Active filters

FILTER DESIGN USING OPAMP

1. Filters Ideal Filter Responses Passive Filters and Active Filters Active Filters LOW PASS FILTER HIGH PASS FILTER BAND PASS FILTER BAND STOP FILTER LINEAR INTEGRATED CIRCUITS 19ECE46 RAJESH G Sr. Asst. Prof/ECE

2. I n t r o d uc t ion  F il t e r s a r e c i r c u its t h a t a r e c a p a b le o f p a ss i n g s i g n a ls wit h in a b a n d o f fr e que n cies w h i le r e jec t i n g o r b l o cki n g s i g n a ls o f f r e qu e n cies ou t s i d e t h is b a n d . Th i s p r o p e r ty o f f ilt er s is a l s o called “ f r e qu e n cy se lecti v i ty”. F ilt e r can b e p a s s i v e o r acti v e f i l t e r .  P a ssi v e f i l t e r s : T h e c i r c u i t s bu i lt us ing R C , R L , o r R L C ci r c u i ts . A c t i v e f il t er s : Th e ci r cui t s t h at e m p loy on e o r m o r e o p- a m p s r e s i s t o r s in t h e d e s i g n a n a d di t i o n to a n d c a p aci t o r s

3. Types o f F i lters • T h ere are t w o b road cat e go ri e s o f fi lt ers: – – A n a n al o g f i lt e r pr o cess es c o n ti n u o u s -t i m e s ig n a ls A d i g ital filt e r p r o c e sse s di s cr e t e - ti m e s i g n a l s . • T h e an a l o g or d i g i tal filters can be sub divided into four categories: – – – – L o w p as s F ilt e rs H i g h p as s F il t e rs Ba n d Ba n d stop F i l t e rs p as s F il t e rs

4. A n alog Filt e r Resp ons es H ( f ) H ( f ) f f f f c c I d e a l “ b r i ck w a ll” f ilt e r Pra c t ic a l f ilter

5. I d eal Filt er s L o w p as s F i lt e r H ighp as s F i l t e r c c B a nd s top F il t e r B a ndp a s s F i l t e r c 1 c 2 c 1 c 2 S t opband Pa s sband S t opband M( ) Pa s s b and S t opband Pa s sband S t opband Pa s s b and M( ) Pa s s b and S t opband

6. Pas s ive Fil t e r s • M a de up of p ass ive c o m pon e nts - r e s i s to r s , ca p a c i tors indu c tors N o a m plify i ng e l e m e n ts ( tr a n s i s tor s , op- a mp s , e t c ) N o s ig n a l g a in 1 s t ord e r - d e s i gn is s imp l e ( ju s t u s e s t a nd a rd e qu a tions f i n d r e s on a nt f r e qu e n c y o f the c ir c uit) a nd • • • to • • • ● 2 nd o r d e r - c omp l e x e qu a tions R e qu i re no po w e r s upp l i e s B u f f e r a mp l ifi e r s m ight be r e qui r e d De s i r a b l e t o u s e indu c to r s w ith h igh qu a lity f ac to r s

7. I ndu ct o r - BIG PROBLEM! • • P hy s i c a l s i ze , a nd l a rge indu c t a n c e v a l u e s a re r e qui r e d . T uning i n d u c t o rs t o the r e qui r e d v a lu e s is tim e - c on s uming a n d e xp e n s ive for l a rg e r qu a nti t i e s of f il t e r s . O ft e n proh i b i tiv e ly e xp e n s i v e . • ● D if f i c u l t L o s s y to im p l e m e n t a t f r e qu e n c i e s b e l o w 1 k H z . ●

8. Active Fil t er • • • • • N o indu c t ors M a de up of op - a mp s , r e s i s tors a nd ca p a c i t ors P rovi d e s a rbi t r a ry g a in Ge n e r a l ly e a s i e r t o d es ign H igh input im p e d a n c e pr e v e nts e x ces s ive lo a ding s ou r c e of the driv i ng • L ow output i m p e d a n c e pr e v e nts the fi l t e r f r om b e ing a ff ec t e d by the lo a d E a s y t o a d ju s t o v e r a w i de f r e qu e n c y r a nge w i t hout a lt e ri n g the d e s i r e d r e s pon s e •

9. Op Amp A dv ant a g es • A dv a n t ages o f acti v e RC f i l t ers i n c l u d e: – – – Re d u c ed s i z e a n d w e i g ht Incr eas ed r e l i a b ility a n d imp r o v e d perform a n c e S impl e r d e sign t h a n f o r p ass i ve f i lt e rs a n d c an r e ali z e a w i d e r ran g e of fu n c ti o ns as w ell as p r ovi d ing v olt a ge g a in In l a r g e q u a n t iti e s, t h e c o s t of a n IC is le s s t h a n i ts p ass i ve c o u nterp a r t –

10. Op A m p Disad v an t ages • A c t ive R C f ilt e r s a lso h a ve s ome d i s a d v a n t a ge s : – li m i t e d b a n d w i dth of ac ti v e d e vic e s l i m its the h ig h es t a tt a in a b le p o le f r e q u e ncy a nd t h e r e f o re a p p li c a t io n s n ea r by 100 k H z ( p as sive RL C fi l t e rs c a n b e u se d up to 5 00 M H z ) r e q ui r e p o w e r sup p li e s (u n li k e pa ss i v e fi l t e rs) – – in c r eas ed se n s it i vity to v a r i a ti o ns in ci rc u it p a r a m et e rs ca us e d by e n vi r o nm e ntal c hanges filt e r s . c omp a red to p as sive • F or m a ny app l i c a t i ons, p a r t i c ularly in v oice a n d d a ta c om m u n i c a t io n s , the e con o m ic a nd p e rf o r m an c e a d v a ntag e s of ac t i ve RC f ilt e rs f a r o u t w e i g h th e ir dis a d v a ntag e s.

