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 ```Antenna Element Losses I thought I might follow up on the discussion of "losses" due to traps with some quantification via modeling. This will graphically illustrate the fact that the insertion of loads in an antenna element results in lesser gain just from the reconfiguration of the element, even when there are no ohmic losses, and also give an indication of additional loss of gain occasioned by ohmic losses related to the Q of the load. To do this, I created a model of a 20 meter dipole. Then I shortened it from roughly 34' to 24' (about 70% normal length). To reresonate the dipole, I inserted various types of loads. I then added, where relevant, some ohmic losses to the load elements. All models are in free space. The full size model used 21 segments; the 70% models used 15 segments so that distance between current check points is about the same as in the full size model. The data can be looked at in at least two very useful ways. First, there are the standard numbers associated with gain and feedpoint impedance. Second, we can examine the pattern of current levels along the elements. I shall list the current levels from the feedpoint to the end for only one side of the dipole, since they are the same on the other side. Note the abrupt changes from the normal virtually sinusoidal curve of currents wherever loads are present. Use caution in interpreting these numbers. First, gain figures are in dBi, which means that you should never think such things as "This version has only 50% of the gain of that one," if the gains are 2 dBi and 1 dBi, respectively. Rather, version 2 is down 1 dB from version 1, and would be so over real ground of any sort (where the numbers might be 8 dBi and 7 dBi, respectively). Second, when applied to multi-element arrays, the differentials are roughly--but not exactly, additive. For dipoles with a 0.5 dB differential, a 3 element beam might show about 1.5 dB differential, but with due allowance for other design factors that can modify this rough measure. Third, the models use a fairly radical element shortening: 30%. Traps in a 10-15-20 meter beam, on 20 meters, do not approach this level of shortening. On 15 and 10 meters, the situation is more complex, since part of the gain reduction may stem from a trap appearing as an inductive load and part from trap inefficiency in terminating the element. Finally, note that currents are at the center of segments of these NEC models; hence, the current closest to the feed point will be less than 1.0 and the current in the last segment will be greater than zero. Currents are for a set power level to the feedpoint of 100 Watts. You will have to mentally add the line beneath the readings to create the linear element along which these current levels exist. Time for some numbers. All models are of copper wire (#12) at 14.174 MHz. "Current" = the current with a feedpoint power of 100 watts; "C (I=1)" = the current with a preset feedpoint current of 1A. 1. Full size dipole: gain 2.09 dBi; Z = 73.0 + j1.0 ohms Current: 1.16 1.12 1.06 .98 .88 .75 .61 .46 .29 .10 C (I=1): .99 .96 .91 .84 .75 .64 .52 .39 .25 .09 2. Capacity hat loading at 70% point: gain 1.97 dBi; Z = 59.7 + 0.0 ohms Current: 1.28 1.25 1.18 1.09 .98 .86 .72 (load begins here) C (I=1): .99 .96 .91 .84 .76 .66 .56 Note that the current level for 100 watts is higher due to the lower feedpoint impedance. Relative current distribution is shown by the "C (I=1)" line where the current is set to 1 A at the feedpoint. Otherwise note that the current remains at normal levels until those levels have decreased to the point of adding little to the antennas radiation. The current continues to decrease in the hat elements, but radiation from those elements cancels itself due to being of equal magnitudes but opposite phase. Gain is down by 0.12 dB from the full size dipole. 