Modeling and Budgeting of Timing Jitter
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What is the primary focus of the chapter on modeling and budgeting of timing jitter and noise?

  • Managing timing and voltage noise for multi-Gb/s design (correct)
  • Evaluating performance using oscilloscopes
  • Understanding the fundamental principles of electrical engineering
  • Improving the efficiency of low-speed interfaces

    • What are the key metrics introduced in evaluating a signaling interface through the eye diagram?

  • Eye width and eye height (correct)
  • Bandwidth and latency
  • Frequency response and gain margin
  • Signal amplitude and phase shift

    • Which phenomenon degrades the eye width in high-speed signaling?

  • Jitter (correct)
  • Signal attenuation
  • Interference from analog signals
  • Low bandwidth

    • How does the chapter propose to create a system noise budget?

    <p>By identifying sources of voltage noise and analyzing their impact</p> Signup and view all the answers

    What does the peak distortion analysis (PDA) technique account for?

    <p>Both timing and voltage noise while considering signal integrity</p> Signup and view all the answers

    Which aspect of high-speed digital design is directly linked to the bit error rate (BER)?

    <p>Amount of voltage and timing noise allowed</p> Signup and view all the answers

    What are the limitations detailed in the peak distortion analysis methods?

    <p>Assumptions made about worst-case scenarios</p> Signup and view all the answers

    Which type of noise is mentioned as degrading the eye height in signaling interfaces?

    <p>Voltage noise</p> Signup and view all the answers

    What is primarily represented on the horizontal axis of an eye diagram?

    <p>Time</p> Signup and view all the answers

    Which aspect of the eye diagram indicates system performance margins?

    <p>Eye width</p> Signup and view all the answers

    What effect does distortion have on an eye diagram?

    <p>It causes the eye to close.</p> Signup and view all the answers

    Which method is used to evaluate if the eye meets system timing and noise requirements?

    <p>Eye mask application</p> Signup and view all the answers

    In terms of evaluating link performance, what do the minimum height and width of the eye represent?

    <p>Required voltage levels and timing compliance</p> Signup and view all the answers

    What is represented by the term Bit Error Rate (BER)?

    <p>The ratio of erroneous received bits to transmitted bits</p> Signup and view all the answers

    How can the Bit Error Rate (BER) be impacted?

    <p>By varying the sampling point and voltage level</p> Signup and view all the answers

    What type of interfaces do eye diagrams apply to?

    <p>Both single-ended and differential interfaces</p> Signup and view all the answers

    What is a key metric for assessing timing requirements in an eye diagram?

    <p>Minimum eye width</p> Signup and view all the answers

    What happens when the receiver samples data at the edge of the eye?

    <p>The Bit Error Rate (BER) increases significantly.</p> Signup and view all the answers

    What does the peak distortion analysis (PDA) method help determine?

    <p>Minimum eye height and width under distortion</p> Signup and view all the answers

    What is necessary for the receiver to resolve input signals into digital values?

    <p>Sufficient height and width of the eye diagram</p> Signup and view all the answers

    Why is the eye diagram important in high-speed designs?

    <p>To evaluate system performance visually</p> Signup and view all the answers

    What increases the mean time between errors to 10 years?

    <p>Average traffic on the bus unlikely to exceed 50%</p> Signup and view all the answers

    What is represented by ρT in the bit error rate equation?

    <p>The proportion of logic transitions to total bits</p> Signup and view all the answers

    Which of the following statements about deterministic jitter is correct?

    <p>It can be modeled using dual Dirac distributions.</p> Signup and view all the answers

    Why is the dual Dirac model used despite its limitations?

    <p>It provides an approximation for low BER estimation.</p> Signup and view all the answers

    What does the total jitter PDF, JT(t), result from?

    <p>Convolution of deterministic jitter and random jitter models.</p> Signup and view all the answers

    Which scenario suggests a bimodal distribution of jitter?

    <p>Combining Gaussian and bounded jitter sources.</p> Signup and view all the answers

    What is the expected bit error rate as a result of the given jitter conditions?

    <p>$10^{-19}$</p> Signup and view all the answers

    In the context of timing uncertainties, what is the primary limitation of high-speed signaling?

    <p>Ability to maintain adequate margins</p> Signup and view all the answers

    How is the probability density function for deterministic jitter defined mathematically?

