EE247 Lecture 8. Summary Lecture 7

Transcription

1 EE47 Lecture 8 Continuoutime filter deign conideration Monolithic highpa filter Active bandpa filter deign Lowpa to bandpa tranformation Example: 6 th order bandpa filter GmC bandpa filter uing imple diff. pair Variou GmC filter implementation Performance comparion of variou continuoutime filter topologie Introduction to witchedcapacitor filter EECS 47 Lecture 8: Filter 00 H.K. Page Summary Lecture 7 Automatic onchip filter tuning (continued from lat lecture) Continuou tuning (continued) eplica ingle integrator in a feedback loop locked to a reference frequency DC tuning of reitive timing element Periodic digitally aited filter tuning Sytem where filter i followed by ADC & DSP, exiting hardware can be ued to periodically update filter freq. repone EECS 47 Lecture 8: Filter 00 H.K. Page

2 LC Highpa Filter Any LC lowpa and value derived from table can be converted to highpa by: eplacing all C by L and L Norm HP = / C Norm LP eplacing all L by C and C Norm HP = / L Norm LP L HP =L r / C Norm LP, C HP =C r / L Norm LP where L r = r /w r and C r =/( r w r ) L4 V in C C4 L C3 V in L C L3 Lowpa Highpa EECS 47 Lecture 8: Filter 00 H.K. Page 3 Integrator Baed HighPa Filter t Order Converion of imple highpa C filter to integratorbaed type by uing ignal flowgraph technique V in C V o Vo C Vin C EECS 47 Lecture 8: Filter 00 H.K. Page 4

3 t Order Integrator Baed HighPa Filter Signal Flowgraph V Vin VC VC IC C V in C I C V C V I V o Vo V IV SFG IC I V in V C V V o C I C I EECS 47 Lecture 8: Filter 00 H.K. Page 5 V in t Order Integrator Baed HighPa Filter SGF C V o VC V V in C SGF V o V in V o Note: Addition of an integrator in the feedback path High pa frequency haping EECS 47 Lecture 8: Filter 00 H.K. Page 6

4 Addition of Integrator in Feedback Path Let u aume flat gain in forward path (a) Effect of addition of an integrator in the feedback path: V in a Vo a V in af Vo a t /t Vin a / t t / a a int g zero@ DC & wpole a wo t Note: For large forward path gain, a, can implement high pa function with high corner frequency Addition of an integrator in the feedback path DC axw 0 intg Thi technique ued for offet cancellation in ytem where the low frequency content i not important and thu dipoable V o EECS 47 Lecture 8: Filter 00 H.K. Page 7 Bandpa Filter Bandpa filter two cae: Low Q or wideband (Q < 5) Combination of lowpa & highpa Lowpa H jw w Highpa H jw w Bandpa H jw Q<5 w High Q or narrowband (Q > 5) Direct implementation H jw Bandpa Q>5 w EECS 47 Lecture 8: Filter 00 H.K. Page 8

5 NarrowBand Bandpa Filter Direct Implementation Narrowband BP filter Deign baed on lowpa prototype Same table ued for LPF are alo ued for BPF Lowpa Freq. Mak Bandpa Freq. Mak w Q c wc c B B EECS 47 Lecture 8: Filter 00 H.K. Page 9 Lowpa to Bandpa Tranformation Splane Comparion Lowpa pole/zero (plane) Bandpa pole/zero (plane) x x x x x Pole Zero x From: Zverev, Handbook of filter ynthei, Wiley, 967 p.56. EECS 47 Lecture 8: Filter 00 H.K. Page 0

6 Lowpa to Bandpa Tranformation Table Lowpa LC filter tructure & table ued to derive bandpa filter Q Q filter LP BP BP Value C C L L C QC w r r QC w r r From: Zverev, Handbook of filter ynthei, Wiley, 967 p.57. L L C L C C &L are normilzed LP value r QL w QL w r r r EECS 47 Lecture 8: Filter 00 H.K. Page Lowpa to Bandpa Tranformation Example: 3 rd Order LPF 6 th Order BPF Lowpa Bandpa Vin V o L C C3 L Vin C L L C L3 C3 V o L Each capacitor replaced by parallel L& C Each inductor replaced by erie L&C EECS 47 Lecture 8: Filter 00 H.K. Page

