EE247 Lecture 9 Continuous time filters continued Various Gm C filter implementations Performance comparison of various continuous time filter topologies Switched capacitor filters Emulating a resistor by using a switched capacitor Tradeoffs in choosing sampling rate Effect of sample and hold Switched capacitor network electronic noise Switched capacitor integrators DDI integrators LDI integrators EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 1 Correction to Lecture 4 Slide 48 Transmission Zero Generation Opamp RC Integrator Vin3 Vin2 Vo Vin1 Vin2 Vo s C Cx R1 R2 R f 1 Vin3 Vin1 EECS 247 Lecture 9 R2 R1 Cx C Cx Switched Capacitor Filters Rf Cx C Cx Vo 2008 H K Page 2 BiCMOS Gm C Integrator M1 2 triode mode Q1 2 hold Vds of M1 2 constant Current source ID used to tune filter critical frequency by varying Vds of M1 2 and thus controlling gm of M1 2 M3 M4 operate in triode mode and added to provide common mode feedback Needs higher supply voltage compared to the previous design since quite a few devices are stacked vertically Ref R Alini A Baschirotto and R Castello Tunable BiCMOS Continuous Time Filter for HighFrequency Applications IEEE Journal of Solid State Circuits Vol 27 No 12 pp 19051915 Dec 1992 EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 3 BiCMOS Gm C Integrator M5 M6 configured as capacitors added to compensate for RHP zero due to Cgd of M1 2 moves it to LHP size of M5 6 1 3 of M1 2 1 2CGSM1 1 3CGSM1 M5 M1 M6 M2 Ref R Alini A Baschirotto and R Castello Tunable BiCMOS Continuous Time Filter for HighFrequency Applications IEEE Journal of Solid State Circuits Vol 27 No 12 pp 19051915 Dec 1992 EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 4 BiCMOS Gm C Filter For Disk Drive Application Using the integrators shown in the previous page Biquad filter for disk drives gm1 gm2 gm4 2gm3 Q 2 Tunable from 8MHz to 32MHz Ref R Alini A Baschirotto and R Castello Tunable BiCMOS Continuous Time Filter for HighFrequency Applications IEEE Journal of Solid State Circuits Vol 27 No 12 pp 1905 1915 Dec 1992 EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 5 Summary Continuous Time Filters Opamp RC filters Good linearity High dynamic range 60 90dB Only discrete tuning possible Medium usable signal bandwidth 10MHz Opamp MOSFET C Linearity compromised typical dynamic range 40 60dB Continuous tuning possible Low usable signal bandwidth 5MHz Opamp MOSFET RC Improved linearity compared to Opamp MOSFET C D R 50 90dB Continuous tuning possible Low usable signal bandwidth 5MHz Gm C Highest frequency performance at least an order of magnitude higher compared to other integrator based active filters 100MHz Dynamic range not as high as Opamp RC but better than Opamp MOSFET C 4070dB EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 6 Switched Capacitor Filters SC filters are sampled data type circuits operating with continuous signal amplitude quantized time Emulating resistor via switched capacitor network 1st order switched capacitor filter Switch capacitor filter considerations Issue of aliasing and how to prevent aliasing Tradeoffs in choice of sampling rate Effect of sample and hold Switched capacitor filter electronic noise EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 7 Switched Capacitor Resistor Capacitor C is the switched capacitor Non overlapping clocks 1 and 2 control switches S1 and S2 respectively vIN 1 2 S1 S2 vOUT C vIN is sampled at the falling edge of 1 Sampling frequency fS Next 2 rises and the voltage across C is transferred to vOUT Why does this behave as a resistor EECS 247 Lecture 9 1 2 T 1 fs Switched Capacitor Filters 2008 H K Page 8 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 i fS C vIN vOUT 2 EECS 247 Lecture 9 T 1 fs Switched Capacitor Filters 2008 H K Page 9 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 vIN ivOUT 1 f sC Example f s 100kHz C 0 1pF Req 100Mega 1 Note Can build large time constant in small area EECS 247 Lecture 9 2 Switched Capacitor Filters T 1 fs 2008 H K Page 10 Switched Capacitor Filter Let s build a switched capacitor filter REQ vIN vOUT C2 Start with a simple RC LPF Replace the physical resistor by an equivalent switched capacitor resistor 3 dB bandwidth C 3dB 1 f s 1 ReqC2 C2 C f 3dB 1 f s 1 2 C2 EECS 247 Lecture 9 vIN 1 2 S1 S2 vOUT C1 Switched Capacitor Filters C2 2008 H K Page 11 Switched Capacitor Filter Advantage versus Continuous Time Filter 1 Vin S1 Req 2 S2 C1 Vout Vin C2 C2 f 3 dB f 3dB 1 f s C1 2 C2 Corner freq proportional to System clock accurate to few ppm C ratio accurate 0 1 Vout 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 2008 H K Page 12 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 2008 H K Page 13 Uniform Sampling Continuous time signal xc t Sampling interval T Sampling frequency fs 1 T Sampled signal xd kT x k Amplitude Nomenclature xd kT xc 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 Note Samples are the waveform values at kT instances and undefined in between EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 14 voltage Sampling Sine Waves T 1 s fs 1 T 1MHz fin 101kHz time y nT v t cos 2 fi n t Sampled data domian t n T or t n fs fi n 101kHz n cos 2 n v n cos 2 fs 1MHz EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 15 Sampling Sine Waves Aliasing voltage T 1 s fs 1 T 1MHz fin 899kHz time 101kHz 89 9 k H z 1 0 0 0 k Hz 1 0 1k Hz n c o s 2 n c o s 2 n v n c o s 2 1M Hz 1M Hz 1M Hz 101kHz n c os 2 1MHz EECS 247 Lecture 9 Switched Capacitor Filters 2008 H K Page 16 Sampling Sine Waves Aliasing voltage T 1 s fs 1 T 1MHz fin 1101kHz time 1000kHz 101kHz 1101kHz n co s 2 n v n cos 2 1MHz …
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