3. Center loading coil of infinite Q (no ohmic losses). Load = j458 ohms. Gain 1.86 dBi; Z = 29.2 + j1.3 ohms Current: 1.70 1.51 1.29 1.04 .78 .49 .18 C (I=1): .92 .82 .70 .56 .42 .27 .10 Note: the gain reduction is 0.23 dB just from the missing high current portion of the antenna element unavailable for radiation. (Modeling software treats inductive loads as non-radiating. They do radiate a little, but too little to affect the results here.) 4. Center loading coil: Q=100. Load = 4.58 + j458 ohms Gain 1.23 dBi; Z = 33.8 + j1.3 ohms Current: 1.58 1.40 1.20 .97 .72 .46 .16 5. Center loading coil: Q=50. Load 9.16 + j458 ohms Gain 0.68 dBi; Z = 38.4 + j1.3 ohms Current: 1.49 1.32 1.12 ..91 .68 .43 .15 Note that the current distribution remains the same for a present feedpoint value of 1.0. However, element gain is down significantly due to additional power being lost in the center load resistive losses, as indicated by the decreased current levels in 4. and 5. Again, remember that relative to a trap element, this is a very high loading value. Modern traps may (or may not) achieve coil Q values higher than 100. However, a more accurate reflection of their action come from models of mid-element loading coils. 6. Mid-element loading coil: infinite Q (no ohmic losses). Loads = j478 ohms (x2). Gain 1.89 dBi; Z = 46.1 + 0.47 ohms Current: 1.46 1.42 1.36 1.24 .93 .59 .21 C (I=1): .99 .96 .92 .84 .64 .40 .14 Coil Position: ^ Note that although mid-element loading coils yield a slightly higher gain (0.03 dB) than a center loading coil, the difference is not significant. Each coil must actually be larger than a single center loading coil for resonating the same length of element. Compare the current distribution to that of the full size dipole and the rapid drop of current past the loading coil. 7. Mid-element loading coil: Q=100. Loads = 4.78 + j478 (x2) Gain 1.29 dBi; Z = 53.0 + 0.1 ohms Current: 1.36 1.32 1.27 1.16 .88 .55 .20 8. Mid-element loading coil: Q=50. Loads = 9.56 + j478 (x2) Gain 0.76 dBi; Z = 59.8 - 0.2 ohms Current: 1.28 1.25 1.19 1.10 .82 .52 .19 Note that again, the current distribution is the same as in the lossless load case, although the gain is down significantly (1.33 dB for Q=50; 0.80 for Q=100). For a constant power, current levels are down along the element compared to a set of lossless loads. Again, the much smaller values of trap coils may occasion far lower losses. Note that we have been focusing on current distribution and on currents from a constant power level. We did this to sort out the questions of gain related to load configuration and reactance from the questions of gain related to resistive losses. Constant-power current figures are comparable only within a model type, where feedpoint impedances are close enough to make the current levels meaningfully similar. Plugging these numbers into a spreadsheet and making simple line graphs can display the discontinuities occasioned by loading elements even more vividly. That however, and in the words of all those pretentious textbooks, I leave to the reader as an exercise. If you use a trap beam, you can estimate for 20 meters a total equivalent midelement loading coil by seeing what value of inductive reactance is necessary to resonate the element on 20 at its manufactured length. Actually performance will additionally depend on the Q of the coil(s) functioning as coils rather than as part of a tuned circuit, since the capacitor has little effect. (However, ultra precision would also take into account signal coupling through the capacitor--of very high Q but of significant capacitive reactance.) Loosely, you can do the same for 15 meters by measuring the element from 15 meter trap to 15 meter trap. On 10 meters, the element should be full length. However, trap efficiencies come into play for these bands, and that is another topic entirely. -73- LB, W4RNL L. B. Cebik, W4RNL /\ /\ * / / / (Off)(423) 974-7215 1434 High Mesa Drive / \/ \/\ ----/\--- (Hm) (423) 938-6335 Knoxville, Tennessee /\ \ \ \ / / || / (FAX)(423) 974-3509 37938-4443 USA / \ \ \ \ || cebik@utk.edu -- FAQ on WWW: http://www.contesting.com/towertalkfaq.html Submissions: towertalk@contesting.com Administrative requests: towertalk-REQUEST@contesting.com Problems: K7LXC@contesting.com Sponsored by Akorn Access, Inc & N4VJ / K4AAA ```