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Bode plots for 2nd Order systems
2nd Order Systems
• Everything applies, except the break point
• Magnitude and Phase with s=jω
22
2
02
)(nn
n
ssCsG
“Double” Breakpoint at ωn
2nd Order Systems
• Everything applies, except the break point
• Magnitude and Phase with s=jω
22
2
02
)(nn
n
ssCsG
“Double” Breakpoint at ωn
Bode Plots Approximations
• Because Double break point at ωn
• If in s2+2ξωns+ωn2 in denominator
• -40 db/decade in denominator at ωn
• -180 deg shift (starting a decade below, to decade above at ωn )
• -90 deg at break point at ωn
G(s)=9/(s2+2s+9)
-80
-60
-40
-20
0
20M
agnitu
de (
dB
)
10-1
100
101
102
-180
-135
-90
-45
0
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
G(s)= 9/(s3+2s2+9s)
-150
-100
-50
0
50
Magnitu
de (
dB
)
10-1
100
101
102
-270
-225
-180
-135
-90
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
G(s)= (s+1)/ (s2+2s+100)
-40
-30
-20
-10
0M
agnitu
de (
dB
)
10-2
10-1
100
101
102
-90
-45
0
45
90
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
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