EE247 Lecture 8. Lowpass to bandpass transformation Example: Gm-C BP filter using simple diff. pair

Transcription

1 EE47 Lecture 8 Summary of lat lecture Continuoutime filter Bandpa filter Lowpa to bandpa tranformation Example: GmC BP filter uing imple diff. pair Linearity & noie iue Variou GmC Filter implementation Comparion of continuoutime filter topologie Switchedcapacitor filter EECS 47 Lecture 8: Filter 006 H.K. Page Summary Lat Lecture Automatic onchip filter tuning (continued from lat lecture) Continuou tuning Reference integrator locked to a reference frequency Error due to integrator DC offet and cancellation method DC tuning of reitive timing element Periodic digitally aited tuning Sytem where filter i followed by ADC & DSP, exiting hardware can be ued to periodically update filter freq. repone Continuoutime filter High pa filter EECS 47 Lecture 8: Filter 006 H.K. Page

2 Bandpa Filter Bandpa Filter: Low Q (Q < 5) Combination of lowpa & highpa Lowpa H( jω) ω Highpa H( jω) ω Bandpa H( jω) Q<5 ω High Q or narrowband (Q > 5) Direct implementation H( jω) Bandpa Q>5 ω EECS 47 Lecture 8: Filter 006 H.K. Page 3 NarrowBand Bandpa Filter Direct Implementation Narrowband BP filter Deign baed on lowpa prototype Same table ued for LPF are ued for BPF Lowpa Freq. Mak Bandpa Freq. Mak ω Q c ωc Ω Ω Ω Ωc ΩB ΩB EECS 47 Lecture 8: Filter 006 H.K. Page 4

3 Lowpa to Bandpa Tranformation Lowpa pole/zero (plane) Bandpa pole/zero (plane) Pole Zero From: Zverev, Handbook of filter ynthei, Wiley, 967 p.56. EECS 47 Lecture 8: Filter 006 H.K. Page 5 Lowpa to Bandpa Tranformation Table Lowpa filter tructure & table ued to derive bandpa filter Q = Q filter LP BP BP Value C C L C = QC R ω Rr L = QC ω r r r From: Zverev, Handbook of filter ynthei, Wiley, 967 p.57. L L C L C C &L are normilzed LP value Rr = QL ω = QC R ω r r r EECS 47 Lecture 8: Filter 006 H.K. Page 6

4 Lowpa to Bandpa Tranformation Example: 3 rd Order LPF 6 th Order BPF Lowpa Bandpa Vin R V o L C C3 RL Vin R C L L C L3 C3 V o RL Each capacitor replaced by parallel L& C Each inductor replaced by erie L&C EECS 47 Lecture 8: Filter 006 H.K. Page 7 Lowpa to Bandpa Tranformation Example: 3 rd Order LPF 6 th Order BPF C = QC R ω R L = ω QC QL 3 QC C = Rω R L = QL ω 0 C3 = QC3 Rω R L = ω 0 Vin Where: R C L L C L3 C3 V o RL C, L, C 3 Normalized lowpa value Q Bandpa filter quality factor Filter center frequency ω 0 EECS 47 Lecture 8: Filter 006 H.K. Page 8

5 Lowpa to Bandpa Tranformation Signal Flowgraph L C V o Vin R C L L3 C3 RL 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 ) 4Ue tate pace decription to draw SFG 5 Convert all current node to voltage EECS 47 Lecture 8: Filter 006 H.K. Page 9 Signal Flowgraph 6 th Order Bandpa Filter V V in V 3 V V out * * R R R C * L R * R L C * R * R L3 C * 3R * R RL 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 8 The reulting SFG i: EECS 47 Lecture 8: Filter 006 H.K. Page 0

