Basic Elements Of Electrical Circuits II.. Basic Laws.[r]
(1)Electric Circuit Theory
(2)Contents
I. Basic Elements Of Electrical Circuits II. Basic Laws
III Electrical Circuit Analysis IV Circuit Theorems
V Active Circuits
VI Capacitor And Inductor VII First Order Circuits VIII.Second Order Circuits
IX Sinusoidal Steady State Analysis X AC Power Analysis
XI Three-phase Circuits
XII Magnetically Coupled Circuits
XIII.Frequency Response
(3)Frequency Response
1 Transfer Function 2 The Decibel Scale 3 Bode Plots
4 Series Resonance 5 Parallel Resonance 6 Passive Filters
(4)(5)Transfer Function (2)
( ) in ω I
+
–
( ) in ω V
( ) out ω I
+
–
( ) out ω V
( )ω
H
( ) ( )
( )
ω ω
ω
= Out
H
In
1
( )ω = →0 z z, , (zeros) Out
1
(6)Transfer Function (3)
Ex 1
vs = 100sinωt (V) Find the transfer function Vo/Vs and sketch its frequency response.
+ – + – ( ) s v t o v 5Ω 2 H + – + – s V o V 5 2 j ω 2 5 2 s o j j ω ω = + V V 2 ( ) 5 2 o v s j j ω ω ω → = = + V H V 2
2 (5 2 ) 4 10
(5 2 )(5 2 ) 25 4 25 4 v
j j j H j j ω ω ω ω ω ω ω ω − = = + =
+ − + + φv
4
1
16 100 5
; tan
4 25 2
v v
H ω ω φ
ω − ω
+
= =
(7)Transfer Function (4)
Ex 1
vs = 100sinωt (V) Find the transfer function Vo/Vs and sketch its frequency response.
+
– +
–
( ) s
v t
o
v
5Ω 2 H
4
1
16 100 5
; tan
4 25 2
v v
H ω ω φ
ω − ω
+
= =
+
0 10 15 20 25 30 35 40 45 50 0.2
0.4 0.6 0.8
ω
( )
v
H ω
0 10 15 20 25 30 35 40 45 50 10
20 30 40 50 60 70 80 90
( )
v
φ ω
(8)Transfer Function (5)
Ex 2
vs = 100sinωt (V) Find the transfer functions Vo/Vs, Io/Ii, Vo/Ii, & Io/Vs.
+
– +
–
( ) s
v t
o
v
5Ω
2 H 1mF
o
i
i
(9)Frequency Response
1 Transfer Function 2 The Decibel Scale 3 Bode Plots
4 Series Resonance 5 Parallel Resonance 6 Passive Filters
(10)The Decibel Scale
2 10
1
log P
G
P
=
2 10
1
10 log
dB
P G
P
=
2 10
1
20 log
dB
V G
V
=
2 10
1
20 log
dB
I G
I
(11)Frequency Response
1 Transfer Function 2 The Decibel Scale 3 Bode Plots
4 Series Resonance 5 Parallel Resonance 6 Passive Filters
(12)Bode Plots (1)
Semilog plots of the magnitude (in decibels) and phase (in degrees) of a transfer function versus frequency
H
=
H φ 20 log H10
φ
→
1 2 3 H1
= =
H H H H ( φ1)(H2 φ2 )(H3 )
( )
3
1 2 3
H H H
φ
= φ φ φ1 + + +2 3
10 10 1 10 2 10 3
1 2 3
20log 20log 20 log 20log
H H H H
φ φ φ φ
= + + +
→
= + + +
(13)Bode Plots (2) 1 2 2
( ) 1 1
( )
2
1 1
k k
n n
j j j
K j
z
j j j
p ω ζ ω ω ω ω ω ω ω ζ ω ω ω ω ± + + + = + + + H : gain K 1
: pole at the origin
jω
: zero at the origin
jω
1
1
: simple pole 1 j
p
ω
+
1
1 j : simple zero
z ω + 2 1
: quadratic pole 2
1
n n
j ζ ω jω
ω ω + + 2
1 : quadratic zero
k k
j ζ ω jω
ω ω
+ +
(14)Bode Plots (3) 10
20 log ( )
0
dB
H K
K
ω
φ
=
= →
=
H
H
10
20 log K
0.1 1 10 100 ω
φ
0
(15)Bode Plots (4)
0.1 1 10 ω 20
0 20
− H
0.1 1 10 ω
o
90 −
o
0 φ
10 o
20 log 1
( )
90
dB
H j
ω ω
ω φ
= −
= →
= −
(16)Bode Plots (5)
0.1 1 10 ω 20
0 20
− H
0.1 1 10 ω
o
90
o
0 φ
10 o
20 log ( )
90
dB
H
j ω
ω ω
φ
=
= →
=
(17)Bode Plots (6)
10
1
1
1
20 log 1 1
( )
1 tan
dB
j H
p j
p p
ω
ω ω
ω
φ −
= − +
= →
+ = −
H
-25 -20 -15 -10 -5
0
ω
1
0.1p p1 10 p1
(18)Bode Plots (7)
10
1
1
1
20 log 1 1
( )
1 tan
dB
j H
p j
p p
ω
ω ω
ω
φ −
= − +
= →
+ = −
H
ω
1
0.1p p1 10 p1
φ 100 p1
-90 -80 -70 -60 -50 -40 -30 -20 -10
(19)Bode Plots (8)
10
1
1 1
1
20 log 1 ( ) 1
tan
dB
j H
z j
z
z
ω ω
ω
ω
φ −
= +
= + →
=
H
-5 10 15 20 25
ω
1
0.1z z1 10z1
(20)Bode Plots (9)
10
1
1 1
1
20 log 1 ( ) 1
tan
dB
j H
z j
z
z
ω ω
ω
ω
φ −
= +
= + →
=
H
ω
0.1z z 10z
φ
0 10 20 30 40 50 60 70 80 90 100