Help graphing Bode Plot

Discussion in 'Homework Help' started by TripleDeuce, Jan 31, 2011.

  1. TripleDeuce

    Thread Starter New Member

    Sep 20, 2010
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    0
    I need to graph a bode plot of this transfer function

    H(jω) = (1.5 x 10^-3 *(1+jω/10)) / ((1+jω/100)(1+jω/500))

    and I have no idea how to do so. I'm trying to follow an example my professor did in his notes. I replace jω with an "s" so the equation looks like this

    H(s) = (1.5 x 10^-3 *(1+s/10)) / ((1+s/100)(1+s/500))

    It seems he graphed each component of a transfer function separately, so I'll try to do the same

    Gain of 1.5 x 10^-3 is 20log(1.5 x 10^-3) = -56.5db.

    It's graph is just a horizontal line at height -56.5db for all ω. The x axis is where ω is.

    (1+s/10) has corner frequency at ω = 10. So it contributes 20db/decade asymptote started at ω=10.

    (1+s/100) has corner frequency at ω = 100. Since it is in the denominator, it contributes -20db/decade asymptote started at ω=100.

    (1+s/500) has corner frequency at ω = 500. Since it is in the denominator, it contributes -20db/decade asymptote started at ω=500.

    Now how do I physically add all the plots to give me an overall bode plot?
     
  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    I think you are over-complicating it a bit.

    The X axis is frequency
    The Y axis is amplitude (dB/Volts/Power/etc)

    Calculate the Y for several values of X, most concentrating on the corner frequency(/ies) area(s). Then connect the dots.

    The 20dB/decade numbers are what can be read from the bode plot by the steepness of the amplitude curve, dB/octave or dB/decade do not need to be calculated for each sample, only the actual amplitude value from the top formula.

    Does that make sense?
     
  3. TripleDeuce

    Thread Starter New Member

    Sep 20, 2010
    26
    0
    You're saying that to indicate a slope of 20db/decade, I would just go up an amplitude of 20db and go across one decade? What do you mean by

    I'm graphing this on a semilog plot by the way.

    Oh, and since I was going to start a thread to ask this question, do you also know how to graph a bode asymptotic phase angle plot of the function?
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    If I was asked to draw that plot in Uni, they would require me to do pretty much what the OP did.

    First calculate the DC gain (@ ω=0). Then go level until you find a pole or zero that will add or subtract inclination to your plot. You don't have to plot more that two or three decades after the final pole/zero.

    Also take a moment to visit this very useful site:
    http://www.williamsonic.com/BodePlot/
     
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