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## [TowerTalk] Self C and L for inductors

 To: "Towertalk" [TowerTalk] Self C and L for inductors "Jim Lux" Sat, 22 Nov 2003 07:44:24 -0800
 ```For those of you thrashing out the issue of parasitic C, and applying circuit theory to loaded antennas, I've run some calculations on typical loading coils. I've used the Wheeler approximations for the inductance, and the Medhurst approximation for self capacitance. The former is the typical equation you'll see in the ARRL handbook. The latter is essentially the self C of a conducting cylinder in free space. I note that the ARRL antenna book doesn't discuss the effect of the self C of the loading coil (except in the context of self resonant frequency of the coil). From an antenna tuning standpoint, the effect is probably fairly small, and would be overwhelmed by the effect of surroundings, and would be accounted for in the inevitable "pruning" to resonance. And, for that matter, the self C of the coil is probably not too far from the self C of an equivalent length of wire; a statement, the verification of which, is left to the interested reader (meaning, I'm too lazy to do it) I have taken the design examples from page 16-5 in the 20th ed of the ARRL antenna book. It's an 8 foot mobile whip in all cases. I cut and pasted from an Excel spreadsheet so the columns might not line up. The #N/A is because my handy table for the K factor in Medhurst's equation doesn't deal with short fat coils. The Wheeler L and the ARRL L don't match, probably because the ARRL calculated the desired inductance, then took the nearest integer number of turns and round numbers for dimensions that added up. I've also added a column for the reactance of the L and C at the frequency of interest. Note that these reactances are all in the few hundred or thousand ohms, which is significant if you're calculating currents. You'll need to do some serious cutting and pasting to get the table to look right, because most mail clients wrap the lines. F L N AWG Dia Length H/D Wheeler L Med. K C Self Res Xl Xc MHz uH turns inch inch uH pF MHz ohm ohm Base 1.8 345 135 18 3 10 3.33 361.29 0.646 4.92 3.77 4086 17962 3.8 77 75 14 2.5 10 4.00 79.00 0.72 4.57 8.37 1886 9161 3.8 77 29 12 5 4.25 0.85 80.87 #N/A #N/A #N/A 1931 #N/A 7.2 20 17 16 2.5 1.25 0.50 19.01 #N/A #N/A #N/A 860 #N/A 7.2 20 22 12 2.5 2.75 1.10 19.52 0.462 2.93 21.03 883 7535 14.2 4.5 10 14 2 1.25 0.63 4.65 #N/A #N/A #N/A 415 #N/A 14.2 4.5 12 12 2.5 4 1.60 4.39 0.476 3.02 43.69 392 3708 Center 1.8 700 190 22 3 10 3.33 715.64 0.646 4.92 2.68 8094 17962 3.8 150 100 16 2.5 10 4.00 140.45 0.72 4.57 6.28 3353 9161 7.2 40 28 16 2.5 2 0.80 39.20 #N/A #N/A #N/A 1773 #N/A 7.2 40 34 12 2.5 4.25 1.70 33.60 0.482 3.06 15.69 1520 7222 14.2 8.6 16 14 2 2 1.00 8.83 0.46 2.34 35.04 788 4796 14.2 8.6 15 12 2.5 3 1.20 8.52 0.464 2.95 31.76 760 3804 If anyone wants, I can post the excel spreadsheet on the web. Jim W6RMK _______________________________________________ See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless Weather Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any questions and ask for Sherman, W2FLA. _______________________________________________ TowerTalk mailing list TowerTalk@contesting.com http://lists.contesting.com/mailman/listinfo/towertalk ```
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