Bài giảng Tín hiệu và hệ thống: Chương 7 (Lecture 18) – Trần Quang Việt (2017)

404001 - Tín hi u và h th ng

Lecture-18
áp

ng t n s và b l c tương t

áp ng t n s c a h th ng LTIC
Bi u
Bode
Thi t k b l c tương t
B l c Butterworth
B l c Chebyshev
Các phép bi n i t n s
phé

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

B l c Butterworth

Coefficients of Butterworth Polynominal Bn(s)=sn+an-1sn-1+…+a1s+1
n

a1

a2

a3

a4

a5

a6

a7

a8

a9

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

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B l c Butterworth

Butterworth Polynominal in Factorized Form
n

Bn (s)

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

B l c Butterworth
Các bư c thi t k b l c thông th p Butterworth:
Bư c 1: Xác
Bư c 2: Xác

ωc ≥

(10

− G /10
lo g  (1 0 − G s / 1 0 − 1) /(1 0 p
− 1) 


nh n ≥
2 lo g ( ω s / ω p )

nh ωc:
ωp

− G p / 10

− 1)

1/ 2 n

và

ωc ≤

ωs
(10

− G s /10

− 1)1/ 2 n

Bư c 3: Xác

nh H(s): dùng n (bư c 1) tra b ng (ho c tính)

Bư c 4: Xác

nh H(s):

H ( s)

s ← s / ωc

H (s)

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

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B l c Chebyshev
Chebyshev Filter Coefficients of the Denominator Polynominal
'
C n = s n + a n −1 s n −1 + a n − 2 s n − 2 + ... + a1 s + a 0

n

a0

a1

a2

a3

a4

a5

a6

0.5 d B ripple
r = 0 .5 d B

1 d B ripple
r = 1d B

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

B l c Chebyshev
Chebyshev Filter Coefficients of the Denominator Polynominal
'
C n = s n + a n −1 s n −1 + a n − 2 s n − 2 + ... + a1 s + a 0

n

a0

a1

a2

a3

a4

a5

a6

2 dB ripple
r = 2dB

3 dB ripp le
r = 3dB

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

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B l c Chebyshev
Chebyshev Filter Poles Locations
n r = 0 .5 dB
r = 1d B

r = 2dB

r = 3dB

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

B l c Chebyshev
Chebyshev Filter Poles Locations
n r = 0 .5 dB
r = 1d B

r = 2dB

r = 3dB

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

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B l c Chebyshev
Các bư c thi t k b l c thông th p Chebyshev:
Bư c 1: Xác

nh: n ≥

Bư c 2: Ch n ε:

1
cosh − 1 (ω s / ω p )

cosh

 10 − G s /10 − 1 


r /10
−1 
 10

1 0 − G s /10 − 1
≤ε ≤
c o sh [ n c o s h − 1 ( ω s / ω p )]

N u ε sao cho r=0.5dB, 1dB, 2dB ho c 3dB
n u không th a tính C’n(s):

s k = − sin

−1

( 2 k −1) π
2n

sinh x + j cos

k = 1, 2, 3, ..., n ; x =

1
n

1/ 2

1 0 r /10 − 1

tra b ng C’n(s);

( 2 k −1) π
2n

cosh x

1
sinh − 1 ( ε )

'
C n ( s ) = ( s − s1 )( s − s 2 )...( s − s n )
Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

B l c Chebyshev

Các bư c thi t k b l c thông th p Chebyshev:
Bư c 3: Xác

nh H(s): H ( s ) =

a0

K n =  a0
 1+ε 2

Bư c 4: Xác

nh H(s):

Kn
C n' ( s )

n odd
n even

H ( s)

s ← s / ωp

H (s)

Signal & Systems - Tran Quang Viet – FEEE, HCMUT – Semester: 02/09-10

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