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2 Port Networks - Impedance Parameters

  1. Aug 30, 2012 #1
    1. The problem statement, all variables and given/known data
    see attached


    2. Relevant equations



    3. The attempt at a solution
    $$\eqalign{
    & {V_1} = {Z_{11}}{I_1} + {Z_{12}}{I_2} \cr
    & {V_2} = {Z_{22}}{I_2} + {Z_{21}}{I_1} \cr
    & {\rm{ - - - - - - - - - - - - - - - - - - - - - - - - - - - }} \cr
    & 2\angle 30 = 8{I_1} - j4{I_2} \cr
    & 0 = - j4{I_1} + 8{I_2} & \to {I_1} = {{8{I_2}} \over {j4}} = - j2{I_2} \cr
    & 2\angle 30 = - j16{I_2} - j4{I_2} \cr
    & {{2\angle 30} \over {20\angle - 90}} = {I_2} \cr
    & {I_2} = 0.1\angle 120{\rm{ A}} \cr} $$

    As I2 is incorrect I haven't bothered with I1. Can somebody point out where the error is?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Aug 30, 2012 #2

    NascentOxygen

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    Staff: Mentor

    [strike]Z11 is 6 ohms. EDIT: Oops, I failed to notice you'd included the 2 ohms there.[/strike]

    Where it says 2∠30°, change it to 20∠30°. :wink:
     
    Last edited: Aug 30, 2012
  4. Aug 31, 2012 #3

    rude man

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    Homework Helper
    Gold Member

    Check the relation between I1 and I2. There's a sign error there!

    Plus the magnitudes are wrong anyway unless you change the input to 20V or reduce the answers by a factor of 10 ...

    Plus, the angle of I1 is off by 10 deg.

    Not a good day for the quizmaster.
     
    Last edited: Aug 31, 2012
  5. Sep 1, 2012 #4
    Thanks guys.

    I have learned a lot from this book in spite of the many errors.
     
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