ELG439: Op Amp-baed Actve Flter Advantage: educed ze and weght, and therere paratc. Increaed relablty and mprved perrmance. Smpler degn than r pave lter and can realze a wder range unctn a well a prvdng vltage gan. In large quantte, the ct an IC le than t pave cunterpart. Dadvantage: Lmted bandwdth actve devce lmt the hghet attanable ple requency and therere applcatn abve 00 kz pave LC lter can be ued up t 500 Mz. The achevable qualty actr al lmted. equre pwer upple unlke pave lter. Increaed entvty t varatn n crcut parameter caued by envrnmental change cmpared t pave lter. Fr applcatn, partcularly n vce and data cmmuncatn, the ecnmc and perrmance advantage actve C lter ar utwegh ther dadvantage.
Frt-Order Lw-Pa Flter B B C C C C C V V / A lw-pa lter wth a dc gan /
v t t C 0 v n t dt
Frt-Order gh-pa Flter B B B C C C C C C C v v / / A hgh-pa lter wth a hgh requency gan /
gher Order Flter n B n n n /
Sngle-Ple Actve Flter Degn gh Pa Lw Pa v v ut n C C C C C / C / C v v ut n / C / C
Tw-Ple Sallen-Key Flter Lw Pa Flter gh Pa Flter C +V +V + C C + v n v n C - vut - vut -V -V 7
Three-Ple Lw-Pa Flter Stage Stage C +V + +V v n C - -V 3 C 3 + - 3 v ut -V 4 8
Tw-Stage Band-Pa Flter C 4 +V v n C + - -V C 4 C 3 3 + - +V v ut -V 3 Stage Tw-ple lw-pa Stage Tw-ple hgh-pa 4 A v Stage repne BW Stage repne BW = Q = 0 / BW 9
Multple-Feedback Band-Pa Flter C +V C - v n + v ut -V 0
Traner unctn Traner Functn V V V V Im e Im e e Im tan 0 e e Im tan 80 0 e
Frequency Traner Functn Flter L L and 0 Pa Flter Band - III 0 Pa Flter - gh II 0 Pa Flter Lw - I a pecc phae repne ha r all Pa r phae- ht Flter - All V and 0 Band - Stp Ntch Flter IV L L
Bde Plt T undertand Bde plt, yu need t ue Laplace tranrm! V n The traner unctn the crcut : A v A v V V n C / C / C C where c called the break requency, r crner requency, and gven by: C b c C
4 Bde Plt Sngle Ple C 0 0 0lg 0lg db db 0 0lg Fr >> C V V Sngle ple lw-pa lter
0dB 6dB Fr ctave apart, Fr decade apart, db 0lg 0 x 0 0 x x 6dB 0dB lg lpe -6dB/ctave -0dB/decade 5
6 Bde Plt Tw-Ple C C v v 0 0lg
Crner Frequency The gncance the break requency that t repreent the requency where A v = 070.7-45 Th where the utput the traner unctn ha an ampltude 3-dB belw the nput ampltude, and the utput phae hted by -45 relatve t the nput. Therere, c al knwn a the 3-dB requency r the crner requency.
Bde plt ue a lgarthmc cale r requency, where a decade dened a a range requence where the hghet and lwet requence der by a actr 0.
A v Magntude the Traner Functn n db / b A v db 0lg 0lg 0lg 0lg / / 0lg / b b b / b See hw the abve expren change wth requency: at lw requence << b, Av db = 0 db lw requency aymptte at hgh requence >> b, Av db = -0 lg / b hgh requency aymptte
eal Flter Butterwrth Flter Flat Pa-band. 0n db per decade rll-. Chebyhev Flter Pa-band rpple. Sharper cut- than Butterwrth. Ellptc Flter Pa-band and tp-band rpple. Even harper cut-. Beel Flter Lnear phae repne.e. n gnal dtrtn n pa-band.
