EECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 1EE247Lecture 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-idealitiesEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 2Sampling Sine WavesFrequency Spectrumf /fsAmplitudefs1MHz…fAmplitudefin100kHz2fs600kHz1.2MHzContinuous-TimeDiscrete TimeSignal scenariobefore samplingSignal scenarioafter samplingKey point: Signals @ nfS±fmax__signalfold back into band of interestÆAliasing0.50.10.40.21.7MHz0.3EECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 3timeVoOutput Frequency Spectrum prior to holdfs2fsf-3dBFirst Order S.C. FilterVinVoutC1S1 S2φ1φ2C2VintimeSwitched-Capacitor Filters Æ problem with aliasing|H(f)|EECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 4timeVoOutput Frequency Spectrum prior to holdAntialiasing Pre-filterfs2fsf-3dBFirst Order S.C. FilterVinVoutC1S1 S2φ1φ2C2VintimeSwitched-Capacitor Filters Æ problem with aliasingAnti-Aliasing FilterEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 5Sampled-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 Æfmax< fs /2 )• Usually, anti-aliasing filter Æ included on-chip as continuous-time filter with relaxed specs. (no tuning)EECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 6Antialiasing Pre-filterfs2fsf-3dBExample : Anti-Aliasing Filter Requirements• 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 Æ 0 to 4kHz < 0.05dB– Allow +-30% variation for anti-aliasing filter corner frequency (no tuning) Need to find minimum required filter orderEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 7Oversampling Ratio versus Anti-Aliasing Filter OrderÆ2ndorder ButterworthÆNeed to find minimum corner frequency for mag. droop < 0.05dBMaximum Aliasing Dynamic Rangefs/fin_maxFilter Order* AssumptionÆanti-aliasing filter is Butterworth typefs/fin =256K/4K=64EECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 8Example : Anti-Aliasing Filter SpecificationsFrom: Williams and Taylor, p. 2-37Stopband Attenuation dBΝοrmalized ω• Normalized frequency for 0.05dB droop: need perform passband simulationÆ normalized ω=0.34Æ 4kHz/0.34=12kHz • Set anti-aliasing filter corner frequency for minimum corner frequency 12kHz Æ Find nominal corner frequency: 12kHz/0.7=17.1kHz• Check if attenuation requirement is satisfied for widest filter bandwidth Æ 17.1x1.3=22.28kHz• Find (fs-fsig )/f-3dBmaxÆ252/22.2=11.35Æ make sure enough attenuation• Check phase-error within 4kHz signal band for min. filter bandwidth via simulation 0.05dB droopEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 9Antialiasing Pre-filterfs2fsf-3dBExample : Anti-Aliasing Filter• 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)Æ2-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 10Summary• Sampling theorem Æ fs> 2fmax_Signal• Signals at frequencies nfS±fsigfold back down to desired signal band, fsigÆ 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 shapeÆ 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 informationEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 11Switched-Capacitor Network Noise•During φ1high: 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:Q2 = C2V2 = C2. kT/C = kTC•φ1low: S1 open ÆThis charge is sampledvINvOUTCS1 S2φ1φ2RonS1CvINEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 12Switched-Capacitor NoisevINvOUTCS1 S2φ1φ2RonS2C•During φ2high: Resistance of switch S2 contributes to an uncorrelated noise charge on C at the end of φ2: with variance kT/C• Mean-squared noise charge transferred from vINto vOUT per sample period is:Q2=2kTCEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page 13• The mean-squared noise current due to S1 and S2’s kT/C noise is :• This noise is approximately white and distributed between 0 and fs /2 (noise spectra Æ single sided by convention) The spectral density of the noise is found:ÆS.C. resistor noise = a physical resistor noise with same value!Switched-Capacitor Noise()2Q22Since i then i Qf 2k TCfsBst=→==222k TCfiBs4k TCf Bsffs224k T1iBSince R then: EQfC f RsEQ==Δ==ΔEECS 247 Lecture 9 Switched-Capacitor Filters © 2009 H. K. Page
View Full Document
Unlocking...