7 Lowpa to Bandpa Tranformation Example: 3 rd Order LPF 6 th Order BPF C QC w L QC C QL QL L C L 3 QC3 3 QC w w w 0 w w 0 Vin Where: C, L, C 3 Q w 0 C L L C L3 C3 V o L Normalized lowpa value Bandpa filter quality factor Filter center frequency EECS 47 Lecture 8: Filter 00 H.K. Page 3 Lowpa to Bandpa Tranformation Signal Flowgraph L C V o Vin C L L3 C3 L Voltage & current named for all component Ue KCL & KVL to derive tate pace decription 3 To have BMF in the integrator form Cap. voltage expreed a function of it current V C =f(i C ) Ind. current a a function of it voltage I L =f(v L ) 4 Ue tate pace decription to draw SFG 5 Convert all current node to voltage EECS 47 Lecture 8: Filter 00 H.K. Page 4

8 Signal Flowgraph 6 th Order BPF veru 3 rd Order LPF BPF V in V V 3 V V out * * * L C * L C * C * 3 * L3 * L V V V 3 Vin V V * * * C * C * L 3 L V V V 3 LPF Vo EECS 47 Lecture 8: Filter 00 H.K. Page 5 Signal Flowgraph 6 th Order Bandpa Filter V V in V 3 V V out * * * L C * L C * * L3 C * 3 * L V V V 3 Note: each C & L in the original lowpa prototype replaced by a reonator Subtituting the bandpa L, C,.. by their normalized lowpa equivalent from page 3 The reulting SFG i: EECS 47 Lecture 8: Filter 00 H.K. Page 6

9 Signal Flowgraph 6 th Order Bandpa Filter V in V V 3 V V out * QC w 0 QC QL QC 3 w 0 QLw 0 w 0 QC3 * L V V V 3 Note the integrator different time contant atio of time contant for two integrator in each reonator loop~ Q Typically, require high component ratio Poor matching Deirable to modify SFG o that all integrator have equal time contant for optimum matching. To obtain equal integrator time contant ue node caling EECS 47 Lecture 8: Filter 00 H.K. Page 7 Signal Flowgraph 6 th Order Bandpa Filter V in V QL V /(QL ) QL V 3 V out * QC V /(QC ) QC V QC3 V 3 /(QC 3 ) * L QC3 All integrator timecontant equal To implify implementation chooe L==* EECS 47 Lecture 8: Filter 00 H.K. Page 8

10 Signal Flowgraph 6 th Order Bandpa Filter V in QL QL V out w 0 QC QC3 QC QC3 Let u try to build thi bandpa filter uing the imple GmC tructure EECS 47 Lecture 8: Filter 00 H.K. Page 9 Second Order GmC Filter Uing Simple SourceCouple Pair GmCell Center frequency: M, gm wo C Q function of: M, g Q m g M 3,4 m int g Ue thi tructure for the t and the 3 rd reonator Ue imilar tructure w/o M3, M4 for the nd reonator How to couple the reonator? EECS 47 Lecture 8: Filter 00 H.K. Page 0

11 Coupling of the eonator Additional Set of Input Device V in QL QL V out w 0 QC QC3 QC QC3 Coupling of reonator: Ue additional input ource coupled pair for the highlighted integrator For example, the middle integrator require 3 et of input EECS 47 Lecture 8: Filter 00 H.K. Page Example: Coupling of the eonator Additional Set of Input Device Add one ource couple pair for each additional input Coupling level ratio of device width Diadvantage extra power diipation Coupling Input Main Input coupling V in M main V in M3 C int g M4 M V o EECS 47 Lecture 8: Filter 00 H.K. Page

12 Coupling of the eonator Modify SFG Bidirectional Coupling Path Vin Q CL Q C3L V out w 0 QC QC 3 Q C L C QC3 L Modified ignal flowgraph to have equal coupling between reonator In mot filter cae C = C 3 Example: For a butterworth lowpa filter C = C 3 & L = Aume deired overall bandpa filter Q=0 EECS 47 Lecture 8: Filter 00 H.K. Page 3 Sixth Order Bandpa Filter Signal Flowgraph Vin V out w 0 w 0 Q Q Where for a Butterworth hape Since in thi example Q=0 then: Q 4 EECS 47 Lecture 8: Filter 00 H.K. Page 4

