Continuous-Time Filters

Transcription

1 tuute Flter.0 Operatal Tracductace Aplfer (OTA Z Z ut (a (b (c (d Fgure. deal all gal equvalet crcut f Sgle eded OTA ad Fully dfferetal OTA pleetat Ug Sgle eded OTA. Fgure (a h the ybl f gle eded OTA. t deal equvalet crcut h Fgure (b. t perat gve by: v (v v Z Z ut

2 That, t utput pedace hch 0 fr deal pap. A fully dfferetal OTA h Fgure (c ca be pleeted ug t gle eded OTA th tce the tracductace. t cect h Fgure (d. The equvalecy ca be h a fll: ( ( (. OTA Sple Buldg Blck rcut R R Z (a (b (c Z Z Z L (d (e Z L Fgure OTA ple buldg blck Fgure (a h a ple vltage ptve ga aplfer. t ga derved a fll: R R A R Z, ce the put pedace f OTA, ad Z R, ce the utput pedace f OTA. Fgure (b the ae a Fgure (a except fr the put ver reultg egatve ga. Fgure (c,

3 A ; ce Z Z Fgure (d the ae a Fgure (a th a lad R/. A R A Fgure (a, the put ad utput pedace f Fgure (d are: Z ; Z Fgure (e, Z Z L L A Z L ZL Z Z L That, the put pedace the recprcal f the lad pedace. f the lad pedace capactve, the the put pedace ductve. Th crcut a pedace cverter. Sce the utput pedace f OTA ad the put pedace f OTA are bth, the crcut utput pedace : Z Z L

4 Thee are uarzed the fllg table. Table : OTA Sple Buldg Blck rcut. rcut Type Av Z Z ltage aplfer th R R ptve ga, Fg (a ltage aplfer th R R egatve ga, Fg (b OTA Retace, Fg (c / / ltage aplfer ug / / OTA retace, Fg (d OTA pedace cverter, Fg (e Z L /( Z L Z L. Frt Order Flter Buldg Blck rcut (b LP( (c HP( (d TF( Ftype LP 0 HP 0 (e (f Fgure. Frt Order Flter SgleEded OTA Buldg Blck. 4

5 Fgure h the frt rder flter buldg blck. The t lpa flter pleetat Fgure (a ad (b ll be h t be the ae. Al, ly Fgure (a ca be cverted t fully dfferetal ta pleetat h Fgure 4(a. Fgure (a, / / ( Fgure (b, ( / / That, Fgure (a ad (b pleet the ae trafer fuct. Fgure (c, ( / Fgure (d, 0 a a ] /( [ ] /( [ ] /( [ ( ( ( 5

6 Table : OTA Frt Order Flter. rcut Type Trafer Fuct W Frt rder Lpa, Fg (a,(b / / / Frt rder Hghpa, Fg (c / / eeral Frt rder Fg (d [ /( ] [ /( ] [ /( ] /( A uveral frt rder flter ca be pleeted a h Fgure (e. The uveral flter ha fur teral,,, ad. The lpa flter ca be elected by cectg the put t ad t grud. The hghpa flter elected by cectg the put t ad t grud. Thee are uarzed Fgure (f. ' " (a (b (c Fgure 4. Dfferetal OTA pleetat f FrtOrder Flter. 6

7 Fgure 4 h the fully dfferetal OTA pleetat f the frt rder flter. t h the uber ad value f capactr dubled. equetly, t ll cue re LS real etate. Hever, a fully dfferetal crcut pleetat have the advatage f better e uty ad dtrt prperte. The equvalete f the t pleetat ll be llutrated fr the frt rder lpa ad hghpa flter. That, the trafer fuct f Fgure 4(a ll be h t be detcal t that f Fgure (a r (b. Fgure 4(a: / / ( ( ( ( ( " ' " ' ( ( The hgh pa flter h Fgure 4(b th e fully dfferetal ta pleetat ll be h t have the ae trafer fuct a the gleeded ta Fgure (c. The dervat fll: / ] [ ( ] ( [( Addg the abve t equat ad equatg th the frt equat, ( ( ( The geeral frt rder flter h Fgure 4(c ca larly be derved. Nte that lpa flter eed t fully dfferetal ta, hle fr hghpa flter requre ly e. The calculat depedet f hether ug lpa r hghpa trafer fuct. The lpa flter trafer fuct ll be ued fr llutrat. The trafer fuct t be pleeted gve by: L( 7

