Frequency response 2012 mk
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Electric Circuit Theory
Electric
Circuit
Theory
Frequency Response
Contents
1. Basic Elements Of Electrical Circuits
2. Basic Laws
3. Electrical Circuit Analysis
4. Circuit Theorems
5. Active Circuits
6. Capacitor And Inductor
7. First Order Circuits
8
SdOdCiit
8
.
S
econ
d
O
r
d
er
Ci
rcu
it
s
9. Sinusoidal Steady State Analysis
10. AC Power Analysis
11
Three
phase Circuits
11
.
Three
-
phase
Circuits
12. Magnetically Coupled Circuits
13. Frequency Response
14
The Laplace Transform
14
.
The
Laplace
Transform
15. Two-port Networks
Frequency Response - sites.google.com/site/ncpdhbkhn
2
Frequenc
y
Response
•
Transfer Function
Transfer
Function
• The Decibel Scale
•
Bode Plots
•
Bode
Plots
• Series Resonance
•
Parallel Resonance
•
Parallel
Resonance
• Passive Filters
A ti Filt
•
A
c
ti
ve
Filt
ers
• Scaling
Frequency Response - sites.google.com/site/ncpdhbkhn
3
Transfer Function (1)
()
in
I
()
out
I
+
()
in
V
+
()
out
V
()
H
–
–
()
()
Out
H
()
()
H
In
()
V
()
I
()
()
()
out
voltage
in
V
H
V
()
()
()
out
current
in
I
H
I
()
()
out
V
H
()
()
out
I
H
Frequency Response - sites.google.com/site/ncpdhbkhn
4
()
()
()
out
impedance
in
H
I
()
()
()
out
admittance
in
H
V
Transfer Function (2)
()
in
I
()
out
I
+
()
in
V
+
()
out
V
()
H
–
–
()
()
Out
H
()
()
H
In
12
( ) 0 , , (zeros)
z
z
Out
() 0 (poles)
pp
In
Frequency Response - sites.google.com/site/ncpdhbkhn
5
12
() 0
, ,
(poles)
pp
In
Transfer Function (3)
Ex. 1
v
s
= 100sinωt (V). Find the transfer function
+
–
+
5
V
o
/V
s
and sketch its frequency response.
–
()
s
vt
o
v
2H
2
52
s
o
j
j
V
V
52
o
j
j
2
()
5
2
o
v
s
j
j
V
H
V
5
s
j
V
2
22
2(5 2) 4 10
(5 2 )(5 2 ) 25 4 25 4
v
jj
jH
jj
v
+
–
+
s
V
V
5
2
j
42
1
16 100 5
H
Frequency Response - sites.google.com/site/ncpdhbkhn
6
–
s
o
V
2
j
1
2
16 100 5
;tan
425 2
vv
H
Transfer Function (4)
Ex. 1
v
s
= 100sinωt (V). Find the transfer function
+
–
+
5
V
o
/V
s
and sketch its frequency response.
–
()
s
vt
o
v
2H
42
1
2
16 100 5
;
tan
vv
H
2
;
425 2
vv
1
80
90
0.6
0.8
()
v
H
50
60
70
80
0.2
0.4
10
20
30
40
()
v
Frequency Response - sites.google.com/site/ncpdhbkhn
7
0 5 10 15 20 25 30 35 40 45 50
0 5 10 15 20 25 30 35 40 45 50
10
Transfer Function (5)
Ex. 2
v
s
= 100sinωt (V). Find the transfer functions
+
–
+
5
o
i
i
i
V
o
/V
s
, I
o
/I
i
, V
o
/I
i
, & I
o
/V
s
.
–
()
s
vt
o
v
2H
1mF
Frequency Response - sites.google.com/site/ncpdhbkhn
8
Frequenc
y
Response
•
Transfer Function
Transfer
Function
• The Decibel Scale
•
Bode Plots
•
Bode
Plots
• Series Resonance
•
Parallel Resonance
•
Parallel
Resonance
• Passive Filters
A ti Filt
•
A
c
ti
ve
Filt
ers
• Scaling
Frequency Response - sites.google.com/site/ncpdhbkhn
9
The Decibel Scale
P
2
10
1
log
P
G
P
2
10
1
10log
dB
P
G
P
2
10
1
20log
dB
V
G
V
2
10
1
20log
dB
I
G
I
Frequency Response - sites.google.com/site/ncpdhbkhn
10
1
I
Frequenc
y
Response
•
Transfer Function
Transfer
Function
• The Decibel Scale
•
Bode Plots
•
Bode
Plots
• Series Resonance
•
Parallel Resonance
•
Parallel
Resonance
• Passive Filters
A ti Filt
•
A
c
ti
ve
Filt
ers
• Scaling
Frequency Response - sites.google.com/site/ncpdhbkhn
11
Bode Plots (1)
Semilo
g
p
lots of the ma
g
nitude
(
in decibels
)
and
p
hase
(
in de
g
rees
)
g
pg()p(g)
of a transfer function versus frequency
10
20log
H
H
H
10
20log
H
123 1
HHHHH
12
H
23
H
3
123
HHH
123
123
HHH
123
10 10 1 10 2 10 3
20log 20log 20log 20log HH H H
Frequency Response - sites.google.com/site/ncpdhbkhn
12
123
Bode Plots (2)
2
1
1
2
() 1 1
jj j
Kj
1
2
2
() 1 1
()
2
1 1
kk
Kj
z
jj j
H
1 nn
p
:gainK
1
: pole at the origin
j
1
: simle pole
1
j
2
2
1
: quadratic pole
2
1
jj
:
z
e
r
oatt
h
eo
ri
g
in
j
1
p
1:simlezero
j
1
nn
2
1
2
1 : quadratic zero
jj
Frequency Response - sites.google.com/site/ncpdhbkhn
13
:eoatteog
j
1
z
1 : quadratic zero
kk
Bode Plots (3)
10
20log
()
dB
HK
K
H
()
0
K
H
H
10
20log K
0
0.1
1
10 100
0.1
1
10 100
Frequency Response - sites.google.com/site/ncpdhbkhn
14
Bode Plots (4)
10
20log
1
()
dB
H
H
o
()
90
j
H
H
01
1
10
20
0
01
1
10
o
0
0
.
