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1 EE47 Lecture 0 Switched-capacitor filter Switched-capacitor network electronic noie Switched-capacitor integrator DDI integrator LDI integrator Effect of paraitic capacitance Bottom-plate integrator topology Reonator Bandpa filter Lowpa filter Termination implementation Tranmiion zero implementation Switched-capacitor filter deign conideration Switched-capacitor filter utilizing double ampling technique Effect of non-idealitie EES 47 Lecture 0: S Filter 006 H. K. Page Summary of lat lecture ontinuou-time filter continued Variou Gm- filter implementation omparion of continuou-time filter topologie Switched-capacitor filter Emulating reitor via witched-capacitor network t order witched-capacitor filter Switch-capacitor filter conideration: Iue of aliaing and how to avoid it Sample at high enough frequency o that the entire range of ignal including the paraitic are at freq < f / Ue of anti-aliaing prefilter Effect of ample and hold EES 47 Lecture 0: S Filter 006 H. K. Page

2 Switched-apacitor Network Noie φ φ During φ high: Reitance of witch S (R on S ) produce a noie voltage on with variance kt/ (lecture - firt order filter noie) v IN S S v OUT The correponding noie charge i: R on S Q = V =. kt/ = kt φ low: S open Thi charge i ampled EES 47 Lecture 0: S Filter 006 H. K. Page 3 Switched-apacitor Noie φ φ During φ high: Reitance of witch S contribute to an uncorrelated noie charge on at the end of φ : with variance kt/ v IN S S v OUT Mean-quared noie charge tranferred from v IN to v OUT per ample period i: R on S Q =kt EES 47 Lecture 0: S Filter 006 H. K. Page 4

3 Switched-apacitor Noie The mean-quared noie current due to S and S kt/ noie i : ( ) Since i= Q then i = Qf k Tf t = B Thi noie i approximately white and ditributed between 0 and f / (noie pectra ingle ided by convention) The pectral denity of the noie i: k Tf i = B = 4k B Tf Δf f i 4k B T Since R EQ = then: = f Δf R EQ S.. reitor noie = a phyical reitor noie with ame value! EES 47 Lecture 0: S Filter 006 H. K. Page 5 Sampling Noie from S S/H Periodic Noie Analyi SpectreRF Netlit ahdl_include "zoh.def" Netlit imoption option reltol=0u vabtol=n iabtol=p Vclk 00n 00kOhm R S Vrc ZOH Vrc_hold PNOISE Analyi PNOISE weep from 0 to 0.0M (037 tep) pf ZOH T = 00n SpectreRF PNOISE: check 00kOhm R noietype=timedomain ltage NOISE VNOISE noietimepoint=[ ] pf a alternative to ZOH. noiekipcount=large might peed up thing in thi cae. PSS p period=00n maxacfreq=.5g errpreet=conervative PNOISE ( Vrc_hold 0 ) pnoie tart=0 top=0m lin=500 maxideband=0 EES 47 Lecture 0: S Filter 006 H. K. Page 6

4 Sampled Noie Spectrum Denity of ampled noie including inc ditortion Sampled noie normalized denity corrected for inc ditortion EES 47 Lecture 0: S Filter 006 H. K. Page 7 Total Noie Sampled imulated noie in 0 f /: 6.μV rm (expect 64μV for pf) EES 47 Lecture 0: S Filter 006 H. K. Page 8

Switched-apacitor Integrator - φ φ φ φ I - T=/f for fignal<< fampling f V 0 = V dt in I ω 0 = f I Main advantage: No tuning needed critical frequency function of ratio of capacitor & clock freq.

5 Switched-apacitor Integrator - φ φ φ φ I - T=/f for fignal<< fampling f V 0 = V dt in I ω 0 = f I Main advantage: No tuning needed critical frequency function of ratio of capacitor & clock freq. EES 47 Lecture 0: S Filter 006 H. K. Page 9 Switched-apacitor Integrator φ I φ - φ φ T=/f φ I φ - - I φ High harged to φ High harge tranferred from to I EES 47 Lecture 0: S Filter 006 H. K. Page 0

6 ontinuou-time veru Dicrete Time Analyi Approach ontinuou-time Dicrete-Time Write differential equation Laplace tranform (F()) Let =jω F(jω) Plot F(jω), phae(f(jω) Write difference equation relate output equence to input equence Ue delay operator z - to tranform the recurive realization to algebraic equation in z domain Set z= e jωt [(n )T ] V o(nt ) = V i... ( ) Z = z V i ( z)... Plot mag./phae veru frequency EES 47 Lecture 0: S Filter 006 H. K. Page Dicrete Time Deign Flow Tranforming the recurive realization to algebraic equation in z domain: Ue delay operator z : nt... (n )T... z (n /)T /... z (n )T... z (n /)T /... z * Note: z = e jωt = co(ωt ) j in(ωt ) EES 47 Lecture 0: S Filter 006 H. K. Page

