Lecture 25
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EE 508 Lecture 25 Integrator Design Review from last time Parasitic Capacitances on Floating Nodes Floating Node Not Floationg Node Z2 Zk Z1 CP2 CP1 CP Parasitic capacitances ideally have no affect on filter when on a non-floating node but directly affect transfer function when they appear on a floating node Parasitic capacitances are invariably large, nonlinear, and highly process dependent in integrated filters. Thus, it is difficult to build accurate integrated filters if floating nodes are present Generally avoid floating nodes, if possible, in integrated filters Review from last time Which type of Biquad is really used? Not Floationg Node Floating Node R2 C1 R1 VOUT K -K R1 C2 VIN VIN R3 C1 Sallen-Key Type (Dependent Sources) C1 R3 R1 C2 R2 VIN VOUT Infinite Gain Amplifiers RQ R1 C2 C1 R0 R2 RA RA VIN VOUT Integrator Based Structures C2 R2 VOUT Review from last time Filter Design/Synthesis Considerations VIN Cascaded Biquads T1(s) T2(s) Tk(s) Tm(s) Biquad Biquad Biquad Biquad VOUT T s T1T2 Tm Leapfrog VIN I1(s) I2(s) Integrator Integrator Integrator VOUT I4(s) Ik-1(s) Ik(s) Integrator Integrator Integrator I3(s) a1 a2 Multiple-loop Feedback – One type shown XIN α0 α2 α1 αF αk T1(s) T2(s) Tk(s) Biquad Biquad Biquad XOUT Observation: All filters are comprised of summers, biquads and integrators And biquads usually made with summers and integrators Integrated filter design generally focused on design of integrators, summers, and amplifiers (Op Amps) Will now focus on the design of integrators, summers, and op amps Basic Filter Building Blocks (particularly for integrated filters) • Integrators • Summers • Operational Amplifiers Integrator Characteristics of Interest XIN I0 s XOUT I0 I s = s Properties of an ideal integrator: I jω = I0 ω I jω = -900 I jI 0 = 1 Gain decreases with 1/ω Phase is a constant -90o Unity Gain Frequency = 1 How important is it that an integrator have all 3 of these properties? Integrator Characteristics of Interest I0 s XIN I0 I jω = ω I0 I s = s XOUT I jω = -900 I jI 0 = 1 How important is it that an integrator have all 3 of these properties? Consider a filter example: T s XIN I0 s I 0 s α XO2 XO1 Q= - I02 s2 + αI0s + I02 1 ω0 = I0 Band edges proportional to I0 Phase critical to make Q expression valid In many (most) applications it is critical that an integrator be very nearly ideal (in the frequency range of interest) Some integrator structures C VIN I s VOUT R Inverting Active RC Integrator Are there other integrator structures? VIN IOUT gm VOUT C IOUT = - gm VIN VOUT IOUT Termed an OTA-C or a gm-C integrator 1 sC I s gm sC I0 gm C 1 RCs I0 1 RC Some integrator structures Are there other integrator structures? VBB IOUT IOUT VOUT VOUT VIN C V1 gm VIN gmV1 C IOUT = gm VIN VOUT IOUT I0 Termed a TA-C integrator VC C VIN RMOS 1 sC I s VOUT I s 1 sCRMOS I0 Termed MOSFET-C integrator 1 RFETC gm C gm sC Some integrator structures Are there other integrator structures? C IIN V1 V2 V2 = V1 I IN R IOUT IOUT 1 sC V2 - V1 R I s IOUT 1 IIN sRC ZL I0 • Output current is independent of ZL • Thus output impedance is ∞ so provides