EE247 Lecture 10. EECS 247 Lecture 10 Switched-Capacitor Filters 2010 H. K. Page 1. DDI Switched-Capacitor Integrator 1 2 C I. Vin. Cs 1.

Transcription

1 EE247 Lecture 0 Switched-capacitor filter (continued) DDI integrator LDI integrator Effect of paraitic capacitance Bottom-plate integrator topology Switched-capacitor reonator Bandpa S.. filter Lowpa S.. filter Switched-capacitor filter deign conideration Termination implementation Tranmiion zero implementation Effect of non-idealitie Switched-capacitor filter utilizing double ampling technique EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page DDI Switched-apacitor Integrator Vin V o z jt ( z ), z e I I V z z in j T / 2 j j e ince : in e e I jt I jt / 2 jt / 2 e e e 2j jt / 2 j e I 2inT / 2 T / 2 jt / 2 e I jt int / 2 Ideal Integrator Magnitude Error EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 2

2 DDI Switched-apacitor Integrator Vin j T / 2 ( z ) T / 2 e I j T in T / 2 V in Example: Mag. & phae error for: - f / f =/2 Mag. error = % or 0.dB Phae error=5 degree Q intg = f / f =/32 Mag. error=0.6% or 0.04dB Phae error=5.6 degree Q intg = -0.2 DDI Integrator: magnitude error no problem phae error major problem EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 3 5 th Order Low-Pa Switched apacitor Filter j Built with DDI Integrator j -plane oare View -plane Fine View Example: 5th Order Elliptic Filter Ideal Pole Singularitie puhed Ideal Zero - toward RHP due to DDI Pole integrator exce phae DDI Zero EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 4

3 H j Paband Peaking Switched apacitor Filter Build with DDI Integrator S DDI baed Filter Zero lot! f / 2 ontinuou-time Prototype Frequency (Hz) f 2f f EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 5 Switched-apacitor Integrator Output Sampled on 2 Vin Sample output ½ clock cycle earlier Sample output on 2 EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 6

4 (n-3/2)t Switched-apacitor Integrator Output Sampled on 2 (n-)t (n-/2)t nt (n+/2)t 2 2 (n+)t lock Vin V 2 F Q [(n-)t ]= V i [(n-)t ], Q I [(n-)t ] = Q I [(n-3/2)t ] F 2 Q [(n-/2) T ] = 0, Q I [(n-/2) T ] = Q I [(n-3/2) T ] + Q [(n-) T ] F _ Q [nt ] = V i [nt ], Q I [nt ] = Q I [(n-) T ] + Q [(n-) T ] F 2 Q [(n+/2) T ] = 0, Q I [(n+/2) T ] = Q I [(n-/2) T ] + Q [n T ] EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 7 (n-3/2)t Switched-apacitor Integrator Output Sampled on 2 (n-)t (n-/2)t nt 2 2 (n+)t lock Vin V Q I [(n+/2) T ] = Q I [(n-/2) T ] + Q [n T ] V o2 = - Q I / & V i = Q / V o2 [(n+/2) T ] = V o2 [(n-/2) T ] - V i [n T ] Uing the z operator rule: V o2 z / 2 ( z ) V o2 z = /2 V o2 z -/2 I z - V i V in EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 8

5 LDI Switched-apacitor Integrator LDI (Lole Dicrete Integrator) ame a DDI but output i ampled ½ clock cycle earlier LDI V o2 z / 2 jt ( z ), z e I V z in Vin e jt / 2 I jt I jt / 2 jt / 2 e e e j I 2 int / 2 I j T Ideal Integrator T / 2 int / 2 Magnitude Error No Phae Error! For ignal at frequencie << ampling freq. Magnitude error negligible EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 9 H j Zero Preerved Switched-apacitor Filter Built with LDI Integrator f /2 Frequency f (Hz) 2f f EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 0

6 Switched-apacitor Integrator Paraitic apacitor Senitivity Vin 2 p2 p + p3 - Effect of paraitic capacitor: - p3 driven by opamp o.k. 2- p2 at opamp virtual gnd o.k. 3- p harge to Vin & dicharge into, p include the MOS witch junction capacitor which are voltage dependent, not only affect ratio but reult in non-linearitie Problem paraitic capacitor enitivity EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page Paraitic Inenitive Bottom-Plate Switched-apacitor Integrator Senitive paraitic cap. p rearrange circuit o that p charge/dicharge = p grounded doe not 2= p at virtual ground 2 - Vi+ p p2 + Vi- Solution: Bottom plate capacitor integrator EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 2