7 Switched-apacitor Integrator Output Sampled on φ φ φ I - φ φ φ φ φ φ lock V EES 47 Lecture 0: S Filter 006 H. K. Page 3 (n-3/)t Switched-apacitor Integrator (n-)t (n-/)t nt (n/)t (n)t φ φ φ φ φ lock V Φ Q [(n-)t ]= V i [(n-)t ], Q I [(n-)t ] = Q I [(n-)t ] Φ Q [(n-/) T ] = 0, Q I [(n-/) T ] = Q I [(n-) T ] Q [(n-) T ] Φ _ Q [nt ] = V i [nt ], Q I [nt ] = Q I [(n-) T ] Q [(n-) T ] Since V o = - Q I / I & V i = Q / I V o (nt ) = I V o [(n-) T ] - V i [(n-) T ] EES 47 Lecture 0: S Filter 006 H. K. Page 4

8 Switched-apacitor Integrator Output Sampled on φ φ φ I - φ I V o(nt ) = I (n )T V in (n )T V o(nt ) = (n )T V I in (n )T V o(z) = Z V o(z) Z V I in (Z) V o Z (Z) = V I Z in DDI (Direct-Tranform Dicrete Integrator) EES 47 Lecture 0: S Filter 006 H. K. Page 5 z-domain Frequency Repone LHP ingularitie in -plane map into inide of unit-circle in z-domain RHP ingularitie in -plane map into outide of unitcircle in z-domain The jω axi map onto the unit-circle Particular value: f = 0 z = f = f / z = - imag. axi in -domain f = f / LHP in -domain z-plane f = 0 EES 47 Lecture 0: S Filter 006 H. K. Page 6

9 z-domain Frequency Repone The frequency repone i obtained by evaluating H(z) on the unit circle at: z = e jωt = co(ωt ) j in(ωt ) Once z=- (f /) i reached, the frequency repone repeat, a expected The angle to the pole i equal to 360 (or π radian) time the ratio of the pole frequency to the ampling frequency (co(ωt ),in(ωt )) πf f S z-plane EES 47 Lecture 0: S Filter 006 H. K. Page 7 Switched-apacitor Direct-Tranform Dicrete Integrator φ I φ - φ V o V in (z) = z I z I z = EES 47 Lecture 0: S Filter 006 H. K. Page 8

10 DDI Integrator Pole-Zero Map in z-plane z -=0 z = on unit circle f Pole from f 0 in -plane mapped to z = A frequency increae z domain pole move on unit circle (W) f = f / f increaing (z-) Once pole get to: z=- (f=f /) frequency repone repeat z-plane EES 47 Lecture 0: S Filter 006 H. K. Page 9 DDI Switched-apacitor Integrator I φ φ I - φ z jωt (z) =, z= e I V z in j T / j j e ω α α = = ince: inα = e e I jωt I jωt / jωt / e e e j jωt / = j e I in( ωt/) ωt/ jωt / = e I jω T in( ωt/) Phae Error Ideal Integrator Magnitude Error EES 47 Lecture 0: S Filter 006 H. K. Page 0

11 DDI Switched-apacitor Integrator I φ φ I - φ Example: Mag. & phae error for: - f / f =/ Mag. error = % or 0.dB Phae error=5 degree Q intg = f / f =/3 Mag. error=0.6% or 0.04dB Phae error=5.6 degree Q intg = -0. DDI Integrator: magnitude error no problem phae error major problem EES 47 Lecture 0: S Filter 006 H. K. Page 5 th Order Low-Pa Switched apacitor Filter jω Built with DDI Integrator jω ω -plane oare View -plane Fine View σ σ Example: 5th Order Elliptic Filter Ideal Pole Singularitie puhed Ideal Zero -ω toward RHP due to DDI Pole integrator exce phae DDI Zero EES 47 Lecture 0: S Filter 006 H. K. Page

12 H( jω) Paband Peaking Switched apacitor Filter Build with DDI Integrator S DDI baed Filter Zero lot! f / ontinuou-time Prototype Frequency (Hz) f f f EES 47 Lecture 0: S Filter 006 H. K. Page 3 Switched-apacitor Integrator Output Sampled on φ I φ φ I - φ Sample output ½ clock cycle earlier Sample output on φ EES 47 Lecture 0: S Filter 006 H. K. Page 4