8 all the ubequet exaple, t ll aued that the value f 6.8*0 5 crrepdg t a frequecy f 00kHz. The capactace value fr a gve 85.44u btaed a fll: 85.44E pF 6.8E 5 The geeral flter trafer fuct t be pleeted ha a ple at fp00khz, ad zer at fz00khz ad th D ga f 0.5. That, 0.5( π e 5 TF( ( πe 5 (0.5 πe 5 ( πe 5 a a [ /( ] [ /( ] [ /( ] a a a 0 Aue a a a 85.44e 6 ( a ( pF πe 5 a a a 0 a ( gve (67.99pF 67.99pF 0.5 a e 6 (πe 5 πe e 6 8

9 . Frt Order Flter Sulat Frt Order Lpa Flter Trafer Fuct *Fleae "lp.cr" *Frt rder lpa flter f00k.param 6.8e5 0 D 0 A R 0 E0 E 0 LAPLAE {(}{/(} Rut 0 k * Aaly.A DE 0 Hz 00MegHz.PROBE.END Frt Order Hghpa Flter Trafer Fuct *Fleae "hp.cr" *Frt rder lpa flter f00k.param 6.8e5 0 D 0 A R 0 E0 E 0 LAPLAE {(}{/(} Rut 0 k * Aaly.A DE 0 Hz 00MegHz.PROBE.END eeral Frt Order Flter Trafer Fuct *Fleae "ge.cr" *eeral frt rder flter p00khz, z00khz.param p6.8e5 *.PARAM z*p.param z.5664e5 0 D 0 A R 0 E0 E 0 LAPLAE {(}{0.5*(z/(p} Rut 0 k * Aaly.A DE 0 Hz 00MegHz.PROBE.END 9

10 deal Frt Order Lpa Flter Repe deal Frt Order Hghpa Flter Repe 0

11 deal eeral Frt Order Flter Repe Uveral Frt Order Flter Sgleeded OTA pleetat *Fleae "uv_.cr", ee Fgure e *Uveral Frt rder flter. f00k *Ug Sgleeded OTA 0 D 0 A *LP *Xflt 0 SFLT *HP Xflt 0 SFLT R 0 E0.SUBKT SFLT v v v0.param 5.98pF Xta v v0 v0 WSOTA v0 v {} 0.SUBKT WSOTA ut 0 ut 85.44U * Aaly.A DE 00 Hz 00MegHz.PROBE.END eeral Frt Order Flter Sgleeded OTA pleetat *Fleae "ge_.cr", ee Fgure d *eeral Frt rder flter. p00khz, z00khz *Ug Sgle Eded OTA

12 .PARAM 67.99pF 0 D 0 A Xta 0 WSOTA Xta 0 WSOTA 0 {} {} R 0 E0.SUBKT WSOTA ut 0 ut 85.44U * Aaly.A DE 00 Hz 00MegHz.PROBE.END Frt Order Lpa Flter Repe

13 Frt Order Hghpa Flter Repe eeral Frt Order Flter Repe Fully Dfferetal OTA pleetat f Frt Order Flter Uveral pleetat t pble ug fully dfferetal OTA. Lpa flter requre t fully dfferetal OTA, hle hghpa flter ly eed e. Fully Dfferetal OTA pleetat f Frt Order Lpa Flter

