EE247 Lecture 7. Example Gm-C BP filter using simple diff. pair. Various Gm-C Filter implementations Comparison of continuous-time filter topologies

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1 Summary lat lecture EE247 Lecture 7 Continuoutime filter Bandpa filter Example GmC BP filter uing imple diff. pair Linearity Noie Variou GmC Filter implementation Comparion of continuoutime filter topologie EECS 247 Lecture 7: Filter 2004 H.K. Page Summary lat lecture Automatic onchip filter tuning Continuou tuning Materlave tuning Periodic offline tuning Sytem where filter i followed by ADC & DSP, exiting hardware can be ued to periodically update filter freq. repone EECS 247 Lecture 7: Filter 2004 H.K. Page 2

MaterSlave Frequency Tuning Reference VoltageControlledOcillator (VCO) Intead of VCF a voltagecontrolledocillator (VCO) i ued VCO made or

Tan and P.R. Gray, Fully integrated analog filter uing bipolar FET technology, IEEE, J. SolidState Circuit, vol. SC3, no.6, pp.

Page 3 MaterSlave Frequency Tuning Reference Filter (VCF) Replica Filter (Mater) Main Filter (Slave) Vo Vin R* R Phae Comparator Amp.

2 MaterSlave Frequency Tuning Reference VoltageControlledOcillator (VCO) Intead of VCF a voltagecontrolledocillator (VCO) i ued VCO made or replica integrator Tuning circuit operate exactly a a conventional phaelocked loop (PLL) Tuning ignal ued to tune main filter Ref: K.S. Tan and P.R. Gray, Fully integrated analog filter uing bipolar FET technology, IEEE, J. SolidState Circuit, vol. SC3, no.6, pp. 8482, December EECS 247 Lecture 7: Filter 2004 H.K. Page 3 MaterSlave Frequency Tuning Reference Filter (VCF) Replica Filter (Mater) Main Filter (Slave) Vo Vin R* R Phae Comparator Amp. Filter τ τ0 VLP τ 2 τ0 Q Vtune τ 3 τ 4 R* R τ 5 Vr e f Ref: H. Khorramabadi and P.R. Gray, High Frequency CMOS continuoutime filter, IEEE Journal of SolidState Circuit, Vol.SC9, No. 6, pp , Dec EECS 247 Lecture 7: Filter 2004 H.K. Page 4 L

3 Reference C/Gm Locked to Ref. Frequency P2 high S2 cloed Vref Gm S2 I=Gm*Vref C S3 C2 A Charge C with I=Gm*Vref P2 VC VC Gm Vref T2 C T T2 EECS 247 Lecture 7: Filter 2004 H.K. Page 5 Reference C/Gm Locked to Ref. Frequency P3 high S3 cloed Vref Gm S2 C S3 C2 A T T2 Charge on C hared with C2 Feedback force Gm to aume a value: VC= VC2 = Vref ince: VC = Gm Vref T2 C then: Vref = Gm V ref T2 C or: C = T2= N/fclk Gm EECS 247 Lecture 7: Filter 2004 H.K. Page 6

4 Reference C/Gm Locked to Ref. Frequency Incorporating Offet Cancellation P2 P3 Vref/2 Vcm Vref/2 P2B P2B C3a C3b P P2 P2 P C P3 P3 C2 P2 P3 Vtune Gmcell two et of input pair Aux. input pair C3a,b Offet cancellation Same clock timing EECS 247 Lecture 7: Filter 2004 H.K. Page 7 DC Tuning of Reitive Timing Element Rext ued to lock Gm or onchip R I Gm Vtune Feedback force Gm=/Rext Account for Cap. variation in the gmc implementation by trimming Rext. I Ref: C. Laber and Gray, A 20MHz 6th Order BiCOM Paraitic Inenitive Continuoutime Filter and Second Order Equalizer Optimized for Dik Drive Read Channel, IEEE Journal of Solid State Circuit, Vol. 28, pp , April 993 EECS 247 Lecture 7: Filter 2004 H.K. Page 8

5 Offline Frequency Tuning Example:Wirele Receiver Baeband Filter A/D RF Amp IF Stage ( 0 to 2 ) Oc. p 2 A/D Digital Signal Proceor (DSP) Sytem where filter i followed by ADC & DSP Take advantage of exiting digital ignal proceor to periodically update the filter critical frequency Filter tuned only at the outet of each data tranmiion eion (offline tuning) EECS 247 Lecture 7: Filter 2004 H.K. Page 9 Offline Filter Tuning Concept EECS 247 Lecture 7: Filter 2004 H.K. Page 0