13 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification Vin V out Q Q EECS 47 Lecture 8: Filter 00 H.K. Page 5 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification For narrow band filter (high Q) where frequencie within the paband are cloe to w 0 narrowband approximation can be ued: Within filter paband: w jw The reulting SFG: EECS 47 Lecture 8: Filter 00 H.K. Page 6

14 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification Vin V out Q Q Bidirectional coupling path, can eaily be implemented with coupling capacitor no extra power diipation EECS 47 Lecture 8: Filter 00 H.K. Page 7 Sixth Order GmC Bandpa Filter Utilizing Simple SourceCoupled Pair GmCell Ck Cint gck Cint g Ck / 4 Ck Cint g 3 Paraitic cap. at integrator output, if unaccounted for, will reult in inaccuracy in EECS 47 Lecture 8: Filter 009 H.K. Page 8

15 Sixth Order GmC Bandpa Filter NarrowBand veru Exact Frequency epone Simulation Q=0 egular Filter epone EECS 47 Lecture 8: Filter 009 H.K. Page 9 DC gain (integrator Q) Simplet Form of CMOS GmCell Nonidealitie M, g a m M, g 0 g load L a q Vg Vth M, Small Signal Differential Mode HalfCircuit Where a denote DC gain & q i related to channel length modulation (l)by: q l L Seem no extra pole! EECS 47 Lecture 8: Filter 009 H.K. Page 30

16 CMOS GmCell HighFrequency Pole Cro ection view of a MOS tranitor operating in aturation Ditributed channel reitance & gate capacitance Ditributed nature of gate capacitance & channel reitance reult in infinite no. of highfrequency pole EECS 47 Lecture 8: Filter 009 H.K. Page 3 CMOS GmCell HighFrequency Pole effective P i Pi effective P.5 w M, t High frequency behavior of an MOS tranitor operating in aturation region w M, Vg V M, gm 3 th M, t / 3C WL ox L Ditributed nature of gate capacitance & channel reitance reult in an effective pole at.5 time input device cutoff frequency EECS 47 Lecture 8: Filter 009 H.K. Page 3

17 Simple GmCell Quality Factor a q L Vg Vth M, Vg Vth M, effective 5 P 4 L Q int g. real a wo p i i Note that phae lead aociated with DC gain i inverely prop. to L Phae lag due to highfreq. pole directly prop. to L For a given w o there exit an optimum L which cancel the lead/lag phae error reulting in high integrator Q q V g V th M, 4 w o L int g. Q L 5 Vg Vth M, EECS 47 Lecture 8: Filter 009 H.K. Page 33 Simple GmCell Channel Length for Optimum Integrator Quality Factor L. 5 opt. 4 / 3 qvg Vth M, wo Optimum channel length computed baed on proce parameter (could vary from proce to proce) EECS 47 Lecture 8: Filter 009 H.K. Page 34

18 SourceCoupled Pair CMOS GmCell Tranconductance For a ourcecoupled pair the differential output current (I d ) a a function of the input voltage(v i ): vi v i V g V th 4 V g V th Id I M, M, / Note : For mall v I i d V g V th vi M, I Note : A v d i increae or the vi effective tranconductance decreae g M,M m v V V i i i I I I d d d EECS 47 Lecture 8: Filter 009 H.K. Page 35 SourceCoupled Pair CMOS GmCell Linearity Ideal G m =g m Large ignal G m drop a input voltage increae Give rie to nonlinearity EECS 47 Lecture 8: Filter 009 H.K. Page 36

19 Meaure of Linearity Vout Vin Vin Vin amplitude3 rd harmonicdit. comp. HD3 amplitude fundamental 3 Vin 4... Vin Vout w w w 3w w amplitude3 rd order IM comp. IM 3 amplitude fundamental Vin Vin... w Vin Vout w w w w w w w w w EECS 47 Lecture 8: Filter 009 H.K. Page 37 SourceCoupled Pair GmCell Linearity vi v i I I () V g V th 4 V g V th d M, M, 5 3 d i i 3 i I a v a v a v... Serie expanion ued in ( ) I a & a 0 V g V thm, I a 3 & a V g V th a I 8 V g V th M, 5 M, & a 0 6 / EECS 47 Lecture 8: Filter 009 H.K. Page 38