14 *Fleae "lp_d.cr", ee Fgure 4a *Frt rder flter f00k *Ug fully dfferetal OTA D 0 A.PARAM 5.98pF Xta 4 DFFOTA Xta 4 4 DFFOTA 0 {*} {*} 0 R 0 E0 R 0 E0 R 0 E0 R4 4 0 E0 * Fully Dfferetal OTA pleetat * by deft.subkt DFFOTA ut ut 0 ut 85.44U 0 ut 85.44U * Aaly.A DE 00 Hz 00MegHz.PROBE.END Fully Dfferetal OTA pleetat f Frt Order Hghpa Flter *Fleae "hp_d.cr", ee Fgure 4b *Frt rder flter. f00k *Ug Fully Dfferetal OTA D 0 A.PARAM 5.98pF Xta 4 4 DFFOTA {*} 0 4 {*} 0 R 0 E0 R 0 E0 R 0 E0 R4 4 0 E0 * Fully Dfferetal OTA pleetat * by deft.subkt DFFOTA ut ut 0 ut 85.44U 0 ut 85.44U * Aaly.A DE 00 Hz 00MegHz.PROBE.END Fully Dfferetal OTA pleetat f eeral Frt Order Flter *Fleae "ge_d.cr", ee Fgure 4c *Frt rder flter fp00khz, fz00khz *Ug fully dfferetal OTA 4

15 D 0 A.PARAM 67.99pF Xta 4 DFFOTA Xta 4 4 DFFOTA 0 {*} {*} 0 {*} 0 4 {*} 0 R 0 E0 R 0 E0 R 0 E0 R4 4 0 E0 * Fully Dfferetal OTA pleetat * by deft.subkt DFFOTA ut ut 0 ut 85.44U 0 ut 85.44U * Aaly.A DE 00 Hz 00MegHz.PROBE.END Frt Order Lpa Flter Repe 5

16 Frt Order Hghpa Flter Repe eeral Frt Order Flter Repe 6

17 4. Secd Order Flter Buldg Blck rcut (a LP( (b HP( (c BP( (d BR( Fgure 5. Secd Order Flter pleetat th fxed Q ad OTA each. There are t ecd rder flter buldg blck. Oe requrg t OTA ad the ther OTA. The elect deped hether a adjutable Q requred r t. 7

18 Fxed Q pleetat Fgure 5 h the ecd rder flter pleetat ug OTA. The pleetat ha a adjutable Q, ce the capactve cpet had bee detered. The trafer fuct dervat ll be detrated fr the lpa crcut. Fgure 5(a: ( ( ( ( parg the trafer fuct th the tadard lpa trafer fuct gve Table. The ad Q are btaed a fll: ; f Q Slvg fr Q, Q Nte that fr a gve value f ad, Q fxed but ca be adjuted by chagg. The expre fr the ther crcut ca be derved a lar ay. The reult are uarzed Table 4. 8

19 Table. Secd Order Flter Trafer Fuct. rcut Type Trafer Fuct Lpa Hghpa Badpa Badreject ( /Q ( /Q ( /Q ( /Q ( /Q Table 4. Secd Order OTA pleetat Flter Paraeter. rcut Type Trafer Fuct * Q Lpa Adjutable ( / Q Fxed, Fg 5(a ( / ( / Hghpa Adjutable Q Fxed, Fg 5(b ( / ( / Badpa Adjutable Q Fxed, Fg 5(c ( ( / / ( / Badreject Adjutable Q Fxed, Fg 5(d ( ( / ( / / * Aue The capactace ca be cputed fr ay f the fur trafer fuct. The lpa trafer fuct ll be ued fr th purpe. The trafer fuct t be pleeted : L( 0.680* * ( /Q 9

20 The capactace are cputed a fll: 0.0E.680(5.98E Q Q 84.04E 5.98E.680 Q 5.98pF 5.98E 5 6.8E E Q Q Q * 0.680* Q 0.680* Q 0

21 Adjutable Q pleetat (a LP( (b HP( (c BP( (d BR( Fgure 6. Secd Order Flter pleetat th adjutable Q ad OTA each. Fgure 6 h the ecd rder flter pleetat ug OTA. The pleetat ha adjutable Q, t value detered by the thrd OTA. The trafer fuct dervat ll be detrated fr the lpa crcut. Fgure 6(a:

22 ( ( ( [ ] ( The ad Q ca be derved by cparg th trafer fuct th the tadard lpa trafer fuct gve Table. Q ; f ad Slvg fr Q Q NOTE fr a gve capactr value, Q ad ca be adjuted depedetly f each ther. Q ca be adjuted by ad by. The expre fr the ther crcut Fgure 6 ca larly be derved. The reult are uarzed Table.

