In our examination of J-poles using parallel wires as the radiator section--with and without connections at either the top of the bottom, we did not present some of the large body of data collected to establish various considerations. Some of the data involves the sorted radiation and transmission-line currents of the J-pole models SJ-1 through SJ-5. Only the last model, with its seeming aberrant current distribution received a full table of information.
In addition, we also made some basic claims about the performance of current-fed folded dipoles, both closed and open (that is, with an end gap). This set of claims deserves a fuller justification on its own ground, simply to further develop an understanding of the operation of these types of antenna elements. This appendix will provide the missing data collection, with a minimum number of notes along the way to set the data context.
Models SJ-1 through SJ-5
Relative to the appearance of composite current magnitude curves, such as those provided by modeling software, we noted that only the closed folded dipole version (SJ-5) of the J-pole showed transmission-line currents in sufficient magnitude to seriously distort the patterns from their appearance if we had shown only radiation currents. See Fig. 7 in the main text to review the composite current magnitude distribution curves. For our purposes, we need only refer to Fig. 1 to review the configurations of each of the five models.
The models for these versions of the J-pole showed very similar performance values, despite the differences in the radiator sections. As a convenience to data gathering, all of the long radiator-section wires use 14 segments, with segment 1 always at the bottom, that is, closest to the matching section, whether or not directly connected. Therefore, segment 14 is always at the top. The modeling tables will appear in reverse order, starting with model SJ-5. All but the last model (SJ-1) will use 4 columns to present the composite current values provided by NEC-4 software as the starting point in the analysis. Each pair of columns presents the current magnitude and phase angle on each of the two wires. Of course, model SJ-1 is the exception, since it has only 1 wire, and its currents are entirely radiating currents. Hence, Table 5 is complete with only 2 columns of data.
The last 4 columns for Table 1 through Table 4 present the total radiating current and transmission-line current at each pair of facing segments as we move up the wires. Each current has a magnitude and a phase angle. We shall begin with Table 1 and model SJ-5, the closed folded dipole. The notes at the bottom of the table apply to each of the succeeding tables. As I suggested in the main text, note the relatively constant transmission-line current phase angle throughout the length of the radiator. Also note that the transmission-line current reaches a minimum magnitude at about the mid-point of the radiator.
When we turn to Table 2 and model SJ-4, we find a relatively constant transmission-line current phase angle, but one that is quite different from the average value for SJ-5. In fact, the phase angles differ by about 60 degrees from each other. Remember that the ends of the second wire in SJ-4 are not connected at either end to the first wire that is continuous with the matching section. Hence, in model SJ-4, the second wire has a parasitic relationship to the first wire, with moderate transmission-line current magnitudes along the entire length.
Model SJ-3 is the so-called slim-jim configuration, connected at the top between the radiator long wires, but open at the bottom end. Hence, the configuration feeds the end of one of the two long wires. The transmission-line current phase angles in Table 3 do not show as tight a grouping as in the closed folded dipole (SJ-5), but the range is small compared to the range of phase angles shown by the radiating currents. The average phase angle is negative relative to the values shown by models SJ-5 and SJ-4. In addition, the transmission line current magnitude shows a parallel structure to the curve created by model SJ-5, with the minimum value about at the midpoint of the radiator section of the J-pole.
Model SJ-2 reverses the connection by bringing it to the bottom of the radiator, so that the two radiator wires form parallel-connected branches for the matching section, if we treat it as the simple source of energy. Table 4 shows a relatively constant transmission-line current phase angle of about 22 degrees. Note that, like model SJ-4, the maximum transmission line current magnitude occurs about mid-element, but the value of the peak transmission-line current is considerably lower than we find on SJ-4.
Model SJ-1 (Table 5), provides the simplest case, since it has only radiating currents.
The maximum value for the radiating current on model SJ-1 is higher than the values that we calculate for the two-wire radiators, but if we reduce it to about 0.7 of its tabular value, we may create a graphs of radiating current magnitude values for all of the models in the group. Fig. 2 supplies the graph. The values for SJ-1 still rise more rapidly than on the other models because SJ-1 does not undergo either element termination or current division at the junction of the radiator section with the matching section. Otherwise, for the entire collection of double-wire radiators, the radiation current magnitudes show virtually no differences. Model SJ-4, with a wholly unconnected second wire shows a current magnitude graph shape that is more similar to SJ-1 than to the other two-wire models.
