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Berkeley ELENG 247A - Lecture Notes

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EECS 247 Lecture 7: Filters © 2005 H.K. Page 1EE247 Lecture 7• Summary last lecture• Automatic on-chip filter tuning (continued from last lecture)• Continuous tuning– Reference integrator locked to a reference frequency– DC tuning of resistive timing element• Periodic digitally assisted tuning– Systems where filter is followed by ADC & DSP, existing hardwarecan be used to periodically update filter freq. response• Continuous-time filters – Bandpass filters• Example: Gm-C BP filter using simple diff. pair– Linearity & noise issues– Various Gm-C Filter implementations– Comparison of continuous-time filter topologiesEECS 247 Lecture 7: Filters © 2005 H.K. Page 2Summary last lecture• Continuous-time filters– Opamp MOSFET-C filters– Opamp MOSFET-RC filters– Gm-C filters• Frequency tuning for continuous-time filters– Trimming via fuses– Automatic on-chip filter tuning• Continuous tuning– Utilizing VCF built with replica integrators– Use of VCO built with replica integratorsEECS 247 Lecture 7: Filters © 2005 H.K. Page 3Master-Slave Frequency TuningReference Integrator Locked to Reference FrequencytuneVGmCVin•Replica of main filter integrator e.g. Gm-C building block used •Utilizes the fact that a DC voltage source connected to the input of the Gm cell generates a constant current proportional to the transconductance and the voltage reference I = Gm.VrefReplica of main filter Gm-C VoutVrefI=Gm*VrefEECS 247 Lecture 7: Filters © 2005 H.K. Page 4Reference Integrator Locked to Reference FrequencyC1refVGmVTC1=××tuneVGmC1Vin•Consider the following sequence:§ Integrating capacitor is fully discharged @ t=0 § At t=0 the integrator input is connected to the output of the Gm cell then:VoutVC1TVrefI=Gm*Vreft=0timeEECS 247 Lecture 7: Filters © 2005 H.K. Page 5Reference Integrator Locked to Reference FrequencyclkCNTGmf==C1refVGmVTC1≈××tuneVGmCVinSince at the end if the period T:If VC1 is forced to be equal to Vref then:How do we manage to force VC1=Vref?à Use feedback!VoutVC1TVrefI=Gm*Vreft=0timeC1refVGmVTC1≈××EECS 247 Lecture 7: Filters © 2005 H.K. Page 6Reference Integrator Locked to Reference FrequencyS2S1S3GmC1C2VrefA• Three clock phase operation • To analyze à study one phase at a timeReplica of main filter Gm Ref: A. Durham, J. Hughes, and W. Redman- White, “Circuit Architectures for High Linearity Monolithic Continuous-Time Filtering,” IEEE Transactions on Circuits and Systems, pp. 651-657, Sept. 1992.EECS 247 Lecture 7: Filters © 2005 H.K. Page 7Reference Integrator Locked to Reference Frequency P1 highà S1 closedS2S1S3GmC1C2VrefC1 à dischargedC2 à retains its previous chargeAEECS 247 Lecture 7: Filters © 2005 H.K. Page 8Reference Integrator Locked to Reference FrequencyP2 high à S2 closedS2S3GmC1C2VrefAI=Gm*VrefP2VC1C1refVGmVT2C1=××T1T2C1 à charged with constant current: I=Gm*VrefC2 à retains its previous chargeEECS 247 Lecture 7: Filters © 2005 H.K. Page 9Reference Integrator Locked to Reference Frequency P3 high à S3 closedC1 charge shares with C2Few cycles following startup à Feedback forces C1/Gm to assume:S2S3GmC1C2VrefAC1C2C1refrefrefVVVrefsinceVGmVT2C1then:VGmVT2C1C1or:T2N/fclkGm:===××=××==T1T2EECS 