1
1
10
20
0
.
1
1
10
o
90
Frequency Response - sites.google.com/site/ncpdhbkhn
15
Bode Plots (5)
10
20log
()
dB
H
j
H
o
()
90
j
H
H
o
90
20
0
H
o
90
o
0
0.1
1
10
0
20
0.1
1
10
o
0
Frequency Response - sites.google.com/site/ncpdhbkhn
16
Bode Plots (6)
10
20log 1
1
dB
j
H
p
1
1
1
1
1
()
1
tan
p
j
p
p
H
H
0
5
-10
-5
-20
-15
Frequency Response - sites.google.com/site/ncpdhbkhn
17
-25
1
0.1p
1
p
1
10 p
Bode Plots (7)
10
20log 1
1
dB
j
H
p
1
1
1
1
1
()
1
tan
p
j
p
p
H
1
0.1
p
1
p
1
10
p
1
100
p
-10
0
-40
-30
-20
80
-70
-60
-50
Frequency Response - sites.google.com/site/ncpdhbkhn
18
-100
-90
-
80
Bode Plots (8)
10
20log 1
dB
j
H
z
j
1
1
1
1
() 1
tan
z
j
z
z
H
H
20
25
10
15
0
5
Frequency Response - sites.google.com/site/ncpdhbkhn
19
-5
1
0.1z
1
z
1
10z
Bode Plots (9)
10
20log 1
dB
j
H
z
j
1
1
1
1
() 1
tan
z
j
z
z
H
80
90
100
40
50
60
70
10
20
30
40
Frequency Response - sites.google.com/site/ncpdhbkhn
20
1
0.1z
1
z
1
10z
0
10
1
100z
Bode Plots (10)
2
2
10
2
20log 1
1
dB dB
jj
HH
2
2
1
2
22
1
()
2
2/
1
tan
1/
nn
n
nn
n
jj
j
H
10
20
2
0.05
2
0.2
H
-10
0
2
0.707
2
0.4
-30
-20
2
1.5
2
Frequency Response - sites.google.com/site/ncpdhbkhn
21
-40
1
0.1
1
1
10
1
100
Bode Plots (11)
2
2
10
2
20log 1
1
dB dB
jj
HH
2
2
1
2
22
1
()
2
2/
1
tan
1/
nn
n
nn
n
jj
j
H
20
0
1
0.1
1
1
10
1
100
-
80
-60
-40
-
20
2
1.5
2
0707
-
140
-120
-100
-
80
2
0
.
707
2
0.4
2
0.2
Frequency Response - sites.google.com/site/ncpdhbkhn
22
-180
-160
140
2
2
0.05
Bode Plots (12)
2
2
10
2
2
20log 1
2
dB dB
jj
HH
jj
2
1
2
22
2
() 1
2/
tan
1/
nn
nn
n
n
jj
j
H
30
40
2
1.5
H
10
20
2
0.707
2
0.4
-10
0
02
-20
2
0
.
2
2
0.05
1
0.1
1
1
10
1
100
Frequency Response - sites.google.com/site/ncpdhbkhn
23
Bode Plots (13)
2
2
10
2
2
20log 1
2
dB dB
jj
HH
jj
2
1
2
22
2
() 1
2/
tan
1/
nn
nn
n
n
jj
j
H
140
160
180
2
0.05
2
0.2
04
80
100
120
2
0
.
4
20
40
60
2
1.5
2
0.707
Frequency Response - sites.google.com/site/ncpdhbkhn
24
0
20
1
0.1
1
1
10
1
100
Bode Plots (14)
K
()
N
j
1
1
N
j
K
()
N
j
()
N
j
1
j
z
10
20log
K
20 dB/decadeN
1
20 dB/decadeN
1
20 dB/decadeN
z
o
0
o
90N
o
90
N
10
o
90N
o
0
Frequency Response - sites.google.com/site/ncpdhbkhn
25
o
90
N
z
10
z
10
z