6 Summary Filter Frequency Tuning Trimming Expenive Doe not account for variation aociated with temperature and upply etc Automatic frequency tuning Continuou tuning Mater VCF ued in tuning loop Tuning quite accurate Iue reference ignal feedthrough to the filter output Mater VCO ued in tuning loop Deign of reliable & table VCO challenging Iue reference ignal feedthrough Single integrator in negative feedback loop force timecontant to be a function of accurate clock frequency More flexibility in choice of reference frequency le feedthrough iue Locking a replica of the Gmcell to an external reitor DC offet iue Doe not account for integrating capacitor variation Periodic tuning Require digital capability minimal additional hardware Advantage of no reference ignal feedthrough ince tuning performed offline EECS 247 Lecture 7: Filter 2004 H.K. Page Bandpa Filter Bandpa Filter: Q < 5 Combination of lowpa & highpa Lowpa H( jω) ω Highpa H( jω) ω H( jω) Q<5 ω H( jω) Q > 5 Direct implementation Q>5 ω EECS 247 Lecture 2: Filter 2004 H.K. Page 2

7 Direct Implementation Narrow Band Bandpa Filter Lowpa Freq. Mak Bandpa Freq. Mak ωc Ω Ω2 Ω = Q ωc = Ωc ΩB2 ΩB Deign baed on lowpa prototype for narrow band filter Same lowpa table ued EECS 247 Lecture 7: Filter 2004 H.K. Page 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 247 Lecture 7: Filter 2004 H.K. Page 4

8 Lowpa to Bandpa Tranformation Table ( Ω Ω ) a = B2 a = Qfilter B From: Zverev, Handbook of filter ynthei, Wiley, 967 p.57. EECS 247 Lecture 7: Filter 2004 H.K. Page 5 Lowpa to Bandpa Tranformation Lowpa Bandpa Vin R C L2 C3 V o RL Vin R C L L2 C2 L3 C3 V o RL Each capacitor replaced by parallel L& C Each inductor replaced by erie L&C EECS 247 Lecture 7: Filter 2004 H.K. Page 6

9 Lowpa to Bandpa Tranformation ' C = QC R ω R L = ω ' QC 2 ' QL2 3 ' QC C = Rω ' R L2 = QL2 ω 0 ' C3 = QC3 Rω R L = ω 0 Vin R C L L2 C2 L3 C3 V o RL Where: C, L 2, C 3, normalized lowpa value Q bandpa filter quality factor & filter center frequency ω 0 EECS 247 Lecture 7: Filter 2004 H.K. Page 7 Signal Flowgraph 6 th Order Bandpa Filter Vin R C L L2 C2 L3 C3 V o RL Vin V out * R R * R C * L R R * L2 C * 2R * R L3 C * 3R * R RL Note each C & L in the original lowpa prototype replaced by a reonator Subtituting the bandpa L, C,.. by their normalized lowpa equivalent previou page The reulting SFG i: EECS 247 Lecture 7: Filter 2004 H.K. Page 8

10 Signal Flowgraph 6 th Order Bandpa Filter Vin V out * R R ' QC ω 0 QC ' QL ' 2 ' QC 3 ω 0 ' QL2ω 0 ' QC3 * R RL Note the integrator have different time contant Ratio of time contant for each reonator ~/Q 2 typically, require high component ratio poor matching Deirable to convert SFG o that all integrator have equal time contant for optimum matching. Scale node to obtain equal integrator time contant EECS 247 Lecture 7: Filter 2004 H.K. Page 9 Signal Flowgraph 6 th Order Bandpa Filter Vin ' QL 2 ' QL 2 V out ω QC ' 0 ω 0 QC3 ' QC ' QC3 Note: Three reonator All integrator timecontant are equal Let u try to build thi bandpa filter uing the imple GmC tructure EECS 247 Lecture 7: Filter 2004 H.K. Page 20

11 Second Order GmC Filter Uing Simple SourceCouple Pair GmCell Center frequency: M,2 gm ω o = 2 Cintg Q function of: M,2 g Q = m g M3,4 m To ue thi tructure it i eaier to couple reonator through capacitive coupling EECS 247 Lecture 7: Filter 2004 H.K. Page 2 Signal Flowgraph 6 th Order Bandpa Filter Vin Q CL ' ' 2 ' ' Q C3L2 V out ω QC ' 0 ω 0 QC3 Q C ' L ' 2 ' C ' ' QC3 L2 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 2 =2 Aume overall bandpa filter Q=0 EECS 247 Lecture 7: Filter 2004 H.K. Page 22

12 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 2 4 EECS 247 Lecture 7: Filter 2004 H.K. Page 23 Sixth Order Bandpa Filter Signal Flowgraph For narrow band filter (high Q) where frequencie within the paband are cloe to ω 0 narrowband approximation can be ued: The reulting SFG: γ Vin V out Q γ γ Q γ EECS 247 Lecture 7: Filter 2004 H.K. Page 24

