5.1) Current Analysis
If we compare the results of Pocklington's formulae with the results obtained from the measurements of a vector difference current, as in figure 22, the curves are not greatly dissimilar. It is just the general acceptance that an antenna behaves like a transmission line and that the classical explanation for a transmission line is being taken to be correct that throws the antenna theory into error. The classical transmission line explanation does not take into account the fact that the INCIDENT and REFLECTED signals form voltage vector sum and current vector difference patterns that do not directly indicate the actual voltages and currents present. Also, every author in every antenna book studied insists that the antenna end current is zero and virtually ignore the fact that the INCIDENT current can be reflected from the end of the antenna. Reflections are only infrequently mentioned and are then generally with respect to the Rhombic and Beverage antennas. It is also interesting to observe the direction of current flow in Figure 2b (page 1) and to compare it with the reality in Figure 21 (page 6). When Terman wrote the Radio Engineers Handbook in 1943 directional couplers were still in their infancy and it is unlikely that anybody had actually measured current direction in an antenna and the directions shown in Figure 2b must have been logically deduced from the information available.
Figure 22 Comparison of Current Distribution Curves
5.2) Phase Analysis
If the transmission line article is studied, it can be realised that the voltage and current in one direction within a transmission line are virtually always in phase and that differences can only occur at the very extreme ends if there is a mismatch. Also that the signal into an OPEN termination is reflected without any phase change. Therefore any mention of the phase of the voltage and current being in quadrature within an antenna, as stated in many text books, is almost certainly incorrect.
A typical error with phase is shown in Terman's description of figure 2 "The current in the loops on either side of a current minimum are almost exactly 180° out of phase except in the immediate vicinity of the minimum, which is where substantially all of the phase change takes place". This is a total misrepresentation of the real phase change which is linear and continuous over the length of the antenna in both directions. If there was a dramatic phase change in only one position, then this would suggest that the charged particles in this vicinity were moving faster than in the rest of the antenna and they would have to move much faster than the speed of light to achieve such rapid change, which is not possible. There is of course the explanation that the charges move independently of the particles but the need for this illogical concept has already been removed in the study of transmission lines in our article and there is no logical reason that it applies to antennas. It is quite clear from this antenna study that phase change is linear along the length of the antenna and if phase information is important in the calculations required then more error will occur if Terman's model is used.
There has obviously been much discussion as to the accuracy of Pocklington's formula over the years and the version in Eq. 3 is not recognisable from the original in the published paper of 1897, so there have probably been changes. The conclusion reached in this article is reached by a totally different approach to the highly mathematical result obtained originally. In 1897 they did not have the facilities that we have today and there is no sense in criticising the result that the highly intellectual Mr Pocklington arrived at. His work was not wrong, merely unfinished because it was not split into INCIDENT and REFLECTED currents. We can only be grateful that the physicists of the past have led us to the understanding that we have now but at one time tempers must have run high.
ANTENNAS Theory and Practice by Sergei A. Schelkunoff, John Wiley & Sons 1952. In the Preface, page ix Schelkunoff states "Half a century ago Pocklington demonstrated that the current and charge on thin perfectly conducting wires are propagated approximately with the velocity of light and that between any two points of monochromatic excitation the current distribution is approximately sinusoidal. Much of practical antenna theory has been based on this fundamental result. The author of this approximation was apparently forgotten. Some radio engineers call it "a practical engineering approximation" and some theoreticians once called it a colossal fraud".
Most antenna radio text books state that antenna current distribution is sinusoidal as a fact, Schelkunoff appears to use the sinusoidal approximation but also understands that this is not the reality as shown by two of his comments.
1) Page 28 "An element differs from a short antenna in that the current in the element is substantially constant along its length, whereas in the antenna it tapers off linearly toward the ends."
2) Page 214 "* Later we shall find that the difference between the true antenna current and the sinusoidal approximation is largely in quadrature with the main current, and for this reason the effect of the difference on the radiated power is still further reduced."
Schelkunoff devotes a full chapter of his book to Antenna Current and in this chapter page 213, he states "the answers to some questions are relatively insensitive to the errors in the current distribution, whereas the answers to others are very sensitive". It seems therefore that it can be very important to get the current distribution correct but the historical formula used does not show the correct distribution, nor does it take into account the fact that there are two currents going in opposite directions. This deviation from fact is probably reflected in the subsequent calculations made from the current distribution because it is sometimes impossible to reach a final result or significant approximations have to be made. Which suggests that input data to the subsequent formulas represent an impossible situation and therefore, there cannot be a satisfactory result. With the facilities available now for measurement and computer processing, it should be possible to calculate far more accurately the characteristics of an antenna using an improved current distribution model which takes into account linear current loss and current reflections.
The study of antennas will continue with further articles which will reinforce the conclusions reached in this current distribution article and continue with the process of explaining the real radiation mechanism.
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First Published by William J Highton on 21/6/2014
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