The majority of calculations for antenna impedance, resistance, radiation resistance, reactance, radiation pattern etc are based on methods using the overall antenna current distribution curve. The distribution has been traditionally calculated using a formula originated by Hubert Pocklington that was first published in 1897, at the time the existence of electrons was being confirmed, many physicists still believed in the ether and electricity was still the subject of much study. The subsequent antenna calculations generated over many years using the Pocklington current distribution formula as a basis, are generally extremely complicated and only the most gifted and dedicated mathematicians are likely to be able to understand them. During the process of studying some very basic formulas for calculating the radiation resistance of a simple antenna, it became obvious that the current distribution curves given in every antenna book available to me were very similar to the curves given for transmission line current into a mismatch. Having already investigated the transmission line curves and reaching a logical conclusion that does not agree with the text books, it seemed like a good idea to investigate antenna current distribution in a similar manner.
1.2) Conventional Current Distribution
The conventional current distribution for an ideal antenna is described in Radio Engineers Handbook by F E Terman, McGraw-Hill, 1943. Terman is a very well respected engineering academic and this book is still regularly used as a reference by radio engineers. It is reasonable to assume that Terman is using the best calculation methods available to him and they have withstood the test of time. The following is an excerpt from his book, page 772.
"Resonant Antennas - In the case of a wire having an open end, the current will be distributed as in Fig.2a. It is zero at the open end and passes through minima at distances that are a half wavelength away from the end. 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. Since the current minima are quite small with respect to the current maxima, it is common practice to picture the current distribution as in Fig 2b, where the current at the minima is assumed to to be zero instead of merely small, and the currents in adjacent loops are taken as 180° out of phase".
Fig 2.- Actual and schematic current distribution in resonant antennas.
The arrows represent the direction of current flow (i.e. the polarity).
The equation of the resulting current distribution for this idealised case is
Where Io = current at current maximum
x/λ = distance in wavelengths from the open end
ω = 2π x frequency
t = time
The current distribution represented by Eq. (3) is that which would be obtained if the antenna acted exactly as a transmission line with zero losses. This condition is never realised perfectly in practice, because obviously an antenna will radiate some energy and therefore will consume some energy.
1.3) Comparing Current Curves
In order to compare the results of different calculation methods, the curves for current distribution were generated using equation 3 (Pocklington formula) together with a sinusoidal curve and a vector difference of the INCIDENT and REFLECTED currents in a lossless transmission line that is terminated with an OPEN. These are shown in Figure 3 and the calculations are performed in antenna-current.xls on the Curves page. The Vector Difference and Sinusoidal curves are virtually identical and the only difference appears to be in computer calculation accuracy.
It is interesting to compare the curve generated by the Pocklington formula with the curve of the vector Difference. The similarity of the two curves demonstrates that using Pocklington's formula has again thrown a subject into the same trap of simply accepting the patterns generated by the phase relationships of two separate signals and not analysing the two individual currents present. This has caused much confusion with transmission line theory and an indication of what is really happening in a transmission line can be found at 6.2) Phase relationships Along the Length of a Mismatched Transmission Line but it may be necessary to read the whole article in order to gain a fuller understanding of the real behaviour of transmission lines.
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