EE247 Lecture 9 Switched Capacitor Filters 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 EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 1 Capacitor C is the switched capacitor Non overlapping clocks 1 and 2 control switches S1 and S2 respectively vIN is sampled at the falling edge of 1 Next 2 rises and the voltage across C is transferred to v OUT 2 Sampling frequency fS Why does this behave as a resistor EECS 247 Lecture 9 Switched Capacitor Filters vIN EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 2 Switched Capacitor Resistors Switched Capacitor Resistor Emulating resistor via switched capacitor network 1st order switched capacitor filter Switch capacitor filter considerations Issue of aliasing and how to avoid it Tradeoffs in choosing sampling rate Effect of sample and hold Switched capacitor filter electronic noise Switched capacitor integrator topologies Charge transferred from vIN to vOUT during each clock cycle is 1 2 S1 S2 vIN vOUT C Q C vIN vOUT 1 2 S1 S2 vOUT C Average current flowing from vIN to vOUT is 1 i Q t Q fs 1 Substituting for Q 2 i fSC vIN vOUT T 1 fs 2005 H K Page 3 EECS 247 Lecture 9 Switched Capacitor Filters T 1 fs 2005 H K Page 4 Switched Capacitor Resistors i fS C vIN vOUT With the current through the switchedcapacitor resistor proportional to the voltage across it the equivalent switched capacitor resistance is vIN 1 2 S1 S2 Switched Capacitor Filter REQ vOUT C Req 1 f sC Start with a simple RC LPF Replace the physical resistor by an equivalent switchedcapacitor resistor Req 1Mega T 1 fs EECS 247 Lecture 9 Switched Capacitor Filters 3 dB bandwidth C 3dB 1 f s 1 ReqC2 C2 C f 3dB 1 f s 1 2 C2 2 f 1MHz C 1pF Let s build a switched capacitor filter 1 Example 2005 H K Page 5 S1 S2 C1 Vout Vin Vout vOUT C2 vIN 1 2 S1 S2 C1 EECS 247 Lecture 9 Switched Capacitor Filters vOUT C2 2005 H K Page 6 Typical Sampling Process Switched Capacitor Filters Advantage versus Continuous Time Filters 1 Req 2 Vin vIN Continuous Time CT Sampled Data SD ContinuousTime Signal time C2 C2 Sampled Data f 3dB 1 f s C1 2 C2 Corner freq proportional to System clock accurate to few ppm C ratio accurate 0 1 f 3dB 1 1 2 ReqC2 Corner freq proportional to Absolute value of Rs Cs Poor accuracy 20 to 50 Main advantage of SC filters inherent corner frequency accuracy EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 7 Sampled Data ZOH Clock EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 8 Uniform Sampling Sampling Sine Waves Nomenclature EECS 247 Lecture 9 Switched Capacitor Filters time y nT T v t sin 2 101000 t time 2005 H K Page 9 EECS 247 Lecture 9 Switched Capacitor Filters Sampling Sine Waves 2005 H K Page 10 Sampling Sine Waves T 1 s fs 1MHz fin 1101kHz T 1 s fs 1MHz fin 899kHz time v t sin 2 899000 t EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 11 voltage x t Problem Multiple continuous time signals can yield exactly the same discrete time signal Let s look at samples taken at 1 s intervals of several sinusoidal waveforms voltage x t T fs 1 T x kT x k voltage Continuous time signal Sampling interval Sampling frequency Sampled signal T 1 s fs 1 T 1MHz fin 101kHz x kT x k time v t sin 2 1101000 t EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 12 Sampling Sine Waves Frequency Spectrum Time domain Voltage Sampling Sine Waves Problem fs 1 T Identical samples for EECS 247 Lecture 9 Switched Capacitor Filters Amplitude fs 1MHz After Sampling Amplitude Amplitude Frequency Domain Interpretation 1101kHz 899kHz fin 2005 H K Page 13 fs fin fs fin 101kHz 2fs f fin 101kHz EECS 247 Lecture 9 Switched Capacitor Filters 2fs f fs 1MHz 2005 H K Page 14 Aliasing Frequency domain fs 2 fs Amplitude fin Signal scenario after sampling filtering Frequency domain Before Sampling Multiple continuous time signals can yield exactly the same discrete time signal Signal scenario before sampling time y nT v t sin 2 fint v t sin 2 fin fs t v t sin 2 fin fs t 2fs f Frequency domain fin fs 2 fs 2fs f Key point Signals nfS fmax signal fold back into band of interest Aliasing EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 15 Multiple continuous time signals can produce identical series of samples The folding back of signals from nfS fsig down to ffin is called aliasing Sampling theorem fs 2fmax Signal If aliasing occurs no signal processing operation downstream of the sampling process can recover the original continuous time signal EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 16 How to Avoid Aliasing 1 Sample fast enough to cover all spectral components including parasitic ones outside band of interest 2 Pre filter signal to eliminate signals above 2 Limit fmax Signal through filtering fs 2 then sample EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 17 Switched Capacitor Filter Amplitude Anti Aliasing Filter 0 Case1 B fmax Signal Brickwall Anti Aliasing Pre Filter fs 2 fs Frequency domain fin fs 2 2fs fs f 2005 H K Page 18 Desired Signal Band Anti Aliasing Filter f fs 2 Oversampling 2005 H K Page 19 Parasitic Tone Switched Capacitor Filter Case2 B fmax Signal Non practical since an extremely high order anti aliasing filter close to an ideal brickwall filter is required Practical anti aliasing filter Nonzero filter transition band In order to make this work we need to sample much faster than 2x the signal bandwidth EECS 247 Lecture 9 Switched Capacitor Filters fs new f 2fs old fs old Practical Anti Aliasing Filter Realistic Anti Aliasing Pre Filter 2fs fin EECS 247 Lecture 9 Switched Capacitor Filters Anti Aliasing Filter Considerations Desired Signal Band Frequency domain Amplitude 1 Push sampling frequency to x2 of the highest freq In most cases not practical Must obey sampling theorem fmax Signal fs 2 Two possibilities Amplitude How to Avoid Aliasing 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 Attenuation 0 0 EECS 247 Lecture 9 Switched Capacitor Filters B B fs 2 fs B fs f f 2005 H K Page 20 Tradeoff Effect of Sample Hold Oversampling Ratio versus Anti Aliasing Filter Order Maximum Aliasing Dynamic Range
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