Summary Last Lecture. EE247 Lecture 6. Use of MOSFETs as Resistors Single-Ended Integrator. Use of MOSFETs as Resistors Differential Integrator

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1 EE247 ecture 6 Summary lat lecture ontinuoutime filter Opamp MOSFET filter Opamp MOSFET filter filter Frequency tunin for continuoutime filter Trimmin via fue utomatic onchip filter tunin ontinuou tunin Materlave tunin Periodic offline tunin Sytem where filter i followed by D & DSP, exitin hardware can be ued to periodically update filter freq. repone Ue of MOSFET a eitor SinleEnded nterator 2 D µ ox d ( th ) d 2 2 i µ ox ( D th ) i 2 D G µ ox ( th i) i Problem: Sinleended MOSFET nterator Effective nonlinear Note that the nonlinearity i mainly 2 nd order type D G Tunable by varyin G: EES 247 ecture 6: Filter 2005 H.K. Pae EES 247 ecture 6: Filter 2005 H.K. Pae 3 Summary at ecture Ue of MOSFET a eitor Differential nterator ontinuoutime filter Effect of interator nonidealitie on continuoutime filter behavior Fact about monolithic & and it effect on interated filter characteritic Opamp filter Opamp MOSFET filter Frequency tunin for continuoutime filter Frequency adjutment by makin proviion to have variable or d D µ ox th d 2 i i D µ ox th 4 2 i i D2 µ ox th 4 2 D D2 µ ox ( th ) i ( D D2) G µ ox th i ( ) Nonlinear term cancelled! dmittance independent of i Problem: Threhold voltae dependence i/2 i/2 G D M D2 OpampMOSFET ut EES 247 ecture 6: Filter 2005 H.K. Pae 2 EES 247 ecture 6: Filter 2005 H.K. Pae 4

2 MOSFET nterator Example: Opamp MOSFET Filter For the Opamp interator, opamp input tay at 0 (virtual nd.) For the MOSFET interator, opamp input tay at the voltae x which i a function of 2 nd order MOSFET nonlinearitie i/2 i/2 i/2 i/2 0 0 G x x ut ut Suitable for low frequency application ue with linearity inearity achieved ~4050dB Need tunin 5 th Order Elliptic MOSFET PF with 4kHz Bandwidth ommonmode voltae enitivity Y. Tividi, M.Banu, and J. Khoury, ontinuoutime MOSFET Filter in S, EEE Journal of Solid State ircuit ol. S2, No. Feb. 986, pp. 530 EES 247 ecture 6: Filter 2005 H.K. Pae 5 EES 247 ecture 6: Filter 2005 H.K. Pae 7 Ue of MOSFET a eitor ue MOS xtor operatin in triode reion ro ection view Ditributed channel reitance & ate capacitance Ditributed nature of ate capacitance & channel reitance reult in infinite no. of hihfrequency pole exce phae Filter performance mandate wellmatched MOSFET lon channel device Exce phae increae with 2 Tradeoff between matchin and interator Q Thi type of filter limited to low frequencie mproved MOSFET nterator d D µ ox th d 2 G i i D µ ox th 4 2 M i i i/2 D D3 µ ox 2 th 4 2 X D D3 i µ i ox i/2 i D2 i X2 µ ox X X2 µ ox ( 2 ) i ( X X2) G µ ox ( 2) i No threhold dependence Firt order ommonmode nonlinearity cancelled inearity achieved in the order of 6070dB Z. zarnul, Modification of the BanuTividi ontinuoutime nterator Structure, EEE Tranaction on ircuit and Sytem, ol. S33, No. 7, pp. 7476, July 986. D3 D4 M4 G2 X X2 ut EES 247 ecture 6: Filter 2005 H.K. Pae 6 EES 247 ecture 6: Filter 2005 H.K. Pae 8

