EE247 Lecture 8 Continuous time filters continued Various Gm C filter implementations Comparison of continuous time filter topologies Switched Capacitor Filters Analog sampled data filters Continuous amplitude Quantized time Applications First commercial product Intel 2912 voice band CODEC chip 1979 Oversampled A D and D A converters Stand alone filters E g National Semiconductor LMF100 x2 biquads EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 1 Summary Last Lecture Automatic on chip filter tuning continued from previous 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 hardware can be used to periodically update filter freq response Continuous time filters Highpass filters 1st order integrator in the feedback path Bandpass filters Cascade of LP and HP for Qfilter 5 Direct implementation for narrow band filter via LP to BP transformation EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 2 Simplest Form of CMOS Gm Cell Nonidealities DC gain integrator Q a a g0M 1 2 gload 2L Vgs Vth M 1 2 Small Signal Differential Mode Half Circuit Where a denotes DC gain is related to channel length modulation by M 1 2 gm L Seems no extra poles EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 3 CMOS Gm Cell High Frequency Poles Cross section view of a MOS transistor operating in saturation Distributed channel resistance gate capacitance Distributed nature of gate capacitance channel resistance results in infinite no of high frequency poles EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 4 CMOS Gm Cell High Frequency Poles effective P2 1 1 i 2 P i effective 2 5 tM 1 2 P2 tM 1 2 High frequency behavior of an MOS transistor operating in saturation region g mM 1 2 3 2 3CoxWL 2 Vgs Vth M 1 2 2 L Distributed nature of gate capacitance channel resistance results in an effective pole at 2 5 times input device cut off frequency EECS 247 Lecture 8 2007 H K Page 5 Filters Gm C S C Simple Gm Cell Quality Factor a 2L P2effective Vgs Vth M 1 2 int g Qreal 1 1 o a 1 int g Q 15 4 Vgs Vth M 1 2 2 L 1 p i 2 i Vgs Vth M 1 2 2L o L2 4 1 5 V V g s th M 1 2 Note that phase lead associated with DC gain is inversely prop to L Phase lag due to high freq poles directly prop to L For a given there exists an optimum L which cancel the lead lag phase error resulting in high integrator Q EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 6 Simple Gm Cell Channel Length for Optimum Integrator Quality Factor 1 3 2 V V M 1 2 gs th L opt 1 5 4 o Optimum channel length computed based on process parameters could vary from process to process EECS 247 Lecture 8 2007 H K Page 7 Filters Gm C S C Source Coupled Pair CMOS Gm Cell Transconductance For a source coupled pair the differential output current Id as a function of the input voltage vi vi Id I ss V V gs th vi 1 1 4 Vgs Vth M 1 2 M 1 2 2 1 2 vi Id Note F or small V V gmM 1 M 2 v i gs th M 1 2 Id Not e A s vi in c re a se s o r t he vi e ffe c tiv e tra n sc o nd u c ta n c e de c re a se s EECS 247 Lecture 8 Filters Gm C S C vi Vi1 Vi2 Id Id1 Id 2 2007 H K Page 8 Source Coupled Pair CMOS Gm Cell Linearity Ideal Gm gm Large signal Gm drops as input voltage increases Gives rise to nonlinearity EECS 247 Lecture 8 2007 H K Page 9 Filters Gm C S C Measure of Linearity Vout 1Vin 2 Vin 2 3Vin 3 Vin amplitude 3rd harmonicdist comp HD 3 amplitude fundamental 1 3 Vin 2 4 1 amplitude 3rd order IM comp amplitude fundamental 3 3 25 5 Vin 2 Vin 4 4 1 8 1 IM 3 EECS 247 Lecture 8 1 2 Filters Gm C S C Vout 1 Vin 1 Vout 3 1 1 2 2 1 2 2 2 1 2007 H K Page 10 Source Coupled Pair Gm Cell Linearity vi I d I ss V V gs th vi 1 1 4 Vgs Vth M 1 2 M 1 2 2 1 2 1 I d a1 vi a2 vi 2 a3 vi3 Se rie s expansion used in 1 I ss a1 a2 0 Vgs Vth M 1 2 I ss a3 a4 0 3 8 Vgs Vth a5 M 1 2 I ss 128 Vgs Vth 5 a6 0 M 1 2 EECS 247 Lecture 8 2007 H K Page 11 Filters Gm C S C Linearity of the Source Coupled Pair CMOS Gm Cell 3a3 2 25a5 4 v v 4a1 i 8a1 i Su bstitu ting for a1 a3 IM3 2 4 v i v i IM3 3 25 32 VGS Vth 1024 VGS Vth v i max 4 VG S Vth 2 IM 3 3 I M 3 1 VG S Vth 1V V inrms 23 0m V Key point Max signal handling capability function of gate overdrive voltage EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 12 Simplest Form of CMOS Gm Cell Disadvantages Max signal handling capability function of gate overdrive IM 3 VGS Vth 2 Critical freq is also a function of gate overdrive o M 1 2 gm 2 Cint g W V V gs th L Vgs Vth since gm Cox then o Filter tuning affects max signal handling capability EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 13 Simplest Form of CMOS Gm Cell Removing Dependence of Maximum Signal Handling Capability on Tuning Can overcome problem of max signal handling capability being a function of tuning by providing tuning through Coarse tuning via switching in out binaryweighted cross coupled pairs Try to keep gate overdrive voltage constant Fine tuning through varying current sources Dynamic range dependence on tuning removed to 1st order Ref R Castello I Bietti F Svelto High Frequency Analog Filters in Deep Submicron Technology International Solid State Circuits Conference pp 74 75 1999 EECS 247 Lecture 8 Filters Gm C S C 2007 H K Page 14 Dynamic Range for Source Coupled Pair Based Filter IM 3 1 VGS Vth 1V Vinrms 230mV Minimum detectable signal determined by total noise voltage It can be shown for the 6th order Butterworth bandpass filter fundamental noise contribution is given by vo2 3Q k T Cint g Assumin g Q 10 Cint g 5 pF rms vnoise 160 V rms since vm a x 230mV 3 …
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