"Owen Duffy" wrote in message
...
Well, we all like Distortionless Lines, almost all ham discussion
and indeed much if not most textbook discussion is about one
special case of a Distortionless Line, the Lossless Line.

Nevertheless, we apply one property of Distortionless Lines to
real lines, the property that Zo=Ro+j0, and that Zo is independent
of frequency.

Or, in other words, the Heaviside Condition is met.

C/G = L/R

This is met in lossless lines with R and G being zero, and the
characteristic
impedance being real.
_____________________ _____
Zo = v((R + j?L)/(G + j?C)) = v(L/C)

But, a real Distortionless Line (real excludes Lossless) doesn't
have much application for us.

Consider that with real inductors and capacitors, the permeability,
µ, and the permittivity, e, are themselves often complex.

µ = µ' + jµ" and e = e' + je"

Of the two, I am most familiar with dielectric properties of
polymers as a function of frequency. With plastics like
polyethylene and polytetrafluoroethylene, e' (the real part) remains
fairly constant from low frequencies well into the microwave region,
and e" (the imaginary part) is quite low. Plastics like
polyvinylchloride, on the other hand, show an increasing e" with
frequency due to rotational hindrances of strong dipoles in the
polymer.

Similar frequency dependencies are seen at optical frequencies,
where the refractive index is a function of wavelength. Chromatic
aberration, the failure of a lens to focus all colors to the same
point, is caused by this change of refractive index with
wavelength. In general, the refractive index of a material
increases with increasing frequency. In the infrared and visible
portions of the spectra, we see large changes in permittivity
because of vibrational resonances in the polymer groups.

Though I haven't had my hands on a Distortionless Line, it occurs
to me that increasing L/m is a means of diminishing the effect of
changing R/m, making G/m higher is another means of making Zo
real, and if the materials make R/m(f) track G/m(f) closely ...
then the problem is mostly solved.

With typical commercial coaxial cables, the ratio of shunt
conductance to shunt capacitance is generally much lower than the
ratio of series resistance to series inductance (all per unit
length). This makes the characteristic impedance complex, and the
cable causes distortion.

In the weird cable I described earlier, the resistance of the wire
would increase linearly with the number of turns per unit length but
the inductance would increase as the square of the turns per unit
length. So there would be merit here. Increasing the shunt
conductance will also help — at the expense of making the cable
extremely lossy.

While we have been talking about conventional electrical
transmission lines, we can also analyze nerves as a transmission
line. A nerve is essentially an electrical transmission line with
chemical transducers on each end. When a receptor synapse detects
a neurotransmitter, like serotonin or norepinephrin, it sends an
electrical signal down the neuron. The neuron is the transmission
line. It is essentially an ionic conductor covered with a fatty
substance known as myelin. The result is a distributed resistance-
capacitance line. In diabetics, the myelin sheath is partially
destroyed and replaced with sorbitol, a sugar alcohol. In addition
to being more conductive than myelin, sorbitol has a far higher
dielectric constant. Viewing the neuron as a distributed RC line,
we have both added shunt conductance and increased the capacitance.
It is no wonder that nerve conduction velocity and amplitude both
decrease resulting in such things as peripheral neuropathy, usually
associated with diabetics.

--
73, Dr. Barry L. Ornitz WA4VZQ