13 (n-3/)t Switched-apacitor Integrator Output Sampled on φ (n-)t (n-/)t nt (n/)t φ φ φ φ φ (n)t lock V Φ Q [(n-)t ]= V i [(n-)t ], Q I [(n-)t ] = Q I [(n-3/)t ] Φ Q [(n-/) T ] = 0, Q I [(n-/) T ] = Q I [(n-3/) T ] Q [(n-) T ] Φ _ Q [nt ] = V i [nt ], Q I [nt ] = Q I [(n-) T ] Q [(n-) T ] Φ Q [(n/) T ] = 0, Q I [(n/) T ] = Q I [(n-/) T ] Q [n T ] EES 47 Lecture 0: S Filter 006 H. K. Page 5 Switched-apacitor Integrator Output Sampled on φ (n-3/)t (n-)t (n-/)t nt (n)t φ φ φ φ φ lock V Q I [(n/) T ] = Q I [(n-/) T ] Q [n T ] V o = - Q I / I & V i = Q / I V o [(n/) T ] = I V o [(n-/) T ] - V i [n T ] Uing the z operator rule: V o z / (z) = I V o z / = I V o z -/ - V I i V z in EES 47 Lecture 0: S Filter 006 H. K. Page 6

14 LDI Switched-apacitor Integrator LDI (Lole Dicrete Integrator) ame a DDI but output i ampled ½ clock cycle earlier LDI V o z / jωt (z) =, z= e I V z in e jωt / = = I jωt I jωt/ jωt/ e e e = j I in( ωt/) I φ φ I - φ = I jω T Ideal Integrator ωt/ in( ωt/) Magnitude Error No Phae Error! For ignal at frequencie << ampling freq. Magnitude error negligible EES 47 Lecture 0: S Filter 006 H. K. Page 7 Frequency Warping Frequency repone 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? z H S.. (z) = int z = int jinπ ft EES 47 Lecture 0: S Filter 006 H. K. Page 8

15 T S Integrator omparion H R T Integrator S Integrator () = z τ H S (z) = int z = π jf R τ = int jinπ f S T Identical time contant: int τ = R = f Set: H R (f R ) = H S (f S ) f R f f = π π in f S EES 47 Lecture 0: S Filter 006 H. K. Page 9 LDI Integration f S /f /π f R /f Slope= f R f f = π π in f S R frequencie up to f /π map to phyical (real) S frequencie Frequencie above f /π do not map to phyical frequencie Mapping i ymmetric about f / (aliaing) Accurate only for f R << f EES 47 Lecture 0: S Filter 006 H. K. Page 30

16 H( jω) Switched-apacitor Filter Built with LDI Integrator Zero Preerved f / Frequency f (Hz) f f EES 47 Lecture 0: S Filter 006 H. K. Page 3 Switched-apacitor Integrator Paraitic Senitivity φ I φ - p p3 p Effect of paraitic capacitor: - p - driven by opamp o.k. - p - at opamp virtual gnd o.k. 3- p3 harge to & dicharge into I Problem paraitic enitivity EES 47 Lecture 0: S Filter 006 H. K. Page 3

17 Paraitic Inenitive Bottom-Plate Switched-apacitor Integrator Senitive paraitic cap. p rearrange circuit o that p charge/dicharge φ= p grounded doe not φ= p at virtual ground φ φ I EES 47 Lecture 0: S Filter 006 H. K. Page 33 Bottom Plate Switched-apacitor Integrator Vi φ φ - Note: Different delay from Vi & Vi- to either output Special attention needed for input/output connection I φ φ Vi on φ p - Vi p Vi- Solution: Bottom plate capacitor integrator Vi- Vion φ Output/Input z-tranform on φ on φ z z I z I z z I I z z EES 47 Lecture 0: S Filter 006 H. K. Page 34

18 Bottom Plate Switched-apacitor Integrator z-tranform Model Vi φ φ I z -z z z z Input/Output z-tranform z z Viφ φ Vi Vi- I I z z z z LDI EES 47 Lecture 0: S Filter 006 H. K. Page 35 LDI Switched-apacitor Ladder Filter - τ 3 τ 4 τ z z I I z z z I z z z z z z I z I I Delay around integrator loop i (z -/. z / =) LDI function EES 47 Lecture 0: S Filter 006 H. K. Page 36

19 Switched-apacitor LDI Reonator Reonator Signal Flowgraph ω φ φ ω φ φ ω f = = R eq ω f 3 = = R eq3 4 4 EES 47 Lecture 0: S Filter 006 H. K. Page 37 Fully Differential Switched-apacitor Reonator φ φ φ φ EES 47 Lecture 0: S Filter 006 H. K. Page 38