23 Table 5. Secd Order OTA pleetat Flter Paraeter. rcut Type Trafer Fuct * Q Lpa Adjutable ( / Q Adjutable, ( / ( / Fg 6(a Hghpa Adjutable Q Adjutable, ( / ( / Fg 6(b Badpa Adjutable ( / Q Adjutable, ( / ( / Fg 6(c Badreject ( Adjutable / Q Adjutable, ( / ( / Fg 6(d * Aue ; The OTA pleetat ll tllutrated ug the ae trafer fuct L( a the OTA pleetat. Q 85.44E pF 6.8E * Q * 0.680* 85.44E 6 5.8E 6 Q.680 A the frt rder flter, uveral flter pleetat f ecd rder flter Fgure 5 ad fgure 6 are h Fgure 7(a ad 7(c repectvely. The crrepdg prgrag are h Fgure 7(b ad 7(d repectvely.

24 (a Ftype LP 0 0 HP 0 0 BP 0 0 BR 0 (b (c Ftype LP 0 0 HP 0 0 BP 0 0 BR 0 Fgure 7. Uveral Secd Order Flter pleetat. (d 4

25 4. Secd Order Flter Sulat Secd Order Lpa Flter Trafer Fuct *Fleae "LP.cr" *Secd rder lpa flter.param 6.8e5 0 D 0 A * thrd bquad R 0 E0 E 0 LAPLAE {(}{(*/(*0.680***} *utput Rut 0 k * Aaly.A DE 00 Hz 00MegHz.PROBE.END Secd Order Hghpa Flter Trafer Fuct *Fleae "HP.cr" *Secd rder hghpa flter.param 6.8e5 0 D 0 A * thrd bquad R 0 E0 E 0 LAPLAE {(}{(*/(*0.680***} *utput Rut 0 k * Aaly.A DE 00 Hz 00MegHz.PROBE.END Secd Order Badpa Flter Trafer Fuct *Fleae"BP.cr" *Secd rder badpa flter.param 6.8e5 0 D 0 A * thrd bquad R 0 E0 E 0 LAPLAE {(}{(0.680**/(*0.680***} *utput Rut 0 k * Aaly.A DE 00 Hz 00MegHz.PROBE.END Secd Order Badreject Flter Trafer Fuct *Fleae"BR.cr" 5

26 *Secd rder badreject flter.param 6.8e5 0 D 0 A * thrd bquad R 0 E0 E 0 LAPLAE {(}{(**/(*0.680***} *utput Rut 0 k * Aaly.A DE 00 Hz 00MegHz.PROBE.END deal Secd Order Lpa Flter Repe 6

27 deal Secd Order Hghpa Flter Repe deal Secd Order Badpa Flter Repe 7

28 deal Secd Order Badreject Repe Uveral Secd Order Flter Ug deal OTA per Flter *Fleae "uv_.cr", ee Fgure 7a *Bquad d rder flter. f00k 0 D 0 A *LP *Xflt 0 0 SFLT *HP *Xflt 0 0 SFLT *BP *Xflt 0 0 SFLT *BR Xflt 0 SFLT R 0 E0.SUBKT SFLT v v v v0.param 5.98pF.PARAM Q.680 Xta v v0 WSOTA Xta v0 v0 WSOTA v {/Q} 0 v0 v {Q*} 0 R 0 E0.SUBKT WSOTA ut 0 ut 85.44U 8

29 * Aaly.A DE 00 Hz 00MegHz.PROBE.END Uveral Secd Order Flter Ug deal OTA per Flter *Fleae "uv_.cr", ee Fgure 7c *Bquad d rder flter. f00k 0 D 0 A *LP *Xflt 0 0 SFLT *HP *Xflt 0 0 SFLT *BP *Xflt 0 0 SFLT *BR Xflt 0 SFLT R 0 E0.SUBKT SFLT v v v v0.param 5.98pF Xta v v0 WSOTA Xta 0 v0 WSOTA Xta v v0 v0 WSOTA 0 {} 0 v0 v {} 0 R 0 E0.SUBKT WSOTA ut 0 ut 85.44U.SUBKT WSOTA ut 0 ut 5.8U * Aaly.A DE 00 Hz 00MegHz.PROBE.END 9

