BODE PLOT - S-PLANE REVIEW
NONINVERTING DC GAIN
INVERTING DC GAIN
+K
TERM IN H(s)
"K
jω
jω
S-PLANE
σ
σ
!
!
(NOT VISIBLE IN S-PLANE)
(NOT VISIBLE IN S-PLANE)
+K = K
"K = K
BODE PLOT:
LET s = jω
MAGNITUDE
|H|
[dB]
!
|H|
[dB]
!
20log(K )
20log(K )
ω
!
ω
!
H
[deg]
H
[deg]
ω
0°
ω
PHASE
-180°
K = tan"1 (0 /K ) = 0
"K = tan"1 (0 /" K ) = "180
TERM IN H(s)
LHP ZERO
ZERO AT ORIGIN (DERIVATIVE)
RHP ZERO
1+ s" ZL
s" ZO
1" s# ZR
jω
jω
jω
S-PLANE
σ
!
σ
!
"1
# ZL
1+ j"# ZL = 12 + ("# ZL )
BODE PLOT:
LET s = jω !
!
|H|
[dB]
σ
!
2
1
" ZR
1" j#$ ZR = 12 + (#$ ZR )
0 + j"# ZO = "# ZO
+20dB/dec
ω
|H|
[dB]
!
+20dB/dec
ω
!
|H|
[dB]
!
2
+20dB/dec
ω
MAGNITUDE
1
" ZL
H
[deg]
PHASE
+90°
+45°!
1
H
[deg]
" ZO
H
[deg]
1
" ZR
+90°
ω
!
ω
!
ω
-45°
-90°
1+ j"# ZL = tan$1 ("# ZL )
% "# (
0 + j"# ZL = tan$1' ZL * = +90 o
& 0 )
1" j#$ ZR = tan"1 ("#$ ZR )
TERM IN H(s)
LHP POLE
POLE AT ORIGIN (INTEGRATOR)
1
1+ s" PL
1
s" PO
jω
RHP POLE
1
1" s# PR
jω
jω
S-PLANE
σ
!
|H|
[dB]
-20dB/dec
!
PHASE
ω
1
" PL
H
[deg]
!
σ
!
1
" PR
1
1
=
2
1+ j"# PL
12 + ("# PL )
BODE PLOT:
MAGNITUDE
!
"1
# PL
LET s = jω !
σ
1
1
=
0 + j"# PO "# PO
|H|
[dB]
H
[deg]
ω
-45°
-90°
-20dB/dec
!
!
|H|
[dB]
ω
1
1
=
2
1" j#$ PR
12 + (#$ PR )
!
-20dB/dec
!
1
1
" PO
" PR
H
[deg]
ω
+90°
+45°!
ω
ω
-90°
1/(1+ j"# PL ) = $tan$1 ("# PL )
1 (0 + j"# PO ) = $tan$1 ("# PO 0) = $90 o
1/(1" j#$ PR ) = tan"1 (#$ PR )
GENERAL TRANSFER FUNCTION
ZERO AT
ORIGIN
LHP
ZERO
RHP
ZERO
s" ZO L (1+ s" ZL )L (1# s" ZR )
H(s) = ± K
s" PO L (1+ s" PL )L (1# s" PR )
POLE AT
ORIGIN
!
LHP
POLE
RHP
POLE
(UNSTABLE MODE!)