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

ELECRAFT BL2 Balun Measurements

The ELECRAFT BL2 BALUN Return Loss and Balance were measured as shown in the referenced links. The Balance measurements were performed according to W7EL's referenced document. Refer to pg 163 paragraph named 'Current Balun'.

Elecraft BL2 BALUN Specifications & Operating Manual

BALUNS. What they do and how they do it. W7EL

Test Configurations and BALUN Schematic

Return Loss Measurements

Balance Measurements

Test Fixture 1

Test Fixture 2

Test Fixture 3