Bode Plots by hand ... cont'd (2.010)

Bode Plots by hand ... cont'd

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.

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 co-located 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