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Low pass filter (arctan domain)

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data
    when i'm trying to calculate and show the graphic of the phase characteristic i don't understand why the domain range of the arctan function is [0,90] :


    2. Relevant equations
    aa4a.gif




    image392.gif


    3. The attempt at a solution
    shouldn't be the domain of arctan function between [-Pi/2,Pi/2]?
    z_tri59.png
     
    Last edited: Nov 26, 2012
  2. jcsd
  3. Nov 26, 2012 #2

    berkeman

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    Staff: Mentor

    The value of the phase shift is the range of the function, not the domain. The domain is the input range to the function and the range is the output values of the function.

    The phase shift for a single-pole LPF varies from 0 to -90 degrees, as shown in the diagram. It is 0 at low frequencies in the passband of the filter, and drops to -90 degrees past the cutoff of the LPF.
     
  4. Nov 26, 2012 #3

    berkeman

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    Staff: Mentor

    I see that you've edited your post to add the red arctan curve. I think it may be the shape of the phase response in the first plot that is confusing you. I don't think it is plotted very well -- it make is look like the full arctan() curve, when it is really only half of it.

    When ω = 0, you get the arctan(0) which is zero. As the frequency increases, you get half of the arctan() function, going negative because of the sign being negative.

    Does that make more sense now?

    http://www.electronics-tutorials.ws/filter/filter_2.html

    .
     
  5. Nov 26, 2012 #4
    thank you, the link was helpful too!
     
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