7 Bottom Plate Switched-apacitor Integrator Vi+ 2 Note: Different delay from Vi+ & Vi- to either output Special attention needed for input/output connection to enure LDI realization - + Vi- 2 2 Output/Input z-tranform 2 on on 2 z z 2 Vi+ I I on z z Vion 2 I I z z z 2 EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 3 Bottom Plate Switched-apacitor Integrator z-tranform Model Vi+ Vi- I 2 z -z 2 z z + z 2 Input/Output z-tranform z z 2 2 Vi+ I I z 2 z 2 z Viz 2 2 LDI EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 4

8 LDI Switched-apacitor Ladder Filter z 2 2 z z z 2 2 z z z 2 z 2 z 2 2 z z z 2 To tet whether LDI or DDI Need to examine delay around the integrator loop Delay around integrator loop i (z -/2. z +/2 =) LDI function EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 5 Switched-apacitor LDI Reonator Reonator Signal Flowgraph f R eq 2 2 f 3 2 R eq3 4 4 EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 6

9 Fully Differential Switched-apacitor Reonator Note: Two et of S.. bottom plate network for each differential integrator 2 2 EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 7 Switched-apacitor LDI Bandpa Filter Utilizing ontinuou-time Termination V i Bandpa Filter Signal Flowgraph 0 V o -/Q V o2 Q V o 0 V o2 Feedback in the amount of -/Q provided from V o2 to V o via the addition of capacitor Q 3 f f Q 2 Q V i EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 8

10 Magnitude (db) Example: 2 nd Order S.. Bandpa Filter -Plane veru z-plane -plane j z-plane EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 9 Switched-apacitor LDI Bandpa Filter ontinuou-time Termination f f f Df 0 Q Q f dB Df Both f 0 and Df accurately determined by cap ratio & clock frequency f 0 Frequency 0. 0 EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 20

11 Fifth Order All-Pole LDI Low-Pa Ladder Filter omplex onjugate Termination Termination Reitor Termination Reitor omplex conjugate termination (alternate phae witching) Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 2 Fifth-Order All-Pole Low-Pa Ladder Filter Termination Implementation Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 22

12 Sixth-Order Elliptic LDI Bandpa Filter Tranmiion Zero Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 23 Ue of T-Network V V 2 2 V2 4 V High Q filter large cap. ratio for Q & tranmiion zero implementation To reduce large ratio required T-network utilized Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 24

13 Sixth Order Elliptic Bandpa Filter Utilizing T-Network Q implementation Zero T-network utilized for: Q implementation Tranmiion zero implementation Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 9 Switched-apacitor Filter 200 H. K. Page 25 Effect of Opamp Nonidealitie on Switched apacitor Filter Behavior Opamp finite gain Opamp finite bandwidth Source of ditortion Finite lew rate of the opamp Non-linearity aociated with opamp output/input characteritic apacitor non-linearity- uually inignificant, imilar to cont. time filter harge injection & clock feedthrough (will be covered in the overampling data converter ection) EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 26

14 Effect of Opamp Non-Idealitie Finite D Gain H( ) f f I a o H( ) o a Qint g a Vi+ Vi Input/Output z-tranform D Gain = a Finite D gain ame effect in S.. filter a for.t. filter If D gain not high enough lowing of overall Q & droop in paband EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 27 Effect of Opamp Non-Idealitie Finite Opamp Bandwidth Vi+ Vi Input/Output z-tranform Unity-gainfreq. V o 2 ettling error time = f t T=/f Aumption- Opamp doe not lew (will be reviited) Opamp ha one pole only exponential ettling Ref: K.Martin, A. Sedra, Effect of the Opamp Finite Gain & Bandwidth on the Performance of Switched- apacitor Filter," IEEE Tran. ircuit Syt., vol. AS-28, no. 8, pp , Aug 98. EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 28

