The effect of coupler imbalance on VSWR readings

Discussion in 'Antennas, Feedlines, Towers & Rotors' started by G1OJS, May 25, 2019.

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  1. G1OJS

    G1OJS XML Subscriber QRZ Page

    Hi all,

    I've been thinking about what happens when VSWR meters don't agree, and why VSWR seems to change cyclically as transmission line length is changed. I say "seems to" because, whilst measured VSWR reduces as a lossy line is lengthened, it doesn't change cyclically (despite some information on the web!).

    I've read that common-mode currents can cause odd VSWR reading behaviour, and it certainly makes sense to say that if the feedline has become part of the antenna then changing its length is bound to affect the (now extended) antenna impedance and hence VSWR - however I've seen no theoretical treatment of this and I wonder how significant the effects can be; significant enough to perpetuate stories of VSWR varying cyclically with transmission line length? Seems a stretch but maybe.

    What I've discovered after a day of experimenting is that VSWR meters can be brought into alignment, so that they agree across a range of frequencies and complex load impedance, and read 1.0:1, i.e. correctly, into a dummy load where they didn't before, by adjusting the coupler balance. In the case of the Bruene coupler there is often a variable capacitor on the input voltage divider to allow this adjustment.

    This prompted me to create a little numerical model of the Bruene coupler, which confirmed as I suspected that the indicated VSWR varies (and, cyclically) with the phase of the reflection coefficient if (and only if) the coupler balance is incorrect by some percentage. So - if your coupler is a little off balance, then changing the line length will give a change in VSWR reading. I've put some results from my model below & this shows that the effect can be significant - e.g. with the coupler 30% out of balance, adding a 1/4 wave of line(*) would show an indicated VSWR change from just under 4:1 to about 2.3:1, where in reality the VSWR is constant at 3:1 (this example is in the second picture). Also, perhaps obviously, if the coupler is out of balance, a VSWR of 1.0:1 will not be seen even into a matched load, and - tbc - can never be seen into any load (proving this might be a challenge!).

    Anyway - I hope this provides food for thought and sheds some light on some of the tales that float around. I've not seen any analysis like this elsewhere?

    The maths is scrappy hand-written notes currently but ends up with:

    upload_2019-5-25_16-0-11.png
    where Z is the load impedance (normalised here i.e. assuming Zo = 1.0) and K a constant which rolls up all of the usual voltage divider, inductance turns ratio & load resistance values etc into one constant that characterises coupler balance and is 1.0 for perfect balance).

    So the graphs below are produced from that equation above by making a complex reflection coefficient suitable for some chosen values of *actual* VSWR across 360 degrees of reflection coefficient phase, working out the Z load that must be associated with it, and plugging that Z in above.

    The legend on each graph indicates the *actual* VSWR.

    (*) adding a 1/4 wave of lossless line has the same effect as changing the load impedance such that the reflection coefficient magnitude stays the same but the phase increases by 180 degrees.

    upload_2019-5-25_15-51-35.png

    upload_2019-5-25_15-52-1.png
     
    Last edited: May 25, 2019
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  2. WB5WPA

    WB5WPA Ham Member QRZ Page

    WELCOME to the world of what is known as COUPLER DIRECTIVITY ...

    The HP on-line calculator gives the range of uncertainty for a known directivity coupler, too.

    http://hpmemoryproject.org/pict/technics/applet/slide_rule/reflectometer.htm

    Note for a 26 dB directivity coupler the range of possible, *actual* SWR values range from 1.11 to 1.31 and RL (Return Loss) from 16.5 and 25.8 dB

    HP_Reflectometer_sliderule_Zoom.jpg

    And, of course, it gets worse for even smaller values of "directivity".

    .
     
    Last edited: May 25, 2019
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  3. G1OJS

    G1OJS XML Subscriber QRZ Page

    Thanks - typical of me to work something out for myself and then find out it's already been looked into in depth! Still - it was a useful exercise. That slide rule (following the link and selecting relevant numbers) confirms my example too, which is nice :)
     
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  4. SM0AOM

    SM0AOM Ham Member QRZ Page

    Nice plots, and they show very well what is going on.
    The key to understanding the effects of non-perfect coupler directivity is to see both reflection coefficient and coupler directivity as vector quantities.

    Once this is grasped, the relations are quite easy both to derive and understand.

    I certainly like the looks of the Excel plots, such tools during my Uni days in the late 70s would have rendered my lab reports in Microwave Measurements far more legible, as we had to work out the numerics using slide rules and the occasional scientific calculator...

    73/
    Karl-Arne
    SM0AOM
     
  5. W5LZ

    W5LZ Ham Member QRZ Page

    One thing to keep in mind is -where- that meter placed in the feed line. If its placed at the transmitter end, then the feedline's impedance can certainly affect the reading! So, bare that in mind.
    (all puns intended!)
     
  6. WB5WPA

    WB5WPA Ham Member QRZ Page

    re: "One thing to keep in mind is -where- that meter placed in the feed line. If its placed at the transmitter end, then the feedline's impedance can certainly affect the reading!"

    The old "magic cable length" trick (from radio to antenna) is real after all then?

    /sarc

    (
    See, in a 50 Ohm system, the standing waves, created by the superposition of by an incident and a reflected wave, would remain at the same ratio -for lossless line- whether at the beginning of the line or at the end of the line.)
     
    Last edited: May 25, 2019
  7. G1OJS

    G1OJS XML Subscriber QRZ Page

    Thank you. I like the graphs too and wonder if this effect is one of the things that keeps the "magic feedline length" meme alive (true transmission line transformer designs excepted of course).

    Yes I remember being asked to print out plots from one analyser and pull data points off with a ruler to put them into a PC for analysis, at which point I looked in the appendix of the analyser manual detailing the IEEE-488 interface and wrote a PC control program for it - I'd rather experience pain once than several times :). Having done that implementing 3-term calibration was straightforward (after I'd gone through the tedium of complex arithmetic in Basic or Pascal or whatever we had on that machine!). That seems a lifetime ago though!
     
  8. SM0AOM

    SM0AOM Ham Member QRZ Page

    Non-ideal directional couplers certainly are a part of the persistent myth of the "feedline length dependent SWR", but I also suspect an underlying general ignorance of transmission line basics. The impedance transformation properties of non-flat lines are quite mysterious to more than one radio amateur, and coupled with the inherent difficulty of accurately measuring small values of reflection coefficient makes it worse.

    If someone using a coupler with, say, 20 dB directivity gets obsessed with SWR, and finds that moving the meter by 1/4 wavelength could reduce the indication from 1:1.5 to 1:1 without making any adjustments to the load, it is understandable that they fall for the temptation...

    Writing software procedures for handling network analyser calibration and error-correction was (and is) a quite common project task, and I remember assigning such homework when I taught Microwave Measurements in the early 80s.

    I sometimes stressed that my students were lucky having access to an automatic network analyser, previous classes had to make do with slotted lines, pen and paper and slide-rule.

    73/
    Karl-Arne
    SM0AOM
     
    Last edited: May 25, 2019
  9. W5LZ

    W5LZ Ham Member QRZ Page

    No, there's no "magic" cable length as such. But the feedline's impedance combined with the antenna's input impedance is what you will 'see' on the meter. The only 50 ohm input impedance I've ever seen was when connecting a dummy load to the transmitter with 50 ohm coax. But it was only -close-! There is no 'perfect' match, only close.
     

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