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RC Networks and complex numbers

  1. Feb 1, 2012 #1
    Hello.

    I maybe should have put this in the maths section, but it is related to electronics, so I figured here.

    I am reading Microwave Engineering by Pozar, and in one of the examples, it says that the series RC load impedance is ZL = 60 - j80, so the resistance is 60 Ohms and the capacitance is 0.995pF. But is doesn't expalin how that C value was arrived at.

    I was initially thinking that this was arrived at by comverting to polar form, but that doesn't seem to be it.

    Could someone please help me with this?

    Thanks.

    -S
     
  2. jcsd
  3. Feb 1, 2012 #2
    The impedance of a capacitor is given by,
    [tex]Z_C=\frac{1}{j\omega{C}}[/tex]
    which given a RC network, would be associated with the imaginary component on the complex plane.
     
  4. Feb 1, 2012 #3
    Thanks :)

    Okay, so, I know the frequency is 2GHz, which gets me ω. But what is Zc, is that the 80 in the complex number?

    -S
     
  5. Feb 1, 2012 #4
    Yes. The impedance of a network is given in the form Z=R+jX, where resistances are the real parts, and inductors and capacitors are the imaginary part. By plugging your values into the equation I gave you, you will indeed see that it is -j80!
     
  6. Feb 1, 2012 #5
    I get it now.

    Many thanks!

    -S
     
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