current output Termed active RC current-mode integrator 1 RC Some integrator structures VBB C IIN IOUT V1 VOUT V2 C R VIN IOUT ZL 1 I s sRC gm 1 sRC VC VOUT C I s gm sC VOUT R I s IOUT I s C VIN VIN gm C gm sC VIN VOUT RMOS I s There are other useful integrator structures (some will be introduced later) There are many different ways to build an inverting integrator 1 sRMOSC Integrator Functionality C VIN I s VOUT R Basic Active RC Inverting Integrator Rn RA VINn C VIN C VIN1 1 sRC R VOUT R1 n 1 VINk CR s k k 1 VOUT RA Noninverting Integrator VOUT Summing Integrator I s 1 sRC RF C C R VINdiff + - + VOUTdiff - Axis of Symmetry R C Fully Differential Integrator VOUTdiff 1 VINdiff CRs VIN R VOUT VOUT RF R V IN 1+CRFs Lossy Integrator Many different types of functionality from basic inverting integrator Same modifications exist for other integrator architectures Integrator-Based Filter Design C VIN C IIN VOUT R VBB V1 V2 IOUT VOUT R IOUT C ZL XIN I0 s I 0 s α gm VIN XO2 XO1 VIN VIN T0(s) T1(s) T2(s) Tk(s) Tm(s) FirstOrder Biquad Biquad Biquad Biquad VOUT IOUT gm VOUT C VIN I1(s) I2(s) Integrator Integrator a1 I3(s) Integrator I4(s) Ik-1(s) Ik(s) Integrator Integrator Integrator VOUT a2 VC C VIN RMOS VOUT Any of these different types of integrators can be used to build integrator-based filters Are new integrators still being invented? Example – OTA-C Tow Thomas Biquad VIN XIN I0 s I 0 s IOUT gm C XO2 α VOUT XO1 VOUT gm3 gm2 = 2 VIN s C1C2 sgm4C2 +gm1gm2 V1 VOUT gm2 gm1 C1 VIN Assume gm1=gm2=gm, C1=C2=C C2 VOUT VIN gm3 gm4 gm3 gm2 gm C2 = 2 gm4 gm gm2 s s + 2 g m C C express as VOUT sC2 =gm2 V1 V1sC1= -gm1VOUT gm3 VIN gm4 V1 gm3 2 ω0 gm VOUT = VIN 2 ω0 +ω02 s s Q where ω0 = gm C Q= gm gm4 Basic Integrator Functionality XIN XOUT I0 s Noninverting XIN I0 s+α XOUT I 0 s XIN Inverting XOUT XIN I0 s+α XOUT Lossy Inverting Lossy Noninverting XIN1 I0k s XINk XOUT n I Ok XOUT k 1 XINn s Summing (Multiple-Input) Inverting/Noninverting XIN1 I0k s+ k XINk XOUT n I Ok XOUT k 1 s+α k XINn Summing (Multiple-Input) Lossy Inverting/Noninverting + XIN XIN + - I0 + s - X+ OUT XOUT I0 + + + X+ XIN XIN OUT XOUT s Balanced Differential XINdiff + - + I0 + + - s - Fully Differential XOUTdiff I XOUTdiff 0 XINdiff s Basic Integrator Functionality XIN I0 s Noninverting XOUT XIN I 0 s XOUT Inverting • An inverting/noninverting integrator pair define a family of integrators • All integrator functional types can usually be obtained from the inverting/noninverting integrator pair • Suffices to focus primarily on the design of the inverting/noninverting integrator pair since properties of class primarily determined by properties of integrator pair Example – Basic Op-Amp Feedback Integrator RA C VIN R C VOUT VOUT VIN R VOUT RA 1 VIN CRs VOUT Inverting Integrator of Family 1 VIN CRs Noninverting Integrator Rn VINn C VIN1 R1 n 1 VINk k1 CRk s VOUT VOUT Summing Inverting Integrator Example – Basic Op-Amp Feedback Integrator Rn C VIN VINn VOUT R VOUT 1 VIN CRs Inverting Integrator of Family n 1 VINk k1 CRk s VOUT C VIN1 VOUT R1 Summing Inverting Integrator VINn VINn-1 Rn Rn-1 C VIN1 R1 VOUT n1 R n VINk R k 1 k VINn Rn 1+CRns VOUT Lossy Summing