    <p>Via a dual Dirac delta function.</p> Signup and view all the answers

    What indicates a potential increase in error rates in high-speed signaling?

    <p>High levels of noise in the system.</p> Signup and view all the answers

    What is the role of the Dirac delta function in jitter modeling?

    <p>To simplify the convolution of different jitter distributions.</p> Signup and view all the answers

    In high-speed signaling, how can the jitter distribution be visually represented?

    <p>Through histograms of zero crossing points.</p> Signup and view all the answers

    What primary factor can impact the transition density ratio, ρT?

    <p>The time intervals between transitions.</p> Signup and view all the answers

    What is the primary purpose of the delay line in the AGP source synchronous transmitter?

    <p>To offset the clock signal from the data signal</p> Signup and view all the answers

    What limits the maximum transmission rate of a source synchronous system in theory?

    <p>The setup-and-hold window of the receiver</p> Signup and view all the answers

    Which timing margin equation represents the setup condition in the AGP source synchronous link?

    <p>tmarSu = UI / 2 - (tTxSu + tchanSu + tRxSu)</p> Signup and view all the answers

    What is the unit interval (UI) for the AGP 8X system operating at 533 Mb/s?

    <p>1875 ps</p> Signup and view all the answers

    Which factor contributes to variations in the timing of the transmitter delays?

    <p>Clock distribution path differences</p> Signup and view all the answers

    How does the worst-case approach treat sources of timing uncertainty?

    <p>As bounded sources not exceeding specified amounts</p> Signup and view all the answers

    What degradation in maximum transfer rate occurs due to variations in transmitter and interconnect delays?

    <p>It decreases the transfer rate to approximately 3.4 Gb/s</p> Signup and view all the answers

    Which of these is characterized as having a Gaussian distribution regarding timing uncertainties?

    <p>Phase-locked loop (PLL) jitter</p> Signup and view all the answers

    What is the impact of a high bit error rate (BER) of $10^{-18}$ on mean time between errors for the AGP data bus?

    <p>It increases the mean time between errors to approximately five years</p> Signup and view all the answers

    What does the probability function $RJ(t)$ represent in the context of timing jitter?

    <p>The probability of having a timing jitter of $t$ ps</p> Signup and view all the answers

    What is the total window for setup and hold time at the receiver for the AGP 8X system?

    <p>295 ps</p> Signup and view all the answers

    Which variation is NOT included in the timing margins for the AGP source synchronous link?

    <p>Environmental temperature change</p> Signup and view all the answers

    What is the consequence of mismatches in data signal delays and clock signal delays in source synchronous designs?

    <p>Decreased performance due to timing errors</p> Signup and view all the answers

    What is the result of combining the jitter from the transmitter, channel, receiver, and clock in a CDR circuit?

    <p>It results in a total jitter expression</p> Signup and view all the answers

    Which step in the design methodology involves negotiating initial targets?

    <p>Step 1</p> Signup and view all the answers

    What is the purpose of evaluating design options for individual components?

    <p>To satisfy the targets for jitter and other metrics</p> Signup and view all the answers

    What is the main purpose of conducting final simulations before hardware is built?

    <p>To verify that the design meets timing requirements</p> Signup and view all the answers

    Which of the following is NOT a step in the design flow for managing jitter budgets?

    <p>Manufacture the hardware immediately</p> Signup and view all the answers

    Which element contributes to the overall deterministic jitter in a PCI Express system?

    <p>Reference clock jitter</p> Signup and view all the answers

    Which aspect is likely to require multiple iterations during the design process?

    <p>Adjusting component designs</p> Signup and view all the answers

    How does voltage noise affect high-speed signaling systems?

    <p>It causes timing jitter, reducing performance</p> Signup and view all the answers

    What does the total periodic jitter function represent?

    <p>The sum of effects from multiple jitter sources.</p> Signup and view all the answers

    What is the formula for calculating the system random jitter ($\sigma_{RMS(sys)}$)?

    <p>$ ext{√(σ²_Tx + σ²_channel + σ²_Rx + σ²_clock)}$</p> Signup and view all the answers

    Which mathematical representation is used for the probability density function of periodic jitter?