6 Signal Flowgraph 6 th Order Bandpa Filter V in V 3 V V V out * R R QC ω 0 QC QL QC 3 ω 0 QLω 0 ω 0 QC3 * R RL V V V 3 Note the integrator different time contant Ratio of time contant for two integrator in each reonator ~ Q Typically, require high component ratio Poor matching Deirable to convert SFG o that all integrator have equal time contant for optimum matching. To obtain equal integrator time contant cale node EECS 47 Lecture 8: Filter 006 H.K. Page Signal Flowgraph 6 th Order Bandpa Filter V in V QL V /(QL ) QL V 3 V out * R R QC V /(QC ) QC V QC3 V 3 /(QC 3 ) * R RL QC3 All integrator timecontant equal To implify implementation chooe RL=R=R* EECS 47 Lecture 8: Filter 006 H.K. Page

7 Signal Flowgraph 6 th Order Bandpa Filter V in QL QL V out ω 0 QC QC 3 QC QC3 Let u try to build thi bandpa filter uing the imple GmC tructure EECS 47 Lecture 8: Filter 006 H.K. Page 3 Second Order GmC Filter Uing Simple SourceCouple Pair GmCell Center frequency: M, gm ω o = Cintg Q function of: M, g Q = m g M3,4 m 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 006 H.K. Page 4

8 Coupling of the Reonator Additional Set of Input Device V in QL QL V out ω 0 QC QC 3 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 006 H.K. Page 5 Example: Coupling of the Reonator 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 V main in M3 C int g M4 M V o EECS 47 Lecture 8: Filter 006 H.K. Page 6

9 Coupling of the Reonator Modify SFG Bidirectional Coupling Path Vin Q CL Q C3L V out ω 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 006 H.K. Page 7 Sixth Order Bandpa Filter Signal Flowgraph Vin γ γ V out ω 0 ω 0 Q Q γ γ Where for a Butterworth hape Since Q=0 then: γ γ = Q 4 EECS 47 Lecture 8: Filter 006 H.K. Page 8

10 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification Vin γ V out Q γ γ Q γ EECS 47 Lecture 8: Filter 006 H.K. Page 9 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification For narrow band filter (high Q) where frequencie within the paband are cloe to ω 0 narrowband approximation can be ued: Within filter paband: ω = jω γ γ γ The reulting SFG: EECS 47 Lecture 8: Filter 006 H.K. Page 0

11 Sixth Order Bandpa Filter Signal Flowgraph SFG Modification Vin γ V out Q γ γ Q γ Bidirectional coupling path, can eaily be implemented with coupling capacitor no extra power diipation EECS 47 Lecture 8: Filter 006 H.K. Page Sixth Order GmC Bandpa Filter Utilizing Simple SourceCoupled Pair GmCell γ γ Ck = Cint g Ck = /4 Ck = 3 Cint g Paraitic cap. at integrator output, if unaccounted for, will reult in inaccuracy in γ EECS 47 Lecture 8: Filter 006 H.K. Page

12 Sixth Order GmC Bandpa Filter NarrowBand veru Exact Frequency Repone Simulation Q=0 Regular Filter Repone NarrowBand Approximation EECS 47 Lecture 8: Filter 006 H.K. Page 3 DC gain (integrator Q) Simplet Form of CMOS GmCell Nonidealitie M, g a = m g M, 0 g load a = θ L ( Vg Vth ) M, Small Signal Differential Mode HalfCircuit Where a denote DC gain & θ i related to channel length modulation by: θ λ = L Seem no extra pole! EECS 47 Lecture 8: Filter 006 H.K. Page 4

13 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 006 H.K. Page 5 CMOS GmCell HighFrequency Pole effective P i= Pi High frequency behavior of an MOS tranitor effective P.5 ω ω M, t μ ( Vg Vth ) M, M, gm 3 t = = C WL ox L M, Ditributed nature of gate capacitance & channel reitance reult in an effective pole at.5 time input device cutoff frequency EECS 47 Lecture 8: Filter 006 H.K. Page 6

14 Simple GmCell Quality Factor a = θ L ( Vg Vth ) M, ( Vg Vth ) M, μ effective 5 P = 4 L Q intg. real a ωo p i= i ( V V ) θ g th M, 4 ωol intg. Q L 5 μ ( Vg Vth ) M, Note that the phae lead aociated with DC gain i inverely prop. to L The phae lag due to highfreq. pole directly prop. to L For a given ω ο there exit an optimum L which cancel the lead/lag phae error reulting in high integrator Q EECS 47 Lecture 8: Filter 006 H.K. Page 7 Simple GmCell Channel Length for Optimum Integrator Quality Factor L. 5 opt. 4 θμ ( VgVth) ωo /3 M, Optimum channel length computed baed on proce parameter (could vary from proce to proce) EECS 47 Lecture 8: Filter 006 H.K. Page 8

