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Magnitude and Phase Bode Plot Help

  1. Mar 22, 2012 #1
    Hi all, on a current homework I have been given a transfer function and asked to draw the straight-line (asymptotic) magnitude (dB) and phase (degrees) Bode plot. I first learned Bode plots roughly a year ago, and while being on spring break and my notebook from last year is at school, I'm having difficulty remembering some techniques. I do know how to plot these when given a zero frequency, but in this specific problem, this transfer function has no zeros and has three poles. Judging from my notes from this class, I tried my best to dictate what to do for the magnitude, but was posting here to check and make sure I plotted the magnitude properly. My handwork to show the breakpoints and slopes is in Attachment 2 - Handwork, and the magnitude plot can be seen through Attachment 3 - Magnitude Plot.

    My question though is for the phase plot. As seen in my handwork, I think that because the numerator is second order, it's slope should be +90°/decade, but am I supposed to include that in the phase plot because there is no zero frequency? Also, I'm a little fuzzy as to how I find out where I begin my plot in degrees - I have been taught that you begin with a slope of 0°/decade and end with a slope of 0°/decade, but how do I know where to begin my plot for phase?

    Any help on this topic would be greatly appreciated!

    1. The problem statement, all variables and given/known data

    (Attachment 1 - Problem)

    2. Relevant equations

    None.

    3. The attempt at a solution

    (Attachment 2 - Handwork)

    (Attachment 3 - Magnitude Plot)
     

    Attached Files:

  2. jcsd
  3. Mar 22, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Hi NHLspl09. I took a quick look at your transfer function and plot. If I'm not mistaken I think that the magnitude plot should probably peak at about 80dB in the neighborhood of 104 Hz.

    The phase plot looks to be an interesting beast. Sort of a water-slide ride from 180° down to about -90° with a plateau of near zero phase shift coinciding with that of the magnitude plot. Does this sound like what you're getting?
     
  4. Mar 23, 2012 #3
    Interesting, if you don't mind me asking, how did you come up with a peak at around 80dB around 104 Hz? I didn't think that could be possible if my break frequencies aren't within that bound of 104 Hz?

    And my main problem with the phase plot is I can't remember for the life of me on how to find where I start my plot. Looking at my notes is it: j(2∏Tm)f? Although I could be entirely wrong about that.
     
  5. Mar 23, 2012 #4

    gneill

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    Staff: Mentor

    Well, I cheated, of course :smile: I used MathCad to plot the magnitude. You should be able to verify by plugging in the corresponding jω value for that frequency and finding the magnitude.
    I'm not sure about a rule of thumb for this; I usually just find the angle for a very low frequency far from any critical frequencies (ideally in the limit as f → 0) and begin there.
     
  6. Mar 25, 2012 #5
    Wish I could use that and call it a day :tongue: I'm interested to see which is correct - which yours is I'm sure because of MathCad, but using the methods my professor taught I'm interested to see what I did wrong. I suppose I'll find out tomorrow!
     
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