    <p>$PDFPJ(t) = \frac{1}{\pi}\sqrt{A^2 - t^2}$</p> Signup and view all the answers

    What should be done if the predicted jitter does not meet the targets?

    <p>Revise timing targets or modify the design</p> Signup and view all the answers

    Which noise source significantly reduces signal-to-noise ratio according to the Shannon–Hartley theorem?

    <p>Voltage noise</p> Signup and view all the answers

    Which type of jitter results from variations in logic state durations, such as rise and fall time mismatches?

    <p>Duty Cycle Distortion (DCD) jitter</p> Signup and view all the answers

    What characterizes the probability density function for ISI jitter in a non-equalized channel?

    <p>It has multiple peaks.</p> Signup and view all the answers

    In the PCI Express system jitter model, which component is associated with an initial jitter of 60.6 ps?

    <p>Transmitter</p> Signup and view all the answers

    What role do statistical analysis methods play during the design process?

    <p>They help minimize iterations and enhance design understanding</p> Signup and view all the answers

    What is the peak-to-peak value of the deterministic jitter calculated in the example provided?

    <p>62 ps</p> Signup and view all the answers

    What is Bounded Uncorrelated Jitter (BUJ) primarily associated with?

    <p>Crosstalk between neighboring signals.</p> Signup and view all the answers

    The RMS value of random jitter in the example is given as what?

    <p>2.5 ps</p> Signup and view all the answers

    For duty cycle distortion jitter, the PDF is represented as a sum of which mathematical functions?

    <p>Delta functions</p> Signup and view all the answers

    What does the total jitter (PDFTJ(t)) calculation involve?

    <p>The convolution of deterministic jitter and random jitter PDFs</p> Signup and view all the answers

    In which statistical measure is the amplitude of periodic jitter indicated in the example?

    <p>Amplitude</p> Signup and view all the answers

    When equalization is applied to a channel, the ISI jitter distribution resembles what shape?

    <p>Truncated Gaussian distribution</p> Signup and view all the answers

    What is a significant source of periodic jitter identified in the context of transmission lines?

    <p>Signal reflections</p> Signup and view all the answers

    What effect does a 10% duty cycle variation (DCD) introduce to jitter?

    <p>It generates sharp peaks in the jitter distribution.</p> Signup and view all the answers

    In the context of ISI, what role does equalization play?

    <p>It mitigates amplitude variations caused by reflections.</p> Signup and view all the answers

    What is the expected rejection percentage of supply noise by the combination of high transmitter impedance and differential receiver?

    <p>Over 99%</p> Signup and view all the answers

    What is the effect of superposition on a transmitted second pulse at t = 4 ns?

    <p>It reduces the signal level of the second pulse due to negative ISI.</p> Signup and view all the answers

    Which system had a projected worst-case noise of 835 mV?

    <p>Single-ended system</p> Signup and view all the answers

    What is the noise margin for the differential system?

    <p>0.286 V</p> Signup and view all the answers

    How does the addition of a pulse at t = 8 ns affect the worst-case bit pattern?

    <p>It requires expansion of the worst-case bit pattern to 1000101.</p> Signup and view all the answers

    What does the worst-case bit pattern indicate about the logical 1 in the presented example?

    <p>Logical 1 may be adversely affected by surrounding pulses.</p> Signup and view all the answers

    Which source contributes to the lowest noise in the differential system according to the budget analysis?

    <p>Equalizer resolution</p> Signup and view all the answers

    Which of the following best describes the term 'postcursor' as used in the context of ISI?

    <p>It indicates the time intervals after the initial pulse.</p> Signup and view all the answers

    How is the noise immunity defined?

    <p>Ratio of signal swing to worst-case noise</p> Signup and view all the answers

    What is the primary cause of random jitter (RJ)?

    <p>Thermal noise and shot noise</p> Signup and view all the answers

    Which of the following statements about deterministic jitter (DJ) is true?

    <p>Its peak-to-peak maximum is never exceeded.</p> Signup and view all the answers

    What is the noise immunity ratio of the differential system?

    <p>3.5:1</p> Signup and view all the answers

    What is the primary challenge mentioned regarding finding the worst-case bit pattern?

    <p>It is often inefficient to create numerous waveforms.</p> Signup and view all the answers

    What function is used to calculate the bit error rate (BER) from the leading edge?

