EE247 Lecture 9 Switched capacitor filters Tradeoffs in choosing sampling rate Effect of sample and hold Switched capacitor network electronic noise Switched capacitor integrators DDI integrators LDI integrators Effect of parasitic capacitance Bottom plate integrator topology Resonators EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 1 Summary of last lecture Continuous time filters continued Various Gm C filter implementations Comparison of continuous time filter topologies Switched capacitor filters Emulating resistor via switched capacitor network 1st order switched capacitor filter Switch capacitor filter considerations Issue of aliasing and how to avoid it Sample at high enough frequency so that the entire range of signals including the parasitics are at freqs fs 2 Use of anti aliasing prefilters EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 2 Sampling Sine Waves Problem Identical samples for v t cos 2 fint v t cos 2 n fs fin t v t cos 2 n fs fin t n integer Multiple continuous time signals can yield exactly the same discrete time signal EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 3 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 2007 H K Page 4 How to Avoid Aliasing Must obey sampling theorem fmax Signal fs 2 Note Minimum sampling rate of fs 2xfmax Signal is called Nyquist rate Two possibilities 1 Sample fast enough to cover all spectral components including parasitic ones outside band of interest 2 Limit fmax Signal through filtering attenuate out of band components prior to sampling EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 5 How to Avoid Aliasing 1 Sample Fast Amplitude Frequency domain fin fs old 2fs old fs new f Push sampling frequency to x2 of the highest frequency signal to cover all unwanted signals as well as wanted signals In vast majority of cases not practical EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 6 How to Avoid Aliasing 2 Filter Out of Band Signal Prior to Sampling Amplitude Frequency domain fin fs 2fs Filter Frequency domain Amplitude fin fs 2 f fs 2fs f Pre filter signal to eliminate attenuate signals above fs 2 then sample EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 7 Anti Aliasing Filter Considerations Desired Signal Band Switched Capacitor Filter Amplitude Anti Aliasing Filter Brickwall Anti Aliasing Pre Filter 0 fs 2 fs Realistic Anti Aliasing Pre Filter 2fs f Case1 B fsigmax fs 2 Non practical since an extremely high order anti aliasing filter close to an ideal brickwall filter is required Practical anti aliasing filter Non zero filter transition band In order to make this work we need to sample much faster than 2x the signal bandwidth Oversampling EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 8 Practical Anti Aliasing Filter Switched Capacitor Filter Anti Aliasing Filter Case2 B fmax Signal Parasitic Tone fs 2 More practical anti aliasing filter Preferable to have an antialiasing filter with The lowest order possible No frequency tuning required if frequency tuning is required then why use switched capacitor filter just use the prefilter EECS 247 Lecture 9 Desired Signal Band Attenuation 0 B 0 B fs fs 2 fs B fs 0 5 Switched Capacitor Filters f f fs 2007 H K Page 9 Tradeoff Oversampling Ratio versus Anti Aliasing Filter Order Maximum Aliased Signal Rejection Filter Order fs fin max Assumption anti aliasing filter is Butterworth type not a necessary requirement Tradeoff Sampling speed versus anti aliasing filter order Ref R v d Plassche CMOS Integrated Analog to Digital and Digital to Analog Converters 2nd ed Kluwer publishing 2003 p 41 EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 10 Effect of Sample Hold Sample Hold Tp Ts Ts Using the Fourier transform of a rectangular impulse H f T p sin fT p EECS 247 Lecture 9 fT p Ts sin x shape x Switched Capacitor Filters 2007 H K Page 11 Effect of Sample Hold on Frequency Response 1 0 9 H f abs H f 0 8 Tp Ts 0 7 T p sin fT p fT p Ts f Tp f s Ts f fs sin More practical H f 0 n integer Tp 0 5Ts 0 4 Ts T H f nf s s 0 Tp 0 6 0 5 Tp 0 3 0 2 0 1 0 0 EECS 247 Lecture 9 0 5 1 1 5 f fs 2 2 5 Switched Capacitor Filters 3 2007 H K Page 12 Sample Hold Effect Reconstruction of Analog Signals Time domain Magnitude droop due to sinx x effect EECS 247 Lecture 9 time ZOH Amplitude Tp Ts voltage Tp Ts H f fin sin fTs fTs Frequency domain 2fs f fs Switched Capacitor Filters 2007 H K Page 13 Sample Hold Effect Reconstruction of Analog Signals Droop 1dB Voltage Case 1 fsig fs 4 Time domain time Amplitude Magnitude droop due to sinx x effect 1dB fin EECS 247 Lecture 9 Frequency domain fs Switched Capacitor Filters f 2007 H K Page 14 Sample Hold Effect Reconstruction of Analog Signals Time domain Magnitude droop due to sinx x effect 1 0 8 0 6 0 4 Case 2 0 2 Amplitude fsig fs 32 0 0 2 0 4 0 6 0 8 sampled data after ZOH 1 0 0 5 1 1 5 2 2 5 3 Time Insignificant droop High oversampling ratio desirable EECS 247 Lecture 9 0 0035dB Amplitude Droop 0 0035dB fin 3 5 x 10 5 Frequency domain fs f Switched Capacitor Filters 2007 H K Page 15 Sampling Process Including S H H Z e g S C F Sampler S H Vi Time Domain t Freq Domain Freq Domain General Signal fin fB EECS 247 Lecture 9 f fs 2fs fs 2fs fs 2fs fs 2fs Switched Capacitor Filters fs fs 2fs 2fs 2007 H K Page 16 1st Order Filter Transient Analysis 1st Order RC versus SC LPF fs 1MHz f 3dB 50kHz fin 3 6kHz SC response extra clock cycle delay steps with finite rise time exaggerated EECS 247 Lecture 9 Switched Capacitor Filters 2007 H K Page 17 1st Order Filter S C versus C T Transient Analysis 1st Order RC versus SC LPF fs 1MHz f 3dB 50kHz fin 3 6kHz R1 3 2MOHM SC response extra clock cycle delay steps with finite rise time due to Rsw VO RC C2RC 1pF VIN 2 1 S1 S2 Rsw C1 314 2fF EECS 247 Lecture 9 VO SC C2SC 1pF Switched Capacitor Filters 2007 H K Page 18 1st Order Filter Transient Analysis ZOH ZOH Emulates an ideal S H pick signal after settling usually at end of clock phase Adds delay and sin x x shaping When in doubt use a ZOH in periodic ac simulations EECS …
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