[TowerTalk] Series Section Transmission Line Matching

[David Gilbert]

I have a question for the math and/or transmission line experts on this 
list.

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?

73,
Dave   AB7E

p.s.  I loaded the formulas into a very simple EXCEL spreadsheet if 
anyone is interested ...