20 Switched-apacitor LDI Bandpa Filter Utilizing ontinuou-time Termination Bandpa Filter Signal Flowgraph ω0 V i -/Q V o Q V o ω0 3 ω f 0 = = 4 Q = Q V o V i EES 47 Lecture 0: S Filter 006 H. K. Page 39 -Plane veru z-plane Example: nd Order LDI Bandpa Filter -plane jω z-plane σ EES 47 Lecture 0: S Filter 006 H. K. Page 40

21 Switched-apacitor LDI Bandpa Filter ontinuou-time Termination f f 0 = π f Δ f = 0 Q Q = f π 4 Both accurately determined by cap ratio & clock frequency 0-3dB Magnitude (db) Δf 0. 0 f 0 Frequency EES 47 Lecture 0: S Filter 006 H. K. Page 4 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 47 Lecture 0: S Filter 006 H. K. Page 4

22 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 47 Lecture 0: S Filter 006 H. K. Page 43 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 47 Lecture 0: S Filter 006 H. K. Page 44

Ue of T-Network 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.

23 Ue of T-Network 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 47 Lecture 0: S Filter 006 H. K. Page 45 Sixth Order Elliptic Bandpa Filter Utilizing T-Network Q implementation Zero T-network utilized for: Q implemention 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 47 Lecture 0: S Filter 006 H. K. Page 46

24 Switched-apacitor Reonator φ φ φ φ Regular ampling Each opamp buy ettling only during one of the two clock phae Idle during the other clock phae EES 47 Lecture 0: S Filter 006 H. K. Page 47 Switched-apacitor Reonator Uing Double-Sampling Double-ampling: nd et of witche & ampling cap added to all integrator While one et of witche/cap ampling the other et tranfer charge into the intg. cap Opamp buy during both clock phae Effective ampling freq. twice clock freq. while opamp bandwidth requirement remain the ame EES 47 Lecture 0: S Filter 006 H. K. Page 48

25 Double-Sampling Iue f clock f = f clock Iue to be aware of: - Jitter in the clock - Unequal clock phae -Mimatch in ampling cap. 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 47 Lecture 0: S Filter 006 H. K. Page 49 Double-Sampled Fully Differential S.. 6 th Order All-Pole Bandpa Filter 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 47 Lecture 0: S Filter 006 H. K. Page 50

time termination (Q) implementation -Folded-acode opamp with f u = 00MHz ued -enter freq. 3.MHz, filter Q=55 -lock freq.

26 Sixth Order Bandpa Filter Signal Flowgraph γ γ V out ω 0 ω 0 Q ω0 ω0 ω0 ω0 Q γ γ EES 47 Lecture 0: S Filter 006 H. K. Page 5 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, filter Q=55 -lock freq..83mhz effective overampling ratio 8.7 -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., No. 6, pp , Dec EES 47 Lecture 0: S Filter 006 H. K. Page 5

27 Effect of Opamp Nonidealitie on Switched apacitor Filter Behaviour Opamp finite gain Opamp finite bandwidth Finite lew rate of the opamp EES 47 Lecture 0: S Filter 006 H. K. Page 53 Effect of Opamp Non-Idealitie Finite D Gain φ φ I H() f I f I a ωo H() ω o a Vi Vi- - D Gain = a Input/Output z-tranform Q a Finite D gain ame effect in S.. filter a for.t. filter EES 47 Lecture 0: S Filter 006 H. K. Page 54

28 Effect of Opamp Non-Idealitie Finite Opamp Bandwidth Vi Vi- φ φ I - Input/Output z-tranform Unity-gain-freq. = f t V o φ ettling error time T=/f Aumption- Opamp doe not lew (will be reviited) Opamp ha only one pole 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 55 Vi Vi- φ φ Effect of Opamp Non-Idealitie Finite Opamp Bandwidth - Input/Output z-tranform Unity-gain-freq. = f t I k k I H actual (Z) H e e Z ideal(z) I where k = π I ft I f ft Opamp unity gain frequency, f lock frequency 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-8, no. 8, pp. 8-89, Aug 98. V o φ ettling error T=/f time EES 47 Lecture 0: S Filter 006 H. K. Page 56

29 Effect of Opamp Finite Bandwidth on Filter Magnitude Repone Τ non-ideal / Τ ideal (db) Magnitude deviation due to finite opamp unity-gainfrequency Active R f c /f =/3 f c /f =/ Example: nd order bandpa with Q=5 f c /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 57 Effect of Opamp Finite Bandwidth on Filter Magnitude Repone Τ non-ideal / Τ ideal Example: For db magnitude repone deviation: - f c /f =/ f c /f t ~0.04 f t >5f c - f c /f =/3 f c /f t ~0.0 f t >45f c (db) Active R f c /f =/3 f c /f =/ 3- ont.-time f c /f t ~/700 f t >500f c fc /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 58