247 Lecture 7: Filters © 2005 H.K. Page 10SummaryReference Integrator Locked to Reference FrequencyFeedback forces Gm to vary so that :S2S3GmC1C2VrefAintgintg0C1N/fclkGmorGmfclk/NC1τω====• Integrator time constant locked to an accurate frequency• Tuning signal used to adjust the time constant of the main filter integratorsTo MainFilterEECS 247 Lecture 7: Filters © 2005 H.K. Page 11IssuesReference Integrator Locked to Reference FrequencyProblems to be aware of:à Tuning error due to master integrator DC offsetS2S3GmC1C2VrefATo MainFilterintg0Gmfclk/NC1ω ==EECS 247 Lecture 7: Filters © 2005 H.K. Page 12Issues Reference Integrator Locked to Reference FrequencyWhat is DC offset?Simple example: For the differential pair shown here, any mismatch in input device characteristics would cause DC offset:àVo = 0 requires a non-zero input voltageOffset could be modeled as a small DC voltage source at the input Example: Differential PairoVinV-++-M1 M2VosEECS 247 Lecture 7: Filters © 2005 H.K. Page 13Gm-Cell Offset Induced Error()C1C2C1refC1osrefosrefVVVrefIdealVGmVT2C1withoffset:VGmVVT2C1VC1or:T21GmV:===××=×−×=−VrefVosS2S3GmC1C2AI=Gm(Vref-Vos)•Effect of Gm-cell DC offset: Voltage sourcerepresenting DC offsetEECS 247 Lecture 7: Filters © 2005 H.K. Page 14Gm-Cell Offset Induced ErrorosrefosrefVC1T21GmVVfor1/10V10%errorintuning!=−=VrefVosS2S3GmC1C2AI=Gm(Vref-Vos)•Example:EECS 247 Lecture 7: Filters © 2005 H.K. Page 15Issues Gm-Cell Offset Induced ErrorintgC•Assume differential integrator•Add a pair of auxiliary inputs to the input stage for offset cancellation purposesoVmaininV+-+-M1 M2M3M4-+aux.inV+--++-MainInputAux.InputEECS 247 Lecture 7: Filters © 2005 H.K. Page 16Gm-cell à two sets of input pairs Aux. input pair +C3a,bà Offset cancellation Same clock timingReference Integrator Locked to Reference FrequencyOffset Cancellation Incorporated+--+P2P2B-+P3P1+-+-P1P2P3P2BP3P2P3P2Vcm+Vref/2-Vref/2Vtune C1C2C3aC3bEECS 247 Lecture 7: Filters © 2005 H.K. Page 17Reference Integrator Locked to Reference FrequencyP3 High (Update & Store offset)outosVV=osV+--+-++-+-Vcm+Vref/2-Vref/2Vtune C1C2C3aC3bGm-cell à Unity gain configuration via aux. inputsC3a,b à Store Gm-cell offsetC1, C2 à Charge sharingEECS 247 Lecture 7: Filters © 2005 H.K. Page 18Reference Integrator During Offset Cancellation PhaseoutosVV=osV+--++-VcmC3aC3bGm-cell à Unity gain configuration via aux. inputs, main input shortedàC3a,b acquire charge equal to Vosà Store Gm-cell offsetosC3a,bVV=−+--++-VcmC3aC3boutosVV=outosVV=*Note: This technique can be used in various other applicationsEECS 247 Lecture 7: Filters © 2005 H.K. Page 19Reference Integrator Locked to Reference FrequencyP1 High (Reset)+--+-++-+-Vcm+Vref/2-Vref/2Vtune C1C2C3aC3bGm-cell à Reset.C1 à DischargeC2 à Hold ChargeC3a,b à Hold Chargeà Offset stored on C3a,b cancels gm-cell offsetosVosC3a,bVV=−EECS 247 Lecture 7: Filters © 2005 H.K. Page 20Reference Integrator Locked to Reference FrequencyP2 High (Charge)osV+--+-++-+-Vcm+Vref/2-Vref/2Vtune C1C2C3aC3bosC3a,bVV=−Gm-cell à Charging C1 C3a,b à Store Gm-cell offsetC2 à Hold


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Berkeley ELENG 247A - Lecture Notes

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