BODE PLOT - S-PLANE REVIEWusers.wpi.edu/~mcneill/handouts/Bode_plot_guide.pdf · bode plot: let s =...
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BODE PLOT: LET s = jω MAGNITUDE PHASE BODE PLOT - S-PLANE REVIEW + K TERM IN H(s) S-PLANE σ jω ω |H| [dB] ω H [deg] 0° +K = K K = tan "1 0/ K ( ) = 0 NONINVERTING DC GAIN (NOT VISIBLE IN S-PLANE) 20log K ( ) "K σ jω ω |H| [dB] ω H [deg] -180° "K = K "K = tan "1 0/ " K ( ) = "180 INVERTING DC GAIN (NOT VISIBLE IN S-PLANE) 20log K ( )
Transcript of BODE PLOT - S-PLANE REVIEWusers.wpi.edu/~mcneill/handouts/Bode_plot_guide.pdf · bode plot: let s =...
BODE PLOT:
LET s = jω
MAGNITUDE
PHASE
BODE PLOT - S-PLANE REVIEW
!
+KTERM IN H(s)
S-PLANEσ
jω
ω
|H|[dB]
ω
H[deg]
0°
!
+K = K
!
K = tan"1 0 /K( ) = 0
NONINVERTING DC GAIN
(NOT VISIBLE IN S-PLANE)
!
20log K( )
!
"K
σ
jω
ω
|H|[dB]
ω
H[deg]
-180°
!
"K = K
!
"K = tan"1 0 /"K( ) = "180
INVERTING DC GAIN
(NOT VISIBLE IN S-PLANE)
!
20log K( )
BODE PLOT:
LET s = jω
MAGNITUDE
PHASE
!
1+ s"ZLTERM IN H(s)
S-PLANEσ
jω
!
"1
#ZL
ω
|H|[dB]
ω
H[deg]
+90°+45°
+20dB/dec!
1+ j"# ZL = 12 + "# ZL( )
2
!
1+ j"# ZL = tan$1 "# ZL( )
!
1
"ZL
!
s"ZO
σ
jω
ω
ω
+20dB/dec!
0 + j"# ZO ="# ZO
!
0 + j"# ZL = tan$1 "# ZL
0
%
& '
(
) * = +90
o
!
1
"ZO
!
1" s#ZR
σ
jω
!
1
"ZR
ω
ω
+20dB/dec!
1" j#$ ZR = 12 + #$ ZR( )
2
!
1" j#$ ZR = tan"1 "#$ ZR( )
!
1
"ZR
|H|[dB]
H[deg]
+90°
|H|[dB]
H[deg]
-45°-90°
LHP ZERO RHP ZEROZERO AT ORIGIN (DERIVATIVE)
BODE PLOT:
LET s = jω
MAGNITUDE
PHASE
!
1
1+ s"PL
TERM IN H(s)
S-PLANEσ
jω
!
"1
#PL
ω
|H|[dB]
ω
H[deg]
+90°+45°
-20dB/dec
!
1
1+ j"#PL=
1
12 + "#PL( )
2
!
1
"PL
!
1
s"PO
σ
jω
ω
!
1 0 + j"#PO( ) = $tan$1 "#PO 0( ) = $90o
!
1
1" s#PR
σ
jω
!
1
"PR
ω
!
1/ 1+ j"#PL( ) = $tan$1 "#PL( )
H[deg]
-90°
H[deg]
-45°-90°
LHP POLE POLE AT ORIGIN (INTEGRATOR) RHP POLE
ω
|H|[dB]
-20dB/dec
!
1
"PO
ω
|H|[dB]
-20dB/dec
!
1
"PR
!
1
0 + j"#PO=
1
"#PO
!
1
1" j#$PR=
1
12 + #$PR( )
2
!
1/ 1" j#$PR( ) = tan"1 #$PR( )
!
H(s) = ± Ks"
ZOL 1+ s"
ZL( )L 1# s"ZR( )
s"PO
L 1+ s"PL( )L 1# s"
PR( )
GENERAL TRANSFER FUNCTION
ZERO ATORIGIN
LHPZERO
RHPZERO
POLE ATORIGIN
LHPPOLE
RHPPOLE
(UNSTABLE MODE!)