15 SourceCoupled Pair CMOS GmCell Tranconductance For a ourcecoupled pair the differential output current (ΔI d ) a a function of the input voltage(δv i ): Δvi v Δ i I Δ d = I ( V g V th) 4 ( V V ) M, g th M, / Δvi ΔId Note:For mall = g ( V g V th) Δvi M, ΔId A Δvi increae or the Δvi effective tranconductance decreae M,M m Δ v = V V i i i Δ I = I I d d d EECS 47 Lecture 8: Filter 006 H.K. Page 9 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 006 H.K. Page 30

16 Meaure of Linearity Vout = α Vin α Vin α Vin amplitude3 rd harmonicdit. comp. HD3 = amplitude fundamental α Vin 4 α 3 =... Vin Vout ω ω ω 3ω ω amplitude3 rd order IM comp. IM 3 = amplitude fundamental 3α 5α Vin Vin 4α 8 α =... Vin Vout ω ω ω ω ω ω ω ω ω ω EECS 47 Lecture 8: Filter 006 H.K. Page 3 ( V g V th) SourceCoupled Pair GmCell Linearity Δvi v i I I Δ () ( V g V th) 4 ( V g V th) Δ d = M, M, 3 d i i 3 i Δ I = a Δ v a Δ v a Δ v... Serie expanion ued in () I a = & a = 0 5 M, I a 3 = & a 3 4 = 0 8V a ( g V th) I = 8 V V M, ( g th) 5 M, & a = 0 6 / EECS 47 Lecture 8: Filter 006 H.K. Page 3

17 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) ˆvimax 4 ( VGS Vth) IM3 3 ( ) IM = % & V V = V Vˆ 30mV rm 3 GS th in Key point: Max. ignal handling capability function of gateoverdrive EECS 47 Lecture 8: Filter 006 H.K. Page 33 Simplet Form of CMOS Gm Cell Diadvantage Max. ignal handling capability function of gateoverdrive IM3 ( VGS Vth) Critical freq. function of gateoverdrive too g M, m ωo = Cint g ince then g m = μ C ωo W V g th ox L ( V ) ( Vg Vth ) Filter tuning affect max. ignal handling capability! EECS 47 Lecture 8: Filter 006 H.K. Page 34

18 Simplet Form of CMOS Gm Cell Removing 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) Ref: R.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 006 H.K. Page 35 Dynamic Range for SourceCoupled Pair Baed Filter ( ) rm IM 3 = % & V V = V V 30mV GS th in Minimum detectable ignal determined by total noie voltage It can be hown for the 6 th order Butterworth bandpa filter noie i given by: vo kt 3 Q C intg Auming Q = 0 Cintg = 5pF rm vnoie 60μV rm ince vmax = 30mV Dynamic Range 63dB EECS 47 Lecture 8: Filter 006 H.K. Page 36

19 Improving the Max. Signal Handling Capability of the SourceCoupled Pair GmCell nd ourcecoupled pair added to ubtract current proportional to nonlinear component aociated with the main SCP I I 3 W ( L ) W ( ) L M, M3,4 ( V g V th) ( V g V th) M, = b & = a and thu = b a M3,4 EECS 47 Lecture 8: Filter 006 H.K. Page 37 Improving the Max. Signal Handling Capability of the SourceCoupled Pair Gm Ref: H. Khorramabadi, "HighFrequency CMOS ContinuouTime Filter," U. C. Berkeley, Department of Electrical Engineering, Ph.D. Thei, February 985 (ERL Memorandom No. UCB/ERL M85/9). EECS 47 Lecture 8: Filter 006 H.K. Page 38

