1. ECE 546 – Jose Schutt-Aine 1 Spring 2014 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu ECE 546 Lecture - 20 Jitter

2. ECE 546 – Jose Schutt-Aine 2 Timing uncertainties in digital transmission systems Utmost importance because timing uncertainties cause bit errors There are different types of jitter Jitter Definition Jitter is difference in time of when something was ideally to occur and when it actually did occur.

3. ECE 546 – Jose Schutt-Aine 3 Jitter is a signal timing deviation referenced to a recovered clock from the recovered bit stream Measured in Unit Intervals and captured visually with eye diagrams Two types of jitter –Deterministic (non Gaussian) –Random The total jitter (TJ) is the sum of the random (RJ) and deterministic jitter(DJ) Jitter Characteristics

4. ECE 546 – Jose Schutt-Aine 4 Types of Jitter Deterministic Jitter (DDJ)  Data-Dependent Jitter (DDJ)  Periodic Jitter (PJ)  Bounded Uncorrelated Jitter (BUJ) Random Jitter (RJ)  Gaussian Jitter  f  Higher-Order Jitter

5. ECE 546 – Jose Schutt-Aine 5 Bandwidth Limitations  Cause intersymbol interference (ISI)  ISI occurs if time required by signal to completely charge is longer than bit interval  Amount of ISI is function of channel and data content of signal Jitter Effects Oscillator Phase Noise  Present in reference clocks or high-speed clocks  In PLL based clocks, phase noise can be amplified

6. ECE 546 – Jose Schutt-Aine 6 Jitter Statistics  Most common way to look at jitter is in statistical domain  Because one can observe jitter histograms directly on oscilloscopes  No instruments to measure jitter time waveform or frequency spectrum directly Jitter Histograms and Probability Density Functions (PDF)  Built directly from time waveforms  Frequency information is lost  Peak-to-peak value depends on observation time

7. ECE 546 – Jose Schutt-Aine 7 Jitter Classification

8. ECE 546 – Jose Schutt-Aine 8 Gaussian Random Jitter Random jitter can be described by a Gaussian distribution with the following probability density function : independent value : RMS value : mean of distribution (zero by definition)  Note: the PDF of a Gaussian process is unbounded, i.e, its PDF is not zero unless the jitter  t approaches infinity

9. ECE 546 – Jose Schutt-Aine 9 Gaussian Jitter PDF Can be used to estimate the probability when the deviation of the random jitter variable  t is within a multiple of its  value.

10. ECE 546 – Jose Schutt-Aine 10 Cummulative Density Function Cummulative density function (CDF) is defined as: CDF(t) tells us the probability that the transition occurred earlier than t. For random jitter, we get: erf is the error function

11. ECE 546 – Jose Schutt-Aine 11 PDF and CDF of Random Jitter PDFCDF

12. ECE 546 – Jose Schutt-Aine 12 Crosstalk –Noisy neighboring signals Interference Reflections –Imperfect terminations –Discontinuities (e.g. multidrop buses, stubs) Simultaneous switching noise (SSN) –Noisy reference plane or power rail –Shift in threshold voltages Causes of Deterministic Jitter

13. ECE 546 – Jose Schutt-Aine 13 Data-Dependent Jitter Most commonly encountered DJ type Dominant limiting factor for link channels Due to memory of lossy electrical or optical system Bit transition of current bit depends on the transition times of the previous bits

14. ECE 546 – Jose Schutt-Aine 14 Data-Dependent Jitter DDJ depends on the impulse response of the system that generates the pattern DDJ depends on the input pattern DDJ is a distribution with its sample size equal to the number of transitions of the data patent Duty cycle distortion (DCD) occurs for clock patterns of repeating bits

15. ECE 546 – Jose Schutt-Aine 15 Data-Dependent Jitter Since channel does not have zero-rise time step response or infinite bandwidth, jitter is to be expected Settling time gives good indication of DDJ

16. ECE 546 – Jose Schutt-Aine 16 DDJ Estimation for RC Network Assume an RC time constant of  =RC. The step response for an RC circuit is given by: The DDJ time displacement at the 50% voltage level is: In the frequency domain the transfer function is: The 3dB bandwidth is: The DDJ displacement is:

17. ECE 546 – Jose Schutt-Aine 17 Model for DDJ is the probability for the DDJ value of The generic form for DDJ PDF is: satisfies the condition

18. ECE 546 – Jose Schutt-Aine 18 Periodic Jitter Periodic jitter is a repeating jitter signal at a certain period or frequency. It is described by: : angular frequency : initial phase From a signal perspective, it is the same as any periodic signal in terms of frequency and phase, but its amplitude is jitter in units of timing.

