Overview Of LectureFilters For Amplifier BroadbandingGeneral Broadbanding ConceptsUncompensated PerformanceShunt Peaked AnalysisShunt Peaked ResponseShunt Peaked Frequency ResponsePeaking InvestigationBandwidth And PeakingOptimized Frequency ResponseOptimal Shunt PeakingShunt Peaked Envelope DelayDelay ResponseDelay Frequency ResponseShunt Peaking ExampleExample Frequency ResponseExample Delay ResponseComments On Example ResponsesSeries Peaked AmplifierSeries Peaked AnalysisSeries Peaking ExampleSeries Peaked Frequency ResponseSeries Peaked Delay ResponseComments On Series PeakingSeries-Shunt PeakingSeries-Shunt Peaked AnalysisSeries-Shunt Analysis, Cont’dSeries-Shunt Design ProblemCoupled Inductor PeakingCoupled InductancesAmplifier Equivalent CircuitInput Impedance Analysis StrategyConstant Resistance CriteriaFrequency ResponseCircuit PerformanceCircuit Performance ExampleHSPICE Simulated Design ResultsFilter Section FundamentalsEE 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] For Broadband Circuit CompensationFall 2006 SemesterUniversity of Southern California Choma: EE 541300Overview Of LectureOverview Of Lecturez Fundamental Amplification Topology Circuit Schematic Simplified Small Signal Modelz Broadband Architectures Shunt PeakingMagnitude ResponseDelay ResponseDesign Criteria Series Peaking Series Shunt PeakingWithout Coupled InductorsWith Coupled InductorsUniversity of Southern California Choma: EE 541301Filters For Amplifier BroadbandingFilters For Amplifier Broadbandingz Available Broadband Architectures Inductive Shunt Peaking Inductive Series Peaking Series-Shunt Peaking Coupled Inductor Peakingz Design Issues AdvantagesBroadband Compensation Structures Are Fundamentally LosslessBandwidth Enhancements Of Up To Almost 300% Are PossibleQuality Factor Of Inductors Is Generally Not A Major Concern DisadvantagesChip Surface Area Penalty With “Large” InductorsChip Frequency-Dependent Parasitics Associated With Inductor LayoutCoupled Inductors May Be Required¾Coupling Coefficients Difficult To Predict Analytically¾ Reproducibility Of Coupling Coefficients Is ProblematicUniversity of Southern California Choma: EE 541302M1M2VbiasRsRlV + ViQ sV + VoQ oVo+VddClgVmsroCoRlClz Basic GainStage AndSmall SignalModelz Discussion CascodeTransistor M2 Mitigates Miller Effect Of Gate-Drain Capacitance Of Transistor M1 Model Parametersgm→ Effective Forward Transconductancero→ Effective (Large) Output ResistanceCo→ Effective Output Capacitance¾Includes Bulk-Drain Capacitance (Cbd) Of M2¾ Includes Gate-Drain Capacitance (Cgd) Of M2Cl→ Effective Load CapacitanceGeneral Broadbanding ConceptsGeneral Broadbanding ConceptsUniversity of Southern California Choma: EE 541303()()uol l o1BrR C C=+ovovsuVAA(s)V1sB==+z Gain Function Zero FrequencyGain UncompensatedBandwidthz Compensation Requirements Negligible CapacitancesM1 Gate-Source Capacitance (Cgs)Because Of Small Source Resistance, RsSmall M2 Input Resistance At Source¾M1 Bulk-Drain Capacitance (Cbd)¾ M1 Gate-Drain Capacitance (Cgd)¾ M2 Bulk-Source Capacitance (Cbs)¾ M2 Gate-Source Capacitance (Cgs)Note Gate Bias Port Of M2 Is At Signal GroundIn General, Compensation Applied To Output Port Of Amplifier Requires That Uncompensated Dominant Pole Be Established At This PortM1M2VbiasRsRlV + ViQ sV + VoQ o+VddClVogVmsroCoRlCl()vo m o lAgrR=−Uncompensated PerformanceUncompensated PerformanceUniversity of Southern California Choma: EE 541304mllov2sllo losLgR 1RVA(s)V1sRC sLC+==−++VogVmsCoRlClLz Approximate Circuit Model (ro>> Rl)z TransferFunctionz Parameters Self-ResonantFrequency, ωn Circuit QualityFactor NormalizationsFrequency Normalized ToUncompensated BandwidthGain Normalized To ZeroFrequency gain()nlo1ωLC C=+()()lonulnlnl l oLC Cω LB1QR ω Rω RC C+== ==+uu upsB jω Bjy;yω B=→==n v vo n v voA(s) A (s) A ; A (p) A (p) A==lo l oCCC+Shunt Peaked AnalysisShunt Peaked AnalysisUniversity of Southern California Choma: EE 541305()()242 42 4cb4u2Q 2Q 1 2Q 2Q 1 4QByB2Q+−+ +−+==()ocnb buABAjy ;y2B==()2n22vo2n2voA(p) 1 Q pA(p)A1pQpA(jy) 1 jQ yA(jy)A1Qy jy+=+++=−+z Normalized Transfer Functionz 3-dB Bandwidth, Bc Criterion Resultz Response Quality Zero In Transfer Function Promotes Extended Bandwidth Significant Response Peaking Must Be Avoided Ideally, A Maximally Flat Magnitude Response Is DesiredGives Rise To Extended Bandwidth, Subject To Constraint Of Monotone Decreasing Frequency ResponseZero Must Be Set Optimally For Prudent Bandwidth Enhancement Shunt Peaked ResponseShunt Peaked ResponseUniversity of Southern California Choma: EE 541306Shunt Peaked Frequency ResponseShunt Peaked Frequency Response00.20.40.60.811.21.41.60.10 0.16 0.25 0.40 0.63 1.00 1.58 2.51 3.98 6.31 10.00Normalized Signal FrequencyNormalized Gain MagnitudeQ = 0.5Q = 0.75Q = 1.0Optimal QualityFactor Is PossibleToo Low: Poor BWToo High: ExcessPeakingClose To OptimalUniversity of Southern California Choma: EE 5413072oQ Q 2 1 Q 2 1 0.6436 Q+> > −⇒ =z Mathematics Find Normalized Frequency, ym, Where Transfer Function Slope Is Zero Determine Peaked (Maximal) Value Of Transfer Function At y = ymPeaking Prevails Only For Real ymResultant Maximum Value Of Transfer Functionz See Combined Bandwidth And Peaking PlotsBandwidth Is Extended For All Q And Peaking Is Precluded For Q ≤ Qom2nyy m2dA(jy)QQ 2 10ydyQ=+−==⇒()oo2QQnmQQ22QMA(jy)2Q Q 2 2Q 1>>=+− +Peaking InvestigationPeaking InvestigationUniversity of Southern California Choma: EE 541308Bandwidth And PeakingBandwidth And Peaking11.21.41.61.820 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Quality Factor, QNormalized Bandwidth01020304050Percentage PeakingBandwidthPeakingQo1.722University of Southern California Choma: EE 541309z Design Criterion Maximally Flat Magnitude (MFM) Response First (n-1) Frequency Derivatives Of Transfer Function Are Zero At Zero Frequency Ensures Monotone Decreasing Frequency Response Implication Of Null Derivative Requirementz Optimal Quality Factor()22222n22nvonA(jy) 1 jQ y P(y )A(jy)AP(y ) b y1Qy