20 Improving the Max. Signal Handling Capability of the SourceCoupled Pair Gm Improve maximum ignal handling capability by about db Dynamic range theoretically improved to 63=75dB EECS 47 Lecture 8: Filter 006 H.K. Page 39 Simplet Form of CMOS GmCell Pro Capable of very high frequency performance (highet?) Simple deign Con Tuning affect power diipation Tuning affect max. ignal handling capability (can overcome) Limited linearity (poible to improve) Ref: H. Khorramabadi and P.R. Gray, High Frequency CMOS continuoutime filter, IEEE Journal of SolidState Circuit, Vol.SC9, No. 6, pp , Dec EECS 47 Lecture 8: Filter 006 H.K. Page 40

21 GmCell SourceCoupled Pair with Degeneration μc W I ox d = ( Vg Vth ) Vd V L d I W g d d = μc V ox d L Vg Vth geff = M3 M, g d gm M, M3 for gm >> g d geff M3 g d ( ) Vd mall M3 operating in triode mode ource degeneration determine overall gm EECS 47 Lecture 8: Filter 006 H.K. Page 4 GmCell SourceCoupled Pair with Degeneration Pro Moderate linearity Continuou tuning provided by Vc Tuning doe not affect power diipation Con Extra pole aociated with the ource of M, Low frequency application only Ref: 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 006 H.K. Page 4

22 BiCMOS GmCell Example MOSFET in triode mode: μc W I ox d = ( Vg Vth ) Vd V L d Note that if Vd i kept contant: Id W gm= = μc ox V V L d g Linearity performance keep gm contant function of how contant Vd can be held Need to minimize Node X A g M g B x = m m Since for a given current, gm of BJT i larger compared to MOS preferable to ue BJT Extra pole at node X Vb VcmVin I Iout B X M gm can be varied by changing Vb and thu Vd EECS 47 Lecture 8: Filter 006 H.K. Page 43 Alternative Fully CMOS GmCell Example BJT replaced by a MOS tranitor with booted gm 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 006 H.K. Page 44

23 BiCMOS GmC Integrator Differential need commonmode feedback ckt Freq.tuned by varying Vb Deign tradeoff: Extra pole at the input device drain junction Input device have to be mall to minimize paraitic pole Reult in high inputreferred offet voltage could drive ckt into nonlinear region Small device high /f noie Cintg/ Cintg/ Vout EECS 47 Lecture 8: Filter 006 H.K. Page 45 7 th Order Elliptic GmC LPF For CDMA RX 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 006 H.K. Page 46

24 Comparion of 7 th Order GmC veru OpampRC LPF GmC filter require 4 time le intg. cap. area compared to OpampRC For lownoie application where filter area i dominated by C, could make a ignificant difference in the total area OpampRC linearity uperior compared to GmC Power diipation tend to be lower for GmC ince output i high impedance and thu no need for buffering V in Vin A B A B GmC Filter OpampRC Filter A B A B A C B A B A B V o Vout EECS 47 Lecture 8: Filter 006 H.K. Page 47 Ued to build filter for dikdrive application Since high frequency of operation, timecontant enitivity to paraitic cap ignificant. Opamp ued M & M3 added to compenate for phae lag (provide phae lead) BiCMOS GmOTAC Integrator Ref: C. Laber and P.Gray, A 0MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read Channel, IEEE Journal of Solid State Circuit, Vol. 8, pp , April 993. EECS 47 Lecture 8: Filter 006 H.K. Page 48

25 6th Order BiCMOS Continuoutime Filter & Second Order Equalizer for Dik Drive Read Channel GmCopamp of the previou page ued to build a 6 th order filter for Dik Drive Filter conit of 3 Biquad with max. Q of each Performance in the order of 40dB SNDR achieved for up to 0MHz corner frequency Ref: C. Laber and P.Gray, A 0MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read Channel, IEEE Journal of Solid State Circuit, Vol. 8, pp , April 993. EECS 47 Lecture 8: Filter 006 H.K. Page 49 GmCell SourceCoupled Pair with Degeneration Gmcell intended for low Q dik drive filter Ref: I.Mehr and D.R.Welland, "A CMOS ContinuouTime GmC Filter for PRML Read Channel Application at 50 Mb/ and Beyond", IEEE Journal of SolidState Circuit, April 997, Vol.3, No.4, pp EECS 47 Lecture 8: Filter 006 H.K. Page 50

