Path: utzoo!utgpu!news-server.csri.toronto.edu!rutgers!uwm.edu!rpi!dali.cs.montana.edu!uakari.primate.wisc.edu!sdd.hp.com!hplabs!hpfcso!hpfcdj!myers
From: myers@hpfcdj.HP.COM (Bob Myers)
Newsgroups: sci.electronics
Subject: Re: Ridiculous Impedance
Message-ID: <17660092@hpfcdj.HP.COM>
Date: 24 Aug 90 18:51:35 GMT
References: <1770009@otter.hpl.hp.com>
Organization: Hewlett Packard -- Fort Collins, CO
Lines: 38

>	50, 75 and 93 ohm coaxial cable are merely common values that have
>been standardized upon for many commercial and military applications.  They
>are not "magic" numbers for any particular reason.

Hmmmmmm.  It always struck me as odd that certain of these numbers work very
nicely in the good ol' quarter-wave matching section formula, when dealing
with some very basic antenna types.  Remember, the formula is

                Zm = SQRT (Zload x Zline)

where Zload is the feedpoint impedance of the antenna, Zline is the char.
impedance of the feedline to which you are matching, and Zm is the impedance
of the matching section (one-quarter wave long).

Now, a simple dipole has a feedpoint impedance of around 72-73 ohms, and
- surprise! - RG-59 or any other "75 ohm" cable provides and excellent match.
A quarter-wave vertical has a feedpoint impedance half that of a dipole -
about 37 ohms - and applying the above formula says that to match it to
75-ohm line would require a 53-ohm matching section.  (And does anyone
remember when we called RG-8 fifty-TWO ohm line?)

I don't know that any of this had anything to do with the selection of
standard values - as Larry said, the characteristic impedance of any
reasonable coax is going to be about in this range.  But perhaps the selection
wasn't *completely* random.

As far as the 61.8 ohm question goes: I also note that the geometric mean of
75 and 50 is close to this number - it's 61.2 - but that's on the wrong
side of the formula, as it would be the impedance required of the matching
section, not the main line.  (In other words, a 61.2 ohm section would
match a 50 ohm load to a 75 ohm line, and vice versa.)  Does this have
anything at all to do with it?  Did somebody just happen to have a few
thousand miles of 61.8 ohm cable that they wanted to get rid of? :-)


Bob Myers  KC0EW   HP Graphics Tech. Div.|  Opinions expressed here are not
                   Ft. Collins, Colorado |  those of my employer or any other
myers@fc.hp.com                          |  sentient life-form on this planet.