19. ECE 546 – Jose Schutt-Aine 19 Define the overall phase by: Phase  has a uniform distribution if it is observed over a few periods. Its PDF is given by The inverse function of  t is: Periodic Jitter

20. ECE 546 – Jose Schutt-Aine 20 Using the rule for PDF of related variables, the PDF for PJ  t is given by Which can be approximated by Periodic Jitter After substitution and differentiation, we get

21. ECE 546 – Jose Schutt-Aine 21 Periodic Jitter PDF for single sinusoidal

22. ECE 546 – Jose Schutt-Aine 22 Periodic Jitter There are 3 common waveforms for the theoretical analysis of periodic jitter Rectangle Periodic Jitter Triangle Periodic Jitter

23. ECE 546 – Jose Schutt-Aine 23 Periodic Jitter Sinusoidal Periodic Jitter

24. ECE 546 – Jose Schutt-Aine 24 Rectangular Periodic Jitter PDF CDF

25. ECE 546 – Jose Schutt-Aine 25 Triangular Periodic Jitter PDF CDF

26. ECE 546 – Jose Schutt-Aine 26 Sinusoidal Periodic Jitter PDF CDF

27. ECE 546 – Jose Schutt-Aine 27 PDF of Two PJs  A single PJ does not depend on its initial phase if it is observed over many periods.  In the case of 2 PJs, the relative phase is important  When two PJs with the same magnitude, frequency and phase are added together, they form another PJ with twice the amplitude  When two PJs with the same magnitude, frequency and opposite phase are added together, their sum is zero.  The sum of two PJs can have totally different shapes depending on their phase relationships Periodic Jitter

28. ECE 546 – Jose Schutt-Aine 28 Phase Noise & Phase Jitter Phase noise in clock oscillators  Phase offset term that continually changes timing of signal signal waveform with phase noise undistorted signal phase noise Example:

29. ECE 546 – Jose Schutt-Aine 29 Phase Noise clean signal noisy signal 2 GHz phase noise

30. ECE 546 – Jose Schutt-Aine 30 Phase jitter in digital systems  Variability in timing of transition in digital systems is called phase jitter  Phase jitter is digital equivalent of phase noise  Always defined relative to the ideal position of the transitions Phase Jitter For a jittered digital signal is the actual time of the nth transition is the ideal timing value of the nth transition is the time offset of the transition  phase jitter term Example: 10 Gbits/s  T n has bit intervals of 100 ps. Transitions take place at 0, 100, 200 ps

31. ECE 546 – Jose Schutt-Aine 31 Phase Jitter clean signal noisy signal

32. ECE 546 – Jose Schutt-Aine 32 Phase jitter causes bit periods to contract and expand Actual bit periods are given by the time difference between 2 consecutive transitions Ideal bit period: Period jitter: Cycle-to-Cycle Jitter

33. ECE 546 – Jose Schutt-Aine 33 Cycle-to-cycle jitter: Cycle-to-Cycle Jitter

34. ECE 546 – Jose Schutt-Aine 34 Bounded Uncorrelated Jitter BUJ is primarily due to crosstalk The PDF for BUJ is given by

35. ECE 546 – Jose Schutt-Aine 35 Mix of Random and Periodic Jitters  Obtain convolution of 2 PDFs Gaussian RJ and Rectangle PJ Result is the sum of 2 Gaussian distributions with equal RMS value offset by the PJ peak-to-peak value. It is called the DUAL DIRAC DISTRIBUTION