If we perform a similar graphing venture on models SJ2 through SJ-5 (with model SJ-1 automatically disqualified) using the transmission-line current magnitude values, we obtain Fig. 3. The fully closed folded dipole element (SJ-5) and the slim-jim (SJ-3) show similar shapes to the current magnitude curves, although at vastly different magnitude levels. Connecting the feedpoint (from the matching section) to a single wire end best replicates the transmission-line current distribution of the fully closed folded dipole radiator. In contrast, the parasitic model (SJ-4) and the bottom-connected model (SJ-2) have curves that replicate each other in shape, but the parasitic model shows the higher magnitude of transmission-line currents.
The exercise is both useful and limited. It has revealed the distributions for both radiating and transmission-line current magnitudes and phase angles. Indeed, one may well be able to wrest from the tabular data further insights into multiple-wire radiator performance. In doing so, one should be aware of the limitations of the exercise. The current data used for each segment has undergone calculation through the NEC method-of-moments techniques to yield current magnitude and phase-angle values that appear in rounded form in the tables. The sorting of current types rests on external calculations that also appear in rounded numbers. The methods show slight variations, for example, in the 1 to 3 degree change in the transmission-line current phase angle when the current magnitude values are very small.
In addition, we have been examining the currents on models that contain more electrical differences than the similarity of their physical structures may suggest. The distance from the tapping point to the top of the matching section and the bottom of the radiator differ among models as a function of the different impedances presented to the matching section by changes we make in the radiator structures. Because the top of the matching section and the bottom of the radiator occur in a region of antenna structure in which impedances change rapidly, very small changes in the radiator may make a considerable difference in the current values reported by the NEC software. Although most of these differences will be unlikely to significantly affect performance, they may make a difference to the calculated values of the current phase angles for both types of currents in the radiator sections of the arrays.
Nevertheless, the exercises do show some general properties in the currents within various sorts of 1/2 wavelength radiators that we may use with the J-pole.
Current-Fed Open and Closed Folded Dipoles
The suggestion that the folded dipole provides the best model for analyzing the performance of the slim-jim configuration (model SJ-3) rested on a comparison of the performance and the current distribution of current-fed folded dipoles with both closed and end-gapped structures. Fig. 4 outlines the general idea presented in the main text. Note that we have indicated current feeding by placing the source or feedpoint at the center of one of the two folded dipole wires.
In fact, I had modeled folded dipoles for 146 MHz using two 2-mm (0.079") wire separated by 25 mm (about 1"). I created the open-end model simply by removing one of the end wires from the closed model. As suggested in the main text, to restore resonance, I have to increase the length of the long wires by 3.8 mm (0.15") or about 1/2 of 1 percent. Table 6 summarizes the dimensions and the free-space performance of these two versions of a folded dipole.
As the table suggests, there is no detectable performance difference between the radiation patterns of the two antennas. The feedpoint impedance values differ by only 1/2 of 1 percent, and both values represent the anticipated X4 multiplier over a linear dipole that is resonant at the same frequency. Nevertheless, if we compare the current magnitude distribution curves offered by NEC software, we obtain very different patterns. Fig. 5 gives us a good view of the differences.
The composite current magnitude plot for the closed folded dipole shows the normal peak value in the mid-element region for both long wires. However, the fact that the currents at the ends of the long elements do not go to zero alerts us to the fact that the currents have both radiating and transmission-line components. In contrast, the currents at the open end of the gapped folded dipole do go to zero, as they must at the element's open end. Although we find a peak in current magnitude in the mid-element region, the current magnitude values at the closed end of the structure are far from approaching zero.
We may usefully calculate the radiating and the transmission line currents of both types of folded dipole. Table 7 presents the results for the closed dipole, while Table 8 gives comparable results for the end-gapped version. Note that each dipole long wire uses 27 segments and that both increases in segment number from left to right across graphic representations. For the end-gap model, the gap occurs at the left end, that is, at segment 1.
