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.
The table assumes ω>0. If ω<0, magnitude is unchanged, but phase is altered.
Term  Magnitude  Phase 

Constant: K  20log_{10}(K)  K>0: 0° K<0: ±180° 
Pole at Origin
(Integrator) $\frac{1}{s}$ 
20 dB/decade passing through 0 dB at ω=1  90° 
Zero at Origin
(Differentiator) $s$ 
+20 dB/decade passing through 0 dB at ω=1 (Mirror image, around x axis,of Integrator) 
+90° (Mirror image, around x axis, of Integrator about ) 
Real Pole \[\frac{1}{\frac{s}{\omega_0}+1}\] 


Real Zero \[\frac{s}{\omega_0}+1\] 


Underdamped Poles
(Complex conjugate poles) \[\begin{gathered}\frac{1}{{{{\left( {\frac{s}{{{\omega _0}}}} \right)}^2} + 2\zeta \left( {\frac{s}{{{\omega _0}}}} \right) + 1}} \\ 0 < \zeta < 1 \\ \end{gathered} \] 

You can also look in a textbook for examples 
Underdamped Zeros
(Complex conjugate zeros) \[\begin{gathered} 

You can also look in a textbook for examples. (Mirror image, around xaxis, of Underdamped Pole) 
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 \[\frac{1}{{{{\left( {\frac{s}{{{\omega _0}}} + 1} \right)}^2}}}\] 
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 2019 Erik Cheever This page may be freely used for educational purposes.
Erik Cheever Department of Engineering Swarthmore College