Calculate VSWR for varying Reactance Values X

Great question from Richard N4PBQ as follows:

"So as I'm analyzing my various antennas I understand that my antenna is at resonance when my analyzer reports X=0 for a particular frequency.  But that never seems to be the case outside of my dummy load and even there the reactance is reported as X=7 for 28 MHz.

So is there a rule of thumb for acceptable amount of reactance or some calculation that I can use to determine the loss in DB for a given frequency and the reactance?"

I got to thinking about this. The complex math becomes messy quickly with many possible combinations and permutations if both R and X are allowed to vary for the load impedance ZL. However if one keeps R = 50ohms constant and assume that the source impedance is 50 ohms then the analysis simplifies.

The referenced table shows a range of X values up to 20ohms for a VSWR not exceeding 1.5:1

Simplified math derivation

Calculate VSWR for varying Reactance Values X

Impedance looking into a short coax test lead. What is it?

It is certainly not intuitively obvious to me why the capacitance looking into a coax 50ohm test lead is not factored into account when terminated in the characteristic impedance Zo.

Below shows my confusion.

Why in the case of  the model in Figure 1 would I take the capacitance of the coax into account? (about 30pf per foot) when I terminate in a high impedance? Yet when I terminate the coax in a 50ohm load in the model in  Figure 2 I do not see the capacitance? In other words the model in Figure 3 is incorrect.

Even at a frequency of 2MHz the calculated impedance Zin in Figure 1 is 664ohms magnitude, of course with some phase shift. This means that the capacitive effect of the 3ft coax connecting cable is significant.

Some study of transmission lines is needed to reveal the answer.

Function Generator Output Impedance Calculation

I Question my Function Generator Impedance Measurements