owenduffy.net

Determination of transmission line characteristic impedance from impedance measurements discussed issues with the short circuit and open circuit terminations used with measurement of Zoc and Zsc for calculation of characteristic impedance of a line section.

Included was a model of the effect of small delay offset in one of the termination parts on an example scenario.

This article gives a Simsmith model that readers might find interesting to explore the effects of line length, offset, line characteristics, and frequency.

I have issues with Simsmith modelling of transmission lines, but nevertheless the model is informing.

The above example is 6m of RG58A/U with 5mm offset in the short circuit termination. Continue reading Determination of transmission line characteristic impedance from impedance measurements #2

Measured impedances looking into a uniform transmission line section with short circuit (SC) and open circuit (OC) terminations can provide the basis for calculation of characteristic impedance Z0.

We rely upon the following relationships:

\(Z_{sc}=Z_0 \tanh (\alpha + \jmath \beta )l\\\) and

\(Z_{oc}=Z_0 \coth (\alpha + \jmath \beta )l\\\)

Rearranging the formulas and multiplying, we can write:

\(Z_0^2=\frac{Z_{sc}}{\tanh (\alpha + \jmath \beta )l} \frac{Z_{oc}}{\coth (\alpha + \jmath \beta )l}\\\) \(Z_0^2=\frac{Z_{sc}}{\tanh (\alpha + \jmath \beta )l} Z_{oc}\tanh (\alpha + \jmath \beta )l\\\)

The tanh terms cancel out… provided the arguments are equal. Focus on length l, l for the short circuit measurement might not equal l for the open circuit measurement if the termination parts are not ideal (and they usually are not).

If the tanh terms cancel, we can simplify this to \(Z_0=\sqrt{Z_{sc}Z_{oc}}\). This is commonly parroted, apparently without understanding or considering the underlying assumption that l is equal for both measurements.

Another big assumption is that it is a uniform transmission line, ie that the propagation constant β is uniform along the line… including any adapters used to termination the line.

The third assumption is that the measured impedance values are without error.

Above is a plot of calculated Z0 for a theoretical case of a line of ~10m length of Belden 8267 (RG213A/U) around the frequency of first resonances. This calculation essentially imitates perfect measurements of perfect DUTs. Continue reading Determination of transmission line characteristic impedance from impedance measurements

Most of the changes I have made to NanoVNA-App have been to align it with accepted standards and conventions.

This change is to the format of saved Touchstone, .s1p and .s2p, files.

Though the relevant specification is silent on the permitted decimal separator, the only one shown in examples is “.” so it is reasonable to interpret that the required separator is “.” which makes the file format locale independent (as were the first instruments using Touchstone format.

This release of NanoVNA-App writes “.” decimal separator, independent of locale.

The original reading code which was tolerant of either “.” and “,” is maintained, so it will continue to open files which might have been (incorrectly) saved using “,”.

NanoVNA-App-Setup-v1.1.209-OD15