Path: utzoo!utgpu!news-server.csri.toronto.edu!mailrus!cs.utexas.edu!rutgers!ub!kitty!larry
From: larry@kitty.UUCP (Larry Lippman)
Newsgroups: sci.electronics
Subject: Re: Ridiculous Impedance
Summary: Coaxial line characteristics
Message-ID: <3970@kitty.UUCP>
Date: 25 Aug 90 16:35:25 GMT
References: <1770009@otter.hpl.hp.com> <1770010@otter.hpl.hp.com> <33145@cup.portal.com>
Distribution: na
Organization: Recognition Research Corp., Clarence, NY
Lines: 55

In article <33145@cup.portal.com>, ISW@cup.portal.com (Isaac S Wingfield) writes:
> >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.
>                ^^^^^^^^^^^^^^
> According to some things I read a few years ago, the two values 50 and
> 75 ohms are, in fact  "magic".

	That was probably a misleading choice of words on my part, since
it requires further explanation.  However, this article should fill in a
few details.

> 75 Ohms answers the question "For a given outer diameter, what impedance
> provides the lowest attenuation per unit length"? This is good to know if
> you are going to distribute video or cable TV, for example. The fact
> that dipole antennas are also 75 ohms is coincidental.

	Actually, the answer is 77 ohms (close enough to 75 ohms, though),
but it applies *only* to a coaxial transmission line having AIR as the
dielectric (permittivity of unity).  However, polyethylene, as a typical
dielectric, has a permittivity of around 2.4.  Since characteristic
impedance of a coaxial transmission line at a permittivity of unity is
reduced by the reciprocal of the square root of permittivity, the
characteristic impedance of a coaxial cable having a polyethylene
dielectric and having minimum attenuation per unit length is much *less*
than 77 ohms.

> 50 (or 51, or 51.5) Ohms answers the question "For a given outer
> diameter, what impedance cable can handle the maximum amount of power?"
> The answer is really around 35 ohms, but the minimum is quite broad;
> 50 ohms is only fractionally poorer, and also matches vertical
> quarter-wave antennas, so that's why it was chosen.

	Maximum power transmission with an AIR dielectric is approximately
30 ohms.  The same condition for a polyethylene dielectric is obviously
less than 30 ohms.

	Maximum voltage transmission with an AIR dielectric is approximately
60 ohms.  The same condition for a polyethylene dielectric is obviously
less than 60 ohms.  For this condition, I seem to recall that the ratio
of coaxial outer diameter to inner diameter is e (2.718).

> Reference: Schaum's Outline Series volume on transmission lines.

	A word of caution on the topic of coaxial transmission line
calculations...  Many reference books present explanations, equations
and data based upon AIR as the coaxial dielectric.  Such data may not
be applicable when polyethylene or other plastic is used as the
dielectric, as is the case for common coaxial cables.

	I have learned this, The Hard Way. :-)

Larry Lippman @ Recognition Research Corp.  "Have you hugged your cat today?"
VOICE: 716/688-1231   {boulder, rutgers, watmath}!ub!kitty!larry
FAX:   716/741-9635                  {utzoo, uunet}!/      \aerion!larry