15 Vi+ Effect of Opamp Non-Idealitie Finite Opamp Bandwidth k k I H actual ( Z ) H e e Z ideal( Z ) I where k I ft I f ft Opamp unity gain frequency, f lock frequency Ref: Vi- Input/Output z-tranform Unity-gainfreq.= f t V o 2 ettling error T=/f time K.Martin, A. Sedra, Effect of the Opamp Finite Gain & Bandwidth on the Performance of Switched- apacitor Filter," IEEE Tran. ircuit Syt., vol. AS-28, no. 8, pp , Aug 98. EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 29 Example: For db magnitude repone deviation: - f c /f =/2 f c /f t ~0.04 f t >25f c 2- f c /f =/32 f c /f t ~0.022 f t >45f c 3- ont.-time f c /f t ~/700 f t >700f c Effect of Opamp Finite Bandwidth on Filter Magnitude Repone T non-ideal / T ideal (db) Active R f c /f =/32 f c /f =/2 Ref: f c /f t K.Martin, A. Sedra, Effect of the Opamp Finite Gain & Bandwidth on the Performance of Switched- apacitor Filter," IEEE Tran. ircuit Syt., vol. AS-28, no. 8, pp , Aug 98. EES 247 Lecture 9 Switched-apacitor Filter 2009 H. K. Page 30

16 Effect of Opamp Finite Bandwidth on Filter ritical Frequency Example: For maximum critical frequency hift of <% - f c /f =/32 f c /f t ~0.028 f t >36f c 2- f c /f =/2 f c /f t ~0.046 f t >22f c D c / c Active R f c /f =/32 f c /f =/2 3- Active R f c /f t ~0.008 f t >25f c Ref: f c /f t K.Martin, A. Sedra, Effect of the Opamp Finite Gain & Bandwidth on the Performance of Switched- apacitor Filter," IEEE Tran. ircuit Syt., vol. AS-28, no. 8, pp , Aug 98. EES 247 Lecture 9 Switched-apacitor Filter 2009 H. K. Page 3 Opamp Bandwidth Requirement for Switched- apacitor Filter ompared to ontinuou-time Filter Finite opamp bandwidth caue phae lag at the unity-gain frequency of the integrator for both type filter Reult in negative intg. Q & thu increae overall Q reult in peaking in the paband of interet For given filter requirement, opamp bandwidth requirement much le tringent for S.. filter compared to cont. time filter Lower power diipation for S.. filter (at low freq. only ince other nonidealitie dominate at high freq.) Finite opamp bandwidth caue down hifting of critical frequencie in both type filter Since cont. time filter are uually tuned tuning account for frequency deviation S.. filter are untuned and thu frequency hift could caue problem particularly for narrow-band filter EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 32

17 Effect of Opamp Nonidealitie on Switched-apacitor Filter Performance Opamp finite gain Opamp finite bandwidth Source of ditortion Finite lew rate of the opamp Non-linearity aociated with opamp output/input characteritic apacitor non-linearity- uually inignificant, imilar to cont. time filter harge injection & clock feedthrough (will be covered in the overampling data converter ection) EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 33 What i Slewing? Vin 2 - L V o + 2 Vi- Vi+ Aumption: Integrator opamp i a imple cla A tranconductance type differential pair with fixed tail current, I=cont. I EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 34

18 What i Slewing? I o v.. V in I o I max= +I 2 V o Slope ~ g m V in 2 I o V max I max= -I /2 Vi- I Vi+ V > V max Output current contant I o =I/2 or I/2 ontant current charging/dicharging : V o ramp down/up Slewing After V i dicharged enough to have: V <V max I o =gm V Output Exponential or over/under-hoot ettling EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 35 Ditortion Induced by Opamp Finite Slew Rate Output ltage Multiple pole ettling One pole ettling Slewing Settling Settling (multi-pole) Time EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 36

19 Ideal Switched-apacitor Output Waveform Vin - + lock 2 Vin Vin Vc 2 High harge tranferred from to I EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 37 Slew Limited Switched-apacitor Integrator Output Slewing & Settling lock 2 -ideal -real Slewing Linear Settling Slewing Linear Settling EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 38

20 Ditortion Induced by Finite Slew Rate of the Opamp Ref: K.L. Lee, Low Ditortion Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, Feb. 986 (ERL Memorandum No. UB/ERL M86/2). EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 39 Ditortion Induced by Opamp Finite Slew Rate Error due to exponential ettling change linearly with ignal amplitude Error due to lew-limited ettling change non-linearly with ignal amplitude (doubling ignal amplitude X4 error) For high-linearity need to have either high lew rate or non-lewing opamp HDk ST r k k o T o in V in o T f HD o 3 for fo f HD S 3 rt 5 5Sr f Ref: K.L. Lee, Low Ditortion Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, Feb. 986 (ERL Memorandum No. UB/ERL M86/2). EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 40

