Feedline transformation of Impedance: Resistance and Reactance

Discussion in 'General Technical Questions and Answers' started by W9DTC, Jan 14, 2013.

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  1. W9DTC

    W9DTC Ham Member QRZ Page

    I am working on tuning a new antenna... Using an analyzer, I can measure the resistance and reactance in the shack. Measuring these values at the antenna is quite difficult as it is suspeded in the air.

    Is it possible to calculate the resistance and reactance of the antenna (at the feedpoint) provided I know the length of the coax feedline and the properties of the feedline (velocity factor, etc.)?

    I have seen some formulas that appear to convert the impedance, but I don't see how to use those to calculate the resistive and reactive portions at the antenna given measurements in the shack.
     
  2. KA0HCP

    KA0HCP XML Subscriber QRZ Page

    Yes, what you need to study is known as a "Smith Chart". It is a polar/logarithmic chart which simplifies the calculations.
     
  3. W9DTC

    W9DTC Ham Member QRZ Page

    Yes... the Smith Chart... I have some understanding of what is going on there... but I don't have (I think) enough math skills to derive the formula(s) I need.
     
  4. KL7AJ

    KL7AJ Ham Member QRZ Page

    This is why the Smith Chart was invented.Eric
     
  5. W9DTC

    W9DTC Ham Member QRZ Page

    Yes... the smith chart...

    What I want to do is apply the formula to all of my tested frequencies. I have configured my test to sweep the entire band from 0Mhz to 54Mhz. It is currently configured to take 2000 measurements. Using the smith chart manually, I'd have to perform the transformation 2000 times.

    Clearly the smith chart is insufficient for this task. The math behind it is what I am looking for.
     
  6. KL7AJ

    KL7AJ Ham Member QRZ Page

     
  7. W9GB

    W9GB Ham Member QRZ Page

    In your situation I RECOMMEND: The RF CAFE !
    http://www.rfcafe.com/references/electrical/smith.htm
    A mixture of professional packages for purchase, shareware, and freeware regarding Smith Charts, plus links to websites featuring Smith Chart topics.

    ===
    How does a Smith chart work?
    by Rick Nelson, managing editor EDN
    Test & Measurement World, July 2001, p. 23**
    http://tmworld.com/electronics-news/4384297/How-does-a-Smith-chart-work-

    **A print version of this referenced article (Test & Measurement World, July 2001, p. 23) contains an incorrect value for the nonnormalized load impedence corresponding to point B in Figure 6. The correct value appears in the Web (Internet) version.
    In addition, in the original online version, equation numbers were dropped, and some Greek characters failed to render properly. These problems were corrected on March 7, 2006.

     
    Last edited: Jan 14, 2013
  8. W5DXP

    W5DXP Ham Member QRZ Page

    Assuming you have one of the feedlines on the selectable list, the following transmission line calculator should do it. Enter the type of feedline, length, and frequency. On "mismatch", click on "Zin" and enter the impedance that you measured. Then click "calculate".

    http://www.vk1od.net/calc/tl/tllc.php
     
  9. W9DTC

    W9DTC Ham Member QRZ Page

    HEY!!! I found an excel file on this link that may actually do what I'm trying to do! THANK YOU THANK YOU!

    Note: I haven't had a chance to fully review the file, so I'm not entirely sure... I welcome any other input (unless you are just going to tell me to use a smith chart)
     
  10. W9DTC

    W9DTC Ham Member QRZ Page

    Yes. That site, like the smith chart, does exactly what I'm trying to do. Unfortunately, it will only do it one at a time. I am trying to transform my 2000 data points. I actually entered into quite a dialog with vk1od over email as he had replied via email to a different post I had made on this topic. Apparently, he doesn't post on QRZ for some reason (which can be found on his site). In any case, he and his site were very helpful to my understanding, but ultimately he didn't want to share with me how to perform this calculation... I think he has a "give a man a fish" phobia.
     
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