36. ECE 546 – Jose Schutt-Aine 36 Problem  In tests, we have measured jitter histograms and need to extract the individual jitter components  Ideally, we could use deconvolution into components. However without prior knowledge of deterministic jitter, it is not possible  Use dual Dirac distribution model which would yield the worst case deterministic jitter Jitter Mixing

37. ECE 546 – Jose Schutt-Aine 37 Total Jitter Time Waveform The total jitter waveform is the sum of individual components TJ(t) = PJ(t) + RJ(t)

38. ECE 546 – Jose Schutt-Aine 38 Jitter Statistics TJ(x) = PJ(x) * RJ(x) The total jitter PDF is the convolution of individual components

39. ECE 546 – Jose Schutt-Aine 39 Transfer of Level Noise into the Time Domain  Noise on digital data signals causes jitter because it offsets the threshold crossing point in time Bandwidth Limitations  Primarily caused by intersymbol interference Oscillator Phase Noise  Phase noise present in reference clocks especially in systems based on PLL Jitter Mechanisms

40. ECE 546 – Jose Schutt-Aine 40 Jitter Mechanisms  Transfer of noise into time domain  Bandwidth limitation in channels  Oscillator phase noise rise time pk-pk noise amplitude Hi signal level Lo signal level Jitter Mechanisms

41. ECE 546 – Jose Schutt-Aine 41 Jitter Mechanisms Transfer of voltage noise into time domain – Linear model Random noise caused by thermal effects

42. ECE 546 – Jose Schutt-Aine 42 Jitter Mechanisms Transfer of voltage noise into time domain – First order model Periodic noise: switching power, crosstalk, etc…

43. ECE 546 – Jose Schutt-Aine 43 Jitter Mechanisms Multiple threshold crossing of a signal with high-frequency level noise

44. ECE 546 – Jose Schutt-Aine 44 Bandwidth Limitations 0001111 data pattern

45. ECE 546 – Jose Schutt-Aine 45 0101111 data pattern Bandwidth Limitations

46. ECE 546 – Jose Schutt-Aine 46 Q-Scale Transformation Use CDF Q-scale is defined such that the Gaussian distribution mapped onto the Q-scale is a straight line A Gaussian CDF is a straight line in the Q scale with slope 1/  DJ is given by distance d

47. ECE 546 – Jose Schutt-Aine 47 Q-Scale Transformation PDF CDF Gaussian RJ  = 0.5

48. ECE 546 – Jose Schutt-Aine 48 Q-Scale Transformation PDF CDF Gaussian RJ  = 0.25

49. ECE 546 – Jose Schutt-Aine 49 Q-Scale - Generalization PDF CDF Mixed Gaussian RJ and PJ  = 0.1

50. ECE 546 – Jose Schutt-Aine 50 PDF CDF Q-Scale - Generalization Mixed Gaussian RJ and PJ  = 0.25

51. ECE 546 – Jose Schutt-Aine 51 Dual Dirac Model Mixed Gaussian RJ and Triangular PJ

52. ECE 546 – Jose Schutt-Aine 52 Jitter Classification

53. ECE 546 – Jose Schutt-Aine 53 Measuring Jitter

54. ECE 546 – Jose Schutt-Aine 54 Eye Diagrams Eye diagrams are a time domain display of digital data triggered on a particular cycle of the clock. Each period is repeated and superimposed. Each possible bit sequence should be generated so that a complete eye diagram can be made

55. ECE 546 – Jose Schutt-Aine 55 Eye Diagram

56. ECE 546 – Jose Schutt-Aine 56 High-Speed Oscilloscope 8-bit flash ADCs provide 256 discrete levels along vertical axis

57. ECE 546 – Jose Schutt-Aine 57 Interleaving Architecture

58. ECE 546 – Jose Schutt-Aine 58 High-Speed Scope Digitizers SiGe-Based Technologies  Fastest ADCs run at 3.125 Gsamples/s  Typically 8-16 digitizers CMOS Designs  ADCs sample at lower rate  80 digitizers or more

59. ECE 546 – Jose Schutt-Aine 59 Timing Diagram

60. ECE 546 – Jose Schutt-Aine 60 Once waveform samples have been reassembled into a representation of the waveform, they are stored to digital memory The maximum number of samples is the record length Record length are typically in excess of 100 million samples Sampling Procedure