11. Categ o r i es o f Fil t ers L ow P a s s Fi l t e r s : P as s a ll f r e qu e n c i e s f rom High P a s s Filt er s : P as s a ll f r e qu e n c i e s th a t dc a r e up to the upp e r f r e q u e n c y. A c uto f f a bove i ts l o w e r f r e q u e n c y c u t off A v ( d B ) v ( d B ) { { -3dB -3dB f f f f 2 1 H igh-p as s r e s pon s e L o w - p a s s r es pon s e

12. Categ o r i es B a nd P a s s Filt er s : P as s only t he f r e qu e n c i e s th a t f a ll b e t we e n i t s v a lu e s of t he l o w e r a nd upp e r o f Fil t ers B and S top ( N ot c h) F i lt e r s : E l imin a te a ll s ign a ls w i thin the s t op b a nd w h i le p a ss ing a ll f r e qu e n c i e s b a nd. out s ide this c utoff f r e qu e n c i es . A v ( d B) A v ( d B ) { { - 3 dB -3dB f f f 1 f 2 f 1 f 2 B a nd P as s R es p o n s e Band S top R e s pon s e

13. Filt e r A v Re s p ons e Chara c t er istics f But t e r w o r th B e s s e l C h e b y sh e v

14. ACTIVE LOW PASS FILTER Passive filter

15. ACTIVE LOW PASS FILTER Passive filter and its frequency response

16. ACTIVE LOW PASS FILTER Passive filter and its frequency response

17. ACTIVE LOW PASS FILTER This first-order low pass active filter, consists simply of a passive RC filter stage providing a low frequency path to the input of a non-inverting operational amplifier. The amplifier is configured as a voltage-follower (Buffer) giving it a DC gain of one, Av = +1 or unity gain as opposed to the previous passive RC filter which has a DC gain of less than unity. The advantage of this configuration is that the op-amps high input impedance prevents excessive loading on the filters output while its low output impedance prevents the filters cut-off frequency point from being affected by changes in the impedance of the load. While this configuration provides good stability to the filter, its main disadvantage is that it has no voltage gain above one. However, although the voltage gain is unity the power gain is very high as its output impedance is much lower than its input impedance. If a voltage gain greater than one is required we can use the following filter circuit.

18. ACTIVE LOW PASS FILTER Active First order Low Pass Filter with Amplification

19. ACTIVE LOW PASS FILTER Active First order Low Pass Filter

20. ACTIVE LOW PASS FILTER Analysis

21. ACTIVE LOW PASS FILTER

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23. ACTIVE LOW PASS FILTER Active second order Low Pass Filter

24. ACTIVE LOW PASS FILTER Active second order Low Pass Filter The main feature of the 2 nd order LPF is, the frequency response falls at the rate of 40dB/Decade above the cutoff frequency.

25. ACTIVE LOW PASS FILTER Active second order Low Pass Filter At lower frequencies C 1 and C 2 are more so, no effect on the circuit operation. V = V i , A v = 1. At higher frequencies , C 1 & R 2 causes the o/p to fall of @ 20dB/D as the frequency increases. Phase lag produced by R 2 & C 1 and Phase lead is produced by combined C 2 and [R 1 + R 2] . The result of these phase differences is that the feedback via C 2 produces further fall of 20dB/D. Thus total roll off rate is 40db/D

26. ACTIVE LOW PASS FILTER Design Procedure of 2 nd Low Pass Filter R max = R 1 + R 2 = R 1 = R 2 and R 3 = R 1 + R 2 C 2 = 2*C 1 @ f h and Design of 2 nd order LPF with a cutoff frequency of 100Hz. Draw the circuit diagram.

27. ACTIVE HIGH PASS FILTER 1 ST order HPF

28. ACTIVE HIGH PASS FILTER

29. ACTIVE HIGH PASS FILTER

30. ACTIVE HIGH PASS FILTER Design 1 st order HPF for the cutoff frequency 1KHz.Draw the Circuit diagram.

31. ACTIVE HIGH PASS FILTER 2 nd order HPF

32. ACTIVE HIGH PASS FILTER At higher frequencies C 1 and C 2 are more so, no effect on the circuit operation. C 1 & C 2 << R 1 & R 2 , so V = V i , A v = 1. At lower frequencies , C 2 & R 2 causes the o/p to fall of @ 20dB/D as the frequency increases. Phase lead produced by R 2 & C 2 and Phase lag is produced by combined R 2 and [C 1 + C 2 ] . The result of these phase differences is that the feedback via R 2 produces further fall of 20dB/D. Thus total roll off rate is 40db/D

33. ACTIVE HIGH PASS FILTER Design 2 nd order HPF for the cutoff frequency 120KHz.Draw the Circuit diagram.

34. The “Q” or Quality Factor In a  Band Pass Filter  circuit, the overall width of the actual pass band between the upper and lower -3dB corner points of the filter determines the  Quality Factor  or  Q-point  of the circuit. This  Q Factor  is a measure of how “Selective” or “Un-selective” the band pass filter is towards a given spread of frequencies. The lower the value of the Q factor the wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more “selective” is the filter.