![Page 1: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/1.jpg)
Bi-quad, Filter Machine.
Yuval TaubYuval Millo
Ranon LadnauDotan Ziv
Moshe RodenTomer Zaidenshtein
![Page 2: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/2.jpg)
Biquad scheme
![Page 3: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/3.jpg)
Biquad Configurations.
C1*C2*S^2-------------------------------------
C1*C2* s^2 + gm*C1* s + gm^2
Vin = V3V1,V2 = gnd
High Pass
C1*C2*s^2 + gm^2-------------------------------------
C1*C2* s^2 + gm*C1* s + gm^2
Vin = V1 = V3V2 = gnd
Band Reject
C1*gm*s-------------------------------------
C1*C2* s^2 + gm*C1* s + gm^2
Vin = V2V1,V3 = gnd
Band Pass
gm^2-------------------------------------
C1*C2* s^2 + gm*C1* s + gm^2
Vin = V1V2,V3 = gnd
Low Pass
Transfer FunctionInput ConditionsFilter Type
![Page 4: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/4.jpg)
Stability – Impulse Response
Low pass
Band rejectHigh Pass
Band Pass
![Page 5: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/5.jpg)
Transconductance Amplifier,Used in the Biquad implementation
Voltage Divider
![Page 6: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/6.jpg)
OpAmp specs.
CMRR 34.5 dBCMR 1.3V – 3.25Vgm – 9.42u [1/Ohm]Operating Point – 2.3VVdiffmax – 1VVbias – 5VSlew rate – 24.3(V/uSec)Gain – ~10
![Page 7: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/7.jpg)
CMRR & CMR
V1 rampV2 same ramp + sin
1.3V
3.25V
![Page 8: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/8.jpg)
VDiff-Max – 1.0V
![Page 9: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/9.jpg)
@ 1.5V - reaches saturation
![Page 10: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/10.jpg)
Biquad
![Page 11: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/11.jpg)
Low Pass Filter.Behavioral(matlab) Vs Analog (spice)
21.88Mhz3dB point
![Page 12: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/12.jpg)
High Pass Filter.Behavioral(matlab) Vs Analog (spice)
26.67Mhz3dB point
![Page 13: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/13.jpg)
Band Pass Filter.Behavioral(matlab) Vs Analog (spice)
41.88Mhz3dB point
12.8Mhz3dB point
![Page 14: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/14.jpg)
Band Reject Filter.Behavioral(matlab) Vs Analog (spice)
![Page 15: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/15.jpg)
Band Pass Filter.Time – FFT Example
Input : 3 sinusoids at various
harmonies : 1 Mhz , 30 Mhz &150 Mhz.- Band pass is around
the 12 – 40 Mhzpeak .
![Page 16: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/16.jpg)
Band Pass Filter.Time – FFT Example – I/O & FFTs
![Page 17: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/17.jpg)
Band Pass Filter.Time – FFT Example – Input & FFT
![Page 18: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/18.jpg)
Band Pass Filter.Time – FFT Example – Output & FFT
![Page 19: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/19.jpg)
Band Reject Filter.Time – FFT Example
Input : 3 sinusoids at various
harmonies : 2 Mhz , 10 Mhz &50 Mhz.- Band Reject is
between 7 – 12 Mhz
![Page 20: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/20.jpg)
Band Reject Filter.Time – FFT Example – Analog & FFTs
![Page 21: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/21.jpg)
Band Reject Filter.Time – FFT Example – I/O FFTs
![Page 22: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/22.jpg)
Changing Capacitors –to influence Band Width (LP)
Capacitors increase from 0.25pf to 1pf3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)(spice vs. matlab accordingly)-> about 66% spice & 75% matlab reduction !
![Page 23: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/23.jpg)
Changing Capacitors – cont.
LP transfer function is :Gm^2
-------------------------------------C1*C2* s^2 + Gm*C1* s + Gm^2
2nd order Pole @ gm/(c1c2)1/2
With capacitors at 0.25pf Pole @ 3.76 * 10^7
With capacitors at 1pf Pole @ 9.42 * 10^6
![Page 24: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/24.jpg)
Zero-Pole map & Bode Mag.with 0.25pf capacitors
![Page 25: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/25.jpg)
Zero-Pole map & Bode Mag.with 1pf capacitors
![Page 26: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/26.jpg)
Spice results with 1pf capacitors
Parasitic capacitanceinfluences Band Widthof spice moderesults
![Page 27: Bi-quad, Filter Machine. - huji.ac.il · to influence Band Width (LP) Capacitors increase from 0.25pf to 1pf 3db point decreases from around 21 – 48(Mhz) to around 7.3 – 12(Mhz)](https://reader033.vdocument.in/reader033/viewer/2022060711/6077a98ee972827b5546e4f3/html5/thumbnails/27.jpg)