3 MOSFET nterator G G2 Example: Opamp MOSFET Filter i/2 i/2 M M4 ut 5 th Order Beel MOSFET PF 22kHz bandwidth THD 90dB for 4pp 2kHz input inal mprovement over MOSFET by addin reitor in erie with MOSFET oltae drop primarily acro fixed reitor mall MOSFET d improved linearity & reduced tunin rane inearity in the order of 90dB poible Generally low frequency application UK Moon, and BS Son, Dein of a owditortion 22kHz Fifth Order Beel Filter, EEE Journal of Solid State ircuit, ol. 28, No. 2, pp , Dec Suitable for low frequency application Sinificant improvement in linearity compared to MOSFET Need tunin UK Moon, and BS Son, Dein of a owditortion 22kHz Fifth Order Beel Filter, EEE Journal of Solid State ircuit, ol. 28, No. 2, pp , Dec EES 247 ecture 6: Filter 2005 H.K. Pae 9 EES 247 ecture 6: Filter 2005 H.K. Pae MOSFET oy nterator i/2 i/2 G Neative feedback around the nonlinear MOSFET improve linearity ompromie frequency repone accuracy 2 M M4 G2 ut UK Moon, and BS Son, Dein of a owditortion 22kHz Fifth Order Beel Filter, EEE Journal of Solid State ircuit, ol. 28, No. 2, pp , Dec Operational mplifier (Opamp) veru Operational Tranconductance mplifier (OT) Opamp oltae controlled voltae ource ow output impedance Output in the form of voltae an drive load Good for filter, OK for S filter Extra buffer add complexity, power diipation OT oltae controlled current ource Hih output impedance n the context of filter dein called mcell Output in the form of current annot drive load Good for S & m filter Typically, le complex compared to opamp hiher freq. potential Typically lower power EES 247 ecture 6: Filter 2005 H.K. Pae 0 EES 247 ecture 6: Filter 2005 H.K. Pae 2

4 nterator mplementation Tranconductance & OpampTranconductance Simplet Form of MOS nterator c Half ircuit nt. OT nt. o ωo where ωo M int M0 control 2 int 2 int M M0 control 2 int M half circuit EES 247 ecture 6: Filter 2005 H.K. Pae 3 EES 247 ecture 6: Filter 2005 H.K. Pae 5 Filter Simplet Form of MOS nterator Filter Simplet Form of MOS nterator Tranconductance element formed by the ourcecoupled pair ll MOSFET operatin in aturation reion urrent in M& can be varied by chanin control Tranconductance of M& varied throuh control int M M0 control H. Khorramabadi and P.. Gray, Hih Frequency MOS continuoutime filter, EEE Journal of SolidState ircuit, ol.s9, No. 6, pp , Dec Ue ac half circuit & mall inal model to derive tranfer function: M,2 o m 2int M,2 o m 2int o ω o M,2 m ωo 2 int GS M m 2 int half circuit Small inal model 2 int EES 247 ecture 6: Filter 2005 H.K. Pae 4 EES 247 ecture 6: Filter 2005 H.K. Pae 6

5 Filter Simplet Form of MOS nterator MOSFET in aturation reion: µ 2 ox d ( th ) 2 i iven by: M& d m µ ox th 2 d th ( ) /2 2 µ ox 2 d ( ) d varied via control m tunable via control int M M0 control τ 2 nd Order Bandpa Filter in τ 2 ' 2 ' 3 τ τ 2 EES 247 ecture 6: Filter 2005 H.K. Pae 7 EES 247 ecture 6: Filter 2005 H.K. Pae 9 Filter 2 nd Order Filter 2nd Order nteratorbaed Bandpa Filter Ue the cell to build a 2 nd order bandpa filter M int BP τ2 in 2 ττ 2 βτ2 τ τ 2 β ω0 ττ 2 Q β τ τ2 Q BP τ τ M0 control Frommatchinpointofviewdeirable: τ τ 2 Q ω0 EES 247 ecture 6: Filter 2005 H.K. Pae 8 EES 247 ecture 6: Filter 2005 H.K. Pae 20

