I have a question for the math and/or transmission line experts on this
The ARRL Handbook has some good info on using two different sections of
transmission line, each with different characteristic impedances, to
match an arbitrary load impedance to the main coax run. The discussion
and formulas are on page 16-5 of my old 1990 handbook. I've run a few
examples through the formulas and then checked the result with EZNEC and
everything seems cool.
The Handbook points out that the common quarter wave matching
transformer is just a special case of the series section analysis. A
quarter wave matching section has the very valuable and much-utilized
feature that it converts a voltage forcing function to a current forcing
function (with a 90 degree phase shift) so that you can connect two or
more feedlines in parallel and force equal currents in their respective
loads irrespective of load impedance.
So I got to wondering whether a generic series section matching section,
even though the lengths of the two sections don't add to a quarter
wavelength, might also provide the same current forcing characteristics
as a quarter wave one does. I fantasized there might be some phase
transformation due to the disparate feedline impedances of the matching
sections that would compensate for the actual length. However, as best
I can tell after checking currents and phases with EZNEC, that it not
the case. The phase shift under a matched condition doesn't typically
work out to be 90 degrees, and the actual phase remains simply a
function of section lengths and velocity factors.
Did I get that correct?
p.s. I loaded the formulas into a very simple EXCEL spreadsheet if
anyone is interested ...
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