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From: morrison@cs.uiuc.edu (Vance Morrison)
Newsgroups: sci.electronics
Subject: Re: Signal Propagation, Baud Rate, and Attenuation
Message-ID: <1991Jan2.164234.21958@ux1.cso.uiuc.edu>
Date: 2 Jan 91 16:42:34 GMT
References: <17100010@inmet> <1126@soleil.UUCP> <1991Jan2.055516.14616@NCoast.ORG>
Sender: news@ux1.cso.uiuc.edu (News)
Organization: University of Illinois at Urbana
Lines: 77

In <1991Jan2.055516.14616@NCoast.ORG> bbs@NCoast.ORG (XBBS System) writes:

>Could someone out there explain to me why a signal can physically travel
>further on a metal media at a slower baud rate ?

There are two reasons main reasons for a length restriction for cableing, 
attenuation and dispersion.  

Attenuation is relatively easy to deal with and is independent of baud
rate, it can also be compensated for relatively easily by simply boosting
the signal at the source.  

Dispersion is the limiting factor in your case.  So what is dispersion?
The key is to realize that a cable is NOT a perfect transmitting media,
it also distorts the signal passing through it.   To actually calculate
the distortion of a cable involves essentially solving some partial 
differntial equations (maxwells equations), given the geometry of the
cable.  This sounds nasty, and doing it from first principles is nasty,
but EE's have developed some good 'tricks' that simply the problem greatly.

The first trick is to realise that the cable is simply a linear system
(that is a system with only resistors, capacitors and inductors).  For
such systems, we know if they are fed a sinusoidal waveform, the output
MUST be a sinusoidal waveform of the same frequency.  Thus the only thing
a linear system can do is to change the phase and amplitude of of the
sinusoid.  

The second trick is to realise that ANY particular waveform can be expressed 
as a sum of sinusoids (fourier's theorem).  

The final trick is to realize that since the system linear, superposition
holds, that is, the responce of a sum of two signals is simply the sum
of the responce of each of the signals applied seperately.  

Combining these three tricks we now have a procedure for caclulating the
output of a cable (or any other linear system), given the input.  We simply
decompose the input into a sum of sinusoids (find the fourier series or
transform),  compute how the cable distorts each of the sinusoids (remember
only phase and amplitude can change), and then add the responces back up
(compute the inverse fourier series or transform).

Thus the key to all of this is determining how the cable changes the phase
and amplitude of a sinusoid (this is a much easier problem then the general
case.  

As it turns out to a very good approximation, cables distort sinusoids in
a very predictable way.  Basically all that happens is that the high frequencies
travel faster then the low frequencies  (or the other way around, I can never
keep that straight).   This dependance of signal velocity on frequency is called 
dispersion.

Now it is relatively easy to see what is going on.  If we sent a square 
waveform down a cable, the high frequency components of the waveform will
arrive before the lower frequency components.  Thus the signal does not
'add up' right and the signal is distorted.  This causes a rounding of
the edges of the waveform.  Notice, however, that the longer the cable
the more the high frequencies will be out of phase the the lower frequency
components and the worse the distortion will be.

Now by lowering the baud rate, the reciever will not care so much about
the edges of the waveform and so more phase distortion can be tolerated,
so longer cables can be used.

Note that to a large degree, this distortion is very predictable.  Because
of this it is possible to 'predistort' the signal so that the the cable
distortion is canceled (it can also be done at the receiving end).  Modern
modems do this kind of fancy signal processing.

One final note, RS232 cables have a common ground for all signals, this type
of cable has VERY bad dispersion characteristics and this is why RS232 cables
can only go limited distances.  On the other hand if each signal wire has
its own return (differential mode), (like RS422), the characteristics are
MUCH better and much longer distances (4000 ft), are quite reasonable.

Hope this helps

Vance