61. ECE 546 – Jose Schutt-Aine 61 Frequency Interleaving

62. ECE 546 – Jose Schutt-Aine 62 A signal of bandwidth B that has been sampled at regular intervals T can be exactly recovered if the sampling rate satisfies : Nyquist rate : sampling interval : bandwidth Nyquist Criterion

63. ECE 546 – Jose Schutt-Aine 63 High-Speed Oscilloscopes Oscilloscopes use DSP techniques to:  Extend their analog bandwidth  Flatten their amplitude Practice has benefits However, limitations should be understood

64. ECE 546 – Jose Schutt-Aine 64 Scope Channel Equalization

65. ECE 546 – Jose Schutt-Aine 65 Edge Triggering T OFF is recorded with high resolution but is subject to noise

66. ECE 546 – Jose Schutt-Aine 66 Trigger jitter is the amount of effective timing instability between the trigger path and the signal capture path Trigger Jitter In eye diagram construction, multiple waveform acquisitions are overlayed. Trigger jitter is then an externally introduced noise that cannot be distinguished from the true jitter Typical value: ~ 1 ps RMS

67. ECE 546 – Jose Schutt-Aine 67 Trigger Jitter

68. ECE 546 – Jose Schutt-Aine 68 Much of the timing instability in an oscilloscope is a combination of phase noise in the instrument’s time base and aperture jitter in the track-and-hold circuits Sample Jitter They exhibit a Gaussian probability distribution Interleaving errors from the digitizers are another large source of errors. They are deterministic and are manifested as deterministic jitter  can be calibrated out

69. ECE 546 – Jose Schutt-Aine 69 Oscillator Phase Noise

70. ECE 546 – Jose Schutt-Aine 70 Gaussian Errors  Phase noise  Aperture jitter in track-and-hold circuits Deterministic Errors  Interleaving mismatches  Can be calibrated out Sample Jitter

71. ECE 546 – Jose Schutt-Aine 71 An eye diagram is a time-folded representation of a signal that carries digital information Eye Diagram Eye is horizontally centered on the ideal sampling instant

72. ECE 546 – Jose Schutt-Aine 72 Unit interval (UI) of a bit sequence is typically independent of the waveform sampling interval of the measurement instrument.  Waveform sampling interval must be no more than one half the unit interval to avoid aliasing  Rule of thumb for eye diagrams is to sample 5 to 10 times the bit rate  For 2.5 Gb/s, the sampling rate should be 20 GSamples/s Eye Diagram Large eye openings ensure that the receiving device can reliably decide between high and low logic states even when the decision threshold fluctuates or the decision time instant varies.

73. ECE 546 – Jose Schutt-Aine 73 Eye Diagram Construction Eye diagram construction in real-time oscilloscope is based on hardware clock recovery and trigger circuitry

74. ECE 546 – Jose Schutt-Aine 74 Eye Diagram Construction

75. ECE 546 – Jose Schutt-Aine 75 1. Capture of the Waveform Record 2. Determine the Edge Times Eye Diagram Construction

76. ECE 546 – Jose Schutt-Aine 76 Eye Diagram Construction 3. Determine the Bit Labels

77. ECE 546 – Jose Schutt-Aine 77 4. Clock Recovery Eye Diagram Construction

78. ECE 546 – Jose Schutt-Aine 78 Eye Diagram Construction 5. Slice Overlay 6. Display

79. ECE 546 – Jose Schutt-Aine 79 Eye Diagram Measurements

80. ECE 546 – Jose Schutt-Aine 80 Eye Diagram Measurements

81. ECE 546 – Jose Schutt-Aine 81 Reference Levels

82. ECE 546 – Jose Schutt-Aine 82 Eye Height Eye Height is the measuremnt of the eye height in volts : mean value of eye top : standard deviation of eye top : mean value of eye base : standard deviation of eye base

83. ECE 546 – Jose Schutt-Aine 83 Eye Width Eye Width is the measuremnt of the eye width in seconds Crossing percent measurement is the eye crossing point expressed as a percentage of the eye height

