The sign of reactance – challenge solution

The sign of reactance – a challenge posed a problem, a set of R,|X| data taken with an analyser of a quite simple network and asked readers to solve the sign of X over the range, ie to transform R,|X| to  R,X.

It is widely held that this is a trivial matter, and lots of software / firmware implement algorithms that fail on some scenarios. Though the scenario posed was designed to be a small set that provides a challenging problem, it is not purely theoretical, the characteristics of the data occur commonly in real world problems and the challenge data is derived from measurement of a real network.

Imported and rendered graphically in ZPlots we have:

The network measured is comprised from analyser, a 2.8m length of RG58/CU, a tee piece feeding a 50 resistor on one branch and on the other branch, another 2.8m length of RG58/CU with a 4.7Ω resistor termination.

The challenge is: what is the sign of X across the frequency range?

Above is a plot of the signed data from ZPlots.

If your algorithm / software / firmware cannot reliably solve ALL cases, then the results are not dependable. When you are making a decision about whether to cut something shorter based on unreliable measurement… think again before you cut.

The conundrum is that hams who are less likely to be able to solve a problem such as this lack the knowledge to understand that determining the sign of X from a complete (ie signed) measurement of the complex reflection coefficient inside the instrument is the key to dependable results, and lots of instruments and software misrepresent their capability.