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  20log_{10}(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 


Real Zero 


Underdamped Poles
(Complex conjugate poles) 

You can also look in a textbook for examples 
Underdamped Zeros
(Complex conjugate zeros) 

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 
40 db/dec is used because of order of pole=2. For a third order pole, asymptote is 60 db/dec 
180° is used because order of pole=2. For a third order pole, high frequency asymptote is at 270°. 

© Copyright 2005 to 2014 Erik Cheever This page may be freely used for educational purposes.
Erik Cheever Department of Engineering Swarthmore College