Chris Jewell wrote in
:

Someone asked in a Technician license class *why* 450 ohm window line
has much lower loss than an equal length of 50 ohm coax does at the
same frequency. The instructor knew that it is true, but could not
say why. I have an idea about the answer, and would like to know how
I'm doing. I'm one of those hams who is NOT a EE, so I'm trying to
work this out based on high school physics, which at least back in
1964, covered AC but not RF.

I observe that at higher Z, the voltage is higher while the current is
lower for a given power level. Ohmic losses are proportional to the
square of the current. This is the same reason that long distance
power transmission is done at high voltage.

For example, 100 W through 50 ohms is 1.4A @ 70V, while 100W through
450 ohms is 0.47A @ 212V. That is, 9 times the impedance results in
1/3 the current, which results in 1/9 the ohmic loss through the
resistance of the transmission line.

I expect that we also need to account for the difference in R
resulting from different conductor diameter and skin effect, and
probably difference in the dialectrics, neither of which I yet know
how to calculate. Apart from those factors, is my explanation based
on the current vs. impendance:

1. Basically correct?

2. On the right track, but oversimplified, and thus not much use?

3. Completely out in left field?

Thank you.


Chris,

Your explanation is basically correct if your statements depend on the
assumption that both transmission lines are of the same type and
constructed of the same conductors.

In a practical balanced line, most of the loss at HF is in ohmic loss,
the heat generated when current flows through the conductors, and your
workup applies.

In most practical coaxial lines, most of the loss at HF is in ohmic loss,
the heat generated when current flows through the conductors. It turns
out that most of that loss is in the centre conductor (the RF resistance
of the inside of the outer conductor is typically lower than the RF
resistance of the outer of the inner conductor).

So, back to your unstated assumption of same type and same conductors,
when you make the appropriate corrections for coaxial and balanced line
types, then what you have said applies. Having said that, balanced lines
with extremely close spacing (Zo less than about 100 ohms) suffer from an
additional mechanism affecting effective conductor resistance, it is the
proximity effect that causes current to not flow evenly in the skin as it
would for larger spacings.

The mechanism as you have stated it is broadly correct, but it needs to
include a statement of assumptions, and liberal use of words like "most"
to cover the exceptions. It is easier to make the general statement that
"for the same conductors, an air spaced two wire balanced line of 600
ohms characteristic impedance will have close to half the loss of such a
line of 300 ohms", and your explanation applies.

Owen


, and your workup applies