L4_5_Noise in digital systems_DSE [Compatibility Mode]

ME620139 Digital System Engineering Noise in Digital SystemsHome reading: B2-Ch.6, B1.Ch.9NavigationLecture 1. Course Overview & Introduction (Ch.1 & Ch.4) Lecture 2: Wires as Interconnects in VLSI ( B1 Ch4 & 9) Lecture 3. Interconnect Design –transmission lines (Ch.3) Lecture 4. Noise in Digital Systems (Ch.6, B1 Ch.9)Lecture 5. Noise (continue) (Ch.6)Lecture 6. Signaling Conventions (Ch.7)Lecture 7. Signaling Techniques (Ch.8 & 11)Lecture 8. Power Distribution Design (Ch.5)Lecture 9: Timing Conventions (Ch.9 & B1Ch.10)Lecture 10: Clock Distribution Design (Ch.9 & B1 Ch.10) Lecture 11: Synchronization (Ch.10 B1Ch.10 )Lecture 12: Synchronizer Design (Ch.10)Lecture 13: Signaling and Timing Circuits (Ch.11 & 12)A Quick OverviewNoise–Signals may be corrupted from manysources»power supply noise»cross talk»inter-symbol interference»real noise (thermal and shot)»parameter variation–Proportional and independentPower Supply Noise–Inductance and resistance of supply network cause voltage drops–Variation in space on one supply voltage–Variation in time on voltage betweensupplies Cross Talk–One signal interfering with another signal–Capacitive crosstalk between RC lines on a chip»floating»driven–Coupling between LC transmission lines»near end»far endPower supply noisePower supply noiseThe power supply network has parasiticelements–on-chip: resistive–off-chip: inductiveCurrent draw across these elements inducesa noise voltage–Ri + Ldi/dtInstantaneous current is what matters –may be many times the DC current»10W chip draws 4A at 2.5V»peak current may be 10-20A.VP–+i(t)L RL Ri(t)Types of supply noise Two types of loads–logic loads–signal loadsTwo types of noise–single-supply noise–differential-supply noiseSupply NetworkGround Network iL(t)iS(t)Single supply noiseZ G i GVoltage drops across parasitics cause variation in the voltage of a singlesupply (V DD or GND) from one point in the system to anotherIf a signal is referenced to the local supply, this variation is additivevoltage noiseThe problem can be reduced by using an appropriate reference–reference to receiver supply–send an explicit reference VSVS+iGZG++__ZGiG+_ISRTISRTDifferential supply noiseV P –+i(t)LRL R+_V PLDrops across supply parasitics cause the local supply voltage, V PL , to vary over time–affects the delay of many elements»systems may not meet timing specifications»causes jitter in timing circuitsSingle vs. differential supply noiseCrosstalkCross talkNoise induced by one signal that interferes with another signalCapacitive coupling between on-chip linesCapacitive and Inductive coupling between off-chip linesCoupling over shared signal returnsABAB干涉Cross talk between capacitive linesbacx wires y wires x wires y wiresOn-chip wires have significant capacitance to adjacent wires–on same layer –on adjacent layersWhen adjacent signals change, voltage on a floating line is disturbed–capacitive voltage divider –signal is not restoredab cC c C cC oOC CCC C C k +=222to y wiresa is victim ,b andc are agressorsab C cC oV aR b aτ=R(C c +C o )Capacitive lines with driveIf victim line, a, is driven, a will be disturbed but then restored with time constant τ=R(C c +C o )If rise on aggressor, b, is slow compared to τ, magnitude of disturbance is reduced⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛−−⎟⎠⎞⎜⎝⎛ττr r t t exp 1Capacitive couplingFloating node Coupling to a driven lineCross talk and delayaC cC oV aR Capacitive cross talk can affect delay of RC signalsIf agressor(s) switch in oppositedirection, effective capacitance of C c is doubledIf agressor(s) switch in the same direction, C c is effectively eliminated Can cause 2:1 variation in delay in some casesSignificant cause of