Inverting Integrator RF C VIN1 R1 VOUT VOUT n R F VINk k 1 Rk 1+CRFs Example – Basic Op-Amp Feedback Integrator C VIN VINn VOUT R Rn 1 VOUT VIN CRs RF C VIN1 R1 VOUT VOUT n R F VINk k 1 Rk 1+CRFs Inverting Integrator of Family Lossy Summing Inverting Integrator RF C VOUT VIN R VOUT Lossy Inverting Integrator RF R V IN 1+CRFs Example – Basic Op-Amp Feedback Integrator C VIN VOUT VOUT R 1 VIN CRs Inverting Integrator of Family VIN+ + R + VIN - + VOUT VOUTdiff VINdiff - VOUT C Axis of Symmetry VOUTdiff - VOUT R VOUT 1 VIN CRs 1 VIN CRs C Balanced Differential Inverting Integrator 1 VINdiff CRs Example – Basic Op-Amp Feedback Integrator C VIN VOUT VOUT R 1 VIN CRs Inverting Integrator of Family C R VINdiff + - + VOUTdiff - Axis of Symmetry R C Fully Differential Inverting Integrator VOUTdiff 1 VINdiff CRs Integrator Types VIN I0 s VOUT I VOUT o VIN s IOUT I IOUT o IIN s VOUT I VOUT o IIN s Voltage Mode IIN I0 s Current Mode IIN I0 s Transresistance Mode VIN I0 s IOUT I IOUT o VIN s Transconductance Mode Will consider first the Voltage Mode type of integrators Voltage Mode Integrators • • • • • • Active RC (Feedback-based) MOSFET-C (Feedback-based) OTA-C Sometimes termed “current mode” TA-C Switched Capacitor Will discuss later Switched Resistor Active RC Voltage Mode Integrator C VIN R VOUT VOUT 1 VIN CRs • Limited to low frequencies because of Op Amp limitations • No good resistors for monolithic implementations Area for passive resistors is too large at low frequencies Some recent work by Haibo Fei shows promise for some audio frequency applications • Capacitor area too large at low frequencies for monolithic implementatins • Active devices are highly temperature dependent, proc. dependent, and nonlinear • No practical tuning or trimming scheme for integrated applications with passive resistors MOSFET-C Voltage Mode Integrator VC C VIN RMOS VOUT • • • • • VOUT 1 VIN CRMOSs Limited to low frequencies because of Op Amp limitations Area for RMOS is manageable ! Active devices are highly temperature dependent, process dependent Potential for tuning with VC Highly Nonlinear (can be partially compensated with cross-coupled input A Solution without a Problem MOSFET-C Voltage Mode Integrator VC VC C VIN RMOS VOUT C VOUT 1 VIN C RMOSs VIN VOUT RMOS VC 1 VOUT VIN C RMOSs • Improved Linearity • Some challenges for implementing VC Still A Solution without a Problem OTA-C Voltage Mode Integrator VIN VOUT gm V IN V OU T gm C g V O U T m VIN sC Inverting • • • • • • • C VO U T gm sC VIN Noninverting Requires only two components Inverting and Noninverting structures of same complexity Good high-frequency performance Small area Linearity is limited (no feedback in integrator) Susceptible to process and temperature variations Tuning control can be readily added Widely used in high frequency applications OTA-C Voltage Mode Integrator VIN VOUT gm C IABC VIN VOUT gm C VO U T gm sC VIN VO U T gm sC VIN g m f IA B C Programmable Integrator OTA-C Voltage Mode Integrator VIN VOUT gm VIN gm C VO U T gm sC VIN VOUT C RF VOUT s gmRF = VIN s 1+s RFC Lossy Integrator But RF is typically too large for integrated applications End of Lecture 25
