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## Bode Plots by hand

On ps #1, intuitively knowing how to plot the right SLOPES and PHASE seemed to trip up most people.
This is actually one of the easiest parts of ps #1:

 Delta in Gain slope (dB/dec)... ...with each Pole (or Zero) Delta in Phase (degrees)... ...with each Pole (or Zero) for EACH POLE -20 (db/dec) -90 (degrees) for EACH ZERO +20 (db/dec) +90 (degrees)

The table above summarizes how each pole (or zero) affects the system response to the right (higher frequency).
Examples:
• One pole at zero: Gain always decreasing w/ slope = -20 (dB/dec)... Phase = -90 (degrees)
• Two poles at zero: Gain always decreasing w/ slope = -40 (dB/dec)... Phase = -180 (degrees)
• One pole at non-zero freq: Gain and Phase CHANGE at this freq.:
new_slope = old_slope - 20(dB/dec)
new_phase = old_phase - 90(degrees)
• N poles at non-zero freq: Gain and Phase CHANGE at this freq.:
new_slope = old_slope - N*20(dB/dec)
new_phase = old_phase - N*90(degrees)
Below are several examples of systems w/ multiple poles at the same frequency, to illustrate how simple this is:
 1 Pole 2 Poles 1------(s+10) = 1------(s+10)^2 = 3 Poles 3 Poles? but 1 Zero cancels 1 Pole! 1------(s+10)^3 = (s+10)--------(s+10)^3 =

Notice in the figure at the lower right that a POLE and ZERO colocated at the SAME FREQUENCY have CANCELLED OUT one another...
• LAPLACE DOMAIN (that 's' stuff) is nice for easily manipulating (and noticing the cancel-outs).

 gonzo@mit.edu 2.010 Tutorial #2, 21-Sep-00