Rules for Drawing Bode Diagrams

The table below summarizes what to do for each type of term in a Bode Plot.  This is also available as a Word Document or PDF

Term Magnitude Phase
Constant: K 20log10(|K|) K>0:  0°       
K<0:   ±180°
Pole at Origin

(Integrator)

-20 dB/decade passing through 0 dB at ω=1 -90°
Zero at Origin

(Differentiator)

+20 dB/decade passing through 0 dB at ω=1
(Mirror image of Integrator about 0 dB)		 +90°
(Mirror image of Integrator about 0°)
Real Pole

  1. Draw low frequency asymptote at 0 dB
  2. Draw high frequency asymptote at -20 dB/decade
  3. Connect lines at ω0.
  1. Draw low frequency asymptote at 0°
  2. Draw high frequency asymptote at -90°
  3. Connect with a straight line from 0.1·ω0 to 10·ω0
Real Zero

  1. Draw low frequency asymptote at 0 dB
  2. Draw high frequency asymptote at +20 dB/decade
  3. Connect lines at ω0.
(Mirror image of Real Pole about 0 dB)
  1. Draw low frequency asymptote at 0°
  2. Draw high frequency asymptote at +90°
  3. Connect with a straight line from 0.1·ω0 to 10·ω0
(Mirror image of Real Pole about 0°)
Underdamped Poles

(Complex conjugate poles)
  1. Draw low frequency asymptote at 0 dB
  2. Draw high frequency asymptote at -40 dB/decade
  3. Draw peak at the frequency
        
     with amplitude
       
    Note:
      • the peak only exists for
      • the peak frequency is typically very near ω0.
  4. Connect lines
  1. Draw low frequency asymptote at 0°
  2. Draw high frequency asymptote at -180°
  3. Connect with a straight line from


    (If ζ<0.02 draw phase vertically from 0 to -180° at ω0)

You can also look in a textbook for examples
Underdamped Zeros

(Complex conjugate zeros)
  1. Draw low frequency asymptote at 0 dB
  2. Draw high frequency asymptote at +40 dB/decade
  3. Draw a dip in the response at frequency
      
    with amplitude
       
    Note:
      • the dip only exists for
      • the dip frequency is typically very near ω0.
  4. Connect lines
(Mirror image of Underdamped Pole about 0 dB)
  1. Draw low frequency asymptote at 0°
  2. Draw high frequency asymptote at +180°
  3. Connect with a straight line from
    (If ζ<0.02 draw phase vertically from 0 to +180° at ω0)

You can also look in a textbook for examples.


(Mirror image of Underdamped Pole about 0°)

For multiple order poles and zeros, simply multiply the slope of the magnitude plot by the order of the pole (or zero) and multiply the high and low frequency asymptotes of the phase by the order of the system.

For example:

Second Order Real Pole

  1. Draw low frequency asymptote at 0 dB
  2. Draw high frequency asymptote at -40 dB/decade
  3. Connect lines at break frequency.

-40 db/dec is used because of order of pole=2.  For a third order pole, asymptote is -60 db/dec
  1. Draw low frequency asymptote at 0°
  2. Draw high frequency asymptote at -180°
  3. Connect with a straight line from 0.1·ω0 to 10·ω0

-180° is used because order of pole=2.  For a third order pole, high frequency asymptote is at -270°.

This page is modeled after the one originally found at http://lims.mech.nwu.edu/~lynch/courses/ME391/2002/bodesketching.pdf

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© Copyright 2005-2007 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College