Bode Plots by hand (2.010)

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:

BASIC RULES for BODE PLOTS
	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