# Hypothetical question on signal propagation

1. Oct 15, 2009

### stephen163

If you connected a DC or AC source to the end of an single, infinitely long, straight wire suspended in free space (separated from anything), would propagation occur along the line?

2. Oct 15, 2009

### jasonRF

If the wire has a finite conductivity then it does "guide" waves, although the energy isn't very confined to the wire. I'm pretty sure Stratton's book covers this.

3. Oct 15, 2009

### waht

depends how you define an infinitely long wire?

in infinitely long parallel wires, AC can propagate. however it looks like an open for DC even if the ends are shorted at infinity

sort of a parallel question. suppose that the length of the wires in not infinite but it's zero, how would dc and ac behave?

4. Oct 15, 2009

### vk6kro

If you apply a DC voltage to a transmission line, there will be a wave front propagated along the line at the speed of light times the velocity factor of the line.
It will take a finite time for the wavefront to pass each point along the line. So, you would not be able to measure the voltage until the wave front got to you if you were some distance down the line.

Since the wire is infinitely long, there will be no reflection, but with a shorter wire, there would be a reflection back along the incoming DC.

An AC wave would also propagate along the transmission line and a particular peak or trough would take a finite time to reach a distant point determined by the speed of light times the velocity factor of the line.

AC waves would tend to be radiated by the line and would decrease in amplitude with distance as a result of this radiation. Higher frequency AC would radiate more than lower frequency.

5. Oct 16, 2009

### stephen163

I am talking about a SINGLE wire. A transmission line requires 2 or more conductors. Imagine a single wire with no return path for current.

If you have a battery and a closed loop for current flow, it is easy to understand that there is a constant electric field within the conductor acting upon the electrons. The voltage at any point along the wire is V, the source voltage. Now, if you made that wire loop huge, say millions of kms, and still maintained that it's a perfect conductor with no attenuation, would the voltage at all points of the wire still be V. The electric field must surely take time to reach the electron in the middle part of the conductor loop (speed of light).

I think I realise my confusion now. I was wondering what the point of 2 conductor transmission lines were when you could propagate at speed of light using a long, conventional single conductor circuit. It must be that the attenuation of a long wire is too great over long distances. If this is wrong, please let me know.

6. Oct 16, 2009

### f95toli

You mean like an antenna?

7. Oct 16, 2009

### stephen163

Yes, it would radiate like an antenna. You can make a transmission line behave like this by putting the voltage source in series. Exciting the 2 conductors in differential mode will allow it to behave like a TEM transmission line. Superconducting power lines with very low resistance should then be able to transfer power without having a coupled multi conductor system, like HV transmission lines do (they can use the axial electric field rather than TEM).

Not sure if this is correct though.

8. Oct 16, 2009

### vk6kro

Yes, it would radiate like an antenna. You can make a transmission line behave like this by putting the voltage source in series. Exciting the 2 conductors in differential mode will allow it to behave like a TEM transmission line. Superconducting power lines with very low resistance should then be able to transfer power without having a coupled multi conductor system, like HV transmission lines do (they can use the axial electric field rather than TEM).

Not sure if this is correct though.

No, it isn't correct.
DC will not radiate from a line no matter how long it is.
If you connected just the positive terminal of a battery to a very long wire, eventually the whole wire would be charged positively WITH RESPECT TO THE NEGATIVE TERMINAL but not with respect to anything else. There would be no power available without a connection back to the negative terminal.

AC will not radiate either unless it has a return path. You cannot join one side of a generator to a long wire and expect it to radiate unless you connect the other side of the generator to a ground connection or another long wire going in a different direction.
Then it becomes like a dipole or a centre fed very long wire and it would radiate.

Capturing this radiated power would not be easy, though, since you would need another very long wire very close to the first one. This is because the power would be radiated equally in all directions at right angles to the first wire and another wire would only intercept a small portion of it.

Feeding ac into one end of a pair of parallel wires results in an inefficient radiator. That is what transmission line are used for. They are not perfect, though, and some power is radiated. The further apart they are, the less their fields due to opposite currents cancel out, so the more they radiate.

9. Oct 16, 2009

### stephen163

Obviously, DC won't radiate. A transmission line which is excited by a series alternating voltage and one end shorted would behave like an antenna - why wouldn't it? After all, it isn't a transmission line any more, it is a simple circuit.

10. Oct 16, 2009

### vk6kro

You keep changing the question.
If you connected a DC or AC source to the end of an single, infinitely long, straight wire suspended in free space (separated from anything), would propagation occur along the line?

If you had a length of 2 wire line and connected an AC source to the input (between the lines... see attached diagram) then connect the two wires at the other end together, you would not have an antenna.

That is a shorted stub. How it behaves depends on the frequency.
If it is a quarter wavelength long it will look like an open circuit to the input signal generator.
If it is a half wavelength long, it will look like a short circuit to the input signal generator.

But it will not radiate, because the two currents flowing in the wires are out of phase with each other, so their fields cancel out.

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11. Oct 16, 2009

### Bob S

If I recall correctly, the characteristic impedance of a coaxial transmission line w/o dielectric is

Z = (377/2 pi) Ln(b/a) where a is the inner, and b the outer conductor radii.

So we a discussing a situation where b--> infinity.

So is there a limit to b, and therefore to ln(b/a) and to Z?

Bob S