    <p>Cumulative density function</p> Signup and view all the answers

    Which factor is considered nonproportional noise in the systems discussed?

    <p>Offset and sensitivity</p> Signup and view all the answers

    Why is it important to analyze postcursor ISI in signal transmission?

    <p>It can indicate how earlier pulses affect later ones.</p> Signup and view all the answers

    What does the analysis show about pulse degradation when a fourth pulse is launched at the tenth postcursor position?

    <p>No degradation is observed beyond the tenth postcursor.</p> Signup and view all the answers

    In the context of jitter, what does a bathtub plot typically illustrate?

    <p>The bit error rate as a function of data eye position.</p> Signup and view all the answers

    What does the equation $vNM = vswing - vnoise$ represent?

    <p>System noise margin</p> Signup and view all the answers

    Which characteristic describes periodic jitter (PJ)?

    <p>It occurs at fixed frequencies.</p> Signup and view all the answers

    What voltage level does the second pulse achieve when subject to the effects of negative ISI at t = 4 ns?

    <p>0.864 V</p> Signup and view all the answers

    What is one significant limitation of using the noise margin as a metric?

    <p>It fails to account for the correlation between swing and noise.</p> Signup and view all the answers

    What is the primary focus in peak distortion analysis methods?

    <p>Assessing peak jitter and noise</p> Signup and view all the answers

    What is represented by the variable 'UI' in the context of jitter analysis?

    <p>Unit Interval</p> Signup and view all the answers

    Which type of jitter is described as data-dependent?

    <p>Duty Cycle Distortion (DCD)</p> Signup and view all the answers

    What does the equation $y(t) = \sum_{i} f [x_i (t)] = \sum_{i} y_i (t)$ represent?

    <p>Superposition principle</p> Signup and view all the answers

    Which type of noise is specified as 10−12 in the content?

    <p>Shot noise</p> Signup and view all the answers

    Which of the following is a key characteristic of random jitter?

    <p>Gaussian distribution with zero mean</p> Signup and view all the answers

    What does the abbreviation 'DCD' stand for in jitter analysis?

    <p>Duty Cycle Distortion</p> Signup and view all the answers

    How does the signal swing of the single-ended system compare to the differential system?

    <p>It is five times greater.</p> Signup and view all the answers

    Which equation is used for calculating trailing-edge bit error rate (BER)?

    <p>BERtrail(t) = 0.5[erfc(...)]</p> Signup and view all the answers

    Which budget for crosstalk is mentioned in the content?

    <p>5% of the signal swing</p> Signup and view all the answers

    What is a common representation of how different types of jitter affect signal timing?

    <p>PDF Model</p> Signup and view all the answers

    What does the term 'smearing' refer to in jitter analysis?

    <p>A deviation of signal timing events</p> Signup and view all the answers

    Which of the following jitter types is influenced by signal reflection and transmission mismatches?

    <p>Deterministic Jitter (DJ)</p> Signup and view all the answers

    How does the amount of random jitter need to be accounted for as target BER decreases?

    <p>It increases in terms of sigma</p> Signup and view all the answers

    What does the term 'crossing point' refer to in the context of a bathtub plot?

    <p>The minimum BER a design can meet</p> Signup and view all the answers

    What is the primary source of shot noise?

    <p>Quantization of device current to individual carriers</p> Signup and view all the answers

    How is the RMS voltage due to shot noise calculated?

    <p>$2qiAf$</p> Signup and view all the answers

    What is the probability distribution type for thermal noise and shot noise?

    <p>Gaussian distribution</p> Signup and view all the answers

    What is the formula for calculating the total RMS noise when combining thermal and shot noise?

    <p>$√{(σtherm)^2 + (σshot)^2}$</p> Signup and view all the answers

    For what maximum probability of exceeding noise is a worst-case value often calculated?

    <p>1 in 1 trillion</p> Signup and view all the answers

    What does the symbol 'R' represent in the equation for RMS shot noise?

    <p>Resistance in ohms</p> Signup and view all the answers

    What does the QBER represent in the dual Dirac model?

    <p>The amount of eye closure due to random jitter</p> Signup and view all the answers

    What is the consequence of using the worst-case noise approach when constructing a noise budget?

