EE247 Lecture 11 Switched Capacitor Filters continued Effect of non idealities Bilinear switched capacitor filters Filter design summary Comparison of various filter topologies Data Converters EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 1 Summary Last Lecture Switched capacitor filter design considerations DDI LDI Integrator characteristics Bottom plate LDI integrator overcomes parasitic sensitivity issues Continuous time and complex conjugate terminations Use of T networks to implement high capacitor ratios Switched capacitor filters utilizing double sampling technique Effect of non idealities Opamp finite gain Opamp finite bandwidth this lecture Finite slew rate of the opamp this lecture EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 2 Effect of Opamp Non Idealities Finite Opamp Bandwidth 1 Vo CI 2 settling error Cs Vo Vi Unity gain freq Input Output z transform ft Vi 2 time T 1 fs AssumptionOpamp does not slew will be revisited Opamp has only one pole exponential settling Ref K Martin A Sedra Effect of the OPamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 3 Effect of Opamp Non Idealities Finite Opamp Bandwidth 1 Vo CI 2 settling error Cs Vi Vi Vo Unity gain freq Input Output z transform ft 2 time T 1 fs CI k k Z 1 H actual Z H ideal Z 1 e e CI Cs CI ft where k CI Cs f s ft O p a m p unity gain f r e q u e n c y fs Clock frequency Ref K Martin A Sedra Effect of the OPamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 4 Effect of Opamp Finite Bandwidth on Filter Magnitude Response non ideal ideal dB Magnitude deviation due to finite opamp unity gainfrequency Active RC fc fs 1 32 fc fs 1 12 Example 2nd order bandpass with Q 25 fc ft Ref K Martin A Sedra Effect of the OPamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 5 Effect of Opamp Finite Bandwidth on Filter Magnitude Response non ideal ideal dB Example For 1dB magnitude response deviation 1 fc fs 1 12 fc ft 0 04 ft 25fc Active RC fc fs 1 32 fc fs 1 12 2 fc fs 1 32 fc ft 0 022 ft 45fc 3 Cont Time fc ft 1 700 ft 700fc EECS 247 Lecture 11 SC Filters DACs fc ft 2005 H K Page 6 Effect of Opamp Finite Bandwidth Maximum Achievable Q Max allowable biquad Q for peak gain change 10 Ov ers am Ra pling tio C T filters fc ft Ref K Martin A Sedra Effect of the Opamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 7 Effect of Opamp Finite Bandwidth Maximum Achievable Q Example For Q of 40 required Max allowable biquad Q for peak gain change 10 1 fc fs 1 32 fc ft 0 02 ft 50fc 2 fc fs 1 12 fc ft 0 035 ft 28fc 3 fc fs 1 6 fc ft 0 05 ft 20fc C T filters fc ft Ref K Martin A Sedra Effect of the Opamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 8 Effect of Opamp Finite Bandwidth on Filter Critical Frequency c c Critical frequency deviation due to finite opamp unity gainfrequency Active RC fc fs 1 32 fc fs 1 12 Example 2nd order filter fc ft Ref K Martin A Sedra Effect of the OPamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 9 Effect of Opamp Finite Bandwidth on Filter Critical Frequency Example For maximum critical frequency shift of 1 1 fc fs 1 32 fc ft 0 028 ft 36fc c c Active RC fc fs 1 32 fc fs 1 12 2 fc fs 1 12 fc ft 0 046 ft 22fc 3 Active RC fc ft 0 008 ft 125fc C T filters fc ft Ref K Martin A Sedra Effect of the Opamp Finite Gain Bandwidth on the Performance of SwitchedCapacitor Filters IEEE Trans Circuits Syst vol CAS 28 no 8 pp 822 829 Aug 1981 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 10 Double Sampled Fully Differential 6th Order S C All Pole Bandpass Filter Cont time termination Q implementation Folded Cascode opamp with fu 100MHz used Center freq 3 1MHz filter Q 55 Clock freq 12 83MHz effective oversampling ratio 8 27 Measured dynamic range 46dB IM3 1 Ref B S Song P R Gray Switched Capacitor High Q Bandpass Filters for IF Applications IEEE Journal of Solid State Circuits Vol 21 No 6 pp 924 933 Dec 1986 EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 11 Sources of Distortion in SwitchedCapacitor Filters Distortion induced by finite slew rate of the opamp Opamp output input transfer function nonlinearity Distortion incurred by finite setting time of the opamp Capacitor non linearity Distortion due to switch clock feed through and charge injection EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 12 What is Slewing CI 2 Vin CI Cs CL 2 Vo Vo Cs ViVi Iss Assume opamp is of a simple differential pair class A transconductance type EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 13 What is Slewing Io Iss 2 Slope gm Vmax Vo Vin Iss 2 Io ViVi Class A amplifiers where the maximum output current is limited to Iss Vin Vmax Vin Vmax Io gmVin Io Imax EECS 247 Lecture 11 SC Filters DACs Iss Class A amplifier input stage 2005 H K Page 14 What is Slewing Io CI Iss 2 Vo Slope gm Vmax 2 Vin Cs Iss 2 Io CL ViVi Iss If at the rising edge of 2 Vcs Vmax Output current constant Io Iss 2 Slewing After Vcs is discharged enough to have Vcs Vmax Linear settling EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 15 Distortion Induced by Opamp Finite Slew Rate EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 16 Ideal Switched Capacitor Integrator Output Waveform Vin CI 1 1 Cs Clock Vo 2 Vin CI 2 Vin Cs Vcs Vo Vo 2 High Charge transferred from Cs to CI EECS 247 Lecture 11 SC Filters DACs 2005 H K Page 17 Slew …
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