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Complex Circuit Analysis Simplification

  1. Feb 9, 2012 #1
    I have the following circuit....
    circuit22.jpg

    I have managed to derive an equation for U2:

    u22.jpg

    Now I want to substitute U2 into U1, in order to derive equation for U1

    I have defined U1 as:

    u11.jpg

    Now I substitute U2 into the above equation. This is how far I get.....I am stuck...


    My circuit simulator is saying that U1 is equal to:


    u11sol.jpg


    However I cannot simplify to get this equation. Can someone please help I have spent hours trying to get U1 to look like the U1 that the simulator produces.


    I thank you in advance.
     
  2. jcsd
  3. Feb 9, 2012 #2
    Have you try to replace R1, R2 and E2 with his Thevenine equivalent circuit ?
    Eth = R2/ ( R1 + R2 ) * E1 and Rth = R1||R2

    attachment.php?attachmentid=43692&stc=1&d=1328795691.jpg

    V3 = I * R3

    [tex] I = \frac{Eth}{\sqrt{(Rth + R3)^2 + Xc^2)}} = \frac{E1*\frac{R2}{R1+R2}}{\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]

    And

    [tex] V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]
     

    Attached Files:

    Last edited: Feb 9, 2012
  4. Feb 9, 2012 #3
    No I haven't tried this before, but I did just try it and I still can't derive U1. Perhaps I am being stupid...
     
  5. Feb 9, 2012 #4
    A made a small error instead of V3 I should write U1

    What is the name of your simulation program?
     
  6. Feb 9, 2012 #5
    Thanks for your help Jony, the simulator is giving me this equation:

    u11sol.jpg

    I haven't derived that myself^. When I expand out the equation you derived:


    [tex] V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}} [/tex]

    I still not can get a the equation looking like the simulator one.


    BTW the simulator is called Solve Elec, you can download it for free.

    [URL="http://www.physicsbox.com/indexsolveelec2en.html[/URL] [Broken]
     
    Last edited by a moderator: May 5, 2017
  7. Feb 9, 2012 #6
    Ah done it! you are right I was being stupid. I am upset with myself that I never thought to do a thevin equivalent :( thanks alot for your help. I can sleep peacefully tonight.
     
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