EE247 Lecture 9 Switched capacitor filters continued Example of anti aliasing prefilter for S C filters Switched capacitor network electronic noise Switched capacitor integrators DDI integrators LDI integrators Effect of parasitic capacitance Bottom plate integrator topology Switched capacitor resonators Bandpass filters Lowpass filters Switched capacitor filter design considerations Termination implementation Transmission zero implementation Effect of non idealities EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 1 Sampling Sine Waves Frequency Spectrum Signal scenario before sampling Amplitude Continuous Time 600kHz 1 2MHz fs fin 1MHz 100kHz 1 7MHz 2fs f Signal scenario after sampling Amplitude Discrete Time 0 2 0 4 0 1 0 3 0 5 f fs Key point Signals nfS fmax signal fold back into band of interest Aliasing EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 2 First Order S C Filter Vin Vin 1 2 S1 S2 C1 time Vout Vo time C2 H f f 3dB fs 2fs Output Frequency Spectrum prior to hold Switched Capacitor Filters problem with aliasing EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 3 First Order S C Filter Vin Vin Anti Aliasing Filter 1 2 S1 S2 C1 time Vout Vo time C2 Antialiasing Pre filter f 3dB fs 2fs Output Frequency Spectrum prior to hold Switched Capacitor Filters problem with aliasing EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 4 Sampled Data Systems Filters Anti aliasing Requirements Frequency response repeats at fs 2fs 3fs High frequency signals close to fs 2fs folds back into passband aliasing Most cases must pre filter input to sampled data systems filter to attenuate signal at f fs 2 nyquist fmax fs 2 Usually anti aliasing filter included on chip as continuous time filter with relaxed specs no tuning EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 5 Example Anti Aliasing Filter Requirements Antialiasing Pre filter f 3dB fs 2fs Voice band CODEC S C filter high order low pass with f 3dB 4kHz fs 256kHz Anti aliasing continuous time pre filter requirements Need at least 40dB attenuation of all out of band signals which can alias inband Incur no phase error from 0 to 4kHz Gain error due to anti aliasing filter 0 to 4kHz 0 05dB Allow 30 variation for anti aliasing filter corner frequency no tuning Need to find minimum required filter order EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 6 Oversampling Ratio versus Anti Aliasing Filter Order Maximum Aliasing Dynamic Range Filter Order fs fin max fs fin 256K 4K 64 Assumption anti aliasing filter is Butterworth type 2nd order Butterworth Need to find minimum corner frequency for mag droop 0 05dB EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 7 Example Anti Aliasing Filter Specifications 252 22 2 11 35 make sure enough attenuation Check phase error within 4kHz signal band for min filter bandwidth via simulation EECS 247 Lecture 9 Stopband Attenuation dB Normalized frequency for 0 05dB droop need perform passband simulation normalized 0 34 4kHz 0 34 12kHz Set anti aliasing filter corner frequency for minimum corner frequency 12kHz Find nominal corner frequency 12kHz 0 7 17 1kHz Check if attenuation requirement is satisfied for widest filter bandwidth 17 1x1 3 22 28kHz Find fs fsig f 3dB max 0 05dB droop rmalized From Williams and Taylor p 2 37 Switched Capacitor Filters 2009 H K Page 8 Example Anti Aliasing Filter Antialiasing Pre filter f 3dB fs 2fs Voice band S C filter f 3dB 4kHz fs 256kHz Anti aliasing filter requirements Need 40dB attenuation at clock freq Incur no phase error from 0 to 4kHz Gain error 0 to 4kHz 0 05dB Allow 30 variation for anti aliasing corner frequency no tuning 2 pole Butterworth LPF with nominal corner freq of 17kHz no tuning min 12kHz max 22kHz corner frequency EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 9 Summary Sampling theorem fs 2fmax Signal Signals at frequencies nfS fsig fold back down to desired signal band fsig This is called aliasing usually mandates use of anti aliasing pre filters combined with oversampling Oversampling helps reduce required order for anti aliasing filter S H function shapes the frequency response with sinx x shape Need to pay attention to droop in passband due to sinx x If the above requirements are not met CT signals can NOT be recovered from sampled data networks without loss of information EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 10 Switched Capacitor Network Noise During 1 high Resistance of switch S1 RonS1 produces a noise voltage on C with variance kT C lecture 1 first order filter noise The corresponding noise charge is vIN 1 2 S1 S2 vOUT C vIN RonS1 Q2 C2V2 C2 kT C kTC C 1 low S1 open This charge is sampled EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 11 Switched Capacitor Noise During 2 high Resistance of switch S2 contributes to an uncorrelated noise charge on C at the end of 2 with variance vIN 1 2 S1 S2 vOUT C kT C Mean squared noise charge transferred from vIN to vOUT per sample period is RonS2 C Q2 2kTC EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 12 Switched Capacitor Noise The mean squared noise current due to S1 and S2 s kT C noise is S i n ce i Q t 2 t hen i2 Qfs 2kBT C fs2 This noise is approximately white and distributed between 0 and fs 2 noise spectra single sided by convention The spectral density of the noise is found 2 i2 2kBT C fs 4k T C f B s fs f 2 i2 4kBT f REQ Si nce REQ 1 t hen fsC S C resistor noise a physical resistor noise with same value EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 13 Periodic Noise Analysis SpectreRF Sampling Noise from SC S H Netlist ahdl include zoh def Netlist simOptions options reltol 10u vabstol 1n iabstol 1p Vclk 100ns 100kOhm R Vrc Vrc hold ZOH1 S1 PNOISE Analysis PNOISE1 sweep from 0 to 20 01M 1037 steps C 1pF ZOH1 T 100ns SpectreRF PNOISE check noisetype timedomain noisetimepoints C1 as alternative to ZOH 1pF noiseskipcount large might speed up things in this case PSS pss period 100n maxacfreq 1 5G errpreset conservative PNOISE Vrc hold 0 pnoise start 0 stop 20M lin 500 maxsideband 10 100kOhm R1 Voltage NOISE VNOISE1 EECS 247 Lecture 9 Switched Capacitor Filters 2009 H K Page 14 V sqrt Hz Normalized Noise Density dB Sampled Noise Spectrum Spectral density of sampled noise including sinx x effect EECS 247 Lecture 9 Noise spectral density with sinx x effect taken out Switched Capacitor Filters 2009 H K Page 15 Normalized Total Noise vnT KT C Total Noise
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