It's also possible to use one of the Leeson spreadsheets that John mentioned to
calculate the resonant length for half-wave dipoles and quarter-wave grounded
verticals, although not for other antenna types such as inverted vees, elevated
verticals, or loops. In the link that John gave, the appropriate file is
"Element.wk1" which is in Lotus 1-2-3 format. It can be opened with Excel
although you may have to jump through some hoops to do so. Also, you probably
won't be able to make much sense of it unless you have the Leeson book.
I own both the book and the diskette. Several years ago I created a copy of
Element.wk1 and stripped out all the parts having to do with wind/ice loading
and element to boom clamps, leaving only the "Equivalent Cylindrical Element"
calculations. Here's a screen grab.
http://ac6la.com/adhoc/VertFactor3.png
The Leeson algorithm is implemented in EZNEC as the Stepped Diameter
Correction. In the screen grab above, the section lengths and diameters
correspond to the reflector of Yagi model 20M5ELYA.ez, one of the samples
included with the EZNEC package. If you open that model with EZNEC, show the
"Wires" sub-window, and click Other > Show Stepped Dia Correction you'll see
this.
http://ac6la.com/adhoc/VertFactor4.png
The inconsequential differences in overall element length and diameter are
because EZNEC uses single precision for the calculations whereas Excel uses
double precision.
The Leeson algorithm calculates the equivalent cylindrical element given a
taper schedule. It doesn't directly calculate a resonant length. However, it
does show the reactance for the equivalent element (cell J23) at the specified
frequency so you can try different tip lengths until the reactance is zero.
For "mono-taper" elements like Gary's 4" 80m vertical just use section 1 and
clear all the other sections. (And remember, lengths are set in inches, not
feet.)
Or, instead of manually trying different lengths, you can use the Excel "Goal
Seek" tool. Like this.
http://ac6la.com/adhoc/VertFactor5.png
When you click OK from the Goal Seek dialog Excel will adjust the length (cell
G4, or B4 if only a single section is being used) such that the reactance (cell
J23) is zero at the frequency specified (cell B1). And it'll do it a heck of a
lot faster than you can.
Here's the modified Leeson workbook. It can be used with Excel or Excel clones
like Open Office.
http://ac6la.com/adhoc/LeesonElementPartial.xls
I don't have explicit permission from the ARRL to distribute this workbook but
as long as it's for personal use I don't think they'll mind.
Dan, AC6LA
http://ac6la.com
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