EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 1EE247Lecture 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 integratorsEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 2Correction to Lecture 4 Slide # 48Transmission Zero Generation Opamp-RC IntegratoroVC +Cx-+R1R2RfVin3Vin2Vin1Cx()x12f1in1 in2 oosCC R R Rxin3xVV VVCVCC⎡⎤++⎢⎥+⎣⎦=−−×+EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 3• M1,2 Æ triode mode• Q1,2 Æ hold Vdsof M1,2 constant• Current source ID used to tune filter critical frequency by varying Vdsof 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 verticallyRef: R. Alini, A. Baschirotto, and R. Castello, “Tunable BiCMOS Continuous-Time Filter for High-Frequency Applications,” IEEE Journal of Solid State Circuits, Vol. 27, No. 12, pp. 1905-1915, Dec. 1992.BiCMOS Gm-C IntegratorEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 4• 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 Æ 1/3 of M1,2Ref: R. Alini, A. Baschirotto, and R. Castello, “Tunable BiCMOS Continuous-Time Filter for High-Frequency Applications,” IEEE Journal of Solid State Circuits, Vol. 27, No. 12, pp. 1905-1915, Dec. 1992.BiCMOS Gm-C Integrator1/2CGSM11/3CGSM1M1M2M5M6EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 5BiCMOS Gm-C Filter For Disk-Drive ApplicationRef: R. Alini, A. Baschirotto, and R. Castello, “Tunable BiCMOS Continuous-Time Filter for High-Frequency Applications,” IEEE Journal of Solid State Circuits, Vol. 27, No. 12, pp. 1905-1915, Dec. 1992.• Using the integrators shown in the previous page• Biquad filter for disk drives•gm1=gm2=gm4=2gm3• Q=2• Tunable from 8MHz to 32MHzEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 6Summary Continuous-Time Filters• Opamp RC filters– Good linearity Æ 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 (40-70dB)EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 7Switched-Capacitor Filters• SC filters are sampled-data type circuits operating with continuous signal amplitude & quantized time• Emulating resistor via switched-capacitor network•1storder 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 noiseEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 8Switched-Capacitor Resistor• Capacitor C is the “switched capacitor”• Non-overlapping clocks φ1and φ2control switches S1 and S2, respectively•vINis sampled at the falling edge ofφ1– Sampling frequency fS•Next,φ2rises and the voltage across C is transferred tovOUT• Why does this behave as a resistor?vINvOUTCS1 S2φ1φ2φ1φ2T=1/fsEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 9Switched-Capacitor ResistorsvINvOUTCS1 S2φ1φ2φ1φ2T=1/fs• Charge transferred from vINto vOUTduring each clock cycle is:• Average current flowing from vINto vOUTis:Q = C(vIN –vOUT)i=Q/t = Q . fsSubstituting for Q:i =fS C(vIN–vOUT)EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 10Switched-Capacitor ResistorsWith the current through the switched-capacitor resistor proportional to the voltage across it, the equivalent “switched capacitor resistance” is:Note: Can build large time-constant in small areavINvOUTCS1 S2φ1φ2φ1φ2T=1/fsi = fS C(vIN –vOUT)IN OUTvvi1ReqfCsExample:f100kHz,C 0.1pFsR 100Megaeq−====→= ΩEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 11Switched-Capacitor Filter• Let’s build a “switched- capacitor ”filter …• Start with a simple RC LPF• Replace the physical resistor by an equivalent switched-capacitor resistor• 3-dB bandwidth:vINvOUTC1S1 S2φ1φ2C2vOUTC2REQvINC11fs3d BRCCeq 2 2C11ffs3d B2C2ωπ==×−=×−EECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 12Switched-Capacitor Filter Advantage versus Continuous-Time FilterVinVoutC1S1 S2φ1φ2C2VoutC2ReqVin3dB1s2C1ff2Cπ−=×2eqCR121fdB3×=−π• Corner freq. proportional to:System clock (accurate to few ppm)C ratio accurate Æ <0.1%• Corner freq. proportional to:Absolute value of Rs & CsPoor accuracy Æ 20 to 50%³Main advantage of SC filtersÆinherent corner frequency accuracyEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 13Typical Sampling ProcessContinuous-Time(CT) ⇒ Sampled Data (SD)Continuous-Time SignalSampled Data+ ZOH ClocktimeSampled DataEECS 247 Lecture 9 Switched-Capacitor Filters © 2008 H. K. Page 14Uniform SamplingNomenclature:Continuous time signal xc(t)Sampling interval TSampling frequency fs= 1/TSampled signal xd(kT) = x(k)• Problem: Multiple continuous time signals can
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