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)
( )
inω
I
+
–
( )
inω
V
( )
outω
I
+
–
( )
outω
V
( )
ω
H
( )
( )
( )
ω
ω
ω
=
Out
H
In
1
( )
ω
= →
0
z z
,
, (zeros)
Out
1
(6)Transfer Function (3)
Ex 1
v
s= 100sin
ω
t (V) Find the transfer function
V
o/V
sand sketch its frequency response.
+
–
+
–
( )
sv t
ov
5
Ω
2 H
+
–
+
–
sV
oV
5
2
j
ω
2
5
2
s oj
j
ω
ω
=
+
V
V
2
( )
5
2
o v sj
j
ω
ω
ω
→
=
=
+
V
H
V
22 (5
2 )
4
10
(5
2 )(5
2 )
25 4
25 4
vj
j
j
H
j
j
ω
ω
ω
ω
ω
ω
ω
ω
−
=
=
+
=
+
−
+
+
φ
v4
1
16
100
5
;
tan
4
25
2
v v
H
ω
ω φ
ω
−ω
+
=
=
(7)Transfer Function (4)
Ex 1
v
s= 100sin
ω
t (V) Find the transfer function
V
o/V
sand sketch its frequency response.
+
–
+
–
( )
sv t
o
v
5
Ω
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
v
s= 100sin
ω
t (V) Find the transfer functions
V
o/V
s, I
o/I
i, V
o/I
i, & I
o/V
s.
+
–
+
–
( )
sv t
o
v
5
Ω
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 H
10
φ
→
1
2
3
H
1
=
=
H
H H H
(
φ
1
)
(
H
2
φ
2
)
(
H
3
)
(
)
3
1
2
3
H H H
φ
=
φ φ φ
1
+ + +
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 22
(
)
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
j
ω
: zero at the origin
j
ω
1
1
: simple pole
1
j
p
ω
+
1
1
j
: simple zero
z
ω
+
21
: quadratic pole
2
1
n n
j
ζ ω
j
ω
ω
ω
+
+
2
1
: quadratic zero
k k
j
ζ ω
j
ω
ω
ω
+
+
(14)Bode Plots (3)
1020 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
p
110 p
1 (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
p
110 p
1φ
100 p
1-90 -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
z
110z
1 (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