I've published the same article twice now, once in The VHF'er in 1966
and last year in the proceedings of the 2010 Central States VHF Conference.
So I have it available on line but not in a format that will be found by
I suppose I should work up an html page that could be found by a search
engine and expand it with the history as I have found it.
A fellow who knows the technical staff at ARRL has submitted it as a
joint work to QST Technical Correspondence, but in 4 or 5 months there
has been NO response from Newington.
In my oral presentation at 2010 CSVHF, I presented some history of the
The inverse hyperbolic cosine formula is based on work of Harold Wheeler
in about 1938 on the capacitance between closely spaced wires. He found
that the charges were not distributed equally over the surface of the
wires but are concentrated where the gap is smallest due to the higher
electric field in that gap when the wire diameter is similar to the gap
spacing. Something about in the gap the spacing is 3 times smaller than
from the outside to the outside (neglecting the warp of fringing that
has to accompany the field lines from outside to outside) makes the
electric field 3 times stronger for the same potential difference. Makes
much sense. So far the earliest publication I've found with the correct
formula is the about 1942 "Reference Data for Radio Engineers" from
Standard Telephone and Cables Ltd of London. Unfortunately the book has
no copyright date and shows no references for cable impedances. The book
was mostly copied into the 1943 "Reference Data for Radio Engineers"
under Federal Telephone and Radio, Inc of New York (Both were associated
with International Telephone and Telegraph Company) which is dated and
acknowledges that ST&C source for much of the material.
Unfortunately, about half the professional handbooks show only the 276
log formula that is only valid when the spacing is much larger than the
conductor diameters but without that caveat. The impedance error is long
about 1% in the 250 ohm region.
It would appear Newington having been wrong for at least 68 years and
three generations of technical editors is unwilling to admit error or
that there can be any technical authority other than F.E. Handy. (long
dead QST Technical editor).
I plotted the curves in my article, because the inverse hyperbolic
cosine is not a commonly tabulated function and isn't on many slide
rules and calculators. I have seen one other formula that finagles with
the diameter and spacing elements before doing the log function, but
I've not checked it for accuracy. Its a bit more complex than the simple
120 inv cosh... formula.
On 1/7/2011 3:20 PM, Steve Hunt wrote:
> That's interesting!
> I wrote them last year about exactly the same error in a QST article. I
> got a nice response acknowledging the error, but there was no correction
> ever printed.
> Similar response on half a dozen other issues, either within QST
> articles or the Antenna Book; I've now given up trying :)
> Steve G3TXQ
So today we publish on the internet independently. Unfortunately there
is so much garbage also posted on the internet that we won't necessarily
be taken seriously.
The proceedings of the various US based VHF conferences and MUD plus the
semiannual EME conferences now that they are publishing proceedings can
be good places if one doesn't run into personality conflicts with the
editors and their close neighbors about some faulty projects like the
phase noise of the synthesized LO for microwave gear, now sold by DEMI.
Likely newsletters of the few microwave groups around the world can be
places to publish too.
73, Jerry, K0CQ
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