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Signal flow graph, describing a RC circuit?

  1. Jul 8, 2012 #1
    Signal flow graph, describing a RC circuit?

    Hi, guys. This is my first post on this forum!
    I'm trying to understand this example in my textbook.
    1z19oxf.jpg
    The current and voltage equations are:
    20kerfm.jpg
    where G=1/R, Z(s)=1/Cs, and I1(s)=I1
    Then the text says the following signal flow graph can be obtained:
    kb81s0.jpg
    And finally we can somehow obtain the transfer function:
    125137s.jpg

    First question, why is it necessary to do the substitution for G, Z(s) and I1?
    For the fourth equation, it says V3=I2Z, where Z(s)=1/Cs. Therefore, V3=I2/Cs (voltage=current/capacitance)? Where does this relationship comes from?
    Lastly, how do I know how many equations do I need? And which circuit elements should I describe?

    I might have more questions later, but I couldn't proceed without know the basics.
    Thank you so much!
     
  2. jcsd
  3. Jul 9, 2012 #2
    V3 = I2Z , where Z(s) = 1/Cs this is because voltage across capacitance is given as CdV/dt=I thus taking laplace transform on both the sides we get sC*V(s)=I(s)
    and V(s)=I(s)/sC therefore V3=I2/Cs.
     
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