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Discretization of RC-circuit

  1. Dec 9, 2016 #1
    1. The problem statement, all variables and given/known data

    Derive a discrete formula for an RC circuit for Vab[k] using the forward difference approximation. It should be of the form Vab[k + 1] = α Vab[k], and depend only on T, R, and C. For T = 0.076 s, R = 3 kΩ, and C = 10 mF, what is α?

    T is the period.
    The current is going from a to b.

    2. Relevant equations

    Ohms law
    Forward difference formula

    3. The attempt at a solution

    I cant find the equation editor...

    dVab(t)/dt = (1/c)I(t)

    discretisized:

    dVab[k]/dt = I[k]/c

    which is approximately equal to

    (Vab[k+1] - Vab) / T

    solving for Vab[k+1]

    Vab[k+1] = (T/C)I[k] + Vab[k]

    From Ohm's law for a simple RC circuit we can find that

    I = Vab/R

    thus

    Vab[k+1] = (T/RC)Vab[k] + Vab[k]

    Vab[k+1] = ((T/RC)+1) Vab[k]

    it follows that

    α = (T/RC)+1)

    which yields a result of approximately 1.0025

    however, the solutions manual claims that the answer is 0.9975 which is (1-(T/RC))
     
  2. jcsd
  3. Dec 9, 2016 #2
    I think I solved it. I swapped
    (Vab[k+1] - Vab) / T

    to
    (-Vab[k+1] + Vab) / T

    because of the orientation of the current.
     
  4. Dec 11, 2016 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    There is only ONE RC circuit in the universe? How about showing us a schematic drawing ...
    The problem wording suggests that the output voltage is decaying in which case you know alpha has to be < 1.
     
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