question about butterworth filters

Discussion in 'General Electronics Chat' started by hunterage2000, Mar 25, 2011.

  1. hunterage2000

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    May 2, 2010
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    Can somebody tell me what the f is in the magnitude formula? I know Ho is the dc gain, fB is the 3db cut off frequency and n is the order.
     
  2. hunterage2000

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    May 2, 2010
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    nobody know what f is then?
     
  3. bertus

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    Apr 5, 2008
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    Hello,

    Can you show the formulas?
    The f will most probably be the frequency.
    and fB the border frequency of the filter (-3dB point).

    Bertus
     
  4. hunterage2000

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    May 2, 2010
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    The attached is the formula and the question is:

    Analyse the magnitude and phase characteristics of a 2nd order butterworth lowpass filter

    not sure how to go about this.

    Also forgot to mention that the cutoff frequency is 1000hz
     
    • H0.pdf
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    Last edited: Mar 25, 2011
  5. bertus

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    Hello,

    [​IMG]


    The H0 is the passband gain.
    When f = fB the gain will be
    H0/sqr(1+(f/fB)^2n) =
    H0/srq(1+1^2n) =
    H0/sqr(2)=
    H0/0.707 ,
    wich is - 3dB.

    Bertus
     
  6. hunterage2000

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    doesnt this mean all orders will give the same result? How would magnitude and phase be analysed then?
     
  7. bertus

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  8. hunterage2000

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    looking at the graph on page 5 shows n= 1,4 and 10 and gives different results. so how does this apply to the formula when the magnitude is always 1/root2
     
  9. bertus

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    Hello,

    You mean this graph:

    [​IMG]

    All the lines go through the same point at f/fB =1.
    This is the -3 dB point.

    Bertus
     
  10. hunterage2000

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    May 2, 2010
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    so magnitude for all orders is the same? just the question says analyse magnitudes of 2nd and 4th order.
     
  11. bertus

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    Hello,

    The magnitude is only the same for all at the - 3dB point.
    Before and afther that point the values are diffetent as you can see in the graph.

    Bertus
     
  12. hunterage2000

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    May 2, 2010
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    so what is this formula used for? Can you explain what the magnitude and phase is for 2nd order as an example so I can try other orders
     
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