material1 / different / Chung-Yu Wu - Analog Circuit Design

H(S)=

− (K

2

S 2

+

K

S

+

K

)

=

V

(s)

ωo

1

o

out

S

2

+

2

V (s)

Q

S + ω0

in

S2V

=-[K

S2+K S+K ] V (ω

S

+ ω2 )•V

out

out

2

1

o

in

o Q

0

>Vout=-

1

[(K1+K2S)Vin+( Wo ) •Vout+ ωo •V1)

S

Q

where V1=

1

[(Ko/ωo)

•Vin+ωo •Vout]

S

−ω0

Vin

1

ω0

ω0

Q

− 1

−

Vout

−

K0

S

V

S

ω

0

1

K1 + K2 S

CA =1

−

1

Q ω0

ω0

ω0

−

K0

1

CB =1

Vin

−

ω0

−

Vout

+

1

+

K1

14-21

Step 3: SCF

CHUNG-YU WU

C2

C =1

φ1

A

C4

CB=1

φ2

φ2

C1

-

C3

Vin

-

OP1

φ2

φ2

φ1

φ2

+

OP2

Vout

φ1

φ1

+

φ2

C1'

C1 = T * Ko/ωo=

A

* ωo * T=

A

1

A

Ko

dc

dc

x

dc

ωo

2

C2

= C3=ωo * T=

1

x

C4 = (ωo * T/Q)=

1

>

Q

=

CA

(not suitable for high Q)

Qx

ωoT

C4

C1'= K1

* T =K1

1

ωo x

C1" = K2

1

CA/C2=

ωoT

>

fo=

fs

fo: center (cutoff) frequency

X=

1

2πx

ωoT

C4

-C1Z-1

-1/CA

C3

-1/CB

Vout

Vin

1-Z-1

1-Z-1

C '+C "(1-Z-1)

1

1

Qout (z)

=

−1/ Cf

=

Vout (z) C

Vin (z)

1− z −1

Vin

(z)

Similarly,

C * (1-z-1)

for an unswitched capacitor (e.g. C1")

C

for a non-inverting capacitor (C1', C3, C4)

-C * z-1

for an inverting capacitor (C1, C2)

V (z)

=

−

(C '+C ")z2

+ (C C

−C '−2C ")z + C "

out

1

1

1 3

1

1

V (z)

(1 + C

4

)z

2 + (C

C

3

−C

4

− 2)z +1

in

2

H(z) = -

a

2

* z2

+ a * z + a

0

1

b

* z2

+b * z +1

2

1

K0=K1=0

a0=a2= -

a1

2

K1=0

C1=K0

T/ω0 = (

K0

)ω

T

=

A

ω

T

ω 2

o

dc

0

0

C2

C3 ω0T

C4

1

(instead of

Q

)

ω0T

Q

C2

+

C4 (1− Z −1 )

C

'' (1− Z −1 )

1

+

V

C +

−1 CA

−C3 Z −1

+

−1 CB

Vout

in

1− Z

−1

V

1−Z

−1

1

1

C '' (1− Z −1 )

1

H(Z)= −

C

"Z 2 + (C C

+ C

'C

− 2C

")Z + (C

"−C

'C

)

1

1

3

1

3

1

1

1

3

Z 2 + (C2C3 + C3C4 − 2)Z + (1 −C3C4 )

Choose C2=C3

Coefficient matching:

C2

φ1

φ2

C4

CA

CB

vin

−

φ2

C1

φ1

φ2

C3

φ2

−

vout

φ1

φ2

+

+

φ1

φ1

4

CA=CB=6.3

C1=4

H (S) = S 2 +1.2S +1

C2=1

C3=1

C4=1.2

fc

=

fs

fc: CENTER FRE.

2 •π •CA

fs: SAMPLING FRE.

Example 2: Low-Q Bandpass SCF Biquad

C2

φ1

C4

φ2

CA

CB

vin

−

φ2

φ1

φ2

φ2

−

vout

φ1

φ2

+

C3

+

φ1

φ1

C '

1

CA=CB=6.3

C1'=2

H (S) =

4

2 +1.2S +1

S

fs

fc: CENTER FRE.

C2=1

C3=1

C4=1.2

fc = 2 •π

•C

A

fs: SAMPLING FRE.

C2

φ1

φ2

CA

C4

φ2

C

C

CB

Vin

1

φ2

-

3

-

φ

φ

+

2

1

Vout

φ

φ

1

1

φ2

+

φ

1

CA=CB=6.3

C1=4

H (S) = S2 +

4

S

+1

5.25

C2=1

C3=1

C4=1.2

fc =

fs

2 •π

•C

A

fc: CENTER FRE.

Example 4: High-Q Band-pass SCF Biquad

fs: SAMPLING FRE.

C2

φ1

Vin

C'1

φ2

CA

C4

φ2

-

C3

CB

-

φ

φ

+

2

1

Vout

φ

1

+

φ1

φ2

2S

S2 +1.2S +1

C2=1

C3=1

C4=1.2

fc =

fs

2 •π

•C

A