    <p>Minimized probability of noise problems</p> Signup and view all the answers

    How is the deterministic jitter term, DJδδ, for the dual Dirac model determined?

    <p>Using linear extrapolation at low Bit Error Rate</p> Signup and view all the answers

    Which of the following factors is not explicitly included in the noise budget?

    <p>Crosstalk</p> Signup and view all the answers

    What is the estimated worst-case Gaussian noise calculated based on an RMS noise of 0.233 mV?

    <p>1.7 mV</p> Signup and view all the answers

    What is the significance of the slope in the QBER versus jitter plot?

    <p>It represents the relationship between jitter and BER</p> Signup and view all the answers

    In the example analyzed, what was the output current from the transmitter driving the transmission line?

    <p>25 mA</p> Signup and view all the answers

    In the equation UI = DJδδ(sys) + QBERσRMS(sys), what does UI represent?

    <p>Unit interval that accounts for jitter</p> Signup and view all the answers

    What does the variable 'q' represent in the context of shot noise?

    <p>Charge of an electron</p> Signup and view all the answers

    What causes extra jitter defined as TJTx,gen and TJRx,gen in a PCI Express system?

    <p>Thermal noise and supply noise</p> Signup and view all the answers

    What aspect of noise management ensures proper operation of high-speed signaling systems?

    <p>Noise budget construction</p> Signup and view all the answers

    How is the random jitter for the system expressed?

    <p>Based on the root-sum-of-squares relationship</p> Signup and view all the answers

    What are the approximated jitter values of DJδδ obtained from Figure 13-13?

    <p>27.7 ps and 56.2 ps</p> Signup and view all the answers

    What role does simulation play in understanding noise sources?

    <p>It helps to correlate with actual measurements for better understanding</p> Signup and view all the answers

    What does the term σRMS(sys) signify in the total jitter budget equation?

    <p>The rms value of the total random jitter in the system</p> Signup and view all the answers

    What do PLLs do in the context of jitter propagation?

    <p>They allow high-frequency jitter to pass through</p> Signup and view all the answers

    What was a primary cause for the errors in the comparison of the dual Dirac model and actual system distributions?

    <p>Numerical errors in the convolution algorithm</p> Signup and view all the answers

    What assumption is made about the channel's effect on incoming jitter in a PCI Express link?

    <p>The channel does not noticeably filter incoming jitter</p> Signup and view all the answers

    Which factors are considered when calculating the system jitter budget?

    <p>Jitter from transmitters, receivers, and interconnect channels</p> Signup and view all the answers

    For a BER of $10^{-12}$, what is the approximate total jitter reported?

    <p>91 ps</p> Signup and view all the answers

    In the context of jitter measurements, what does 'erf$^{-1}$' function typically imply?

    <p>An error function that quantifies jitter relationships</p> Signup and view all the answers

    What is the typical value of the threshold voltage for NMOS (VTN)?

    <p>0.43 V</p> Signup and view all the answers

    What is the effect of increasing the device width on the offset of the differential receiver?

    <p>It decreases the offset</p> Signup and view all the answers

    What is the formula for calculating the minimum offset (vt,min) of the differential receiver?

    <p>vt,min = vTN,min + βP,min/βN,max (VDD,min + VT P,min)</p> Signup and view all the answers

    From the calculations provided, what is the approximate input offset for the inverter?

    <p>±201 mV</p> Signup and view all the answers

    What is the typical value of kN for the given 0.25-μm process?

    <p>115 × 10−6 A/V2</p> Signup and view all the answers

    Which of the following is true about ac noise specifications in reference voltages?

    <p>Typical specifications are ±2% of the reference voltage</p> Signup and view all the answers

    What does the variable $v_{t,max}$ represent in the provided equations?

    <p>The maximum offset voltage for the differential receiver</p> Signup and view all the answers

    For a DAC rated with 4 bits, what is the formula for determining the DAC resolution?

    <p>ires = iDAC / 2^{nDAC}</p> Signup and view all the answers

    What is the effect of device feature size variation on offset estimation?

    <p>They can reduce the offset</p> Signup and view all the answers

    In the context of DACs, what is the minimum voltage noise represented by?

    <p>One-half of the resolution of the DAC</p> Signup and view all the answers

    Which parameter must be considered when estimating the thermal noise?