13 Sixth Order GmC Bandpa Filter Utilizing Simple SourceCoupled Pair GmCell Ck γ = 2 Cintg γ = /4 Ck = 7 Cintg Paraitic C at integrator output, if unaccounted for, will reult in inaccuracy in g EECS 247 Lecture 7: Filter 2004 H.K. Page 25 Sixth Order GmC Bandpa Filter Frequency Repone Simulation EECS 247 Lecture 7: Filter 2004 H.K. Page 26

14 Simplet Form of CMOS GmCell Nonidealitie DC gain (integrator Q) g M,2 a = m g M,2 0 g load a = θ 2L ( Vg Vth ) M,2 Small Signal Differential Mode HalfCircuit Where θ i related to channel length modulation by: θ λ = L Seem no extra pole! EECS 247 Lecture 7: Filter 2004 H.K. Page 27 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 247 Lecture 7: Filter 2004 H.K. Page 28

15 CMOS GmCell HighFrequency Pole effective P2 = High frequency behavior of an MOS tranitor i= 2 Pi effective M,2 P2 2.5ω t ω ( Vg Vth ) M,2 µ M,2 gm 3 t = = C WL 2 2 ox L M,2 Ditributed nature of gate capacitance & channel reitance reult in an effective pole at 2.5 time input device cutoff frequency EECS 247 Lecture 7: Filter 2004 H.K. Page 29 CMOS GmCell Quality Factor a = θ 2L ( Vg Vth ) M,2 ( Vg Vth ) M,2 µ effective 5 P 2 = 4 2 L Q intg. real a ωo p i= 2 i ( V V ) θ 2 g th M,2 4 ωo L intg. Q 2L 5 µ ( VgV real th) M,2 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 247 Lecture 7: Filter 2004 H.K. Page 30

16 CMOS Gm Cell Channel Length for Optimum Quality Factor L. 5 opt. 4 θµ ( VgVth) ωo 2 /3 M,2 Optimum channel length computed baed on proce parameter EECS 247 Lecture 7: Filter 2004 H.K. Page 3 Linearity of the SourceCoupled Pair CMOS GmCell Ideal Gm Large ignal Gm drop a input voltage increae Give rie to filter nonlinearity EECS 247 Lecture 7: Filter 2004 H.K. Page 32

17 SourceCoupled Pair CMOS GmCell Linearity 2 vi v i I I () ( V g V th) 4 ( V g V th) d = M,2 M,2 2 3 d i 2 i 3 i I = a v a v a v... /2 Serie expanion ued in() EECS 247 Lecture 7: Filter 2004 H.K. Page 33 Meaure of Linearity Vout = α Vin α Vin α Vin amplitude3 rdharmonicdit. comp. HD3 = amplitude fundamental α 4 α 3 2 = Vin... Vin Vout w w w 3w w amplitude3 rdorderim comp. IM 3 = amplitudefundamental 3α 25 α 4α 8 α = Vin Vin... w Vin Vout w 2 w w w 2 w 2w w 2 2w 2 w EECS 247 Lecture 7: Filter 2004 H.K. Page 34

18 Linearity of the SourceCoupled Pair CMOS GmCell 3 ( ) % & ˆ rm IM = V V = V V 230mV GS th in Key point: Max. ignal handling capability function of gateoverdrive EECS 247 Lecture 7: Filter 2004 H.K. Page 35 ince then Simplet Form of CMOS Gm Cell Diadvantage Max. ignal handling capability function of gateoverdrive 2 IM3 ( VGS Vth ) Critical freq. function of gateoverdrive too g M,2 m ωo = 2 Cintg W g m = µ C V g th ωo ox L ( V ) ( Vg Vth ) Filter tuning affect max. ignal handling capability! EECS 247 Lecture 7: Filter 2004 H.K. Page 36

19 Simplet Form of CMOS Gm Cell Removing Dependence of Maximum Signal Handling Capability on Tuning Can overcome problem of max. ignal handling capability 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 247 Lecture 7: Filter 2004 H.K. Page 37 Dynamic Range for SourceCoupled Pair Baed Filter ( ) rm IM3 = % & V V = V V 230mV GS th in It can be hown for the 6 th order Butterworth bandpa filter noie i given by: v 2 o kt 3Q C intg Auming Q= 0 Cintg = 5pF rm vnoie 60µ V rm ince vmax = 230mV DynamicRange 63dB EECS 247 Lecture 7: Filter 2004 H.K. Page 38

20 Improving the Max. Signal Handling Capability of the SourceCoupled Pair GmCell 2 nd ourcecoupled pair added to ubtract current from the main SCP EECS 247 Lecture 7: Filter 2004 H.K. Page 39 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 247 Lecture 7: Filter 2004 H.K. Page 40