84. ECE 546 – Jose Schutt-Aine 84 Jitter Measurements Jitter peak-to-peak is the peak-to-peak value for the edge jitter in the current horizontal units Jitter root mean square is the RMS value of the edge jitter in the current horizontal units Jitter 6  represents the same measurement reporting the 6  TCross1 value

85. ECE 546 – Jose Schutt-Aine 85 Noise Measurements Noise peak-to-peak is the peak-to-peak value of the noise at the top or base of the signal as specified by the user Noise root mean square is the RMS value of the noise at the top or base of the signal

86. ECE 546 – Jose Schutt-Aine 86 Noise Measurements Signal-to-noise ratio is the ratio of the signal amplitude to the noise at either the top or the base of the signal Duty cycle distortion is the peak-to-peak time variation of the first eye crossing measured at the mid-voltage reference as a percent of the eye period

87. ECE 546 – Jose Schutt-Aine 87 Eye Quality Factor Quality factor is the ratio of the eye size to noise

88. ECE 546 – Jose Schutt-Aine 88 Eye Diagram Specifications PCI Express 2.0 eye diagram specification for full and deemphasized signals

89. ECE 546 – Jose Schutt-Aine 89 Margin Testing Eye diagram with low margin

90. ECE 546 – Jose Schutt-Aine 90 Eye Pattern Analysis

91. ECE 546 – Jose Schutt-Aine 91 Typical Eye Diagrams Eye Diagram

92. ECE 546 – Jose Schutt-Aine 92 BERT Scan The sample delay BERT scan curve is a direct measurement of the jitter cummulative density function (CDF).

93. ECE 546 – Jose Schutt-Aine 93 BERT Scan

94. ECE 546 – Jose Schutt-Aine 94 Bathtub Curve Linear ScaleLogarithmic Scale

95. ECE 546 – Jose Schutt-Aine 95 Problem  In tests, we have measured jitter histograms and need to extract the individual jitter components  Ideally, we could use deconvolution into components. However without prior knowledge of deterministic jitter, it is not possible  Use dual Dirac distribution model which would yield the worst case deterministic jitter Jitter Mixing

96. ECE 546 – Jose Schutt-Aine 96 Random Jitter Extraction Spectrum Analysis  Extract random jitter by using the assumption that it has a piecewise linear spectrum  Impulses are attributed to DJ  Noise floor is due to RJ

97. ECE 546 – Jose Schutt-Aine 97 Extracting Random Jitter Total jitter Random jitter Time domain Statistical domain Spectral domain

98. ECE 546 – Jose Schutt-Aine 98 Jitter Spectrum A longer FFT yields a spectrum with greater frequency resolution and lower noise floor. Time record: 10N Time record: N

99. ECE 546 – Jose Schutt-Aine 99 Random Jitter Extraction Tail-Fit  Extract random jitter under the assumption that its probability density function follows a Gaussian distribution  Make use of the Dual-Dirac Model

100. ECE 546 – Jose Schutt-Aine 100 Dual Dirac Model Equal Amplitudes  Two unknown variables  Linear Problem  Explicit solution - gap between 2 impulses -  for Gaussian distribution Unknowns

101. ECE 546 – Jose Schutt-Aine 101 Dual Dirac Model Unequal Amplitudes  Three unknown variables  Nonlinear Problem  No explicit solution - gap between 2 impulses -  for Gaussian distribution - ratio of 2 impulse amplitudes Unknowns

102. ECE 546 – Jose Schutt-Aine 102 Dual Dirac Model  Obtain convolution of 2 PDFs Assume Gaussian RJ and Rectangle PJ Result is the sum of 2 Gaussian distributions with equal RMS value offset by the PJ peak-to-peak value. It is called the DUAL DIRAC DISTRIBUTION

103. ECE 546 – Jose Schutt-Aine 103 DDJ and DC D DDJ and DCD are correlated to the data pattern For N bits, transmitted at rate F R, the jitter components due to DDJ and DCD will appear in the spectrum at multiple of F R /N F R =1.0625 Gbits/s N=40 bits