30 Secd Order Lpa Flter Repe Secd Order Hghpa Flter Repe 0

31 Secd Order Badpa Repe Secd Order Badreject Repe

32 5. Butterrth Flter pleetat Table 6. Butterrth D( (here H(K/D(; K N D( 4 5 ( ( ( ( ( ( (.680 The ffth rder ralzed Butterrth l pa flter btaed fr the abve table: B5( ( (.680 (.680 T cale the trafer fuct t the dered frequecy f perat, the trafrat / appled t the ralzed trafrat. B5(.680* * 0.680* * T(T(T( Th a cacade deg baed the ple tade tercect N frtrder ad bquad tage. f the tage are teractg, the verall trafer fuct the prduct f the dvdual tage trafer fuct. Nteractg ea that at ay tage, ay the th tage, the utput pedace Zut( t laded by the put pedace Z( f the ucceedg tage,.e., Zut( << Z(. Fr p apbaed actve flter, th heretly atfed, ce p ap ha hgh put pedace ad l utput pedace. But OTA baed actve flter, due t hgh put ad utput pedace requre tertage bufferg. Thee buffer are uually realzed by utyga urce fller tage. addt, utput bufferg requred t drve exteral lad. The capactace ad tracductace f each OTA ll be cputed fr each cacded flter. Fr T(: 85.44E pF 6.8E 5 Fr T(:

33 Q 85.44E pF 6.8E 5.680* Q *.680* 85.44E 6 8.5E 6 Q 0.68 Fr T(: Q 85.44E pF 6.8E * Q * 0.680* 85.44E 6 5.8E 6 Q Ffth Order Butterrth Flter Sulat Ffth Order Butterrth Flter Trafer Fuct *Fleae "butter5.cr" *Ffth rder butterrth flter, f00k.param 6.8e5 0 D 0 A *frt bquad R 0 E0 E 0 LAPLAE {(} {(/(} * ecd bquad R 0 E0 E 0 LAPLAE {(}{(*/(*.680***} * thrd bquad R 0 E0 E 4 0 LAPLAE {(}{(*/(*0.680***} *utput

34 Rut 4 0 k * Aaly.A DE 00 Hz 00MegHz.PROBE.END Ffth Order Butterrth Flter pleetat Ug deal OTA per Flter ( (0 SFLT ( ( (0 SFLT (4 (5 (0 SFLT (6 *Fleae "but5_.cr" *Butterrth 5th rder flter. f00k 0 D 0 A Xflt 0 SFLT Xbuf BUF Xflt SFLT Xbuf 4 5 BUF Xflt SFLT R 0 E0 R 0 E0 R4 4 0 E0 R5 5 0 E0 R6 6 0 E0.SUBKT SFLT v v v0.param 5.98pF Xta v v0 v0 WSOTA v0 v {}.SUBKT SFLT v v v v0.param 5.98pF Xta v v0 WSOTA Xta 0 v0 WSOTA Xta v v0 v0 WSOTA 0 {} 0 v0 v {} 0 R 0 E0.SUBKT SFLT v v v v0.param 5.98pF Xta v v0 WSOTA Xta 0 v0 WSOTA Xta v v0 v0 WSOTA 0 {} 0 v0 v {} 0 R 0 E0.SUBKT WSOTA ut 0 ut 85.44U 4

35 .SUBKT WSOTA ut 0 ut 8.5U.SUBKT WSOTA ut 0 ut 5.8U.SUBKT BUF ut E ut 0 0 * Aaly.A DE 00 Hz 00MegHz.PROBE.END deal Ffth Order Butterrth Flter Repe ( DB deal Ffth Order Butterrth Flter Repe ( 5