20 Linearity of the SourceCoupled Pair CMOS GmCell 3a3 5a5 4 IM3 vˆi v ˆi... 4a 8a Subtituting for a,a, vˆi 5 vˆi IM VGS Vth 04 VGS Vth ˆv i max 4 VGS Vth IM3 3 rm 3 GS th in IM % & V V V Vˆ 30mV Note that max. ignal handling capability function of gateoverdrive voltage EECS 47 Lecture 8: Filter 009 H.K. Page 39 Dynamic ange for SourceCoupled Pair Baed Filter rm IM3 % & VGS Vth V Vin 30mV Minimum detectable ignal determined by total noie voltage It can be hown for the 6 th order Butterworth bandpa filter fundamental noie contribution i given by: vo 3 kt Q C int g Aumin g Q 0 Cint g 5 pf rm vnoie 60V rm ince vmax 30mV 3 Dynamic ange 0log 30x0 6 60x0 63dB EECS 47 Lecture 8: Filter 00 H.K. Page 40

21 Simplet Form of CMOS Gm Cell Diadvantage Max. ignal handling capability function of gateoverdrive IM3 VGS Vth Critical freq. i alo a function of gateoverdrive M, gm wo Cint g W ince g m C ox V g V th L then wo Vg Vth Filter tuning affect max. ignal handling capability! EECS 47 Lecture 8: Filter 009 H.K. Page 4 Simplet Form of CMOS Gm Cell emoving Dependence of Maximum Signal Handling Capability on Tuning Can overcome problem of max. ignal handling capability being a function of tuning by providing tuning through : Coare tuning via witching in/out binaryweighted crocoupled pair Try to keep gate overdrive voltage contant Fine tuning through varying current ource Dynamic range dependence on tuning removed (to t order) ef:.catello,i.bietti, F. Svelto, HighFrequency Analog Filter in Deep Submicron Technology, International Solid State Circuit Conference, pp 7475, 999. EECS 47 Lecture 8: Filter 009 H.K. Page 4

22 Simplet Form of CMOS GmCell Pro Capable of very high frequency performance (highet?) Simple deign Con Tuning affect max. ignal handling capability (can overcome) Limited linearity (poible to improve) Tuning affect power diipation ef: H. Khorramabadi and P.. Gray, High Frequency CMOS continuoutime filter, IEEE Journal of SolidState Circuit, Vol.SC9, No. 6, pp , Dec EECS 47 Lecture 8: Filter 00 H.K. Page 43 GmCell SourceCoupled Pair with Degeneration C W I ox d Vg Vth Vd V L d Id W gd C ox Vg Vth Vd L geff M 3 M, g d gm M, M 3 for gm g d M3 geff g d Vd mall M3 operating in triode mode ource degeneration determine overall gm Provide tuning through varying Vc (DC voltage ource) EECS 47 Lecture 8: Filter 00 H.K. Page 44

23 GmCell SourceCoupled Pair with Degeneration Pro Moderate linearity Continuou tuning provided by varying Vc Tuning doe not affect power diipation Con Extra pole aociated with the ource of M,,3 Low frequency application only ef: Y. Tividi, Z. Czarnul and S.C. Fang, MOS tranconductor and integrator with high linearity, Electronic Letter, vol., pp. 4546, Feb. 7, 986 EECS 47 Lecture 8: Filter 00 H.K. Page 45 MOSFET operating in triode mode (M): BiCMOS GmCell Example C W I ox d Vg Vth Vd V L d M Id W gm C ox V V L d g Note that if V d i kept contant g m tay contant Linearity performance keep gm contant a Vin varie function of how contant V M d can be held Need to minimize node X V M B A x x gm gm Vin Since for a given current, g m of BJT i larger compared to MOS preferable to ue BJT Extra pole at node X could limit max. freq. V b VcmVin I Iout B X M Varying V b change V d M Change g m M adjutable overall tage g m EECS 47 Lecture 8: Filter 00 H.K. Page 46

