Designing first order Butterworth low pass filter

Discussion in 'Homework Help' started by naspek, Feb 17, 2010.

  1. naspek

    Thread Starter Member

    Feb 17, 2010
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    Hey there.. This is my homework..
    i really need someone who can check whether i'm doing
    it right or not.. =)

    Question:
    Design a first order Butterworth low pass filter with cut-off frequency fo = 20 kHz and the gain K = 1

    fo = 20kHz
    K = 1

    When K = 1, we can ignore R1 and Rf
    formula :
    ωo = 1/RC
    2∏fo = 1/RC

    Set R = 1kΩ

    2∏fo = 1 / (1000) C
    C = 1 /
    (1000)(2∏fo)
    C = 7.96nF

    Answer: R = 1k
    Ω ; C = 7.96nF

    My answer is correct? :)

     
  2. Audioguru

    New Member

    Dec 20, 2007
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    Your answer is correct.
     
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  3. naspek

    Thread Starter Member

    Feb 17, 2010
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    ok! done with the first part..
    now is the complete question..

    Design a first order Butterworth low pass filter with cut-off frequency fo = 20 kHz and the gain K = 1. You will need to simulate the circuit using Multisim and shows that the circuit meet the required specification.

    i)Show all calculations steps and assumption made in your circuit design.
    (DONE!)

    ii)Show the circuit schematic with all the resistor and capacitor values labelled.(attachment)

    iii)Perform frequency response analysis on the circuit and obtain the bode diagram. The bode diagram should show the voltage gain (Vout / Vin) in dB vs the signal frequency (0 to 100 MHz). Does the -3dB cut-off frequency match the desired cut-off frequency fo = 20 kHz ? Explain. From the graph, estimate the roll-off rate. (attachment)


    I inserted my schematics and graph.. am i right?
    :)
     
  4. Audioguru

    New Member

    Dec 20, 2007
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    The opamp has nothing to do with the simple RC filter.
     
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  5. naspek

    Thread Starter Member

    Feb 17, 2010
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    what do u mean? :confused:
     
  6. Audioguru

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    Dec 20, 2007
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    The simple first-order lowpass filter is just the resistor and capacitor. It must have a fairly high resistance load. An opamp has a very high input resistance and can be used as an output buffer if needed to drive a fairly low resistance.

    A second-order Butterworth filter must have an active amplifier like a transistor or opamp.
     
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  7. naspek

    Thread Starter Member

    Feb 17, 2010
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    ok... should i add RL in my circuit?
    other than this problem, my circuit is correct?
     
  8. Audioguru

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    Dec 20, 2007
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    The Rl in your circuit is whatever the opamp is driving. The load of your RC lowpass filter is the extremely high input resistance of the opamp.

    Your circuit is correct. It is an RC lowpass filter with an opamp buffering its output.
     
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  9. naspek

    Thread Starter Member

    Feb 17, 2010
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    ok.. so.. the value for RL , can i choose it randomly
    or, there is formula to get the perfect value for RL?
     
  10. Audioguru

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    Dec 20, 2007
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    The value of Rl in your circuit has nothing to do with the simple RC lowpass filter. It is the value of the resistance that the opamp is able to drive.

    There is no perfect value for Rl of an opamp. It is 2k ohms or more for ordinary opamps.
     
  11. naspek

    Thread Starter Member

    Feb 17, 2010
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    is my answer is wrong, if i didn't include the load resistor?
     
  12. Audioguru

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    Dec 20, 2007
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    It is phoney baloney school work, not a real circuit.
    Nobody knows what is the value of the load. It could be anything.
    The quiz should have listed the load resistance if it is important to the calculations of whether the circuit will work or not.
     
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  13. naspek

    Thread Starter Member

    Feb 17, 2010
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    so.. i can ignore the RL right?
     
  14. Audioguru

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    Dec 20, 2007
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    Your schematic does not have an RL so it doesn't matter. The opamp is not needed.
     
  15. naspek

    Thread Starter Member

    Feb 17, 2010
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    so my schematics is correct?
    what about my graph? i use AC Analysis to plot my graph..
     
  16. Audioguru

    New Member

    Dec 20, 2007
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    You zipped the file instead of posting the schematic and graphs. I don't want to unzip it again so I don't know if your schematic is correct.
     
  17. naspek

    Thread Starter Member

    Feb 17, 2010
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  18. naspek

    Thread Starter Member

    Feb 17, 2010
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    the above, is my schematic and graphs.. =)
    really hope you can guide me solving my problem.. =)
     
  19. Audioguru

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    Dec 20, 2007
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    Your schematic shows an opamp without a power supply so it won't work.
    I don't know what you are asking about it because it is extremely simple.
     
  20. naspek

    Thread Starter Member

    Feb 17, 2010
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    where should i placed the power supply?
    i thought V1 is my power supply..
     
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