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Independence of waves
Roy Lewallen wrote in
: Owen, It's a pleasure to have a rational discussion. We will both learn from this, and perhaps some of the readers will also. Thanks Roy. Owen Duffy wrote: .... Extended to transmission lines, I think it means that although we can make an observation at a single point of V and I, and knowing Zo we can state whether there are standing waves or not, we cannot tell if that is the result of more than two travelling waves (unless you take the view that there is only one wave travelling in each direction, the resultant of interactions at the ends of the line). Hm, let's think about this a little. In my free space example, we had two radiators whose fields went through the same point, and those two radiators were equal in magnitude and out of phase. The sum of the two E fields was zero and the sum of the H fields was zero, so there was no field at all where they crossed. But now let's look at a transmission line with waves created by reflections from a single source. I believe that there is no point along the line where both the E and H fields are zero, or where both the current and the voltage are zero. (Please correct me if I'm wrong about this.) That's a different situation from the free space, Yes, I agree with you, and I think the key factor is that waves are only free to travel in two directions, and if multiple coherent waves can travel in the same direction, they are colinear. two-radiator situation I proposed. So in a transmission line, we can find a point of zero voltage (a "virtual short"), say, but discover that there's current there. There will be an H field but no E field. And conversely for a "virtual open". So there is a difference between those points and a point of no field at all. And there is energy in the E or H field. (This also occurs in free space where a wave interferes with its reflection or when waves traveling in opposite directions cross.) Now, if you could feed two equal canceling waves into a transmission line, going in the same direction, then you would have truly zero E and H fields, and zero voltage and current, like the plane bisecting the two free space antennas. You couldn't tell the But is it possible to inject two coherent waves travelling independently in the same direction? Could I not legitimately resolve the attempt at a circuit node (line end node) of two coherent sources to drive the line to be the superposition of the voltages and curents of each to effectively resolve to a single phasor voltage and associated phasor current at that node, and then the conditions on the line would be such as to comply with the boundary conditions at that line end node. Though I have mentioned phasors which implies the steady state, this should be true in general using v(t) and i(t), just the maths is more complex. I can see that we can deal mathematicly with two or more coherent components thought of as travelling in the same direction on a line (by adding their voltages or currents algebraicly), but it seems to me that there is no way to isolate the components, and that questions whether they actually exist separately. So, whilst it may be held by some that there is re-reflected energy at the source end of a transmission line in certain scenarios, a second independent forward wave component to track, has not the forward wave just changed to a new value to comply with boundary conditions in response to a change in the source V/I characteristic when the reflection arrived at the source end of the line? I know that analysis of either scenario will yield the same result, but one may be more complex, and it is questionable whether the two (or more) forward wave components really exist independently. .... I will think some more about the "actual zero field", but that cannot suggest that one wave modified the other, they must both pass beyond that point, each unchanged, mustn't they? Absolutely! If that is so, the waves must be independent Absolutely! , but the resultant at a point is something separate to each of the components and doesn't of itself alter the propagation of either wave. Sorry, I don't fully understand what you've said. But it is true that the propagation of neither wave is affected in any way by the presence of the other. I am saying that resolution of the fields of two independent waves at a point in free space to a resultant is not a wave itself, it cannot be represented as a wave, and it does not of itself alter the propagation of either wave. It may be useful in predicting the influence of the two waves on something at that point, but nowhere else. Having thought through to the last sentence, I think I am agreeing with your statement about free space interference "I maintain that there is actually zero field at a point of superposition of multiple waves which sum to zero, and that no device or detector can be devised which, looking only at that point, can tell that the zero field is a result of multiple waves." And we haven't mentioned power, not once! Owen |
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