6 2nd Order nteratorbaed Bandpa Filter Terminated nterator BP Firt implement thi part ith tranfer function: 0 ω0 Q Q τ τ M half circuit 2int GS o in 2int m M M m m M m m Small inal model 2 int EES 247 ecture 6: Filter 2005 H.K. Pae 2 EES 247 ecture 6: Filter 2005 H.K. Pae 23 M M0 Terminated nterator int M4 M control M half circuit 2int Q 0 ω0 Q Terminated nterator BP τ τ GS M m m Small inal model o in 2int m M M m m M M m ω m 0 & Q 2 int m 2 int Quetion: How to define Q accurately? EES 247 ecture 6: Filter 2005 H.K. Pae 22 EES 247 ecture 6: Filter 2005 H.K. Pae 24

7 Terminated nterator 2nd Order Filter /2 M M M m 2 µ ox d 2 M /2 m 2 µ ox 2 d et u aume equal channel lenth for M, then: M /2 M m d M m d int M4 M M M0 control Simple dein Tunable Q function of device ratio: Q M,2 m,4 m EES 247 ecture 6: Filter 2005 H.K. Pae 25 EES 247 ecture 6: Filter 2005 H.K. Pae 27 Note that: Terminated nterator int M M0 d d M d d umin equal channel lenth for M0, M: M0 M4 d M0 M M d M /2 M M m M0 M M0 control m M Filter Frequency Tunin Technique omponent trimmin utomatic onchip filter tunin ontinuou tunin Materlave tunin Periodic offline tunin Sytem where filter i followed by D & DSP, exitin hardware can be ued to periodically update filter freq. repone EES 247 ecture 6: Filter 2005 H.K. Pae 26 EES 247 ecture 6: Filter 2005 H.K. Pae 28

8 Example: Tunable Opamp Filter Example:Tunable/Trimmable Opamp Filter Pot manufacturin: Uually at waferort tunin performed Meaure 3dB frequency f frequency too hih decrement D to D f frequency too low increment D to D f frequency within 0% of the deired corner freq. top D2 D D Not practical to require enduer to tune the filter Need to fix the adjutment at the factory D2 D D0 nom 7.2K K K K D0 Fue D Fue D2 Fue EES 247 ecture 6: Filter 2005 H.K. Pae 29 EES 247 ecture 6: Filter 2005 H.K. Pae 3 Trimmin omponent trimmin Build fue onchip Baed on waferort blow fue electively by applyin hih current to the fue Expenive Fue rerowth problem! Doe not account for temp. variation & ain aer trimmin Trim component or cut fue by laer Even more expenive Doe not account for temp. variation & ain Fue To witch D Fue not blown D Fue blown D0 utomatic Frequency Tunin By addin additional circuitry to the main filter circuit Have the filter critical frequency automatically tuned Expenive trimmin avoided ccount for critical frequency variation due to temperature, upply voltae, and effect of ain EES 247 ecture 6: Filter 2005 H.K. Pae 30 EES 247 ecture 6: Filter 2005 H.K. Pae 32

9 MaterSlave utomatic Frequency Tunin MaterSlave Frequency Tunin eference Filter (F) Followin fact ued in thi cheme: Ue a replica (mater) of the main filter (called the lave) in the tunin circuitry Place the replica in cloe proximity of the main filter Ue the tunin inal enerated to tune the replica, to alo tune the main filter n the literature, thi cheme i called materlave tunin! rm rm tune K ref P coφ fo f o Q nput Sinal Frequency ωo Q ref P ωo Phae omparator Tune mp. Filter EES 247 ecture 6: Filter 2005 H.K. Pae 33 EES 247 ecture 6: Filter 2005 H.K. Pae 35 MaterSlave Frequency Tunin eference Filter (F) MaterSlave Frequency Tunin eference Filter (F) Ue a biquad for mater filter (F) Utilize the fact the frequency fo the lowpa (or hihpa) output are 90 deree out of phae wrt to input ω ω o 2 o φ 90 2 ωo Qωo pply a inuoid at the deired fo ompare the P output phae to the input Baed on the phae difference ncreae or decreae filter critical freq. ωo Q HP BP P ωo By cloin the loop, feedback tend to drive the error voltae to zero. ock fo, the critical frequency of the filter to the accurate reference frequency Typically the reference frequency i provided by a crytal ocillator with accuracie in the order of few ppm ωo Q ref ωo P Tune mp. Filter Phae omparator EES 247 ecture 6: Filter 2005 H.K. Pae 34 EES 247 ecture 6: Filter 2005 H.K. Pae 36

