, a 65' wire, and a 62' wire representing the coaxial cable shield. The antenna is placed 63' above perfect ground with the dipole horizontal and the feedline hanging down almost touching the ground. Frequency is 3.75 MHz and the loading load is adjusted after each change so the antenna is resonant. The current
magnitudes, at the feedpoint, are:
32' wire 1.0 A
65' wire 0.61A
62' wire 0.67 A
Now we place a ferrite choke in the 65' wire (feedline shield) near the feedpoint. The impedance is half resistive and half reactive. With 300 + j300 ohms the currents are:
32' wire 1.0 A
65' wire 0.92A
62' wire 0.08 A
The feedline current is now about 1/10 that of the long antenna wire.
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Now we move the antenna down 1' so the feedline contacts ground.
32' wire 1.0 A
65' wire 0.94A
62' wire 0.06 A
This configuration does not require feedline choking. Near the feedpoint the feedline shield impedance is high and a very high Z choke would be needed to reduce feedline shield current. The choke would be better placed near the ground end. Note that the feedline shield current is low even though the feedline is along a line of zero E-field potential.
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Now we move the antenna upwards so it is 124' above ground and lengthen feedline so it is 124' and contacts ground.
32' wire 1.0 A
65' wire 0.90A
62' wire 0.21 A
Let's add a feedline choke near the feedpoint. The choke impedance is 300 +j300 ohms.
32' wire 1.0 A
65' wire 0.94A
62' wire 0.07 A
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Conclusion:
To reduce the feedline shield current to <1/10 the antenna current a modest ferrite choke is required. A choke impedance of 300 +j300 is sufficient.
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Notes:
More modeling could be performed.
1) We could explore the E-field near the feedline using the EZNEC near field feature. With this and some math we could gain a good understanding of the E-field inducing feedline shield current.
2) We could connect the feedline shield to the short side of the antenna.
3) We could take the data over the useful VSWR bandwidth of the antenna to see if more or less choking impedance is needed to maintain a 10:1 antenna-to-feedline shield current ratio.