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Transfer function for RC circuit

Discussion in 'Electronics Homework Help' started by evol_w10lv, Mar 21, 2014.

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  1. evol_w10lv

    evol_w10lv

    73
    0
    Feb 19, 2013
    Hey!
    I have got this circuit:
    [​IMG]

    So.. I have to find transfer function to graph logarathmic amplitude-frequency response and logarathmic phase-frequency response.

    As we know H(jw) = output phasor/input phasor
    Input phasor is total impedance (Z). The impedance of a capacitor is 1/(s*C) = 1/(j*w*C)
    By my calculation, Z should be:
    [​IMG]

    Is it correct? And how can I find output phasor? I have to use voltage divider somehow to find it?
     
  2. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    Suppose the capacitors were shorted out of the circuit. Then your formula would be Z=(1/R2 + 1/R1). What does that give you?
     
  3. evol_w10lv

    evol_w10lv

    73
    0
    Feb 19, 2013
    Then R1 || R2 are loads and transfer function looks something like that:
    [​IMG]
    And:
    [​IMG]

    Or am I wrong?
     
  4. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    Just by looking at the circuit you should be able to determine that the magnitude plot is wrong. There should be two corner frequencies, separated by three decades of frequency on a log scale. The first corner @ -3dB will have a frequency of 1/(R2C2). From there the plot will slope down to the left at -20dB/decade until it reaches the second corner frequency, 1/(R1C1). From there the plot will slope down to the left at -40dB/decade. You should not need to do any calculations at all in order to sketch the Bode magnitude plot of this circuit, but the transfer function must provide a refined version of the basic sketch.
     
  5. evol_w10lv

    evol_w10lv

    73
    0
    Feb 19, 2013
    But then it suggests that transfer function H(jw) is wrong.
    [​IMG]

    I draw Bode graph using Matlab:
    [​IMG]

    There I can see only one corner frequency. What am I doing wrong?
     
  6. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    Can you show how the transfer function was derived? Did you start with the node equations? What were they?
     
  7. evol_w10lv

    evol_w10lv

    73
    0
    Feb 19, 2013
    It seems to me that I were doing completely wrong before.
    This time I calculated H(s) using quadripole method and it is:
    [​IMG]

    It gives me:
    [​IMG]

    Here I can see two corner frequencies as you said it should be. Is it looks correct for you as well?
     
  8. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    Looks pretty good to me. I've never used the quadripole method but it seems to work for you.
     
  9. evol_w10lv

    evol_w10lv

    73
    0
    Feb 19, 2013
    I still have some non understanding here. I have to find coefficient k and time constants T1 and T2. Actually, as you said before T1 =R1*C1 and T2=R2*C2, but is it possible in this circuit or it's just theoretically time constants? I'm not sure, but as there is no amplifier in that circuit, capacitors interacts between each other, that's why solution of time constants not so "clear" as we would like to have. Or is it absolutely wrong?

    And now about calculations.
    This is how I found transfer function before:
    [​IMG]

    But I guess, circuit suggests, there is series of two ''inertial differential sections''. Then:
    [​IMG]

    When I compare these transfer functions:
    [​IMG]

    I'm quite sure, that my first transfer transfer should be correct. Maybe second one is more theoretical? What's your opinion about it?
     
    Last edited: Apr 3, 2014
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