EE247 Lecture 9 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 Switched Capacitor Filters Today 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 EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 2 Switched Capacitor Resistor 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 Sampling frequency fS Next 2 rises and the voltage across C is transferred to vOUT vIN 1 2 S1 S2 vOUT C 1 2 Why does this behave as a resistor T 1 fs EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 3 Switched Capacitor Resistors Charge transferred from vIN to vOUT during each clock cycle is vIN Q C vIN vOUT 1 2 S1 S2 vOUT C Average current flowing from vIN to vOUT is i Q t Q fs 1 Substituting for Q 2 i fS C vIN vOUT 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 vOUT C Req 1 f sC Example 1 f s 1MHz C 1pF 2 Req 1Mega T 1 fs EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 5 Switched Capacitor Filter REQ Let s build a switched capacitor filter Start with a simple RC LPF Replace the physical resistor by an equivalent switchedcapacitor resistor 3 dB bandwidth C 3dB 1 f s 1 ReqC2 C2 C f 3d B 1 f s 1 2 C2 EECS 247 Lecture 9 Switched Capacitor Filters vIN vOUT C2 vIN 1 2 S1 S2 C1 vOUT C2 2005 H K Page 6 Switched Capacitor Filters Advantage versus Continuous Time Filters 1 Req 2 Vin S1 S2 C1 Vout Vout Vin C2 C2 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 Typical Sampling Process Continuous Time CT Sampled Data SD ContinuousTime Signal time Sampled Data Sampled Data ZOH Clock EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 8 Nomenclature Continuous time signal Sampling interval Sampling frequency Sampled signal x t T fs 1 T x kT x k x kT x k 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 T time EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 9 Sampling Sine Waves T 1 s fs 1 T 1MHz fin 101kHz voltage Amplitude Uniform Sampling time y nT v t sin 2 101000 t EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 10 Sampling Sine Waves voltage 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 Sampling Sine Waves voltage T 1 s fs 1MHz fin 1101kHz time v t sin 2 1101000 t EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 12 Sampling Sine Waves Problem Identical samples for v t sin 2 fint v t sin 2 fin fs t v t sin 2 fin fs t Multiple continuous time signals can yield exactly the same discrete time signal EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 13 Sampling Sine Waves Frequency Spectrum Voltage Time domain fs 1 T time y nT fs fin 1101kHz fs fin 899kHz fin 101kHz Frequency domain fs 1MHz After Sampling Amplitude Amplitude Before Sampling 2fs f EECS 247 Lecture 9 Switched Capacitor Filters fin 101kHz fs 1MHz 2fs f 2005 H K Page 14 Signal scenario before sampling Amplitude Frequency Domain Interpretation Frequency domain Signal scenario after sampling filtering fs 2 fs Amplitude fin 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 Aliasing 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 Must obey sampling theorem fmax Signal fs 2 Two possibilities 1 Sample fast enough to cover all spectral components including parasitic ones outside band of interest 2 Limit fmax Signal through filtering EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 17 2 Pre filter signal to eliminate signals above fs 2 then sample Frequency domain fin fs new f 2fs old fs old Amplitude 1 Push sampling frequency to x2 of the highest freq In most cases not practical Amplitude How to Avoid Aliasing Frequency domain fin fs 2 EECS 247 Lecture 9 Switched Capacitor Filters fs 2fs f 2005 H K Page 18 Anti Aliasing Filter Considerations Desired Signal Band Switched Capacitor Filter Amplitude Anti Aliasing Filter 0 Case1 B fmax Signal Brickwall Anti Aliasing Pre Filter fs 2 Realistic Anti Aliasing Pre Filter fs 2fs f fs 2 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 Oversampling EECS 247 Lecture 9 Switched Capacitor Filters 2005 H K Page 19 Practical Anti Aliasing Filter Desired Signal Band Anti Aliasing Filter Case2 B fmax Signal Parasitic Tone Switched Capacitor Filter 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 Oversampling Ratio versus Anti Aliasing Filter Order Maximum Aliasing Dynamic Range Filter
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