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When using ladder line to feed an antenna, I've seen it written that

The spacing should not be over 1 percent of the highest-frequency wavelength, and that’s the only real consideration with ladder-line spacing. source

Why is this the limit? Just that the impedance will be too high the spacing is too large a fraction of wavelength?

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1% here is just an overly precise way of saying "really small compared to the wavelength". The problem is that when the conductors are close together, their electrical and magnetic fields cancel; as they get farther apart, there's a larger volume around the line where the fields don't cancel, and the ladder line starts looking more like an antenna than a transmission line.

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