24 BJT replaced by a MOS tranitor with booted g m Alternative Fully CMOS GmCell Example Lower frequency of operation compared to the BiCMOS verion due to more paraitic capacitance at node A & B A B EECS 47 Lecture 8: Filter 00 H.K. Page 47 BiCMOS GmC Integrator Differential need commonmode feedback circuit Frequency tuned by varying Vb Deign tradeoff: Extra pole at the input device drain junction Input device have to be mall to minimize paraitic pole eult in high inputreferred offet voltage could drive circuit into nonlinear region Small device high /f noie Cintg/ Cintg/ Vout EECS 47 Lecture 8: Filter 00 H.K. Page 48

25 7 th Order Elliptic GmC LPF For CDMA X Baeband Application Vin A CB A B A B A B A B B A A B Vout GmCell in previou page ued to build a 7th order elliptic filter for CDMA baeband application (650kHz corner frequency) Inband dynamic range of <50dB achieved EECS 47 Lecture 8: Filter 00 H.K. Page 49 Comparion of 7 th Order GmC veru OpampC LPF GmC filter require 4 time le intg. cap. area compared to OpampC For lownoie application where filter area i dominated by C, could make a ignificant difference in the total area OpampC linearity uperior compared to GmC Power diipation tend to be lower for GmC ince OTA load i C and thu no need for buffering V in A Vin B C A B A GmC Filter A A OpampC Filter A B B B B A B V o Vout EECS 47 Lecture 8: Filter 00 H.K. Page 50

26 BiCMOS GmOTAC Integrator Ued to build filter for dikdrive application Since high frequency of operation, timecontant enitivity to paraitic cap ignificant. Opamp ued M & M3 added provide phae lead to compenate for phae lag due to amp extra pole ef: C. Laber and P.Gray, A 0MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive ead Channel, IEEE Journal of Solid State Circuit, Vol. 8, pp , April 993. EECS 47 Lecture 8: Filter 00 H.K. Page 5 6th Order BiCMOS Continuoutime Filter & Second Order Equalizer for Dik Drive ead Channel GmCopamp of the previou page ued to build a 6 th order filter for Dik Drive Filter conit of cacade of 3 biquad with max. Q of each Tuning DC tuning of gmcell (Lect. 7 page 3) trimming of C Performance in the order of 40dB SND achieved for up to 0MHz corner frequency ef: C. Laber and P.Gray, A 0MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive ead Channel, IEEE Journal of Solid State Circuit, Vol. 8, pp , April 993. EECS 47 Lecture 8: Filter 00 H.K. Page 5

27 GmCell SourceCoupled Pair with Degeneration Gmcell intended for low Q dik drive filter M7,8 operating in triode mode provide ource degeneration for M, determine the overall g m of the cell ef: I.Mehr and D..Welland, "A CMOS ContinuouTime GmC Filter for PML ead Channel Application at 50 Mb/ and Beyond", IEEE Journal of SolidState Circuit, April 997, Vol.3, No.4, pp EECS 47 Lecture 8: Filter 00 H.K. Page 53 GmCell SourceCoupled Pair with Degeneration Feedback provided by M5,6 maintain the gateource voltage of M, contant by forcing their current to be contant help deliver Vin acro M7,8 with good linearity Current mirrored to the output via M9,0 with a factor of k overall gm caled by k Performance level of about 50dB SND at f corner of 5MHz achieved EECS 47 Lecture 8: Filter 00 H.K. Page 54

28 Need higher upply voltage compared to the previou deign ince quite a few device are tacked vertically M, triode mode Q, hold V d of M, contant Current ID ued to tune filter critical frequency by varying V d of M, and thu controlling gm of M, M3, M4 operate in triode mode and added to provide commonmode feedback BiCMOS GmC Integrator ef:. Alini, A. Bachirotto, and. Catello, Tunable BiCMOS ContinuouTime Filter for High Frequency Application, IEEE Journal of Solid State Circuit, Vol. 7, No., pp , Dec. 99. EECS 47 Lecture 8: Filter 00 H.K. Page 55 M5 & M6 configured a capacitor added to compenate for HP zero due to Cgd of M, (move it to LHP) ize of M5,6 /3 of M, BiCMOS GmC Integrator /C GS M M5 M6 /3C GS M M M ef:. Alini, A. Bachirotto, and. Catello, Tunable BiCMOS ContinuouTime Filter for High Frequency Application, IEEE Journal of Solid State Circuit, Vol. 7, No., pp , Dec. 99. EECS 47 Lecture 8: Filter 00 H.K. Page 56

