Cecil Moore wrote:
Reg Edwards wrote:

Instead of messing about calculating the additional loss due to SWR
and then
adding it to the matched loss, I've just had a wonderful idea.

Why not calculate the actual line loss directly and solve all your
problems
at one fell swoop.

What is the formula for the total dB loss?

I don't know of one, but here's a procedure which will get you the answer:

1) Determine the transmission line characteristics R, G, L & C at the
frequency of interest.

2) Determine the transmission line termination impedance (or admittance)
at the frequency of interest.

3) For convenience, define the excitation at the input to the
transmission line. e.g. defined voltage, current, or generator with
defined source impedance.

4) Solve the transmission line equation for both the voltage and
current, as a function of time and position, subject to the imposed
boundary conditions. Use any method you wish, though the usual approach
is the so called method of reflections where the complete solution is
taken as the summation of damped forward and reverse traveling waves.
Calculation of Zo and Gamma require knowledge of R,G,L & C.

The solution can be expressed algebraically in terms of hyperbolic
functions and will be found in any good transmission line reference.

Now known are v(x,t) and i(x,t).

5) Separately calculate the dissipative losses due to series resistance
and shunt conductance (or dielectric power factor) as follows:

a) The loss due to series resistance at any instant in time for some
section of transmission line, is i(x,t)^2 * R * dx, integrated over the
subject transmission line section.

b) The loss due to shunt conductance at any instant in time for some
section of transmission line, is v(x,t)^2 * G * dx, integrated over the
subject transmission line section.

c) The total dissipative power loss is the the sum of the time averaged
series and shunt loss components, integrated over the entire
transmission line length.

Consider:

The SWR (reflection coefficient at the termination) alone is not
sufficient to determine the loss in general. This is an important
concept to understand.

For illustration, assume the limiting case where the shunt conductance
can be disregarded. This is a useful approximation for many
transmission line installations used at HF where the SWR is reasonably
low (50). In such practical cases the losses will be dominated by
series resistance.

Consider a short (45 electrical degrees) transmission line terminated
in a pure resistance which is much less than Ro. The standing wave
pattern will be such that the current will be maximum, and the voltage
minimum, at the termination. The losses can be calculated using the
procedure given above.

Now consider the same transmission line terminated in a pure resistance
larger than Ro such that the SWR is the same as previously. The current
will now be minimum at the termination and the total dissipative loss
will be considerably less than when the termination resistance is low,
even though the SWR is identical.

Transmission line losses depend on both the actual load impedance and
the transmission line parameters. Knowing matched attenuation
(dB/length) and load SWR is not sufficient to calculate losses exactly.
Any formulas using only SWR and matched transmission line loss are
approximations and must be used carefully!

Feeding electrically short antennas with 50 ohm coax as is commonly
attempted by amateurs on 80 & 160m can result in transmission line
losses much larger than predicted using the simple approximations given
in the amateur literature.

bart
wb6hqk