EE247 Lecture 6 Summary last lecture Continuous time filters continued Opamp MOSFET RC filters Gm C filters Frequency tuning for continuous time filters Trimming via fuses or laser Automatic on chip filter tuning Continuous tuning Master slave tuning Periodic off line tuning Systems where filter is followed by ADC DSP existing hardware can be used to periodically update filter freq response EECS 247 Lecture 6 Filters 2009 H K Page 1 Summary Lecture 5 Continuous time filters Effect of integrator non idealities on integrated continuous time filter behavior Effect of integrator finite DC gain non dominant poles on filter frequency response Integrator non linearities affecting filter maximum signal handling capability harmonic distortion and intermodulation distortion Effect of integrator component variations and mismatch on filter response need for frequency tuning Frequency tuning for continuous time filters Frequency adjustment by making provisions to have variable R or C Various integrator topologies used in filters Opamp MOSFET C filters Opamp MOSFET RC filters EECS 247 Lecture 6 Filters 2009 H K Page 2 Integrator Implementation Opamp RC Opamp MOSFET C Opamp MOSFET RC C Vin R Vtune Vin C C Vin Vo Vo Vo o s EECS 247 whe re o Vo Opamp MOSFET C Vin R Opamp RC Vtune Opamp MOSFET RC 1 R eqC Lecture 6 Filters 2009 H K Page 3 Integrator Implementation Transconductance C Opamp Transconductance C C Vin Vin Gm Gm Vo GmC Intg Vo GmC OTA Intg Vo Vin EECS 247 o s G whe r e o m C Lecture 6 Filters 2009 H K Page 4 Gm C Filters Simplest Form of CMOS Gm C Integrator Use ac half circuit small signal model to derive transfer function Vin Gm Vo g m Vin Cint g s Vo gm Vin Cint g s GmC Intg Vo o Vin s o Vin gm Cint g s g mgV minVin Vo Cintg Issue Design is parasitic sensitive EECS 247 Vo Cintg Small signal model Lecture 6 Filters 2009 H K Page 5 Gm C Filters Simplest Form of CMOS Gm C Integrator Transconductance element formed by the source coupled pair M1 M2 All MOSFETs operating in saturation region Current in M1 M2 can be varied by changing Vcontrol Find transfer function by drawing ac half circuit Vin M1 Cint g M10 Vo M2 Vcontrol Ref H Khorramabadi and P R Gray High Frequency CMOS continuous time filters IEEE Journal of Solid State Circuits Vol SC 19 No 6 pp 939 948 Dec 1984 EECS 247 Lecture 6 Filters 2009 H K Page 6 Simplest Form of CMOS Gm C Integrator AC Half Circuit Cint g Vin M1 Cint g Vo M2 Vin Vo Vo Vin M2 M1 M10 V M10V controlcontrol EECS 247 2Cint g2Cint g 2Cintg M1 AC half circuit Vcontrol Lecture 6 Filters 2009 H K Page 7 Gm C Filters Simplest Form of CMOS Gm C Integrator Use ac half circuit small signal model to derive transfer function Vo Vin M 1 2 Vo gm Vin 2Cint g s Vo g M 1 2 m Vin 2Cint g s 2Cintg AC half circuit Vo o Vin s o M1 Vin M 1 2 gm g m Vin CGS 2 Cint g Vo 2Cintg Small signal model EECS 247 Lecture 6 Filters 2009 H K Page 8 Gm C Filters Simplest Form of CMOS Gm C Integrator MOSFET in saturation region Cox W 2 Vgs Vth Id 2 L Gm is given by I W V V M 1 M 2 gm d Cox gs th Vgs L 2 Id Vgs Vth Vin 1 2 W 1 2 Cox I d L 2 M1 Cint g M10 Vo M2 Vcontrol Id varied via Vcontrol gm tunable via Vcontrol EECS 247 Lecture 6 Filters 2009 H K Page 9 Gm C Filters 2nd Order Gm C Filter Use the Gm cell to build a 2nd order bandpass filter Vin M1 Cint g M10 EECS 247 Lecture 6 Filters Vo M2 Vcontrol 2009 H K Page 10 2nd Order Bandpass Filter Vo VR R VL L VC C IR I L IC I in 1 V1 1 Vo 1 R R V1 V2 R sC R sL 1 1 1 V3 Vin Vo 1 R C 2 L R 1 1 s 2 s1 1 R R Vin EECS 247 Lecture 6 Filters 2009 H K Page 11 2nd Order Integrator Based Bandpass Filter VBP VBP 2s Vin s2 s 1 1 2 2 1 R C 2 L R R 0 1 1 2 1 Q 1 1 1Q R LC s s1 2 From matching point of v iew desirable 1 2 1 Q R 0 R EECS 247 1 1 Lecture 6 Filters Vin 2009 H K Page 12 2nd Order Integrator Based Bandpass Filter VBP First implement this part With transfer function 1 1 s s1 1Q V0 1 Vin s 1 0 Q Vin EECS 247 Lecture 6 Filters 2009 H K Page 13 Terminated Gm C Integrator Cint g Vo M3 Vin M1 M4 Vo Vin M2 M1 M3 2Cintg AC half circuit M11 M10 EECS 247 Vcontrol Lecture 6 Filters 2009 H K Page 14 Terminated Gm C Integrator Vo Vin M1 2Cintg M3 M 1V gm in Vin 1 CGS M3 gm 2Cintg Small signal model AC half circuit Vo Vin Vo 1 gM 3 m M1 M1 gm gm V0 1 Compare to Vin s 1 0 Q s 2Cint g EECS 247 Lecture 6 Filters 2009 H K Page 15 Terminated Gm C Integrator VBP 1Q 1 1 Vo 1 CGS s s1 M 1V gm in Vin M3 gm 2Cintg Small signal model V0 1 Vin s 1 0 Q Vin Vo 1 Vin s 2Cint g M1 gm 0 M1 gm 2Cint g gM 3 m M1 gm gM1 Q m M3 gm Question How to define Q accurately EECS 247 Lecture 6 Filters 2009 H K Page 16 Terminated Gm C Integrator 1 2 1 W M1 2 Cox M 1 I dM 1 gm LM 1 2 Cint g 1 2 1 W M3 2 Cox M 3 I dM 3 gm LM 3 2 Let us assume equal channel lengths for M1 M3 then EECS 247 M3 Vin 1 2 M1 I M1 gm W d M1 M3 M3 W gm M 3 Id Vo M4 M1 M2 M11 M10 Lecture 6 Filters VVcontrol control 2009 H K Page 17 Terminated Gm C Integrator Note that I dM 1 I M 10 d I dM 3 I dM 11 Assuming equal channel lengths for M10 M11 I dM 10 I dM 11 EECS 247 Vin WM 11 M1 Lecture 6 Filters M4 M2 M11 1 2 W W M 10 M 1 W M 11 WM 3 Vo M3 WM 10 M1 gm M3 gm Cint g M10 VVcontrol control 2009 H K Page 18 2nd Order Gm C Filter Vo1 Simple design Tunable Q function of device ratios Q EECS 247 Vo2 gmM 1 2 gmM 3 4 Lecture 6 Filters 2009 H K Page 19 Continuous Time Filter Frequency Tuning Techniques Component trimming Automatic on chip filter tuning Continuous tuning Master …
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