EECS 247 Lecture 6: Filters © 2007 H.K. Page 1EE247 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. responseEECS 247 Lecture 6: Filters © 2007 H.K. Page 2Summary Lecture 5• Continuous-time filters– Effect of integrator non-idealities on 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 filterresponse & 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……………to be continued todayEECS 247 Lecture 6: Filters © 2007 H.K. Page 3Improved MOSFET-C IntegratorVG1CNo threshold dependenceLinearity achieved in the order of 50-70dB++--outVVi/2-Vi/2VG3ID1M1M2ID2M3M4ID3ID4IX1IX2()()WVdsCIVVVDox dsgs thL2VVWiiCIVVD1 oxgs1 thL24VVWiiCIVVD3 oxgs3 thL24IIIX1 D1 D3VWViiCVVoxgs1 gs3L22VWViiCIVVX2 oxgs3 gs1L22WVVCII Vgs1 gs3X1 X2 ox iLIIX1 X2Gμμμμμμ⎛⎞=−−⎜⎟⎝⎠⎛⎞=−−⎜⎟⎝⎠⎛⎞=−−+⎜⎟⎝⎠=+⎛⎞=−−⎜⎟⎝⎠⎛⎞=−−⎜⎟⎝⎠−−=∂−=()WVVCgs1 gs3oxVLiμ−=∂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.M1,2,3,4 equal W/LEECS 247 Lecture 6: Filters © 2007 H.K. Page 4R-MOSFET-C IntegratorVG1C•Improvement over MOSFET-C by adding resistor in series with MOSFET•Voltage drop primarily across fixed resistor small MOSFET Vds improved linearity & reduced tuning range•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 © 2007 H.K. Page 5R-MOSFET-C Lossy IntegratorVG1CNegative feedback around the non-linear MOSFETs improves linearity but Compromises 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.R1R1R2R2EECS 247 Lecture 6: Filters © 2007 H.K. Page 6Example: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, low Q applications• Significant improvement in linearity compared to MOSFET-C• Needs tuning5thOrder Bessel MOSFET-RC LPF 22kHz bandwidthTHD -90dB for 4Vp-p , 2kHz input signalEECS 247 Lecture 6: Filters © 2007 H.K. Page 7Operational Amplifiers (Opamps) versus Operational Transconductance Amplifiers (OTA)• Output in the form of voltage• Low output impedance • Can drive R-loads• Good for RC filters,OK for SC filters• Extra buffer adds complexity, power dissipation• Output in the form of current • High output impedance• In the context of filter design called gm-cells• Cannot drive R-loads• Good for SC & gm-C filters• Typically, less complex compared to opamp higher freq. potential• Typically lower powerOpamp OTAVoltage controlled Voltage controlledvoltage source current sourceEECS 247 Lecture 6: Filters © 2007 H.K. Page 8Integrator ImplementationTransconductance-C & Opamp-Transconductance-CinVoVGmoVCinVGmwhereoo moinVGVs Cωω−==-+∫GmC Intg.GmC-OTA Intg.-+EECS 247 Lecture 6: Filters © 2007 H.K. Page 9Gm-C FiltersSimplest 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 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, Dec. 1984. controlVoVinV-++-int gCM1 M2M10EECS 247 Lecture 6: Filters © 2007 H.K. Page 10Simplest Form of CMOS Gm-C IntegratorAC Half Circuitint gCcontrolVoVinV-++-M1 M2M10controlVoVinV-++-int g2CM1M2M10inVintg2CM1oVAC half circuitint gCint g2CcontrolVEECS 247 Lecture 6: Filters © 2007 H.K. Page 11Gm-C FiltersSimplest Form of CMOS Gm-C Integrator• Use ac half circuit & small signal model to derive transfer function:M1,2o m in int gM1,2omin int gooinM1,2moint gVg V2CsVgV2CsVVsg2Cωω=− × ×=−−=→=×inVintg2CoVingVmCGSinVintg2CM1oVAC half circuitSmall signal modelEECS 247 Lecture 6: Filters © 2007 H.K. Page 12Gm-C FiltersSimplest Form of CMOS Gm-C Integrator• MOSFET in saturation region:• Gm is given by:()()()2M1&M2m1/2CWoxVVIgs thd2LIWdVVCggsthoxVLgsId2VVgs th1WC2Iox d2Lμμμ−=∂−==∂=−⎛⎞=⎜⎟⎝⎠Id varied via Vcontrol gm tunable via VcontrolcontrolVoVinV-++-int gCM1 M2M10EECS 247 Lecture 6: Filters © 2007 H.K. Page 13Gm-C Filters2ndOrder Gm-C Filter• Use the Gm-cell to build a 2ndorder bandpass filtercontrolVoVinV-++-int gCM1 M2M10EECS 247
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