ELG3336: Op Amp-based Active Filters

Transcription

1 ELG6: Op Amp-baed Actve Flter Advantage: educed ze and weght, and thereore paratc. Increaed relablty and mproved perormance. Smpler degn than or pave lter and can realze a wder range o uncton a well a provdng voltage gan. In large quantte, the cot o an IC le than t pave counterpart. Dadvantage: Lmted bandwdth o actve devce lmt the hghet attanable pole requency and thereore applcaton above 00 kz pave LC lter can be ued up to 500 Mz. The achevable qualty actor alo lmted. equre power upple unlke pave lter. Increaed entvty to varaton n crcut parameter caued by envronmental change compared to pave lter. For applcaton, partcularly n voce and data communcaton, the economc and perormance advantage o actve C lter ar outwegh ther dadvantage.

2 Frt-Order Low-Pa Flter o C C C C C V V / A low-pa lter wth a dc gan o /

3 v o t t C 0 v n t dt

4 Frt-Order gh-pa Flter o C C C C C C C v v / / A hgh-pa lter wth a hgh requency gan o /

5 gher Order Flter n n n n /

6 Sngle-Pole Actve Flter Degn gh Pa Low Pa v v out n C C C C C / C / C v v out n / C / C

7 Two-Pole Sallen-Key Flter Low Pa Flter gh Pa Flter C +V +V + C C + v n v n C - vout - vout -V -V 7

8 Three-Pole Low-Pa Flter Stage Stage C +V + +V v n C - -V C + - v out -V 4 8

9 Two-Stage and-pa Flter C 4 +V v n C + - -V C 4 C + - +V v out -V Stage Two-pole low-pa Stage Two-pole hgh-pa 4 A v Stage repone W Stage repone W = Q = 0 / W o 9

10 Multple-Feedback and-pa Flter C +V C - v n + v out -V 0

11 Traner uncton Traner Functon V o V V V o Im e Im e e Im tan 0 e e Im tan 80 o 0 e

12 Corner Frequency The gncance o the break requency that t repreent the requency where A v = Th where the output o the traner uncton ha an ampltude -d below the nput ampltude, and the output phae hted by -45 relatve to the nput. Thereore, c alo known a the -d requency or the corner requency.

13 ode plot ue a logarthmc cale or requency, where a decade dened a a range o requence where the hghet and lowet requence der by a actor o 0.

14 eal Flter utterworth Flter Flat Pa-band. 0n d per decade roll-o. Chebyhev Flter Pa-band rpple. Sharper cut-o than utterworth. Ellptc Flter Pa-band and top-band rpple. Even harper cut-o. eel Flter Lnear phae repone.e. no gnal dtorton n pa-band.

15 utterworth Flter The magntude repone o a utterworth lter. Magntude repone or utterworth lter o varou order wth =. Note that a the order ncreae, the repone approache the deal brckwall type tranmon.

16 Chebyhev Flter Sketche o the tranmon charactertc o a repreentatve even- and oddorder Chebyhev lter.

17 Frt-Order Flter Functon

18 Frt-Order Flter Functon

19 Second-Order Flter Functon

20 Second-Order Flter Functon

21 Second-Order Flter Functon

22 Second-Order LC eonator

23 Second-Order Actve Flter: Two-Integrator-Loop Dervaton o an alternatve two-ntegrator-loop bquad n whch all op amp are ued n a ngle-ended ahon. The reultng crcut n b known a the Tow-Thoma bquad.

24 Low-Pa Actve Flter Degn Degn a ourth-order low-pa utterworth lter havng a requency cut-o o 00 z Chooe C 0.F C 5.9k 0.x0 6 00z

25 Low-Pa Actve Flter Degn

26 Low-Pa Actve Flter Degn

27 Innte-Gan Multple-Feedback IGMF Negatve Feedback Actve Flter 4 5 v 0 v y KCL at V V 0 x, V o V V Vx 5 Vx Vx x V x V x 4 5 Vx V o V o V o Subttute nto gve V V V V V V o o o o o

28 rearrangng equaton, t gve, V o V Or n admttance orm: V V o YY Y Y Y Y Y Y Y Flter Value 4 5 LP C 4 C 5 P C C C 4 5 P C C 4 5

29 and-pa: IGMF and-pa Flter K a b To obtan the band-pa repone, we let C C 4 C 4 C C C C C C C 4 5 Th lter prototype ha a very low entvty to component tolerance when compared wth other prototype. C

30 Smpled Degn IGMF Flter C C C C C Comparng wth the band-pa repone P P P Q K It gve, 5 5 Q Q C p p p

31 Example: IGMF and Pa Flter To degn a band-pa lter wth 5z and Q 0 O P C 5 5z C 00 nf Q P ,66, , 70 00nF ,70 - v 00nF n + v o Wth mlar analy, we can chooe the ollowng value: C 0 nf,554 and 5 6,700

32 utterworth epone Maxmally Flat n o where n the order Normalze to o = rad/ utterworth polynomal utterworth polynomal: ˆ n n ˆ

33 Second order utterworth Flter 4 4 ' P P P Q K C C K C C K C C K C C C C Q P Settng = and C = C K K K Q P Now K = + / A v n C 4 v o + - C A A A P K Q For utterworth repone: Q P A P Q We have 44. A We dene Dampng Factor DF a:.44 A P Q DF