    <p>Temperature and resistance</p> Signup and view all the answers

    What is the maximum noise expected on the VREF of a high-speed transceiver logic as defined?

    <p>±18 mV</p> Signup and view all the answers

    What does the variable $i_{res}$ in the DAC noise estimation formula represent?

    <p>The resolvable output current</p> Signup and view all the answers

    What parameter does the equation $PSD_{therm} = 4k_BTR$ describe?

    <p>Root-mean-square power spectral density of thermal noise</p> Signup and view all the answers

    What kind of noise is typically attributed to power dissipation in devices?

    <p>Thermal noise</p> Signup and view all the answers

    What is the primary cause of local supply noise in single-ended systems?

    <p>Transient current demand in I/O circuits</p> Signup and view all the answers

    How do current-mode differential transmitters affect local supply noise?

    <p>They generate essentially zero local supply noise</p> Signup and view all the answers

    Which parameter is NOT included in the calculation of the inverter threshold voltage?

    <p>Device length variation, ∆L</p> Signup and view all the answers

    What does the offset voltage for a differential receiver depend on?

    <p>The matching of devices of the same type</p> Signup and view all the answers

    In which way does the input sensitivity of a differential receiver compare to that of a CMOS inverter-based receiver?

    <p>Differential receiver requires approximately 10 mV</p> Signup and view all the answers

    The maximum offset in the inverter threshold voltage occurs under what conditions?

    <p>One device at a process extreme, the other at a typical condition</p> Signup and view all the answers

    What is the relationship between the device transconductance parameters and threshold variation?

    <p>They can be largely independent of each other</p> Signup and view all the answers

    What voltage range is typical for the input sensitivity of a CMOS inverter-based receiver?

    <p>200 to 250 mV</p> Signup and view all the answers

    Which factor contributes most to the offset voltage in single-ended inverter circuits?

    <p>Mismatch between NMOS and PMOS devices</p> Signup and view all the answers

    What is true about the external supply noise magnitude typically experienced?

    <p>Approximately 5 to 10% of the nominal supply</p> Signup and view all the answers

    The variations in which parameters result in threshold variation for an inverter circuit?

    <p>NMOS and PMOS device characteristics</p> Signup and view all the answers

    How is the input offset for a differential amplifier defined?

    <p>By the matching variance of the identical devices</p> Signup and view all the answers

    What role does the supply voltage, VDD, play in the inverter threshold voltage calculation?

    <p>It directly affects the inverter's threshold voltage</p> Signup and view all the answers

    What is the primary advantage of differential signaling over single-ended signaling?

    <p>Better noise rejection</p> Signup and view all the answers

    What mathematical expression defines the transmitted pulse signal for the ith bit position?

    <p>xi(t) = x(t - i · UI)</p> Signup and view all the answers

    What is the role of the unit interval UI in the waveform construction?

    <p>It is the width of one data bit.</p> Signup and view all the answers

    How is the received signal waveform y(t) defined for an n-bit data sequence?

    <p>y(t) = Σ bi · x(t - i · UI)</p> Signup and view all the answers

    What does intersymbol interference refer to in high-speed signaling?

    <p>Previously received bits affecting future bit signaling.</p> Signup and view all the answers

    Which bit positions are referred to as precursor and postcursor in a pulse response?

    <p>Bits occurring before and after the cursor bit.</p> Signup and view all the answers

    What is the significance of the 'cursor' in pulse response analysis?

    <p>It marks the position of interest for observing bit-level response.</p> Signup and view all the answers

    Why do we need to create multiple waveforms for analyzing high-speed signaling systems?

    <p>To determine the worst-case scenario based on intersymbol interference.</p> Signup and view all the answers

    What do deviations from the ideal pulse response indicate in a signaling system?

    <p>Signal reflections and possible intersymbol interference are present.</p> Signup and view all the answers

    In the context of signal analysis, what characterizes a 'data eye'?

    <p>It is the graphical representation of timing uncertainties and signal integrity.</p> Signup and view all the answers

    What does the process of superposition involve when analyzing pulse responses?

    <p>Adding the individual pulse responses at designated time shifts.</p> Signup and view all the answers

    What does creating 213 different waveforms assist in achieving regarding signal analysis?

