Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Two-integrator-loop biquad

2hp

2 2

0 0

V

V ( / )i

Ks

s s Q

Consider high-pass filter

2

0 0

hp hp hp2

1V V V = V

iK

Q s s

2

0 0

hp hp hp2

1V V V V

iK

Q s s

One circuit configuration for several different second-order filters?

2 2 2

hp hp 0 hp 0V V ( / ) V = V

is s Q K s

(Razavi 14.4.2)

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

2

0 0

hp hp hp2

1V V V V

iK

Q s s

Express the above equation using a block diagram

Biquad Universal Active Filter

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

How to implement biquad?

Vi Vo

0

0

1 -

1- -

1

i

o

o

i

VV

R sC

V

V RCs s

RC

(Ignoring the op-amp offset)

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Use superposition (Vi, Vbp, Vlp)

13

hp

2 3 1

V Vf

i

R RR

R R R

12

bp

2 3 1

Vf

R RR

R R R

lp

1

Vf

R

R

Weighted sum of Vi, Vbp, Vlp

Kerwin-Huelsman-Newcomb (KHN) biquad

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

13 2

hp bp lp

2 3 1 2 3 1 1

V V 1 V V

f f f

i

R R R RR R

R R R R R R R

KHN

hp bp lp

1V V V V

iK

Q

1/ 1

fR R

2

2 3

2 1R

R R Q

3

2 3

2RK

R R

0=?

2hp

2 2

0 0

V

V ( / )i

Ks

s s Q

All of HF, LP and BP characteristics can be obtained!

2 3

22

R RQ

R

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Can be realized by linear combination of Vhp, Vbp, Vlp

How about All-Pass Filter?

KHN

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

All-Pass Filters

hp bp lpV V V VF F F

o

H B L

R R R

R R R

2

hp i2 2

0 0

V V( / )

Ks

s s Q

0 0

bp hp i2 2

0 0

V ( )V V( / )

K s

s s s Q

2 2

0 0

lp hp i2 2 2

0 0

V ( )V V( / )

K

s s s Q

2 2

0 0

2 2

0 0

V ( / ) ( / ) ( / )=

V ( / )

o F H F B F L

i

R R Ks R R K s R R K

s s Q

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

How about All-Pass Filters?

2 2

0 0

2 2

0 0

V ( / ) ( / ) ( / )=

V ( / )

o F H F B F L

i

R R s R R s R RK

s s Q

All-Pass Filter 1,F

H

R

R

1 ,F

B

R

R Q 1F

L

R

R

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

There are several Biquads

V1 V2

2

1

1

1( // )

1//

i

o

V VV QR

R sCR

sC

1

2

3

iV V

V rR r

1

2

1o iV V

VR R sC

Tow-Thomas biquad:

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Tow-Thomas biquad

V1

V2

2 1

2

1 3 2

2

2 2

1 1 1

V=

1 1V

o

i

C rs s

C C R RR C RR

s sQCR C R

0

1

CR

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

2 1

2

1 3 2

2

2 2

1 1 1

V=

1 1V

o

i

C rs s

C C R RR C RR

s sQCR C R

10C

DC Gain:V1

V2

For LP

1,R

HF Gain:

For HP

1,R

3R

2

R

R

2,R

3R

1C

C

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

2 1

2

1 3 2

2

2 2

1 1 1

V=

1 1V

o

i

C rs s

C C R RR C RR

s sQCR C R

V1

V2

For BP

2R

10C

1

1 3

1 1 ra

C R RR

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

2 1

2

1 3 2

2

2 2

1 1 1

V=

1 1V

o

i

C rs s

C C R RR C RR

s sQCR C R

V1

V2

For AP

1R

1C C

3R Qr

2R R

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Homework(1) Determine Vhp(s)/Vi(s), Vbp(s)/Vi(s), Vlp(s)/Vi(s)

Electronic Circuits 2 (15/1)

Lect. 20: Two-Integrator-Loop Biquad

W.-Y. Choi

Homework(2): Determine Vo(s)/Vi(s)

V1 V2