Reg:

[snip]
Vary line length until it is exactly 1/4 wavelengths.

The input impedance of the 1/4-wave length of open-circuited line is also
calculated and displayed.

It will be found that at exact resonance (vary length or frequency very
finely) the input impedance of the line will be a pure resistance ( jXin =
0) equal to half of the of the line end-to-end wire resistance.
[snip]

This is *exactly* what my [and other's as well] line analysis computer
programs do for the analysis of so-called "bridged taps".

"Bridged taps", which are sections of open circuited transmission line
bridged across an operational transmission line, are quite common
in telephony practice. They are often placed deliberately to allow
for extra extension/party lines, or are inadvertently left in place once
a line is taken out of service. There are often several bridged taps
on a given line. These bridged taps don't affect telephony [audio] but
wreak havoc at higher frequencies for broadband signals. For
frequencies where the bridged taps represent a 1/4 wavelength, they
act as traps or notches and "suck out" the desired energy on the main
line. As such bridged taps can ruin the performance of digital subscriber
loops aka "DSL" such as ADSL/VDSL, etc. because they punch holes
in the transmission band. Several companies, and consultants
such as myself, have transmission line programs to evaluate broadband
transmission over lines with cascades of multiple guages/dielectrics and
several bridged taps. In fact several such "standard" line makeups
for evaluating the performance of DSL systems are published
in the Standards literature [ANSI T1E1.4]. My Fortran computer codes
must perforce analyze such 1/4 wave, or any wavelength for that
matter, stubs quite accurately to predict multi-megabit transmission
performance over several thousand feet of such impaired lines. :-)

But until your posting I had never thought to use them to analyze
the driving point impedances of antennas. Neat application!

[snip]
If your own programs significantly disagree then consign them to the junk
box.
[snip]

Can't do that now, since literally millions of DSL modems are now running
around the world over lines that have been accurately analyzed using those
programs, hence they must be "right". I still use the programs in my
consulting
practice for client companies designing DSL modems who use my services.

I have never used these programs to simulate antennas yet, gotta do that
just for fun... I can set any arbitrary distribution of radiation
resistance
along the line in series with the primary parameter R(f) [of R(f), L(f),
C(f)
and G(f)] and so uniform distribution should be easy.

[snip]
. There are no references
except my tattered note books. I came across various useful relationship
around 1960 when researching into methods of locating faults on oceanic
phone cables.
[snip]

Well you certainly predate me, I only started developing my transmission
line
analysis programs around 1971 or so and have kept *improving* them over the
years, mostly to make contributions to my employers, clients and various
transmission standards committees [ANSI, ITU, ETSI, IEEE].

[snip]
But I daresay Heaviside preceded me. I dug up much information
and designed fault locating and other test equipment but very little was
published beyond contract manufacturing information. There were two
articles
in the house engineering journal. I worked alone with a small group of
assistants, a lab and a workshop. I did present a series of lectures
afterwards, twice in Europe. But it was all just in a day's work with
occasional trips aboard cable laying ships and at manufacturers. The
nearest
I got to the States was Newfoundland and Nova Scotia. I then shifted in
succession to several entirely different fields of operations. But no
experience is ever lost.
[snip]

Same here, as you know... I am a "fan" of Oliver's myself... and most of
my work in this area was done "in house" for various clients and never
published. Many times I felt that such work was "all done" and I was ready
to retire it all only to have it called back into service with each round of
higher
bandwidth systems... for various reasons detailed cable/transmission line
analysis seems to come back into favor every decade or so... these days it
is a sadly neglected subject in "skul" curricula and are few "young turks"
who can handle such problems, and so we "old farts" can't retire just yet.
:-)

Newfie and Nova Scotia, eh? Wonderful place in the summer. My wife
and I have a condominium overlooking Halifax harbour and we spend
part of the summers there. My Mom was/is a Newfie and I was
born in Halifax, Nova Scotia myself, although we are both now all
fully certified "Americans".

Did you work for Cable and Wireless at one time?

I suppose you might even have sailed on the "Cyrus Field", no?

Long live the "Telegraphist's Equations"!

--
Peter K1PO
Indialantic By-the-Sea, FL.