Exploiting your antenna analyser #8

Finding resistance and reactance with some low end analysers

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There are some analysers on the market that do not display reactance X or even magnitude of reactance |X| and possibly resistance, but do display VSWR and magnitude of impedance |Z|.

R can be calculated from VSWR, |Z| and Ro:

R=(Ro^2+|Z|^2)*VSWR/(Ro*(VSWR^2+1))

|X| can be calculated from Z| and R:

|X|=(|Z|^2-R^2)^0.5

As for the sign of reactance, it cannot be calculated from |Z|, you need the phase angle and most of this type of instrument does not actually sense the sign of phase.

If you have one of these analysers and have need to extract R and or |X|, you could program these formulas up into your favourite spreadsheet or calculating tool, or use the online calculator at:

Find |Z|,R,|X| from VSWR,|Z|,R,Ro

Let’s work an example. Lets say you measure the mobile antenna discussed in the last article in this series, and you measured  VSWR=4.61 and |Z|=209Ω, we can calculate R and |Z| using the calculator above.

Screenshot - 12_12_2015 , 6_53_27 AM

The results tell us that R is 191Ω, |X| is 84.1Ω, and the magnitude of phase angle of Z |θ| is 23.7°, we are fairly close to a voltage maximum.

Don’t try to work the answers out for the Mini60 demo display at the top of this article, the displayed values are inconsistent, ie physically impossible. If VSWR(50)=1.35, |Z| cannot be less than 50/1.35=37Ω. Alternatively, if R=33Ω and |Z|=34Ω, then |X|=8.2Ω and VSWR=1.58. The values shown on the display are consistent with Zo=40Ω. (Why would you publish a promotional video that questions the quality of the instrument?)

Summary

It is possible to calculate R and |X| from VSWR and |Z|, 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.