10 MaterSlave Frequency Tunin eference Filter (F) MaterSlave Frequency Tunin eference oltaeontrolledocillator (O) eplica Filter (Mater) Main Filter (Slave) o Phae τ mp. Filter τ 2 τ 0 P τ0 Q τ 3 τ 4 τ 5 omparator H. Khorramabadi and P.. Gray, Hih Frequency MOS continuoutime filter, EEE Journal of SolidState ircuit, ol.s9, No. 6, pp , Dec EES 247 ecture 6: Filter 2005 H.K. Pae 37 MaterSlave Frequency Tunin eference Filter (F) ue to be aware of: eference inal frequency wrt filter paband Filter topoloy are in the layout Fully differential topoloie beneficial EES 247 ecture 6: Filter K.S. Tan and P.. Gray, Fully interated analo filter uin bipolar FET technoloy, EEE, J. SolidState ircuit, vol. S3, no.6, pp. 8482, December EES 247 ecture 6: Filter 2005 H.K. Pae 39 MaterSlave Frequency Tunin eference oltaeontrolledocillator (O) ue to be aware of: nput reference tunin inal need to be inuoid à Diadvantae ince clock are uually available a quare waveform eference inal feedthrouh to the output of the filter can limit filter dynamic rane (reported level or about 00µrm) ef. inal feedthrouh i a function of: ntead of F a voltaecontrolledocillator (O) i ued O made of replica interator ued in main filter Tunin circuit operate exactly a a conventional phaelocked loop (P) Tunin inal ued to tune main filter 2005 H.K. Pae 38 Dein of table & repeatable ocillator challenin O operation hould be limited to the linear reion of the amp or ele the operation loe accuracy imitin the O inal rane to the linear reion not a trivial dein iue n the cae of F baed tunin ckt there wa only ref. inal feedthrouh. n thi cae, there i alo the feedthrouh of the O inal!! dvantae over F baed tunin à eference input inal quare wave (not in.) EES 247 ecture 6: Filter 2005 H.K. Pae 40

11 MaterSlave Frequency Tunin hoice of ef. Frequency wrt Feedthrouh mmunity MaterSlave Frequency Tunin eference / ocked to ef. Frequency eplica of main filter Three phae operation Feedback loop force: S2 S3 S 2 N fclk. Gopinathan, et. al, Dein onideration for HihFrequency ontinuoutime Filter and mplementation of an ntialiain Filter for Diital ideo, EEE JSS, ol. S25, no. 6 pp , Dec Durham, J. Huhe, and. edman hite, ircuit rchitecture for Hih inearity Monolithic ontinuoutime Filterin, EEE Tranaction on ircuit and Sytem, pp , Sept EES 247 ecture 6: Filter 2005 H.K. Pae 4 EES 247 ecture 6: Filter 2005 H.K. Pae 43 MaterSlave Frequency Tunin eference / ocked to ef. Frequency eference / ocked to ef. Frequency P hih S cloed eplica of main filter buildin block ued Utilize the fact that a D voltae ource connected to the input of the cell enerate a contant current. f the interatin capacitor i fully dichared and at t0 i connected to the output of the cell then: eplica of main filter out tune S2 S3 S 2 ref T Dichare T f i forced to be equal to then: T N fclk EES 247 ecture 6: Filter 2005 H.K. Pae 42 EES 247 ecture 6: Filter 2005 H.K. Pae 44

