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A transmission line does not radiate when the spacing between the two wires is very small when compared to the wavelength, but the transmission line begins to radiate when the spacing between the lines becomes comparable to the wavelength of the signal. Why is this?

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Twin-lead transmission lines don't radiate because the opposite fields from each conductor cancel, but when the spacing is far apart this does not happen.

First, let's consider the magnetic field around an infinite, straight conductor with uniform current throughout. In this image, the conductor is just right of center, and the current is coming straight out of the page.

field from one conductor with uniform current

Now let's add next to it another conductor, with the current going the other way:

fields from two conductors with opposite uniform current

Add these fields together, and you get:

enter image description here

For distances far away relative to the conductor spacing, the fields are equal but opposite, so when added together they cancel. Radiation is, by definition, a field that extends to infinity. If there are no fields far away, then it can't be radiating.

However, we made an assumption of uniform current. When the spacing between the conductors is small, this is a mostly true assumption. Although the current isn't exactly uniform, we must travel many multiples of the conductor spacing before there's any appreciable change in phase.

However, when the conductor spacing is large, then this is no longer true. Remember, the current is reversing direction periodically, and if we look at the field from just one conductor this means the field is alternating between clockwise and counterclockwise swirl. The changes to this field only propagate at the speed of light, so if we zoom the graph out to be a wavelength wide or more, we'd see those changes propagating away as waves.

enter image description here

In the image above, the wavelength appears to be approximately four units. Now if we add that second conductor, two units away, we get this:

enter image description here

Notice how the fields don't cancel. They don't cancel because on the scale of the conductor spacing (which is not small relative to the wavelength) there can be significant changes in phase. Thus, there are regions of constructive interference where the fields don't cancel. These regions extend out to infinity, and thus, the feedline radiates.


Images were generated with a Javascript vector field grapher by Kevin Mehall

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  • $\begingroup$ This is good. However, depending on the spacing and frequency, there is an approximate distance from the line where the radiation is insignificant. I realize that there are a lot of variables; but --if it's not a lot of trouble-- could you please go a little further and calculate a few real-world numbers using 1", 2.5", and 6" spacing at 3.5 MHz? (160 through 18 would be even better! ;-) Assume that there is no metal near the feedline from the antenna to a good tuner. $\endgroup$ – Mike Waters Sep 25 '18 at 18:56

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