EECS 247 Lecture 6: Filters © 2005 H.K. Page 1EE247 Lecture 6• Summary 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– Master-slave tuning• Periodic off-line tuning– Systems where filter is followed by ADC & DSP, existing hardwarecan be used to periodically update filter freq. responseEECS 247 Lecture 6: Filters © 2005 H.K. Page 2Summary Last Lecture• Continuous-time filters– Effect of integrator non-idealities on continuous-time filter behavior– Facts about monolithic Rs & Cs and its effect on integrated filter characteristics– Opamp RC filters– Opamp MOSFET-C filters• Frequency tuning for continuous-time filters– Frequency adjustment by making provisions to have variable R or CEECS 247 Lecture 6: Filters © 2005 H.K. Page 3Use of MOSFETs as ResistorsSingle-Ended IntegratorProblem: Single-ended MOSFET-C Integratorà Effective R non-linearNote that the non-linearity is mainly 2ndorder type ( )( )( )2ds2iWVCIVVVDoxgsthdsL2WVCVVVIoxgsthiDL2IWDVVVCGgsthioxVLiµµµ=−−=−−∂−−==∂VGoVC-+inVIDàTunable by varying VG:EECS 247 Lecture 6: Filters © 2005 H.K. Page 4Use of MOSFETs as ResistorsDifferential IntegratorOpamp-MOSFET-CVGC• Non-linear term cancelled!• Admittance independent of ViProblem: Threshold voltage dependence++--outVVi/2-Vi/2( )( )( )W VdsCIVVVDoxdsgsthL2VVWiiCIVVD1oxgsthL24VVWiiCIVVD2oxgsthL24WVVCIIVgsthD1D2oxiLIIWD1D2VVCGgsthoxVLiµµµµµ=−−=−−=−−+−−=∂−−==∂ID1M1M2ID2CEECS 247 Lecture 6: Filters © 2005 H.K. Page 5MOSFET-C IntegratorVGCà Common-mode voltage sensitivity++--outVVi/2-Vi/2VxVx++--Vi/2-Vi/2outV0V0V•For the Opamp-RC integrator, opamp input stays at 0V (virtual gnd.)•For the MOSFET-C integrator, opamp input stays at the voltage Vx which is a function of 2ndorder MOSFET non-linearitiesEECS 247 Lecture 6: Filters © 2005 H.K. Page 6Use of MOSFET as Resistor Issues• Distributed nature of gate capacitance & channel resistance results in infinite no. of high-frequency poles à excess phase• Filter performance mandates well-matched MOSFETs à long channel devices• Excess phase increases with L2àTradeoff between matching and integrator QàThis type of filter limited to low frequenciesMOS xtor operating in triode regionCross section viewDistributed channel resistance & gate capacitanceEECS 247 Lecture 6: Filters © 2005 H.K. Page 7Example:Opamp MOSFET-C Filter•Suitable for low frequency applications•Issues with linearity•Linearity achieved ~40-50dB•Needs tuning5thOrder Elliptic MOSFET-C LPF with 4kHz BandwidthRef: Y. Tsividis, M.Banu, and J. Khoury, “Continuous-Time MOSFET-C Filters in VLSI”, IEEE Journal of Solid State Circuits Vol. SC-21, No.1 Feb. 1986, pp. 15-30EECS 247 Lecture 6: Filters © 2005 H.K. Page 8Improved MOSFET-C IntegratorVG1CNo threshold dependenceFirst order Common-mode non-linearity cancelledLinearity achieved in the order of 60-70dB++--outVVi/2-Vi/2VG2ID1M1M2ID2M3M4ID3ID4IX1IX2( )( )WVdsCIVVVDoxdsgsthL2VW ViiCIVVD1oxgs1thL24VW ViiCIVVD3oxgs2thL24IIIX1D1D3VWViiCVVoxgs1gs2L22VWViiCIVVX2oxgs2gs1L22WVVCIIVgs1gs2X1X2oxiLIIX1X2Gµµµµµµ=−−=−−=−−+=+=−−=−−−−=∂−=()WVVCgs1gs2oxVLiµ−=∂CRef: Z. Czarnul, “Modification of the Banu-Tsividis Continuous-Time Integrator Structure,” IEEE Transactions on Circuits and Systems, Vol. CAS-33, No. 7, pp. 714-716, July 1986.EECS 247 Lecture 6: Filters © 2005 H.K. Page 9R-MOSFET-C IntegratorVG1C•Improvement over MOSFET-C by adding resistor in series with MOSFET•Voltage drop primarily across fixed resistor à small MOSFET Vds àimproved linearity & reduced tuning range•Linearity in the order of 90dB possible•Generally low frequency applications++--outVVi/2-Vi/2VG2M1M2M3M4CRef: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,”IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.RREECS 247 Lecture 6: Filters © 2005 H.K. Page 10R-MOSFET-C Lossy IntegratorVG1CNegative feedback around the non-linear MOSFETs improves linearityCompromises frequency response accuracy++--outVVi/2-Vi/2VG2M1M2M3M4CRef: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,” IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.R1R2R2R2EECS 247 Lecture 6: Filters © 2005 H.K. Page 11Example:Opamp MOSFET-RC FilterRef: U-K Moon, and B-S Song, “Design of a Low-Distortion 22-kHz Fifth Order Bessel Filter,” IEEE Journal of Solid State Circuits, Vol. 28, No. 12, pp. 1254-1264, Dec. 1993.•Suitable for low frequency applications•Significant improvement in linearity compared to MOSFET-C•Needs tuning5thOrder Bessel MOSFET-RC LPF -22kHz bandwidthTHD à-90dB for 4Vp-p 2kHz input signalEECS 247 Lecture 6: Filters © 2005 H.K. Page 12Operational Amplifiers (Opamps) versus Operational Transconductance Amplifiers (OTA)• Low output impedance• Output in the form of voltage • Can drive R-loads• Good for RC filters,OK for SC filters• Extra buffer adds complexity, power dissipation• High output impedance• In the context of filter design called gm-cells• Output in the form of current • Cannot drive R-loads• Good for SC & gm-C filters• Typically, less complex compared to opampà higher freq. potential• Typically lower powerOpamp OTAVoltage controlled Voltage controlledvoltage source current sourceEECS 247 Lecture 6: Filters © 2005 H.K. Page 13Integrator ImplementationTransconductance-C & Opamp-Transconductance-CinVoVGmoVCinVGmwhereoomoinVGVsCωω−==-+∫GmC Intg.GmC-OTA Intg.-+EECS 247 Lecture 6: Filters © 2005 H.K. Page 14Gm-C FiltersSimplest Form of CMOS Gm-C Integrator• Transconductance element formed by the source-coupled pair• All MOSFETs operating in saturation region• Current in M1& M2 can be varied by changing Vcontrolà Transconductance of M1& M2 varied through VcontrolRef: 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,
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