Determine the value of the resistor required to get a 12 kHz cut-off frequency.

Discussion in 'Homework Help' started by aaron0000934, Dec 15, 2010.

  1. aaron0000934

    Thread Starter New Member

    Dec 14, 2010
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    Im stuck on the problem below

    A low pass filter is to be made from a resistor and Capacitor shown. Determine the value of the resistor required to get a 12 kHz cut-off frequency.
    Assuming you test this circuit with an input voltage of 10Vpk at 1.2kHz, 12kHz and 120kHz what is the expected output voltages?

    I am unsure how the cut-off frequency affects the resistor. Where do I start?
     
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  2. R!f@@

    AAC Fanatic!

    Apr 2, 2009
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    What is the formula use to calculate the output
     
  3. aaron0000934

    Thread Starter New Member

    Dec 14, 2010
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    if the cutoff frequency formula is fc=1/(2∏RC) than I should be able to solve for resistance R=1/(2∏fcC) ?
     
  4. aaron0000934

    Thread Starter New Member

    Dec 14, 2010
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    how do I solve the expected Vo for the frequencies given?
     
  5. Fraser_Integration

    Member

    Nov 28, 2009
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    5
    you need to derive the transfer function or gain for this circuit, in other words Vo/Vi

    Treat it as a voltage divider but use the impedances of both elements. I will get you started:

    Vo = (Zc / Zr+Zc)Vi

    rearrange this to get Vo/Vi = something, and then substitute in the values for impedance of the circuit elements.

    Oh and the cut-off frequency formula is correct
     
  6. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    Phase shift makes this more complex than you have indicated.
     
  7. Fraser_Integration

    Member

    Nov 28, 2009
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    It didn't ask for phase shift.

    and it's still the same procedure, just leave the j's in! and phase shift = arctan {Im/Re}
     
  8. Georacer

    Moderator

    Nov 25, 2009
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    I 'll agree with Fraser_Integration. Just treat it as a voltage divider with a variable impedance on the capacitor end. Make a universal formula and input the frequency values, or find the impedance for each frequency first and input that to the divider.
     
  9. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    All I'm saying is this:
    At 1.2kHz, the actual Vo/Vs=0.995
    If you calculate Xc/(R+Xc), you get 0.909, which is the wrong answer.

    As Fraser_Integration said, you have to include the j's.
     
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