EE247 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 hardware can be used to periodically update filter freq response EECS 247 Lecture 6 Filters 2005 H K Page 1 Summary Last Lecture Continuous time filters Effect of integrator non idealities on continuoustime 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 C EECS 247 Lecture 6 Filters 2005 H K Page 2 Use of MOSFETs as Resistors Single Ended Integrator I D Cox W V2 Vgs Vth Vds ds L 2 Vin 2 W Vgs Vth Vi Vi ID L 2 I D W V V V Cox G gs th i Vi L Cox C VG ID Vo Tunable by varying VG Problem Single ended MOSFET C Integrator Effective R non linear Note that the non linearity is mainly 2nd order type EECS 247 Lecture 6 Filters 2005 H K Page 3 Use of MOSFETs as Resistors Differential Integrator Vds Vgs Vth Vds 2 W V V I D1 Cox Vgs Vth i i L 4 2 W L VG Vi 2 C ID1 M1 Non linear term cancelled Admittance independent of Vi Vi 2 W V V I D2 Cox Vgs Vth i i L 4 2 W V V I D1 I D2 Cox gs th Vi L I D1 I D2 W V V G Cox gs th Vi L I D Cox Vout ID2 M2 C Opamp MOSFET C Problem Threshold voltage dependence EECS 247 Lecture 6 Filters 2005 H K Page 4 MOSFET C Integrator Vi 2 0V For the Opamp RC integrator opamp input stays at 0V virtual gnd 0V Vout Vi 2 VG C Vi 2 Vx For the MOSFET C integrator opamp input stays at the voltage Vx which is a function of 2nd order MOSFET non linearities Vi 2 Vx Vout Common mode voltage sensitivity EECS 247 Lecture 6 Filters 2005 H K Page 5 Use of MOSFET as Resistor Issues MOS xtor operating in triode region Cross section view Distributed channel resistance gate capacitance Distributed nature of gate capacitance channel resistance results in infinite no of high frequency poles excess phase Filter performance mandates well matched MOSFETs long channel devices Excess phase increases with L2 Tradeoff between matching and integrator Q This type of filter limited to low frequencies EECS 247 Lecture 6 Filters 2005 H K Page 6 Example Opamp MOSFET C Filter Suitable for low frequency applications Issues with linearity Linearity achieved 40 50dB Needs tuning 5th Order Elliptic MOSFET C LPF with 4kHz Bandwidth Ref 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 30 EECS 247 Lecture 6 Filters 2005 H K Page 7 Improved MOSFET C Integrator VG2 VG1 M1 IX1 ID1 I D3 I X 1 I D1 I D3 W V V Cox Vgs1 Vgs2 i i L 2 2 W V V C I X 2 ox Vgs2 Vgs1 i i L 2 2 W V I X 1 I X 2 Cox gs1 Vgs2 Vi L I X 1 I X 2 W V Cox G gs1 Vgs2 Vi L Vi 2 ID M4 4 ID2 M2 C M3 Vi 2 W Vds V V Vds L gs th 2 W V V I D1 Cox Vgs1 Vth i i L 4 2 W V V I D3 Cox Vgs2 Vth i i L 4 2 I D Cox Vout IX2 C No threshold dependence First order Common mode non linearity cancelled Linearity achieved in the order of 60 70dB Ref 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 8 R MOSFET C Integrator VG2 VG1 M1 R C M3 M2 R M4 Vi 2 Vi 2 Vout C 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 Linearity in the order of 90dB possible Generally low frequency applications Ref 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 EECS 247 Lecture 6 Filters 2005 H K Page 9 R MOSFET C Lossy Integrator R2 VG1 VG2 M1 C M3 R1 M2 M4 Vi 2 Vi 2 R2 Vout C R2 Negative feedback around the non linear MOSFETs improves linearity Compromises frequency response accuracy Ref 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 EECS 247 Lecture 6 Filters 2005 H K Page 10 Example Opamp MOSFET RC Filter 5th Order Bessel MOSFET RC LPF 22kHz bandwidth THD 90dB for 4Vp p 2kHz input signal Suitable for low frequency applications Significant improvement in linearity compared to MOSFET C Needs tuning Ref 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 EECS 247 Lecture 6 Filters 2005 H K Page 11 Operational Amplifiers Opamps versus Operational Transconductance Amplifiers OTA Opamp OTA Voltage controlled voltage source 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 EECS 247 Lecture 6 Filters Voltage controlled current source 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 opamp higher freq potential Typically lower power 2005 H K Page 12 Integrator Implementation Transconductance C Opamp Transconductance C C Vin Vin Gm Gm Vo Vo GmC Intg GmC OTA Intg Vo Vin o s G w h e r e o m C EECS 247 Lecture 6 Filters 2005 H K Page 13 Gm C Filters Simplest Form of CMOS Gm C Integrator Transconductance element formed by the source coupled pair Vo All MOSFETs operating in saturation region Current in M1 M2 can be varied by changing Vcontrol Transconductance of M1 M2 varied through Vcontrol Ref Vin M1 Cint g M10 M2 Vcontrol 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 2005 H K Page 14 Simplest Form of CMOS Gm C Integrator Ac …
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