Bode Plot of a Simple Transfer Function

story of inverted pole and zero form

Let’s ask Mathematica to make a Bode plot of a transfer function

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(1)
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(2)
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  • Then at 0.8, you hit the normal pole 1/(1+s/0.8), the slope down rate becomes 40 dB/dec (bend downward; slope at twice the rate)
  • Soon at 20, you hit the zero 1–s/20, the slope goes back to 20 dB/dec (bend upwards; slope rate returns back)
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  • A normal zero would have phase from 0 to 90, but a right-half plane zero flips the phase. It goes from 0 to -90, its phase plot just like that of a normal pole.
  • Both knee points in the phase plot extends a decade above and below the corner frequency points (ω₁ and ω₂), that is, in this case, for the pole, the two knee points are 0.08 and 8. For the zero, the two knee points are 2 and 200.
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(3)
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(4)
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(5)
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(6)
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Conclusion

It’s easy to make Bode plot using a piece of mathematical software. But to extract salient features from a Bode plot so as to help circuit design, it is more useful to factor the transfer function into simple zero, pole form.

Reference

inverted zeros and poles

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