In message 
          The Natural Philosopher  wrote:

> On 24/06/2020 16:22, David Higton wrote:
> >
> > All cables behave as transmission lines.  So do PCB traces.
>
> Well no, they don't. a single signal wire with the earth/return via the
> other side of the  world is so far from a transmission line as to render
> the notion 'not  useful'

You pick an interesting case.  When current flows through a wire, a
magnetic field is created.  We know this is true because, if the
current is high enough, we can see it deflect a compass needle.

The magnetic field contains energy.  This means the wire has
inductance.  That's one of the four components in the standard model
of a transmission line: series inductance, series resistance, shunt
capacitance and shunt resistance.

30-odd years ago I was involved in the design of an audio test set
with integral oscillator.  The distortion residual of oscillator and
analyser was 0.0008% at 1 kHz.  At one stage in development, I saw
that the distortion measured at the load was a little bit higher than
that at the output terminals of the oscillator.  The path went through
reed relays.  I discussed this with the manufacturer of the relays,
who sent me some magnetic wire and a couple of little bar magnets.
I measured the voltage across a length of wire, and discovered that
it was much higher than across a similar length of copper wire - and
that it was proportional to frequency, i.e. I was seeing the effect
of the wire's inductance, which was much higher for the wire with
the built-in magnetic core (the wire was in all cases straight).  I
measured the harmonic distortion of the voltage across the wire,
and found that I could get several percent if I put enough current
through it.  Looking at the distortion residual, it was all odd
harmonics, mostly third harmonic.  Then the real eye-opener: put
a bar magnet close to the wire, and the second harmonic appeared in
large quantity.  (The wire was being pushed closer to magnetic
saturation when the current flowed in one direction than the other.)

All of which is just to remind you that wire does indeed possess
inductance.  So does cable.

Look at the standard mathematical model of transmission lines, and
you'll see the four components I mentioned above.

As for PCB traces: I discovered in the early 1990s, when we were
using 74ABT logic devices, which have nanosecond rise and fall times,
that devices at the far end of a 150mm PCB trace were being clocked
on the rising edge always (as they should be), but often on the
falling edge too.  Looking at it with a fast enough oscilloscope,
both edges had a "dog-leg" or inflection.  The inflection on the
falling edge was just about the threshold of the receiving device,
so it saw a rise there too.  The cure was to terminate the PCB
trace, which as behaving exactly as the mathematical transmission
line model showed it should.

If you can get hold of appropriate kit, these are observations
that you can replicate.

David

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