Lecture OverviewNMOS Floating Voltage CellFloating Voltage RealizationCOMFET Floating Voltage CellCOMFET Linear TransconductorComments On COMFET Linear OTANMOS Linear TransconductorNMOS Transconductor AnalysisSallen-Key Active RC FilterSallen-Key Equivalent CircuitTransfer CharacteristicDesign-Oriented AnalysisBandwidth FunctionFrequency ResponseOptimal Element RatioMulti-Pole Sallen-Key FilterButterworth 4-Pole FilterButterworth 4-Pole Design ExampleDesign Example, Cont’dFinalized DesignFrequency Response SimulationFrequency Response CommentsPulse Response SimulationEE 541Class LectureSupplementProf. John Choma, ProfessorDepartment of Electrical Engineering-ElectrophysicsUniversity of Southern CaliforniaUniversity Park; MC: 0271; PHE #604Los Angeles, California 90089-0271213-740-4692 [USC Office]213-740-7581 [USC Fax][email protected] FilterIssuesFall 2006 SemesterUniversity of Southern California Choma: EE 5412Lecture OverviewLecture Overviewz Operational Transconductor NMOS Floating Voltage CellBasic ConceptCircuit Realization COMFET Floating Voltage Cell COMFET Linear Transconductor NMOS Linear Transconductorz Sallen-Key Filter Basic Architecture ShortfallsPotential InstabilityFinite Amplifier Output Resistance 4-Pole Butterworth ExampleUniversity of Southern California Choma: EE 5413NMOS Floating Voltage CellNMOS Floating Voltage Cell() ()22nnd1 1 2 x hn d2 2 1 x hnKKWWVVVIVVVV2L 2L = −+− = −+−   +−Vx V1M1Id1Vgs1+−+−Vx V2M2Id2Vgs2+−−VssNote:Vgs1= V1–V2+ Vx Vgs2= V2–V1+ Vxz Requirements M1 And M2 Matched Substrates Appropriately Back Biasedz Analysisz Result Linearity Of Differential I/O Relationship Transconductance Tunable By VxIV()()d1 d2 me 1 2me n x hnII GVVWG2K VVL−= −≡−University of Southern California Choma: EE 5414V1M1i Id1 Q+Vx+−V2M2i + Id2 Q−VssM3kI iQd2−M4kI iQd1−Vx+−x k x k(k 1)I+Q(k 1)I+Q+Vdd()()()()()d1 Q d2 Q me 1 2me n x hnnQiI iI GVVWG2K VVL8K W L I+− + = −=−=Floating Voltage RealizationFloating Voltage RealizationRequirement:kIQ>> |id1|, |id2|z Analysisz Comments M3 And M4 Behave As Nominally Constant Floating Voltage Sources All Transistors Matched Except For Indicated Gate Aspect Ratios Substrates Are Reverse Biased Currentsid1, id2Are Signal CurrentsIQIs A Quiescent Current Only n−Channel Transistors Used In Signal Paths()()2QnQxhnxhnn2IKkWkI V V V V2L KWL≈−≈+University of Southern California Choma: EE 5415Parametric Review:pnnn n pp pnpWWKK K KLLhe hn hpVVV=+()2nedgeheKIVV2=−ne nn pp111KKK+COMFET Floating Voltage CellCOMFET Floating Voltage CellId1M1aM1b +−Vx V1Id2M2aM2b+−Vx V2Id1Id2z Analysisz Differential Output Currentz Comments Linear Differential I/O Relationship Effective Transconductance, Gme, Tunable Via Vx Wide Tunability Range Owing To Vhe= Vhn+ Vhp()()22ne ned1 1 2 x he d2 2 1 x heKKIVVVVIVVVV22=−+− =−+−()()d1 d2 me 1 2me ne x heIIGVVG2KVV−= −=−University of Southern California Choma: EE 