Roy Lewallen wrote:
....
At frequencies from at least HF well into the UHF range or higher,
the
loss in transmission lines having decent insulation (e.g., PE or
PTFE)
is almost all due to conductor loss rather than dielectric loss.
Higher
impedance line has lower loss simply because for a given amount of
power
being conveyed, the current is lower. Therefore, the conductor I^2 *
R
loss (which is nearly the total loss) is lower.

If you introduce a dielectric material (other than air) between
conductors, the characteristic impedance drops and the velocity
factor
increases, due to the same effect. Only in that way are they related
in
a ladder line.

Here's a slightly different way to look at the same thing Roy has said.
For a given coaxial cable outer conductor diameter, assuming smooth
copper conductors, there's a particular ratio of D/d (outer to inner
conductor diameters) that gives you the lowest loss. So long as
there's negligible loss in the dielectric, that D/d is independent of
what dielectric you put in there. But since putting in a dielectric
lowers the impedance, the loss goes up as a result of higher current
for a given power level.

You can put numbers on it pretty easily. Assuming no dielectric loss,
the attenuation of the line in dB per unit length is inversely
proportional to the line impedance: dB/100ft = 4.34*Rt/Zo, where Rt is
the total RF resistance of the wires. But Zo is inversely proportional
to the square root of the relative dielectric constant of the
dielectric in the line. Putting the two together, for a given
conductor configuration (D and d in coax), if there's no loss in the
dielectric itself and only loss in the resistance of the wires, the
loss in dB/unit length is proportional to the square root of the net
effective dielectric constant around the line. Since the velocity
factor is inversely proportional to the square root of the same net
effective dielectric constant, then for a given configuration of
conductors, the loss is indeed dependent on the velocity factor, even
with no power dissipated in the dielectric itself. This is true for
coax and open wire line in equal measure. But beware that you are more
likely to have dielectric loss in open-wire line for a variety of
reasons...

For lossless dielectric and a fixed conductor configuration (coaxial,
two-wire, or other TEM line with fixed conductor sizes and spacings),
varying just the dielectric, then,

dB/unit length = k1/v.f. = k2/Zo = k3*sqrt(net effective dielectric
constant)

where k1, k2 and k3 are proportionality constants depending on the
conductor configuration.

Cheers,
Tom