21 HD3 [db] Example: Slew Related Harmonic Ditortion 2 8 o T o in V HD 2 3 SrT f HD o 3 5S r f 2dB Switched-capacitor filter with 4kHz bandwidth, f =28kHz, S r =V/mec, V o =3V Ref: K.L. Lee, Low Ditortion Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, Feb. 986 (ERL Memorandum No. UB/ERL M86/2). EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 4 Ditortion Induced by Opamp Finite Slew Rate Example f / f =/2-80 f / f =/ (Slew-rate / f ) [V] EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 42

22 Ditortion Induced by Finite Slew Rate of the Opamp Note that for a high order witched capacitor filter only the lat tage lewing will affect the output linearity (a long a the previou tage ettle to the required accuracy) an reduce lew limited non-linearitie by uing an amplifier with a higher lew rate only for the lat tage an reduce lew limited non-linearitie by uing cla A/B amplifier Even though the output/input characteritic i non-linear a long a the D open-loop gain i high, the ignificantly higher lew rate compared to cla A amplifier help improve lew rate induced ditortion in S.. filter In cae where the output i ampled by another ampled data circuit (e.g. an AD or a S/H) no iue with the lewing of the output a long a the output ettle to the required accuracy & i ampled at the right time EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 43 More Realitic Switched-apacitor ircuit Slew Scenario Vin L 2 t=0+ L At the intant connect to input of opamp (t=0+) Opamp not yet active at t=0+ due to finite opamp bandwidth delay Feedforward path from input to output generate a voltage pike at the output with polarity oppoite to final tep- pike magnitude function of, L, Spike increae lewing period Eventually, opamp become active - tart lewing followed by ubequent ettling EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 44

23 Switched-apacitor ircuit Opamp not t=0+ Vin L + t=0+ t0 t0 I L eq eq I L harg e haring : V V where DV V V t0 t0 I t0 I out I L eq I L t0 t0 t0 t0 L I eq L L t0 t0 I t0 out L I L Au min g V V V V DV V V Note that DV V V final t0 t0 out I I L EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 45 More Realitic Switched-apacitor ircuit Slew Scenario Vin L + t=0+ L Notice that if L i large ome of the charge tored on i lot prior to opamp becoming effective operation looe accuracy harg e haring : V V where V V V t0 t0 t0 eq t0 t0 I L eq eq I L L I L Partly reponible for S.. filter only good for low-frequency application EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 46

24 More Realitic S.. Slew Scenario _ideal _real _real Including t=0+ pike Slewing Linear Settling Slewing Linear Settling Spike generated at t=0+ Slewing Linear Settling Slewing Ref: R. atello, Low ltage, Low Power Switched-apacitor Signal Proceing Technique," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, Aug. 84 (ERL Memorandum No. UB/ERL M84/67). EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 47 Effect of Opamp Nonidealitie on Switched apacitor Filter Behavior Opamp finite gain Opamp finite bandwidth Source of ditortion Finite lew rate of the opamp Non-linearity aociated with opamp output/input characteritic apacitor non-linearity- uually inignificant, imilar to cont. time filter harge injection & clock feedthrough (will be covered in the overampling data converter ection) EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 48

25 Source of Noie in Switched- apacitor Filter Opamp Noie Thermal noie /f (flicker) noie Thermal noie aociated with the witching proce (kt/) Same a continuou-time filter Precaution regarding aliaing of noie required EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 49 Extending the Maximum Achievable ritical Frequency of Switched-apacitor Filter onider a witchedcapacitor reonator: Regular ampling: Each opamp i buy ettling only during one of the two clock phae Idle during the other clock phae 2 2 Note: During both opamp are idle EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 50

26 Switched-apacitor Reonator Uing Double-Sampling Double-ampling: 2 nd et of witche & ampling cap added to all integrator 2 While one et of witche/cap ampling the other et tranfer charge into the intg. cap Opamp buy during both clock phae 2 Effective ampling freq. twice the clock freq. while opamp bandwidth requirement remain the ame EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 5 Double-Sampling Iue f clock f = 2f clock Iue to be aware of: - Jitter in the clock - Unequal clock phae -Mimatch in ampling cap. Reult in paraitic paband Ref: Tat. hoi, "High-Frequency MOS Switched-apacitor Filter," U.. Berkeley, Department of Electrical Engineering, Ph.D. Thei, May 983 (ERL Memorandum No. UB/ERL M83/3). EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 52