5416Id1IQIQM1aM1bV1Id1M4bM3aIQ−VssVaId2M2aM2bV2Id2M3bM4aIQVb+Vdd+−Vx+−VxCOMFET Linear TransconductorCOMFET Linear Transconductorz Analysisz Results()() ()2QneQxhexhe 1b2ane22ne ned1 1 a he d 2 2 b he2IKIVV V V VV VV2KKKIVVV IVVV22=−⇒=+ =−=−=−− =−−()()d1 d2 me 1 2me ne x he ne QII GVVG2KVV 8KI−= −=−=University of Southern California Choma: EE 5417Comments On COMFET Linear OTAComments On COMFET Linear OTAz All COMFET Pairs Must Be Matched M1a−M1b Matched To M2a−M2b M3a−M3b Matched To M4a−M4b Ideally, All n-Channel And p-Channel Devices Respectively Matchedz Signals Linear Differential I/O Relationship Inner COMFETs Do Not Conduct Signal Currents Inner COMFETs Conduct Current IQ, Which Controls Effective Transconductance, Gmez Biasing All Substrates Back Biased Not Especially Amenable To Low Voltage Applicationsz Applications Moderate Speed OTA For OTA-C Filter Applications Class AB Stage To Improve Slew Rate Of CMOS Op-AmpsUniversity of Southern California Choma: EE 5418NMOS Linear TransconductorNMOS Linear TransconductorM3M7M4M8M6−VssV1V2V VQss−M5M1IdaM2IdbVxIss+Vdd+ − V Q +− VQM1, M2, M5, M6Are Matchedz No Signal Currents In Transistors M3-M4 And M7-M8z Voltage VQ Biases Gate Source Terminals Of M3-M4 And M7-M8 Controls Effective Differential TransconductanceUniversity of Southern California Choma: EE 5419()()()()() ()22nnda 1 x hn 2 Q x hn22nndb 2 x hn 1 Q x hnda db n Q 1 2 me 1 2KKWWI VVV VV VV2L 2LKKWWIVVV VVVV2L 2LWII K VVVGVVL =−−+−−−   =−−+−−−  ⇒−= −= −M3M7M4M8M6−VssV1V2V VQss−M5M1IdaM2IdbVxIss+Vdd+ − V Q +− VQNMOS Transconductor AnalysisNMOS Transconductor AnalysisUniversity of Southern California Choma: EE 54110SallenSallen--Key Active RC FilterKey Active RC Filterz Topology Lowpass Structure Bandpass And HighpassStructures Can Be Realized Lowpass Version Common InBaseband CommunicationSystem Applicationsz Amplifier Simple Voltage Amplifier With Open Loop Gain Of K Desirable To Design Amplifier For Unity GainMaximizes Bandwidth And Unity Gain FrequencyMaximizes Linearity Because Of Reduced Output SwingAvoids Network Instability Issues¾Note Positive Feedback Through Capacitance C1¾Network Can Oscillate For Large Open Loop Voltage GainAmplifier Has Parasitic Output Resistance (Ro) And Capacitance (Co)+−KR2R1C2C1VoutVinViUniversity of Southern California Choma: EE 54111CoR2R1C2C1VoutVinViRo+−KViz Modelz Parameters Resistances: Capacitances: Amplifier: Assume K = 1 Normalized Frequency:p = sRC = sR1C1z Transfer Function, H(p) = Vout/Vin+−KR2R1C2C1VoutVinVi21orRNR NRRkR==21ocCMC MCCkC==()()() ( )2rr23rc r rc rc1pk pkMN.1 pMN 1 k k 1 p MN kMN 1 kk 1 M MN pkkMNH(p)+++++++++++++=SallenSallen--Key Equivalent CircuitKey Equivalent CircuitUniversity of Southern California Choma: EE 54112Transfer CharacteristicTransfer Characteristicz Transfer Relationship Based On Model IdealizedRo= 0 → kr= 0Co= 0 → kc= 0Functionz Comparisons Ideal Response Is Second Order With No Finite