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Homework Help: Wavelengths along a Smith Chart

  1. Jan 27, 2012 #1

    This may be something that is more mathematical than electrical, but I figured here was the best place.

    I am going through a worked example, and there is something I don't understand. The question is as follows

    Find the imput impedance and return loss (in dB) of the loaded line in the last question as seen at the distance l = 5λ/8 from the load

    The solution states that "because the input impedance is a periodic function of the line lenth, we need to decuct all multiples of λ/2 and analyse only the remainder (λ/8)..."

    Now, I understand that λ/2 is a full rotation of the Smith chart, but why is that deducted? And, if you remove λ\2, how are you left with λ\8 ...from an origianl length of 5λ/8?

    The last part may just be some mathematics that is escaping me at the moment, but I just cannot get past this part.

    Thanks for any advice.

    Last edited: Jan 27, 2012
  2. jcsd
  3. Jan 27, 2012 #2
    5/8 - 4/8 = 1/8.

    You deduct it so you don't spin around the chart 4 times for nothing.
  4. Jan 28, 2012 #3

    Ok, that makes sense ...but, where is the 4 coming from? I mean, why not 6 times?

  5. Jan 30, 2012 #4
    1/2 Lambda = 4/8 Lambda.
  6. Jan 31, 2012 #5
    Ahh, okay ...I am with you now!

    That's fantastic. Thanks for your help.

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