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Lecture Electric circuit theory: Frequency response - Nguyễn Công Phương

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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

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