Why are the resistive losses in large antenna structures made from wires or rods, and having possibly a collection of parasitic elements contributing to the radiation, necessarily less than the resistive loss in a smaller structure, perhaps a simple dipole, for the same rod or wire diameters and the same total radiated power?
Well, the total resistive-loss power absorbed by the radiating structure is proportional to the (square of the current) times the (little element of length), integrated over the entire structure. For a properly designed antenna, the radiated power is proportional to [the (element of current) times the (little element of length), integrated over the entire structure, allowing for the relative phases, and then the total integral is squared].
For a larger structure, having a given radiated total power, the local currents will be smaller. The square of the local currents will be smaller still, and when integrated over the same structure give proportionally lower losses.
We have remarked elsewhere that there is no purpose in considering whether the power flow in the Poynting vector may be localised to a little element of area. In the same way, there is no point in considering the power or field strength radiated from a given little current element (I dx) in isolation from the rest of the structure. Neither is there any point in thinking about the contribution to the radiated power from individual accelerated charges.
Since the total power radiated is proportional to the total electric field strength squared (in the far field), and the far field electric field strength is an integral of the current elements over the structure, we are unable to equate radiated power (numbers of photons per second) to individual current elements in the radiating structure. It therefore makes no sense to ask questions like "does the radiation happen only from the ends of the rods, or is it distributed uniformly along the rods?"
The outward travelling wavefront moves away from the antenna structure at the velocity of light, c = 3E8 metres/second. Relativistic considerations tell us that this is true for us no matter how fast we are travelling as observers with respect to the antenna. This is often expressed by the statement "there is no rest frame for a photon". It is clear that, although the antenna is usually considered as stationary, the radiation mechanism involves getting energy from the rest frame of the antenna to a frame moving outwards at velocity c, which is about as relativistic as one can get. And yet, in this frame the photons are not at rest! They will be doppler-shifted but still travelling at velocity c.
Thus antenna radiation problems are intrinsically relativistic, and probably, therefore, not amenable to being thought about by simple mental pictures. The whole panoply of relativistic mechanics and electrodynamics is needed.
Many problems arise in array antenna analysis, from the interpretation of the coupling between adjacent structures as being largely due to electrostatic interactions, whereas the classical antenna radiation calculations for the far-field involve the Lorentz gauge version of the electromagnetic equations, which has the relativistic effects automatically built in.
All radiation can be traced ultimately back to current (maybe in a distant star) somewhere at some time in the past. But that pre-existing radiation can be used to calculate subsequent radiation, in regions where there are no currents.
There are two thoughts about this. One is, that as the fields repeat once every cycle (or wavelength) along the propagation direction, then if you only have a measure of the fields at a single sample point (receive antenna feed, or point in space) you are quite unable to say how far away that radiation originated; it could be from a current nearby, or many light years away. It is only when you can do triangulation that you can get a fix on the origin. In this case, it is quite reasonable to say that displacement current in the propagating wave gives rise to radiation for points further downstream. However, if the displacement current really was a radiating current, it would also give rise to effects (at a later time) upstream, which is a non- causal solution of Maxwell's equations, alloweb by the maths but non-physical. This is a rather abstruse point.
The other thought, is that diffraction by a circular aperture in an opaque insulating screen gives rise to fields in the diffracted beam which would not be present in the undiffracted case, if the screen was not there at all. This can only be explained by Huygen's principle; that is, that the fields in space across the aperture (no conduction currents) give rise to a contribution to the radiated far fields in the diffracted beam. Of course, we might also consider induced conduction or polarisation currents in the screen, but it is my guess that these are not sufficient to explain the phenomenon as the diffraction pattern doesn't depend on what the screen is made from.
As I understand the Maths in W G V Rosser's 1960s book "Classical electromagnetism via relativity" the only correct way to include the radiation effects of displacement current is to integrate them over all 4-d space, in particular along the entire path between the notional star and any observers, for all points and times. When you do this, you can show that the totality of contribution to any subsequent radiation from this displacement current adds up to precisely zero, leaving just the contribution from electron acceleration (mobile or bound) or other charge acceleration.
Now in the case of computing diffraction, we don't do this, but instead we take the displacement currents across a hypothetical surface at the diffraction screen, and it is this intergral that is non-zero. But we have then left out the rest of the 4-d space-time integral.
Copyright © D.Jefferies 2000, 2004.