jitter if timing is criticalbInductive and capacitive couplingC dLL C c C cM MConsider a positive transient on agressor line, ACapacitive coupling induces a voltage on victim line B–positive waves in both forward and reverse directionsInductive coupling induces a current in line B–positive wave in the reverse direction –negative wave in the forward directionABCC k L M k dcx lx ==Near-end and far-end crosstalk Inductive and capacitive coupling addat the near end of the line–both waves are positive–pulse begins at beginning of coupledsection–pulse width equals length of coupledsectionInductive and capacitive coupling subtract at the far end of the line–in a homogeneous mediumcancellation is exact–narrow pulse coincident with wave on agressorinductive coupling capacitive couplingnear farnear far 耦合一致的Transmission line cross talk experimentA BC DABCDSignal InterferenceOverviewSignal Return Crosstalk–current on shared return lines causesinterference between signals–large numbers of signals switchingsimultaneously may result in significantnoiseInter-Symbol Interference–some transmission systems remember their history–residual state from previous bits may distort the current bit»reflections on transmission lines»resonant circuits»slow rise times Managing Noise–divide noise along two axes»proportional vs. independent»bounded vs. statistical–prepare a budget for the bounded sources»net margin is what remains afterbounded sources–compare magnitude of net margin tostandard deviation of statistical sources»the bit-error rate is a function of thissignal-to-noise ratio (SNR)Signal return crosstalkWith single-ended signals returncurrents from several signals oftenshare pathsSuppose N drivers share a path withparasitic inductance L REach driver switches current i in time t r.If all but one output switchsimultaneously noise is (N-1)Ldi/dtNeed a large number of return paths to operate at high speedVaVbVcLRRO•Closely related to power supply cross talkSignal return current crosstalkExample calculation L R=5nHi = 10mAt r= 200psdi/dt = 5 x 107Ldi/dt = 0.25VV RXN= (N-1)Ldi/dt= 0.25(N-1) V LPLGABReturn crosstalk and rise timeReturn crosstalk is inverselyproportional to rise time for resistive loads (transmission lines)Return crosstalk is inversely quadratic with rise time for capacitive loadsNoise can be greatly reduced byslowing down the signal edge (not the clock cycle)i R i CV NL i t RXNr =⎛⎝⎜⎞⎠⎟Q CV it V NL CV t rRXN S r ===⎛⎝⎜⎞⎠⎟242Power supply crosstalkIntersymbol interference Ideally a transmission system ismemoryless–no history of previous bitsIn reality, the state of the system is affected by previous bits–reflections on transmission lines–magnitude and phase of excitedresonances–signals that don’t reach the rails by the end of the cycleThis history affects the transmission of the current bit History A History B编码间干扰上一次信号影响当前信号大小幅度Impedance mismatchesEchos of previous bits reflect up and down transmission linesA mismatch of x gives (to first order) a reflection of k R =x/2Worst-case superposition of entire echo train isk k k k ir Ri i RR ==−=∞∑11Z 0, t lR TInter-symbol interference due to mismatched terminationResonant circuitsTank circuits and resonant sections of transmission lines oscillateOscillations are excited by signaltransitions and may interfere with latertransitionsSlow rise times pump less energy into resonant circuitsResistance damps oscillation VaNext bit starts fromhistory-dependent state共振震荡电路震动Inertial delaySome circuits don’t reach steady-state by the end of the cycleStart of the next bit then depends onhistory–residual voltageLeads to both voltage and timing noiseOften caused by poor design for rise-time controlInertial delayInput bit sequency at A with 1 ns bitperiods: 