29 BiCMOS GmC Filter For DikDrive Application Uing the integrator hown in the previou page Biquad filter for dik drive gm=gm=gm4=gm3 Q= Tunable from 8MHz to 3MHz ef:. Alini, A. Bachirotto, and. Catello, Tunable BiCMOS ContinuouTime Filter for High Frequency Application, IEEE Journal of Solid State Circuit, Vol. 7, No., pp , Dec. 99. EECS 47 Lecture 8: Filter 00 H.K. Page 57 Summary ContinuouTime Filter Opamp C filter Good linearity High dynamic range (6090dB) Only dicrete tuning poible Medium uable ignal bandwidth (<0MHz) Opamp MOSFETC Linearity compromied (typical dynamic range 4060dB) Continuou tuning poible Low uable ignal bandwidth (<5MHz) Opamp MOSFETC Improved linearity compared to Opamp MOSFETC (D dB) Continuou tuning poible Low uable ignal bandwidth (<5MHz) GmC Highet frequency performance at leat an order of magnitude higher compared to other integratorbaed active filter (<00MHz) Typically, dynamic range not a high a Opamp C but better than Opamp MOSFETC (4070dB) EECS 47 Lecture 8: Filter 00 H.K. Page 58

30 SwitchedCapacitor Filter S.C. filter are ampleddata type circuit operating with continuou ignal amplitude & quantized time Firt product including witchedcapacitor filter Intel 9 voiceband CODEC Standalone filter IC: LMF00 from National Semi. Dual S.C. biquad with LP, HP, BP output Other than filter, S.C. circuit are ued in overampled data converter Pioneering work on S.C. filter technology wa motly performed at UC Berkeley EECS 47 Lecture 8: Filter 00 H.K. Page 59 SwitchedCapacitor Filter Emulating reitor via witchedcapacitor network Switchedcapacitor t order filter Switchcapacitor filter conideration: Iue of aliaing and how to prevent aliaing Tradeoff in choice of ampling rate Effect of ample and hold Switchedcapacitor filter electronic noie EECS 47 Lecture 8: Filter 00 H.K. Page 60

31 SwitchedCapacitor eitor Capacitor C i the witched capacitor Nonoverlapping clock and control witche S and S, repectively v IN S C S v OUT v IN i ampled at the falling edge of Sampling frequency f S Next, rie and the voltage acro C i tranferred to v OUT T=/f EECS 47 Lecture 8: Filter 00 H.K. Page 6 SwitchedCapacitor eitor Waveform Continuou Time Signal Vin time Clock VC Vout (auming Vout) EECS 47 Lecture 8: Filter 00 H.K. Page 6

32 SwitchedCapacitor eitor Why doe thi behave a a reitor? Charge tranferred from v IN to v OUT during each clock cycle i: Q = C(v IN v OUT ) v IN S S C v OUT Average current flowing from v IN to v OUT i: i=q/t = Q. f Subtituting for Q: i =f S C(v IN v OUT ) T=/f EECS 47 Lecture 8: Filter 00 H.K. Page 63 SwitchedCapacitor eitor i = f S C(v IN v OUT ) With the current through the witchedcapacitor reitor proportional to the voltage acro it, the equivalent witched capacitor reitance i: V eq IN V i OUT fc v IN S S C v OUT Example: f 00KHz,C 0.pF eq 00Mega Note: Can build large timecontant in mall area T=/f EECS 47 Lecture 8: Filter 00 H.K. Page 64

33 SwitchedCapacitor Filter EQ Let build a witched capacitor filter v IN v OUT Start with a imple C LPF C eplace the phyical reitor by an equivalent witchedcapacitor reitor 3dB bandwidth: v IN v OUT C w f 3dB C eq C C f f 3dB C S S C C EECS 47 Lecture 8: Filter 00 H.K. Page 65 SwitchedCapacitor Filter Advantage veru ContinuouTime Filter eq V in S S V out V in V out C C C f C C 3dB f Corner freq. proportional to: Sytem clock (accurate to few ppm) C ratio accurate < 0.% f3db eq C Corner freq. proportional to: Abolute value of & C Poor accuracy 0 to 50% Main advantage of SC filter inherent critical frequency accuracy EECS 47 Lecture 8: Filter 00 H.K. Page 66