Finding resistance and reactance with some low end analysers #2
Exploiting your antenna analyser #8 was about finding resistance and reactance with some low end analysers that don’t directly display those values of interest. The article showed how to calculate the values starting with |Z| from the analyser and included links to a calculator to perform the calcs.
This article describes an extension to that calculator Find |Z|,R,|X| from VSWR,|Z|,R,Ro to use R, VSWR, and Ro as the starting point. Note that the sign of X and the sign of the phase of Z cannot be determined from this starting point, there just isn’t enough information.
You will probably not find the equation for |X|(R,VSWR,Ro) in text books or handbooks, and the derivation is not shown here but if there is interest, I may publish a separate paper.
Lets say you knew VSWR=2, R=75Ω, Ro=50Ω, what is |X|?
Above, entering the values in the calculator we find that |X|=35.4Ω.
So, if your analyser does not shows VSWR and either |Z| or R, you can find |X| and the rest using the calculator.
An important reminder, like all calculators the output is no better than the input, and if you input nonsense, you are likely to get nonsense out.
An example of nonsense: MFJ-259
If you have the original MFJ-259 you will recall that it has a ‘Resistance’ meter on it, but do you recall this part of the user manual:
- the first sentence tells you it measures resistance;
- then it goes on to tell you that it doesn’t if the load is reactive; and
- then it tells you that at VSWR minima
the load is generally the point of lowest reactance therefore the most accurate point to measure the antenna’s pure resistance.
But is 3 true?
Above is a scan of a G5RV antenna looking into the balun and ‘matching section.’ The cursor is at the VSWR minimum in the 20m band, and the cursor details shows that Z=120.0-j42.2Ω, it is nowhere near purely resistive.
Above is the R,X scan which demonstrates that X does not cross through zero anywhere near 14MHz, and proves that a local VSWR minimum does not imply zero reactance in the general case and MFJ’s instructions are nonsense.
It is possible to calculate R and |X| from VSWR and |Z|, or |Z| and |X| from VSWR and R but tedious.
Check the consistency of instrument results before you put faith in them.
Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.