12 eference / ocked to ef. Frequency P2 hih S2 cloed Summary eference / ocked to ef. Frequency S2 S3 2 S2 S3 2 P2 T T2 hare with T2 nterator time contant locked to an accurate frequency Tunin inal ued to adjut the time contant of the main filter interator Problem to be aware of: Tunin error due to cell D offet Feedback force to vary o that : τint N/fclk or int ω 0 fclk/n EES 247 ecture 6: Filter 2005 H.K. Pae 45 EES 247 ecture 6: Filter 2005 H.K. Pae 47 eference / ocked to ef. Frequency P3 hih S3 cloed ue eference / ocked to ef. Frequency T T2 S2 S3 2 hare on hared with 2 Feedback force to aume a value: 2 ince: T2 then: ref T2 or: T2 N/fclk hat i D offet? Simple example: For the mcell hown here, difference between the threhold voltae of the input device ( M & ) would caue D offet. nonzero voltae hould be applied to input to have o0 Offet i uually model a a mall D voltae ource at the input int M M0 control Example: cell EES 247 ecture 6: Filter 2005 H.K. Pae 46 EES 247 ecture 6: Filter 2005 H.K. Pae 48

13 oltae ource epreentin D offet ell Offet nduced Error o S2 S3 (o) Effect of cell D offet: 2 deal: T2 ( ref o) 2 withoffet: T2 or: T2 o ref /2 cm /2 eference / ocked to ef. Frequency ncorporatin Offet ancellation P2 P2B P2B P2 3a 3b cell two et of input pair ux. input pair 3a,b Offet cancellation Same clock timin P3 P3 P P2 P2 P P3 P3 2 EES 247 ecture 6: Filter 2005 H.K. Pae 49 EES 247 ecture 6: Filter 2005 H.K. Pae 5 eference / ocked to ef. Frequency ell Offet nduced Error eference / ocked to ef. Frequency P3 Hih (Update & Store o) o S2 S3 Example: (o) 2 /2 cm /2 3a 3b out o 2 T2 o ref for o /0 0% errorintunin! cell Unity ain confi. 3a,b Store cell offet, 2 hare harin EES 247 ecture 6: Filter 2005 H.K. Pae 50 EES 247 ecture 6: Filter 2005 H.K. Pae 52

14 eference / ocked to ef. Frequency P Hih (eet) Summary eference / ocked to ef. Frequency /2 cm /2 3a o 3a 3b 2 /2 cm /2 3a o 3a 3b o 2 cell eet. Dichare 2 Hold hare 3a,b Hold hare Offet tored on 3a,b cancel mcell offet cell harin 3a,b Store cell offet 2 Hold chare Key point: Tunin error due to cell offet cancelled EES 247 ecture 6: Filter 2005 H.K. Pae 53 EES 247 ecture 6: Filter 2005 H.K. Pae 55 eference / ocked to ef. Frequency P2 Hih (hare) Summary eference / ocked to ef. Frequency /2 cm /2 3a o 3a 3b o 2 S2 S3 2 cell harin 3a,b Store cell offet 2 Hold chare Key point: Tunin error due to cell offet cancelled Tunin error due to mcell offet voltae reolved Ha the advantae over previou cheme that fclk can be choen to be at much hiher frequencie compared to filter bandwidth (N>) Feedthrouh of attenuated by filter Feedback force to vary o that : τint N/fclk or int ω 0 fclk/n EES 247 ecture 6: Filter 2005 H.K. Pae 54 EES 247 ecture 6: Filter 2005 H.K. Pae 56

15 D Tunin of eitive Timin Element ext ued to lock or onchip Feedback force /ext ccount for ap. variation in the m implementation by trimmin ext.. aber and Gray, 20MHz 6th Order BiMOS Paraitic nenitive ontinuoutime Filter and Second Order Equalizer Optimized for Dik Drive ead hannel, EEE Journal of Solid State ircuit, ol. 28, pp , pril 993 EES 247 ecture 6: Filter 2005 H.K. Pae 57