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 165 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
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