21 Improving the Max. Signal Handling Capability of the SourceCoupled Pair Gm Improve maximum ignal handling capability by about 2dB > Dynamic range theoretically improved to 632=75dB EECS 247 Lecture 7: Filter 2004 H.K. Page 4 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 Solid State Circuit, Vol.SC9, No. 6, pp , Dec EECS 247 Lecture 7: Filter 2004 H.K. Page 42

22 GmCell SourceCoupled Pair with Degeneration µ C W I ox 2 d = 2( Vg Vth ) Vd V 2 L d Id W gd = µ C ox Vg Vth Vd L geff = 2 M3 M,2 g d gm M,2 M3 for gm g d M3 geff g d ( ) Vd mall M3 operating in triode mode, determine the gm EECS 247 Lecture 7: Filter 2004 H.K. Page 43 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,2 Low frequency application only Ref: Y. Tividi, Z. Czarnul and S.C. Fang, MOS tranconductor and integrator with high linearity, Electronic Letter, vol. 22, pp , Feb. 27, 986 EECS 247 Lecture 7: Filter 2004 H.K. Page 44

23 MOSFET in triode mode: BiCMOS GmCell µ C W I ox 2 d = 2( Vg Vth ) Vd V 2 L d Note that if Vd i kept contant: Id W gm= = µ C ox V V L d g Linearity performance function of how contant Vd can be held Node X mut be minimized A g M g B x = m m Since for a given current, gm of BJT i larger compared to MOS preferable to have BJT Extra pole at node X VgVin Vb I Iout B X M gm can be varied by changing Vb and thu Vd EECS 247 Lecture 7: Filter 2004 H.K. Page 45 CMOS Alternative GmCell 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 Ref: D.A. John, K. Martin Analog Integrated Circuit Wiley, 997, p.606 EECS 247 Lecture 7: Filter 2004 H.K. Page 46

24 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/2 Cintg/2 Vout EECS 247 Lecture 7: Filter 2004 H.K. Page 47 7 th Order Elliptic GmC LPF For CDMA RX Baeband Application Vin A CB A B A B A B A B A B 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 247 Lecture 7: Filter 2004 H.K. Page 48

25 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 cap. area 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 A Vin B C A B A B GmC Filter A A OpampRC Filter A B B A B B V o Vout EECS 247 Lecture 7: Filter 2004 H.K. Page 49 Ued to build filter for dikdrive application Since high frequency of operation, timecontant enitivity to paraitic cap ignificant. Opamp ued M2 & M3 added to compenate for phae lag (provide phae lead) BiCMOS GmOTAC Integrator Ref: C. Laber and P.Gray, A 20MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read Channel, IEEE Journal of Solid State Circuit, Vol. 28, pp , April 993. EECS 247 Lecture 7: Filter 2004 H.K. Page 50

26 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 2 each Performance in the order of 40dB SNDR achieved for up to 20MHz corner frequency Ref: C. Laber and P.Gray, A 20MHz 6th Order BiCMOS Paraitic Inenitive Continuoutime Filter & Second Order Equalizer Optimized for Dik Drive Read Channel, IEEE Journal of Solid State Circuit, Vol. 28, pp , April 993. EECS 247 Lecture 7: Filter 2004 H.K. Page 5 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.32, No.4, pp EECS 247 Lecture 7: Filter 2004 H.K. Page 52

27 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,2 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 25MHz achieved EECS 247 Lecture 7: Filter 2004 H.K. Page 53 BiCMOS GmC Integrator Need higher upply voltage compared to the previou deign M5 & M6 configured a capacitor added to compenate for RHP zero due to Cgd of M & M2 (move it to LHP) ize of M56 i /3 of M2 Current ID ued to tune filter critical frequency M3, M4 operate in triode mode and added to provide CMFB Ref: R. Alini, A. Bachirotto, and R. Catello, Tunable BiCMOS ContinuouTime Filter for HighFrequency Application, IEEE Journal of Solid State Circuit, Vol. 27, No. 2, pp , Dec EECS 247 Lecture 7: Filter 2004 H.K. Page 54

28 BiCMOS GmC Filter For DikDrive Application Uing the integrator hown in the previou page Biquad filter for dik drive gm=gm2=gm4=2gm3 Q=2 Tunable from 8MHz to 32MHz Ref: R. Alini, A. Bachirotto, and R. Catello, Tunable BiCMOS ContinuouTime Filter for HighFrequency Application, IEEE Journal of Solid State Circuit, Vol. 27, No. 2, pp , Dec EECS 247 Lecture 7: Filter 2004 H.K. Page 55 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 247 Lecture 7: Filter 2004 H.K. Page 56

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

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