Flter epne Charactertc
Butterwrth Flter The magntude repne a Butterwrth lter. Magntude repne r Butterwrth lter varu rder wth =. Nte that a the rder ncreae, the repne apprache the deal brckwall type tranmn.
Chebyhev Flter Sketche the tranmn charactertc a repreentatve even- and ddrder Chebyhev lter.
Frt-Order Flter Functn
Frt-Order Flter Functn
Secnd-Order Flter Functn
Secnd-Order Flter Functn
Secnd-Order Flter Functn
Secnd-Order LC enatr
Secnd-Order Actve Flter: Inductr eplacement The Antnu nductance-mulatn crcut. b Analy the crcut aumng deal p amp. The rder the analy tep ndcated by the crcled number.
Secnd-Order Actve Flter: Inductr eplacement The Antnu nductance-mulatn crcut. Analy the crcut aumng deal p amp. The rder the analy tep ndcated by the crcled number.
Secnd-Order Actve Flter: Inductr eplacement ealzatn r the varu ecnd-rder lter unctn ung the p amp-c renatr Fg.. b. a LP; b P; c BP, d ntch at 0 ;
The Secnd-Order Actve Flter: Inductr eplacement
Secnd-Order Actve Flter: Tw-Integratr-Lp Dervatn an alternatve tw-ntegratr-lp bquad n whch all p amp are ued n a ngle-ended ahn. The reultng crcut n b knwn a the Tw-Thma bquad.
Lw-Pa Actve Flter Degn Degn a urth-rder lw-pa Butterwrth lter havng a requency cut- 00 z Che C 0.F C B 5.9k 0.x0 6 00z
Lw-Pa Actve Flter Degn
Lw-Pa Actve Flter Degn
Innte-Gan Multple-Feedback IGMF Negatve Feedback Actve Flter 4 5 3 v 0 v By KCL at V V 0 x, V V V Vx 5 Vx Vx x 3 V x V x 3 4 3 5 Vx V V V Subttute nt gve V V V V V V 3 3 3 3 5 5 5 4 5 4
rearrangng equatn 3, t gve, V 3 V Or n admttance rm: V V 5 3 4 3 4 YY 3 Y Y Y Y Y Y Y 5 3 4 3 4 Flter Value 3 4 5 LP C 3 4 C 5 P C C 3 C 4 5 BP C 3 C 4 5
Band-pa: IGMF Band-Pa Flter K a b T btan the band-pa repne, we let 3 C 3 C 3 4 C 4 C 4 5 5 C3 C C C C 3 4 3 4 5 5 C 4 5 Th lter prttype ha a very lw entvty t cmpnent tlerance when cmpared wth ther prttype. C 3
Smpled Degn IGMF Flter C C 5 5 5 C C C Cmparng wth the band-pa repne P P P Q K It gve, 5 5 Q Q C p p p
Example: IGMF Band Pa Flter T degn a band-pa lter wth 5z and Q 0 O P C 5 5z C 00 nf Q P 5 0 5 9,66, 74 55.4 5 6, 70 00nF 55.4 6,70 - v 00nF n + v Wth mlar analy, we can che the llwng value: C 0 nf,554 and 5 6,700
Butterwrth epne Maxmally Flat n where n the rder Nrmalze t = rad/.6 0.6 3.4 5.4 5.4 3.4.85 0.77.6 3.4.6 3 4 5 5 3 4 4 3 3 B B B B B Butterwrth plynmal Butterwrth plynmal: ˆ B n n ˆ
Secnd Order Butterwrth epne Started rm the lw-pa bquadratc unctn P P P Q K Q K p n 4 4 ecnd rder butterwthplynmal Fr
Secnd rder Butterwrth Flter 4 3 3 4 ' P P P Q K C C K C C K 4 3 3 4 3 4 C C K C C C C Q P Settng = and C = C K K K Q P 3 Nw K = + B / A v n C 4 v + - C 3 B A A B A B P K Q 3 3 Fr Butterwrth repne: Q P A B P Q We have 44. A B We dene Dampng Factr DF a:.44 A B P Q DF