In article , Owen Duffy
wrote:

John,

If I understand correctly, Macalpine's work was in finding solutions given
the computation tools readily available.

The approximation of a real transmission line as having Zo that is real can
introduce significant error in some line calcs.

Improving the model to include an estimated X value based on the loss is a
next step that improves calcs. This technique is widely used, and is
revealed by Ro equal to the nominal Zo, whilst Xo is a small negative
quantity for practical low loss cables at HF. This model produces
significantly different results for high line VSWR at lower frequencies.

TLLC (http://www.vk1od.net/calc/tl/tllc.php) goes a step further and
estimates a value for Ro based on the loss. For example, the Zo used for
RG58 at 1MHz is 50.06-j2.31 ohms. This model produces significantly
different results for extreme line VSWR at lower frequencies.

The more detailed models would be computationally unwieldly with log tables
or a slide rule (the tools of Macalpine's day), but TLLC demonstrates that
it is a trivial computational matter today, though not to lose sight of the
fact that mathematical function libraries are often approximations
favouring speed over ultimate accuracy.

Again, we must keep in mind that the uncertainty of the data fed into the
model (including manufacturing tolerances, and through life component
degradation) contributes to uncertainty of the output, and as Roy has
mentioned, the sensitivity of results to input data can be higher than
people might otherwise expect.

Properly implemented, the VNA OSL calibration process and measurement
process should overcome the problem of a sufficiently accurate model of the
actual transmission line used in the 'fixture', though not the phase
stability between calibration and measurement, especially where they are
done under very different environmental conditions.

Owen

Good info, Owen and it should be noted that "VNA" is a vector network
analyzer and "OSL" refers to the open, short, and load (usually 50 or 75
ohms) reference standards used to calibrate the VNA over the frequency
range of ineterest.

The small reactive (imaginary) part of the transmission line
characteristic impedance is covered (as are all things to do with RF
transmission lines) in detail in R.W.P. King's seminal work, "Transmission
Line Theory". King also covers transmission line baluns in depth. 73s,

John Wood (Code 5550) e-mail:
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337