Handout 1: Bode plot rules reminder
Eric Feron
Feb 4, 2004
General: Bode plot is to plot magnitudes using logarithm scale, phases
using log scales. Indeed:
G(jω) =
s
1
s
2
=
r
1
e
jθ
1
r
2
e
jθ
2
=
s
3
r
3
e
jθ
3
Thus |G(jω) =|
Then log
10
|G(jω) =.|
Recall log
10
Ae
jφ
=
In decibels: G|
db
=|
? Bode plots of systems
? The range over which system behavior can be plotted is
? Bode plots can be determined
? Compensation can
jωτ
1
+ 1
Example: KG(jω) =
(jω)
2
(jωτ
a
+ 1)
1
Phase(KG(jω))=
log |KG(jω) =|
in Decibels, |KG(jω)
db
| =
2
Basic terms for transfer functions:
1. K(jω)
n
Bode plot for n = 0, 1, ?1, ?2
3
2. (jωτ + 1)
±1
4
? ?
(
jω
3. )
2
+ 2ζ
jω
+ 1
±1
ω
n
ω
n
5
2000(s + 0.5)
Example: G(s) =
s(s + 10)(s + 50)
Write transfer function in standard form
Bode plot
6
0.01(s
2
+ 0.01s + 1)
Example: G(s) =
s
2
((s/2)
2
+ 0.02(s/2) + 1)
Bode plot
7