10100001001110111000惯性延迟Eye diagram measurementInertial delay reduction by feedbackSignal attenuation•Critical parameter is what fraction ofswing, A is achieved in one bit time•Eye opening is reduced to B = 2A-1•No eye opening at 50% attenuation•Significant degradation of margins atlower levels of attenuation2A-11ABudgeting noiseSome noise is proportional to signal swing–crosstalk–inter-symbol interference–signal return noise–signaling power supply noise–if you increase the signal swing, you increase the noiseNeed to cancel this noise, notoverpower it! Some noise is independent of signal swing–receiver sensitivity–receiver offset–unrelated power supply noise–reference offsets)21(22N NIS NI S N SNI S N N K V V V V K V V V K V −≥+≥+=0246810121416182000.10.20.30.40.5KnV s /V n iManaging noiseWe manage noise using noise budgetsCatagorize noise along two axes–proportional vs. independent–bounded vs. statistical»Some noise sources could go ineither category (e.g., crosstalk toperpendicular lines)Allocate noise to various sourcesConstrain design to meet the budgetProportional Independent BoundedParallel XtalkISIRcvr OffsetRcvr Sens.Perp. XtalkPS NoiseThermal Noise StatisticalNoise budget1ThresholdProportional Sources, 20%Bounded Sources, 50mV Gross Margin 200mVNet margin 70mVSignal Swing 400mVRMS NoiseVSNR 4040Margins and margin ratioGross margin is half the signal swing, V GM Net margin is gross margin less all bounded noise sources, V NMMargin ratio: V NM /V GM is a good figure of merit–indicates proportion by which you can increase noise sources without causing failureTotal noise margin is meaninlessData sheets report gross margin less receiver offset+sensitivity1Threshold Gross MarginSignal Swing Bounded SourcesNet MarginProportional noise budgetsIndependent noise source budgetManaging noiseFixed v. Proportional–fixed noise -independent of signal swing (V NI)–proportional noise -scales with signal swing (K N)Bounded v. Gaussian–bounded -worst-case analysis–gaussian -statistical analysis, unbounded noiseIn a more complicated/real situation:Total Noise = correlated noise (sum linearly, worse case)+ truly uncorrected noise (RMS, statistical analysis)Overall system noise budgetWorst-case analysisNoise sources are an unknownWith worst-case analysis, assume –all noise sources have the greatest possible magnitude–they all sum up in the same direction Unlikely in any single unit at any instant in time but…–if you make enough units–and run them long enough–this case will occur Signal Swing400mV Vni Rcvr off+sense50mV Uncancelled PS noise20mVTOTAL Vni70mv Kn Crosstalk0.1 Reflections0.1TOTAL Kn0.2KnVs80mVGross Margin200mVVni70mVKnVs80mVVn 150mVNet Margin50Margin Ratio0.25Statistical analysis: Gaussian noise and Bit-Error RateFor some noise sources we consider the probability distribution of values rather than the worst-case value–truly random noise sources»thermal noise, shot noise–uncorrelated bounded noise sources»crosstalk, power supply noise Typically we model these sources witha Gaussian distributionMost sources are zero meanThe relevant parameter is theirstandard deviation or root-mean-squared (RMS) valueAdding Gaussian noise sourcesTo sum up zero-mean Gaussian noise sources–sum the variance, not the standard deviationA 10mV RMS source added to a 20mV RMS source gives a 22.4mV RMS sourceV N V RMSi =⎛⎝⎜⎞⎠⎟∑1212Crosstalk 10.0mV (RMS)PS Noise 20.0mV (RMS)TOTAL 22.4mV (RMS)22221...RMSnRMS RMS tot VVVV +++=i.e. total noise power = Power of noise N1 + N2 +…NnBit Error Rate (BER)If the net margin is V NMand the total Gaussian Noise is V GNThe Gaussian signal to noise ratio isVSNR = V NM/V GNWhat is the probability that the noise will exceed the margin?()PVVVVGNNMGNNM error=−⎛⎝⎜⎞⎠⎟<−⎛⎝⎜⎞⎠⎟⎛⎝⎜⎜⎞⎠⎟⎟1122erfexp。