# Z=50 and Xs=0 but SWR is not 1.0:1

I measured an antenna with a VNA and differently to all other cases the SWR isn't low as expected. Here are some screenshot showing this:

Similar situation, on the same antenna in the same measurement session is the one below:

For Z=45.3 and Xs 0.1 I expected SWR 1.10:1 and not 1.99:1

The point where SWR is the lowest is the one below:

My question is: isn't sufficient Z=50 and Xs=0 to get the lower SWR, so what's wrong? What I need to modify to get the resonance then? Thanks

You have a software error or a serious misconception.

See your first image. At he marker1 frequency (=about 28,1 MHz) you have got return loss -6,33dB. If we forgive the minus, the calculated SWR is exactly in harmony with the return loss RL. (see NOTE1)

If we assume your system has 50 Ohm matched port, also Rs and Xs are in harmony with the return loss and the backwards wave phase angle RP (= nearly -180 degrees). RL and Rp the primary measurement results, the others are calculated from it and the assumed system impedance.

You wonder the absolute Z which is nearly =50 Ohm and it shouldn't cause SWR this high. I wonder it too. But the reason is different. As far as I can guess, the absolute Z and angle theta should be the polar form of impedance phasor Rs + jXs. Absolute Z should be got when one inserts Rs and Xs to the Pythagoran formula. But they don't fit. So there's error somewhere.

I made a web search. I found several reflection measurement examples with the same looking screen as yours. There Rs, Xs, absolute Z and theta were in harmony. This make me confirmed that I didn't guess wrong, your software makes errors or you as its user have made a fatal error in some phase.

NOTE1: RL=6.33dB That means the backwards wave has power = 23% of the test input to the antenna. It can also be presented as voltage reflection factor by taking a squareroot. The reflected wave has voltage 48,2% of the test signal wave voltage.

VSWR is the ratio of the max. possible total voltage and the min total voltage in the cable where forward and backward waves occur simultateously. VSWR= (1+0,482)/(1-0,482)=2,86. That's exactly what your analyzer claims in the rightmost column.

If we insert Rs and 50 Ohm to the common formula of the reflection factor and for simplicity we discard the miniscule reactance, we get -48%. That fits well with the measured reflection factor. Nearly resistive impedance means the reflected wave has inverted polarity which fits well with RP.

• Interesting consideration, at this point I wonder if the error is by the VNA itself or maybe measurements could be affected by common mode currents flowing between antenna and analyzer. Do you think might be possible this? – Kevin White Apr 21 '19 at 9:07
• Guessing is useless, make measurements. Make a few test loads which you can verify (=measure them or their parts at the operating frequency) otherwise and compare the results. If you cannot make other RF measurements, use high quality RF resistors and well documented coaxial cable. I suspect software error. Z is calculated, not measured as far as I can understand how analyzers work. But I am not the God. – user287001 Apr 21 '19 at 9:16
• IMHO some parameters of them are... "derived", others measured: that's the point. If I modify the antenna up to reach Rs=50 and Xs=0 the |Z| should be 50. – Kevin White Apr 21 '19 at 9:26
• Yes. Or |Z| means something else. just in your system. At least 50 Ohm resistor with no cable should give |Z| = 50Ohm =Rs and Xs=0, theta=0. But without exact and comprehensive manual this all is guessing. – user287001 Apr 21 '19 at 9:33
• @KevinWhite, be sure to reset your instrument to default settings before you begin your measurements. Maybe someone has set up the instrument for a different system impedance, added a port extension (to de-embed a specified length of feed line), or changed some other obscure setting. – The Photon Apr 21 '19 at 14:46

Your text says "$$\Z=50\$$", but your measurement only shows $$\\left|Z\right|=50\$$.

If $$\Z\$$ is not purely real, the reflection won't go to 0, and VSWR won't go to 1. It's possible to design a 1-port device where $$\Z\$$ is purely imaginary with value $$\\pm 50 j\$$, and get 100% reflection, meaning VSWR approaches $$\\infty\$$.

Your actual situation isn't as bad as that, but you don't have a perfectly radiating antenna, so you don't see a perfect VSWR.