Hi Dave
This method of direct experimental measurement, without any computational artifice and without the risk of modeling errors or theoretical estimations, is simply my own used method, which I have already presented multiple times and illustrated in several recent topics in this IO group. Indeed, this experimental method is very elegant, accurate, and reliable, and involves no computational tricks.
I have specifically presented it as the method for measuring the characteristic impedance of coaxial or twin-lead lines, offering greater precision than other methods already shown in YouTube videos or even the classical recommended techniques that I have come across in this highly respectable IO group.
It has been suggested to me to use the recently introduced macro function by DiSlord called "Measure" + "Cable" in his latest firmware version 1.2.40. This function directly displays the cable¡¯s characteristic impedance, its length, its attenuation in dB, and its specific attenuation in dB/100m. It's already a very good and reliable function, and above all, it's easy to use¡ªthere¡¯s virtually nothing to do except connect the open-ended coax to port 1 for S11 measurements.
This function is indeed useful, but it provides a single Zc value valid across the entire frequency range. It is based on quasi-static C0 measurements, which are more relevant at relatively low frequencies, and it does not fully account for skin effect and other second-order behaviors that are difficult for a typical user¡ªsuch as a radio amateur seeking ohm-level accuracy¡ªto model precisely.
For example, I have already published the different characteristic impedance values of my RG213 cable depending on the frequency band, using the experimental method that involves centering the impedance circle at the center of the Smith chart with a fixed resistive load close to the nominal characteristic impedance of the coax, or by referring to the first-order value displayed by DiSlord¡¯s macro function.
The method is simple, robust, and original because it is based on the very solid foundational concept of the characteristic impedance of an RF transmission line. This is, by definition, the impedance that produces a purely traveling wave and absorbs all the energy without any reflection¡ªas if the line were infinitely long.
Therefore, in practice, we should observe a constant, purely real impedance across the entire measurement band as a first approximation (theoretically, a line¡¯s characteristic impedance may not be purely real, but for low-loss lines it is often very close to real and commonly approximated by the well-known square root of L/C¡ªthis remains a very good first-order approximation).
Thus, for a ferrite balun, it is experimentally straightforward to connect an adjustable resistor in place of the antenna and connect the other side to port 1 for S11 measurements, in order to center the impedance plot across an entire frequency band on real axe dot.
This is entirely feasible for a small balun or a coiled coaxial cable whose second end is accessible in the shack, allowing the connection of an adjustable resistor (non-inductive, of course) in order to find the value that yields the smallest possible Smith chart impedance plot ¡ª ideally, a single point located on the real axis over the entire desired frequency band. This value can then be directly read using the NanoVNA cursor. It's one of the best methods to measure the characteristic impedance (Zc), while also enjoying the clear and safe visual illustration of its fundamental definition on a simple and tangible Smith chart using a compact NanoVNA.
So far, so good ¡ª but unfortunately, this method cannot always be applied so easily, especially when the cable is already deployed in space, fixed in place, and its far end is no longer accessible from the shack near the NanoVNA.
Fortunately, the new firmware by DiSlord (version 1.2.40) offers a solution by allowing the renormalization of the equivalent impedance for Smith chart display purposes. It¡¯s important to understand that the actual impedances values remain exactly the same ¡ª only the graphical representation changes. So, there¡¯s no risk of error introduced by the renormalization of Zc in S11 measurement mode.
The goal is no longer to focus the impedances on a single real point (since we can¡¯t adjust accurately the resistor remotely ¡ª unless two people coordinate via phone), but rather to connect a fixed resistive load that is approximately correct, and then use the Zc renormalization feature of DiSlord to center the impedance circle on the middle of the Smith chart, indeed the impedances are no longer all reals but remain on a small cicle around the renormalized Zc end value.
The value of Zc that centers the impedance circle is the one to retain in the end. that why i appreciate a lot this renormalize graphical option offered By DiSlord firmware 1.2.40 and ask him many times if it"s possible to add a graphical X4 or X6 zoom option around Smith shart center , it will be very usefull , indeed here all is graphical with Smith Shart , zero external computing .
73's Nizar .
