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Help in a passive low pass filter

Discussion in 'Electronics Homework Help' started by ra585ed, Dec 15, 2011.

  1. ra585ed

    ra585ed

    1
    0
    Dec 15, 2011
    Hi everyone..
    Good morning/evening..
    I hope you all fine..
    I need your help..

    I have this RC CIRCUIT
    :[​IMG]
    Assume the following:
    :[​IMG]

    I need to find V(out) (magnitude only), in the Phasor domain, in terms of the frequency ω and I need to show that the cutoff frequency of this circuit is 1/RC.

    Can any body help me with that..? I will be Grateful.
     
  2. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    In order to solve this problem you need to use phasor algebra. Phasor algebra has the advantage that it reduces steady-state sinusoidal circuits to the form of pure resistance circuits. Once the problem has been converted to the frequency domain it is essentially a resistive problem. The only difference is that the real-number algebra used for resistive circuits becomes complex-number algebra for frequency-domain circuits. I will presume you are proficient in doing simple arithmetic (add, subtract, multiply, divide) with complex numbers.

    The circuit is a simple voltage divider in the frequency domain; therefore, structure the solution as a resistor voltage divider but then use impedance instead of resistance. For cutoff frequency I would assume that means the half-power point. Since power is proportional to the square of the voltage, (Vout/Vin)^2=1/2, what is the frequency where Vo/Vi=0.707?
     
  3. Harald Kapp

    Harald Kapp Moderator Moderator

    9,368
    1,903
    Nov 17, 2011
    Note that the formulae in "assume the following" give the cutoff angular frequency omega . If you want the cutoff frequency in terms of cyclic frequency, you'll have to factor in 2*Pi.

    Harald
     
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