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From: rep@genrad.UUCP (Pete Peterson)
Newsgroups: sci.electronics,rec.ham-radio
Subject: Re: Coax cable specifications (General info wanted)
Message-ID: <1346@genrad.UUCP>
Date: Wed, 16-Sep-87 08:33:45 EDT
Article-I.D.: genrad.1346
Posted: Wed Sep 16 08:33:45 1987
Date-Received: Fri, 18-Sep-87 07:11:49 EDT
References: <1284@bgsuvax.UUCP>
Reply-To: rep@genrad.UUCP (Pete Peterson)
Distribution: na
Organization: GenRad, Inc., Concord, Mass.
Lines: 62
Xref: mnetor sci.electronics:1311 rec.ham-radio:2559

In article <1284@bgsuvax.UUCP> hovan@bgsuvax.UUCP (John Hovan) writes:
>
>   Can anyone explain how coax cable specifications are derived?         
>Does 75ohm coax get its designation by ohms per thousand foot or is this 
>a rating given from a measurement of impedance at frequency?
>
The characteristic impedance of a coax cable depends primarily on its
geometry (log of ratio of shield diameter to inner conductor diameter)
and the permittivity (or dielectric constant) of the dielectric material
separating the conductors.  It can also be expressed in terms of the
inductance per-unit-length and capacitance per-unit-length of the cable.

For low-loss cables:

Characteristic impedance: (ohms)
                  Zo=sqrt(L / C)
                        where Zo is in ohms, L is in henrys/meter
                        and C is in farads/meter.
        or       Zo= 138 * sqrt (mu / epsilon) * log10 (b / a)
                        mu = permeability of dielectric in
                        henrys/meter; epsilon = permittivity of
                        dielectric in farads/meter; b = shield diam;
                        a = inner conductor diam.

Propagation velocity: (meters-per-second)
                     Vp = 1 / sqrt(L * C)
        or           Vp = 3.0E8 / sqrt (mu * epsilon)   

Your 75 ohm coax with a resistive load of 75 ohms will look like
75 ohms resistive at the other end independent of the frequency and
the length of the line.  If terminated in any other load, the driving
end will see a complex impedance which depends on the length of the
cable and the frequency (actually the distance in wavelengths modulo
1/2 wavelength).  Also, if the line is terminated in its characteristic
impedance, there are no reflections from the load. Really, these are
equivalent statements.

For the time it takes for the applied signal to get to the load and
back, you will see a 75 ohm resistive load regardless of what's on
the other end of the cable.  

You can use any of the above properties to determine the Zo empirically
depending on what you have for instrumentation.

Note that cables having dielectrics containing newt's eyes and bat's
wings have been shown to give an improved reproduction of the polish
on the floor of the sound stage.  Unfortunately, these cables must
be made only during a particular phase of the moon since the moon
phase at time of manufacture has important effects on the phase
effects in the cable.  This restriction results in limited production
and great cost.

To appreciate the importance of phase errors resulting from differences
in propagation velocity with frequency, you should observe that speaker
cables might have a delay corresponding to a phase shift of a whole
0.1 degrees at 20khz.  The fact that this total phase shift (let alone
variations in it) is negligible compared to phase errors in any
realizable phono-cartridge equalization circuit should, of course,
not disturb you.

	pete peterson
	{decvax,linus,wjh12,mit-eddie,masscomp}!genrad!rep