    <p>Identifying the worst-case bit patterns and their impact.</p> Signup and view all the answers

    Which voltage level indicates a significant distortion in the pulse response graphically?

    <p>-0.247 V</p> Signup and view all the answers

    How can the performance of a high-speed signaling interface be optimally analyzed?

    <p>Through simulation of various signaling patterns and pulse responses.</p> Signup and view all the answers

    Study Notes

    Modeling and Budgeting of Timing Jitter and Noise

    • Eye diagrams are used to evaluate high-speed system performance. Key metrics include eye width and eye height. Wider eyes offer more margin for voltage and timing requirements.
    • Eye diagrams help determine bit error rate (BER). A larger eye opening indicates a lower BER.
    • BER is the ratio of erroneous received bits to total transmitted bits over a long interval. Equation (13-1).
    • The eye diagram shows different BER values based on sampling point variations. Center sampling yields much lower error rates.
    • Worst-case analysis historically treated jitter sources as bounded, a flawed assumption. Random jitter sources exhibit Gaussian distribution. Equation (13-4).
    • This means worst-case timing analysis doesn't have meaning in evaluating random jitter, as a non-zero probability exists of exceeding any bounded value.
    • Modern high-speed design uses BER-based budgeting instead.
    • Equation (13-5) expresses BER as a function of timing jitter distribution.
    • A dual Dirac model (Equation (13-6) and (13-7)) is used to approximate jitter distribution at low BERs, combining deterministic and random jitter components.
    • System jitter is expressed as the sum of the jitter from multiple sources.

    Jitter Sources and Budgets

    • Jitter is the deviation of a signal timing event from its ideal position, causing data eye smearing.
    • Jitter is categorized into deterministic (bounded) and random (unbounded, often Gaussian-distributed) types.
    • Deterministic jitter includes periodic jitter (e.g., spread-spectrum clocking), data-dependent jitter (e.g., duty-cycle distortion (DCD), intersymbol interference (ISI), crosstalk).
    • For a system with multiple periodic jitter sources, total periodic jitter is: PJ(t) = ∑Ai cos(ωi t + θi)
    • Duty cycle distortion jitter's PDF is expressed as a sum of two delta functions. Equation (13-12).
    • ISI jitter's impact depends on the interconnect channel and can vary with equalization.
    • Uncorrelated jitter is caused by crosstalk.
    • Random jitter sources include device effects like thermal and shot noise.
    • System jitter budgets use equation (13-16) to allocate deterministic and random jitter to maintain a desired BER.

    Noise Sources and Budgets

    • Voltage noise, along with timing jitter, limits high-speed system performance. Equation (13-21).
    • Key noise sources include crosstalk, intersymbol interference, supply noise, circuit input offsets, thermal noise, shot noise
    • Supply noise arises from external distribution system noise and locally generated noise from I/O circuits. Differential systems, in contrast to single ended, tend to reject more noise.
    • Receiver offset is due to process variations in transistor characteristics. Offset calculations use equations (13-22), (13-23), (13-24) and (13-25).
    • Differential receivers have lower offsets due to better device matching. This calculation use equation (13-26).
    • Receiver sensitivity describes the required input voltage to generate a specific output voltage.
    • Noise budgets for high-speed designs apply worst-case values to bounded noise sources, and account for probability distributions of Gaussian sources.
    • Noise margin evaluates system robustness against noise (Equation (13-35)). A higher noise margin doesn't automatically imply higher noise immunity.
    • The noise immunity compares the signal swing to the worst-case noise. Equation (13-36).

    Peak Distortion Analysis Methods

    • Peak distortion analysis (PDA) methods use superposition and pulse response data to assess worst-case jitter and voltage noise in complex interconnect channels.
    • Superposition allows calculation of output waveforms for arbitrary input bit patterns using the system's response to a single pulse. Equations (13-37), (13-38), (13-39), & (13-40) express these principles mathematically.
    • Worst-case bit patterns are determined by identifying patterns that lead to minimized eye opening conditions. These patterns consider ISI effects.

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    Description

    This quiz covers the key concepts of timing jitter and noise modeling in high-speed systems, including eye diagrams, eye width, and the significance of bit error rate (BER). It examines how sampling points affect BER and critiques traditional worst-case analysis. Modern practices are discussed, emphasizing BER-based budgeting for effective system performance evaluation.

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