[sci.electronics] Coax cable specifications

hovan@bgsuvax.UUCP (09/11/87)

	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?

Any technical information pertaining to coax cable will be appreciated.


 
				John Hovan
				BGSU 
				Hardware Support
				hovan@bgsuvax.uucp

rep@genrad.UUCP (Pete Peterson) (09/16/87)

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

dje@datacube.UUCP (09/16/87)

The impedance of  coax has  very little  to do  with it's resistance.
The inductance and capacitance per unit length are the most important
factors.  These are dependent  on geometry  of the  center and shield
and the dielectric constant.  

One way to look at cable impedance is that  if you  terminate the far
end in its characteristic  resistance, and  measure  the impedance at
the  near  end,  you'll  get  the  characteristic  impedance  at  any
frequency. It's magic.

 				Dave Erickson
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henry@utzoo.UUCP (Henry Spencer) (09/17/87)

> 	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?

Sort of the latter.  Consider a longish cable with *something* at the
other end.  Suddenly we apply a voltage to the near end.  How much current
flows?  Remember that speed-of-light lag means that the impedance at the
other end is unknown and cannot influence the answer!  The answer is that
the properties of the cable (and its immediate environment) determine a
"characteristic impedance" which is what you plug into Ohm's Law to find
the instantaneous current.

Of course, after speed-of-light lag has had time to occur, then there will
be trouble if the impedance at the other end doesn't equal the cable's
characteristic impedance.  What happens then is "reflections", which
propagate back (and forth) until everything eventually settles down to
the steady-state situation that you would expect if you ignored the
finite speed of light.  Unfortunately, reflections are usually undesirable,
because they can be mistaken for signal changes when fast circuits are
involved.

To avoid reflections, the basic approach is to keep the same impedance all
the way along, from the transmitter output to the other end.  In particular,
this means cable with fairly constant characteristic impedance and a
terminator of that same impedance at the other end.  The c.i. of a single
wire varies a lot depending on what is near it, although various tactics
can limit the variations.  Coax's c.i. is largely insensitive to its
surroundings, making a constant-impedance system much easier to build.

Some of the serious electron-pushers may want to correct or elaborate on
the above; I'm just a software type with one foot in hardware...
-- 
"There's a lot more to do in space   |  Henry Spencer @ U of Toronto Zoology
than sending people to Mars." --Bova | {allegra,ihnp4,decvax,utai}!utzoo!henry

ron@topaz.rutgers.edu (Ron Natalie) (09/17/87)

Yes, remember that the cable termination is to make it appear infinitely
long.