non-real characteristic impedance transmission lines exist? Are they typical?
Yes.
An ideal transmission line has R = 0 and G = 0. This gives a real characteristic impedance. But this is an idealization. These numbers are never actually 0 in reality, so the imaginary part of characteristic impedance is never truly 0.
What does it even mean to have a non-real characteristic impedance?
It means the transmission line is lossy. The sum of output power and reflected power will be (at least slightly) less than the input power.
but if hope to achieve a real Z0 this means carefully matching the non-ideal properties of both the conductor and the dielectric,
This isn't practical.
More often you just try to get R and G low enough that they can be ignored for practical purposes.
Minimizing G means choosing a dielectric material appropriate for the frequencies you're using.
Minimizing R means using a larger conductor (wider trace on a PCB or larger diameter coax). But this also tends to decrease the maximum frequency before the transmission line goes multi-mode. End result: at high frequencies, you just have to use small geometries and deal with the loss.
Due to skin effect, R tends to increase in proportion to \$\sqrt{f}\$, and this will typically dominate the frequency-dependent loss of a transmission line, if the dielectric has been chosen appropriately for the operating frequency band.
R and G don't directly correlate to physical quantities,
R is pretty directly tied to the conductivity of the conductor material. Skin effect also plays an important role. This is why you see silver-plated conductors on coax meant for high frequencies.
G relates to the polarization behavior of the dielectric, so it's harder to tie down to a specific physical mechanism. Generally if you're choosing dielectrics for high frequency designs, you'll see the loss specified as a loss tangent, but it will probably only be specified at a single frequency, which naturally won't be the one you're designing for.
Phil, the real part of the propagation constant is the attenuation constant and this equals: -
\$Re\sqrt{(R+jwL)(G+jwC)}\$ and not the formula you have in your question.
The formula you have used is for characteristic impedance.
This wiki page should confirm this (right at the bottom): -
So, if you do the math at low frequencies (to make life easier) you see that the attenuation constant becomes \$\sqrt{RG}\$ and if R=G=1 then you have a constant of 1 and a lousy highly lossy line. A lossless line has a re(propagation constant) of zero.
Best Answer
You should notice the following: It's not current and voltage that propagates in the transmission line. It's a radiowave.
The wave is in the space between the conductors, not in the metal. The wave has simultaneous electric and magnetic fields that cannot be separated. They exist both, or it's not a wave.
The fields have quite complex spatial structure that can mathematically be expressed only as 3D vector fields. We, the practical electricians do not tease ourselves with 3D vector fields, but follow the wave by observing the voltage of its electric field and the current that is induced into the conductors.
The wave goes along the transmission line because it has such geometrical form. Not all wires or other pieces of metal quide the wave along it. For example, the antennas are optimized for throwing the radiowave into the space or catching the arriving radiowave as well as possible.
The radiowave reflects when it meets an incontinuity that does not be able to suck it. A short circuit in a transmission line is one possible incontinuity that can't store or dissipate the wave
The reflection does not occur, if the incontinuity allows the wave to retain the proportion between it's electric and magnetic field. In coaxial or pair cable that incontinuity is a proper termination resistor or other line with the same impedance (= the ratio E/H). Or a well matched antenna.
A short kills the electric field. The wave does not die, but generates another wave (=the reflected one) that has opposite electric field. Their sum at the short is =zero and no contradiction exists. The short works and the wave continues its life as the reflected wave.