36 pleeted Ffth Order Butterrth Repe ( DB pleeted Ffth Order Butterrth Repe ( 6

37 6. hebyhev Flter pleetat hebyhec D( fr db rpple (Where H(K/D(; K elected t yeld uty D ga N D( ( 04947( ( ( ( ( ( The ffth rder ralzed hebyhev l pa flter btaed fr the abve table: h5( ( ( (0.8949(0.988( ( T cale the trafer fuct t the dered frequecy f perat, the trafrat / appled t the ralzed trafrat * 0.988* 0.49* h5( * * * 0.988* * * 0.49* T(T(T( The capactace ad tracductace f each OTA ll be cputed fr each cacded flter. Fr T(: * Fr T(: 85.44E * 6.8E 469.7pF 5 7

38 Q * * 85.44E * 6.8E * 6.8pF * Q * * 85.44E 6 5.7E 6 Q 5.56 Fr T(: Q 0.49* 0.655* 85.44E * 6.8E * 07.5pF * Q * * 85.44E 6 6.0E 6 Q.4 6. Ffth Order hebyhev Flter Sulat Ffth Order hebyhev Flter Trafer Fuct *Fleae cheby5.cr *heby5 Ffth rder chebyhev flter *Frt rder flter.param 6.8e5 0 D 0 A *frt bquad R 0 E0 E 0 LAPLAE {(} {(0.8949*/(0.8949*} * ecd bquad R 0 E0 E 0 LAPLAE {(}{(0.49**/(*0.4684**0.49**} * thrd bquad 8

39 R 0 E0 E 4 0 LAPLAE {(}{(0.988**/(*0.789**0.988**} *utput Rut 4 0 k * Aaly.A DE 00 Hz 00MHz.PROBE.END Ffth Order hebyhev Flter pleetat Ug deal OTA per Flter *Fleae "chb5_.cr" *hebyhev 5th rder flter. f00k 0 D 0 A Xflt 0 SFLT Xflt 0 0 SFLT Xflt SFLT R 0 E0 R 0 E0 R4 4 0 E0.SUBKT SFLT v v v0.param 469.7pF Xta v v0 v0 WSOTA v0 v {}.SUBKT SFLT v v v v0.param 6.8pF Xta v v0 WSOTA Xta 0 v0 WSOTA Xta v v0 v0 WSOTA 0 {} 0 v0 v {} 0 R 0 E0.SUBKT SFLT v v v v0.param 07.5pF Xta v v0 WSOTA Xta 0 v0 WSOTA Xta v v0 v0 WSOTA 0 {} 0 v0 v {} 0 R 0 E0.SUBKT WSOTA ut 0 ut 85.44U.SUBKT WSOTA ut 0 ut 5.7U.SUBKT WSOTA ut 0 ut 6.0U 9

40 * Aaly.A DE 00 Hz 00MegHz.PROBE.END deal Ffth Order hebyhev Flter Repe ( DB deal Ffth Order hebyhev Flter Repe ( 40

41 pleeted Ffth Order hebyhev Flter Repe ( DB 4

42 pleeted Ffth Order hebyhev Flter Repe ( 7. eeral Bquad pleetat f a eeral Secd Degree Trafer Fuct Fgure 8. eeral Secd Order Flter pleetat. Fgure 8 h the gleeded OTA pleetat f geeral ecd rder flter. The trafer fuct derved a fll: 4

43 ( 4 4 ( ( Q a a a ( ( ( t ll be h that geeral pleetat f 5 OTA reduce t r OTA fr the tadard flter uch a lpa flter. Frt t ll be h fr lpa trafer fuct geeral pleetat reduce t 4 OTA. parg the t trafer fuct, Q ( ( Equatg the ceffcet,

44 pe 0 That ea that bth capactr ad 5 ca be deleted, reultg the crcut h Fgure 9(a. The 4 OTA pleetat ca be reduced t OTA f 4. Th h bel: 4 4 (a (b (c Fgure 9. eeral Bquad Lpa Flter Trafrat: (a 4 OTA, (b OTA, ad (c OTA. 44

45 ( ; 4 That, ad 4 ca be cbed a h Fgure 9(b. ( The OTA ca be reduced t OTA f. Th h a fll: ( ; That, ad ca be cbed a h Fgure 9(c. ( 4 5 Fgure 0. Dfferetal OTA pleetat f eeral ecdrder flter. (b 45