Despite the seemingly radical difference in structures and composite current distribution, the two models show essentially the same transmission-line phase angle across the entire structure--very close to 90 degrees different from the feedpoint current phase angle. Of equal importance is the fact that the radiation currents for each type of folded dipole also show similar phase-current ranges as we move from one end of the structure to the other. We may portray more easily the radiating current magnitudes in graphical form, as shown in Fig. 6.
The only difference in the radiating current magnitude level curves occurs at the open end of the end-gap version, where the current on the final segment more closely approaches zero. This difference would be too small to show up in any performance category.
The transmission-line current magnitude curves in Fig. 7 show the major differences between the operation of each folded dipole type. The closed model shows a smooth and symmetrical curve, centered around the mid-element point, where we located the feedpoint on one wire. In contrast, the gap-end versions shows a magnitude dip at the center, but a steady progression of values toward zero at the open end of the antenna. Note that the transmission-line current magnitude at the closed end of the antenna is about as much higher than the closed dipole at the same point than the open end current is below the level of the closed dipole at that same point.
Despite the radical change in transmission-line current magnitude along the gap-end version, the radiating currents remain very symmetrical. As a result the radiation patterns for both the closed and open ended folded dipoles overlay each other perfectly with no detectable displacement.
Shorting the Folded Dipole Center
For VHF and UHF applications, center-fed folded dipoles of standard design present a challenge for equipment durability and safety. Often mounted in arrays on masts that tower over surrounding objects, ungrounded antenna structures can carry considerable surges to the equipment that they serve. A short-circuit across the center of a folded dipole allows connection of one side of the feedpoint to the feedline ground, changing the DC and lightning potential to the same value as the support structure. Numerous amateurs have wondered whether a center-shorted folded dipole works, and if it does, how it works. We may apply the same analytical tools that we have been using to the center-shorted folded dipole and find a considerable part of the answer.
Modeling a folded dipole with a center short between the long wires requires a small revision in the wires to create a wire junction on both long wires at the center of the structure. Instead of 27 segments from one end to the other, we shall now have 28 segments, and the source segment will be one segment off center. The required resonant length decreases a small amount, down to 943.0 mm, leaving all other dimensions the same as we used with the sample closed and open-ended versions of the antenna. Fig. 8 shows the outline, along with the composite current distribution curves--with the standard center-fed folded dipole presented for comparison.
The free-space gain of the version with the center short is 2.13 dBi, the same value that we derived for the earlier folded dipoles. The feedpoint impedance is 281.8 - j0.0 Ohms, a value that indicates a full folded-dipole impedance transformation when both long wires have the same diameter. The composite current distribution curve for the modified folded dipole should have a familiar look, since it is virtually the mirror image of the curve that we showed for the open-ended or gapped folded dipole. In fact, allowing for the opposite-end presentation, there is no significant difference between the radiation and the transmission-line currents. Table 9 provides the data calculated on the basis of the current reports for facing segments along the parallel long wires.
For both the center-short and the gapped folded dipoles, the radiation currents vary in magnitude from 1.0 at the center down to about 0.1 at the ends (actually, the center of the last segments). The transmission-line current magnitudes vary from a high between 0.7 at one end to less than 0.05 at the other. If we mirror image Fig. 7, it correctly graphs both types of current magnitude on the center-shorted folded dipole. The transmission-line currents are 90 degrees out of phase with the feedpoint or source current.
The short circuit across the center of the folded dipole does not de-activate the wires on the opposite side of the short relative to the source location. With respect to radiation currents, the entire length of the structure participates equally in the current distribution and the radiation pattern. However, the short circuit does alter the pattern of transmission-line current magnitude, replicating the situation that occurs with the gapped folded dipole. The short does permit the inclusion of a significant safety feature within the antenna structure.
Conclusion
The notes in this appendix supplement the main text for those who wish to dig a bit deeper into element operation when the element contains more than one wire and the spacing between the wires is fairly close. Their practical applications may be scant, but they might be useful to modelers trying to understand some of the seemingly strange current values reported along such multi-wire elements by NEC or MININEC software. They may also help to improve our naturalized expectations of performance from folded elements beyond the level normally treated in most texts.
Then again, they may simply be an expression of where my own curiosity has led me.
Updated 11-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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