26 GmCell SourceCoupled Pair with Degeneration M7,8 operating in triode mode determine the gm of the cell Feedback provided by M5,6 maintain the gateource voltage of M, contant by forcing their current to be contant help linearize rd of M7,8 Current mirrored to the output via M9,0 with a factor of k Performance level of about 50dB SNDR at fcorner of 5MHz achieved EECS 47 Lecture 8: Filter 006 H.K. Page 5 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 BiCMOS GmC Integrator Current ID ued to tune filter critical frequency by varying V d of M, and thu gm of M, M3, M4 operate in triode mode and added to provide commonmode feedback Ref: R. Alini, A. Bachirotto, and R. 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 006 H.K. Page 5

27 M5 & M6 configured a capacitor added to compenate for RHP 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 Ref: R. Alini, A. Bachirotto, and R. 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 006 H.K. Page 53 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 Ref: R. Alini, A. Bachirotto, and R. 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 006 H.K. Page 54

28 Summary ContinuouTime Filter Opamp RC 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 MOSFETRC Improved linearity compared to Opamp MOSFETC (D.R. 5090dB) Continuou tuning poible Low uable ignal bandwidth (<5MHz) GmC Highet frequency performance (at leat an order of magnitude higher compared to the ret <00MHz) Dynamic range not a high a Opamp RC but better than Opamp MOSFETC (4070dB) EECS 47 Lecture 8: Filter 006 H.K. Page 55 SwitchedCapacitor Filter Example: Codec Chip f = 04kHz f = 8kHz f = 8kHz f = 8kHz f = 8kHz f = 8kHz f = 8kHz f = 8kHz Ref: D. Senderowicz et. al, A Family of Differential NMOS Analog Circuit for PCM Codec Filter Chip, IEEE Journal of SolidState Circuit, Vol.SC7, No. 6, pp.0403, Dec. 98. EECS 47 Lecture 8: Filter 006 H.K. Page 56

29 SwitchedCapacitor Reitor Capacitor C i the witched capacitor φ φ Nonoverlapping clock φ and φ control witche S and S, repectively v IN i ampled at the falling edge of φ v IN S C S v OUT Sampling frequency f S Next, φ rie and the voltage acro C i tranferred to v OUT φ Why i thi a reitor? φ T=/f EECS 47 Lecture 8: Filter 006 H.K. Page 57 SwitchedCapacitor Reitor Charge tranferred from v IN to v OUT during each clock cycle i: v IN φ φ S S v OUT Q = C(v IN v OUT ) C Average current flowing from v IN to v OUT i: φ i=q/t = Qxf i =f S C(v IN v OUT ) φ T=/f EECS 47 Lecture 8: Filter 006 H.K. Page 58

30 SwitchedCapacitor Reitor i = f S C(v IN v OUT ) φ φ With the current through the witched capacitor reitor proportional to the voltage acro it, the equivalent witched capacitor reitance i: v IN S S C v OUT R eq = fc Example f = MHz, C = pf R eq = MegaΩ φ φ T=/f EECS 47 Lecture 8: Filter 006 H.K. Page 59 SwitchedCapacitor Filter Let build a SC filter We ll tart with a imple RC LPF v IN R EQ v OUT Replace the phyical reitor by an equivalent SC reitor C 3dB bandwidth: φ φ C ω f 3dB = = R C eq C C f f 3dB = π C v IN S C S v OUT C EECS 47 Lecture 8: Filter 006 H.K. Page 60

31 SwitchedCapacitor Filter Advantage veru ContinuouTime Filter φ φ R eq V in S S V out V in V out C C C f C π C 3dB = f Corner freq. proportional to: Sytem clock (accurate to few ppm) C ratio accurate << 0.% f = π 3 db R eq C Corner freq. proportional to: Abolute value of R & C Poor accuracy 0 to 50% Main advantage of SC filter inherent corner frequency accuracy EECS 47 Lecture 8: Filter 006 H.K. Page 6