27 Sixth Order Bandpa Filter Signal Flowgraph Vin V out 0 0 Q Q EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 53 Double-Sampled Fully Differential 6 th Order S.. All-Pole Bandpa Filter - ont. time termination (Q) implementation - Folded-acode opamp with f u = 00MHz ued - enter freq. 3.MHz (Meaured error >%), filter Q=55 - lock freq. 2.83MHz effective overampling ratio Meaured dynamic range 46dB (IM3=%) Ref: B.S. Song, P.R. Gray "Switched-apacitor High-Q Bandpa Filter for IF Application," IEEE Journal of Solid State ircuit, l. 2, No. 6, pp , Dec EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 54

28 Magnitude (db) Switched-apacitor Filter Application Example: ice-band ODE (oder-decoder) hip f = 024kHz f = 28kHz f = 8kHz f = 8kHz f = 28kHz f = 8kHz f = 28kHz f = 28kHz Ref: D. Senderowicz et. al, A Family of Differential NMOS Analog ircuit for PM odec Filter hip, IEEE Journal of Solid-State ircuit, l.-s-7, No. 6, pp , Dec EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 55 ODE Tranmit Path Lowpa Filter Frequency Repone 0 Note: f =28kHz Frequency (Hz) EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 56

29 Magnitude (db) Magnitude (db) ODE Tranmit Path Highpa Filter Frequency (Hz) Note: f =8kHz 0000 EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 57 ODE Tranmit Path Filter Overall Frequency Repone Frequency (Hz) 0000 Low Q bandpa (Q<) filter hape Implemented with lowpa followed by highpa EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 58

30 ODE Tranmit Path locking Scheme Firt filter ( t order R type) perform anti-aliaing for the next S.. biquad The firt 2 tage filter form 3 rd order elliptic with corner 32kHz Anti-aliaing for the next S.. lowpa filter with 3.4kHz corner freq. The tage prior to the high-pa perform anti-aliaing for highpa Notice gradual lowering of clock frequency Eae of anti-aliaing EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 59 S Filter Summary Pole and zero frequencie proportional to Sampling frequency f apacitor ratio High accuracy and tability in repone Long time contant realizable without large R, ompatible with tranconductance amplifier Reduced circuit complexity, power diipation Amplifier bandwidth requirement le tringent compared to T filter (low frequencie only) Iue: Sampled-data filter require anti-aliaing prefiltering EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 60

31 Switched-apacitor Filter veru ontinuou- Time Filter Limitation onidering overall effect: Magnitude Error 5-0MHz ont. Time Filter S.. Filter Filter bandwidth Auming contant opamp f u Limited witched-capacitor filter performance frequency range EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 6 Summary Filter Performance veru Filter Topology Max. Uable Bandwidth SNDR Freq. Tolerance w/o Tuning Opamp-R ~0MHz 60-90dB % -5% Freq. Tolerance + Tuning Opamp finite unitygain-bandwidth Opamp ettling iue Opamp finite lew rate lock feedthru & witch charge injection Switch+ ampling cap. finite timecontant Opamp- MOSFET- Opamp- MOSFET-R ~ 5MHz 40-60dB % -5% ~ 5MHz 50-90dB % -5% Gm- ~ 00MHz 40-70dB % -5% Switched apacitor ~ 0MHz 40-90dB <% _ EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 62

32 Frequency repone Frequency Warping ontinuou time (-plane): imaginary axi Sampled time (z-plane): unit circle ontinuou to ampled time tranformation Should map imaginary axi onto unit circle How do S.. integrator map frequencie? 2 z H S.. ( z ) int z int 2 j in f T EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 63 T Sntegrator omparion T Integrator Sntegrator H 2 R( ) z H S ( z ) int z 2 jf R int j in f S T Identical time contant: int R f Set: H R (f R ) = H S (f S ) f R f f in f S 2 EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 64

33 LDI Integration f S /f / f R /f f R f f in f S R frequencie up to f / map to phyical (real) S frequencie Frequencie above f / do not map to phyical frequencie Mapping i ymmetric about f /2 (aliaing) Accurate only for f R << f EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 65 Material overed in EE247 Where are We? Filter ontinuou-time filter Biquad & ladder type filter Opamp-R, Opamp-MOSFET-, gm- filter Automatic frequency tuning Switched capacitor (S) filter Data onverter D/A converter architecture A/D converter Nyquit rate AD- Flah, Pipeline AD,. Overampled converter Self-calibration technique Sytem utilizing analog/digital interface EES 247 Lecture 0 Switched-apacitor Filter 200 H. K. Page 66