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BodeRules

# BodeRules - Rules for Making Bode Plots Term Constant K...

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© Copyright 2005-2009 Erik Cheever This page may be freely used for educational purposes. Comments? Questions? Suggestions? Corrections? Erik Cheever Department of Engineering Swarthmore College Rules for Making Bode Plots Term Magnitude Phase Constant: K 20·log 10 (|K|) K>0: K<0: ±180° Real Pole: 0 1 s 1 + ω Low freq. asymptote at 0 dB High freq. asymptote at -20 dB/dec Connect asymptotic lines at ω 0 , Low freq. asymptote at 0 °. High freq. asymptote at -90 °. Connect with straight line from 0.1· ω 0 to 10· ω 0 . Real Zero * : 0 s 1 + ω Low freq. asymptote at 0 dB High freq. asymptote at +20 dB/dec. Connect asymptotic lines at ω 0 . Low freq. asymptote at 0 °. High freq. asymptote at +90 ° . Connect with line from 0.1· ω 0 to 10· ω 0 . Pole at Origin: 1 s -20 dB/dec; through 0 dB at ω =1. -90° for all ω . Zero at Origin * : s +20 dB/dec; through 0 dB at ω =1. +90° for all ω . Underdamped Poles: 2 00 1 ss 21 ⎛⎞ + ζ + ⎜⎟ ωω ⎝⎠ Low freq. asymptote at 0 dB. High freq. asymptote at -40 dB/dec. Connect asymptotic lines at ω 0 . Draw peak at freq. 2 r0 12 ω =ω − ζ with amplitude ( ) 2 r1 0 H(j ) 20 log 2 1 ω= − ⋅ ζ − ζ Low freq. asymptote at 0 °. High freq. asymptote at -180 °. Connect with straight line from 10 10 2 log 2 to 2 2 log ζ ω=ω ζ Underdamped Zeros * : 2 + ζ + Draw low freq. asymptote at 0 dB. Draw high freq. asymptote at +40 dB/dec.

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BodeRules - Rules for Making Bode Plots Term Constant K...

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