bi-quad, filter machine. - cs.huji.ac.il · biquad configurations. c1*c2*s^2-----c1*c2* s^2 +...

Bi-quad, Filter Machine.

Yuval TaubYuval Millo

Ranon LadnauDotan Ziv

Moshe RodenTomer Zaidenshtein

Biquad scheme

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

Stability – Impulse Response

Low pass

Band rejectHigh Pass

Band Pass

Transconductance Amplifier,Used in the Biquad implementation

Voltage Divider

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

CMRR & CMR

V1 rampV2 same ramp + sin

1.3V

3.25V

VDiff-Max – 1.0V

@ 1.5V - reaches saturation

Biquad

Low Pass Filter.Behavioral(matlab) Vs Analog (spice)

21.88Mhz3dB point

High Pass Filter.Behavioral(matlab) Vs Analog (spice)

26.67Mhz3dB point

Band Pass Filter.Behavioral(matlab) Vs Analog (spice)

41.88Mhz3dB point

12.8Mhz3dB point

Band Reject Filter.Behavioral(matlab) Vs Analog (spice)

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 .

Band Pass Filter.Time – FFT Example – I/O & FFTs

Band Pass Filter.Time – FFT Example – Input & FFT

Band Pass Filter.Time – FFT Example – Output & FFT

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

Band Reject Filter.Time – FFT Example – Analog & FFTs

Band Reject Filter.Time – FFT Example – I/O FFTs

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 !

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

Zero-Pole map & Bode Mag.with 0.25pf capacitors

Zero-Pole map & Bode Mag.with 1pf capacitors

Spice results with 1pf capacitors

Parasitic capacitanceinfluences Band Widthof spice moderesults