30 Effect of Opamp Finite Bandwidth Maximum Achievable Q Max. allowable biquad Q for peak gain change <0% Overampling Ratio.T. filter f c /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 59 Example: For Q of 40 required Max. allowable biquad Q for peak gain change <0% - f c /f =/3 f c /f t ~0.0 f t >50f c - f c /f =/ f c /f t ~0.035 f t >8f c Effect of Opamp Finite Bandwidth Maximum Achievable Q 3- f c /f =/6.T. filter f c /f t ~0.05 f t >0f c f c /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 60

31 Effect of Opamp Finite Bandwidth on Filter ritical Frequency Δω c /ω c ritical frequency deviation due to finite opamp unity-gainfrequency Example: nd order filter Active R f c /f =/3 f c /f =/ f c /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 6 Effect of Opamp Finite Bandwidth on Filter ritical Frequency Example: For maximum critical frequency hift of <% - f c /f =/3 f c /f t ~0.08 f t >36f c - f c /f =/ f c /f t ~0.046 f t >f c Δω c /ω c Active R f c /f =/3 f c /f =/ 3- Active R f c /f t ~0.008 f t >5f c.t. filter f c /f t 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-8, no. 8, pp. 8-89, Aug 98. EES 47 Lecture 0: S Filter 006 H. K. Page 6

Source of Ditortion in Switched- apacitor Filter Ditortion induced by finite lew rate of the opamp Opamp output/input tranfer characteritic non-linearity apacitor non-linearity Ditortion incurred by

32 Source of Ditortion in Switched- apacitor Filter Ditortion induced by finite lew rate of the opamp Opamp output/input tranfer characteritic non-linearity apacitor non-linearity Ditortion incurred by finite etting time of the opamp Ditortion due to witch clock feed-through and charge injection EES 47 Lecture 0: S Filter 006 H. K. Page 63 What i Slewing? I φ - I L V o Viφ Vi Aumption: Integrator opamp i a imple cla A tranconductance type differential pair with fixed tail current I I EES 47 Lecture 0: S Filter 006 H. K. Page 64

contant I o =I V o ramp up/down Slewing After Vc i dicharged enough to have: V <V max I o

33 What i Slewing? I o Slope ~ g m I V o V max V in φ I o L I max =I Vi- I Vi V > V max Output current contant I o =I V o ramp up/down Slewing After Vc i dicharged enough to have: V <V max I o =gm V Exponential or over-hoot ettling EES 47 Lecture 0: S Filter 006 H. K. Page 65 Ditortion Induced by Opamp Finite Slew Rate EES 47 Lecture 0: S Filter 006 H. K. Page 66

34 Ideal Switched-apacitor Output Waveform φ - I lock φ φ I φ - Vc φ High harge tranferred from to I EES 47 Lecture 0: S Filter 006 H. K. Page 67 Slew Limited Switched-apacitor Output Settling lock φ φ -ideal -real Slewing Linear Settling Slewing Linear Settling EES 47 Lecture 0: S Filter 006 H. K. Page 68

35 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/). EES 47 Lecture 0: S Filter 006 H. K. Page 69 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 ω ( o ) T V 8 o in HD k = ST r πk ( k 4 ) 8( ot o in ω V ) HD3 = ST r 5 π 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/). EES 47 Lecture 0: S Filter 006 H. K. Page 70

36 Ditortion Induced by Opamp Finite Slew Rate Example HD3 [db] V o =V f / f =/3 V o =V f / f =/ V o =V V o =V (Slew-rate / f ) [V] EES 47 Lecture 0: S Filter 006 H. K. Page 7 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 linearity by uing an amplifier with a higher lew rate only for the lat tage an reduce lew limited linearity by uing cla A/B amplifier Even though the output/input characteritic i non-linear the ignificantly higher lew rate compared to cla A amplifier help improve lew rate induced ditortion 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 47 Lecture 0: S Filter 006 H. K. Page 7

EE247 Lecture 10. Switched-Capacitor Integrator C

EE247 Lecture 10. Switched-Capacitor Integrator C EE247 Lecture 0 Switched-apacitor Filter Switched-capacitor integrator DDI integrator LDI integrator Effect of paraitic capacitance Bottom-plate integrator topology Reonator Bandpa filter Lowpa filter