By the way, the inductance is given as: L = imag(Z)/w and not L = -imag(Z)/w as per you equation.
I don't understand the difference between the values calculated using Y instead of Z.
I recommend to test with data from an ideal schematic that you create yourself, with known values.
As a second step, you can then add small parasitics (e.g. shunt capacitance) to see what that does to your extraction.
What confused me is that I expected this trace to be more inductive
It is unclear what you are trying to do, i.e. what you physical device looks like.
Your curve starts from an open circuit (at lowest freq) so obviously it is not a series inductance.
Can you do a two port measurement? From that it is much easier to separate series and shunt path elements.
I guess you know this: https://www.mathworks.com/help/rf/ug/s2rlgc.html
If you can only do 1-port measurement, I would try to extract the shunt capacitance from low frequency S11 measurement, and then use TDR (time domain reflectometry) to get the line impedance, so that you can calculate L' from known C' and Zline. I explicitely mention TDR because then you can measure Zline no matter what the termination is.
BTW, why do you limit calculating C shunt from low frequency?
With the method shown in first post we can see the broad frequency of C from DUT.
So we only used low frequency data where the impedance into the DUT can be evaluated as a lumped component. At low frequency we know the input impedance of the open ended line is effectively shunt C. and not troubled by inductance.
You can create a little testbench in simulation and try yourself.
In this context what is your definition of "low frequency"? did you use a ratio from your max operating frequency? or some other factor?
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