104. ECE 546 – Jose Schutt-Aine 104 Pattern Correlation

105. ECE 546 – Jose Schutt-Aine 105 Pattern Correlation The phase errors from all occurences of each M-bit patterns are averaged together to estimate the phase error due to that M-bit pattern

106. ECE 546 – Jose Schutt-Aine 106 Extracting DDJ Spectral domain Eye DDJ Dominant RJ Dominant DDJ & RJ

107. ECE 546 – Jose Schutt-Aine 107 Periodic Jitter PJ PJ subcomponent Time domain Statistical domain Spectral domain

108. ECE 546 – Jose Schutt-Aine 108 Clock jitter is the single most important degrader of clock performance Clock Jitter In a computer system, the clock is used to provide timing or synchronization for the system. In a communication system, the clock is used to specify when a data switch or bit transaction should be transmitted and received In a synchronized system, a central global clock is distributed to its subsystem

109. ECE 546 – Jose Schutt-Aine 109 Definition Most of the definitions of data jitter (DJ, Rj,…) apply to clock jitter ISI does not apply to clock jitter

110. ECE 546 – Jose Schutt-Aine 110 Clock jitter analysis is subject to fewer sampling constraints compared to data signal jitter; therefore, more direct and versatile methods are possible for clock jitter analysis. Clock Jitter

111. ECE 546 – Jose Schutt-Aine 111 Synchronized System - Initial clock pulse causes A to latch data from input and launch it into channel - Second clock causes B to latch the incoming data

112. ECE 546 – Jose Schutt-Aine 112 Timing Parameters

113. ECE 546 – Jose Schutt-Aine 113 The minimum conditions are that both setup time and hold time margin should be larger than 0 Timing Conditions These give a quantitative description of how clock jitter and clock skew affect the performance of the synchronized system in which a common or global clock for both driver and receiver is used

114. ECE 546 – Jose Schutt-Aine 114 Skew Impact T c_jitter =0, T c_skew >0  The minimum clock period increases. The maximum hold time increases  hold time condition easier to meet T c_jitter =0, T c_skew <0  The minimum clock period decreases. The maximum hold time decreases  hold time condition harder to meet (race condition)

115. ECE 546 – Jose Schutt-Aine 115 Jitter Impact T c_skew =0, T c_jitter >0 (longer cycle)  The minimum clock period increases. The maximum hold time decreases  hold time condition harder to meet T c_skew =0, T c_jitter <0 (shorter cycle)  The minimum clock period decreases. The maximum hold time increases  hold time condition easier to meet

116. ECE 546 – Jose Schutt-Aine 116 1.Positive jitter over one clock period makes both clock period and hold time hard to meet 2.A longer cycle does more harm to system performance 3.When both skew and jitter are present, system performance can be any of the four scenarios just discussed System Performance

117. ECE 546 – Jose Schutt-Aine 117 Asynchronized System The skew of a synchronized system becomes hard to manage when the data rate increases(~1 Gb/s). At multiple Gb/s data rates, an asynchronized system is commonly used.

118. ECE 546 – Jose Schutt-Aine 118 Synchronized System  Global clock is used to update and determine bits Asynchronized System  Only data is sent  Clock is embedded in data  Clock recovery unit (CRU) recovers clock at receiver Clock Types

119. ECE 546 – Jose Schutt-Aine 119 Asysnchronized Link Low-frequency jitter from the transmitter clock can be tracked or attenuated by the clock recovery function if it has a high enough corner frequency. A low phase noise oscillator within a PLL clock recovery also provides smaller random jitter generations.

120. ECE 546 – Jose Schutt-Aine 120 Phase Jitter : timing for nth edge for jittery clock : timing for nth edge for ideal clock : ideal clock period

121. ECE 546 – Jose Schutt-Aine 121 Phase Jitter Phase jitter captures the instance timing deviation from the ideal for each transition. Jitter measured with phase jitter is absolute and accumulates over time. In frequency domain

122. ECE 546 – Jose Schutt-Aine 122 Period Jitter Period jitter is defined as the period deviation from the ideal period. using previous relations in terms of phase units Period jitter and phase jitter are not independent  we can derive one from the other.

123. ECE 546 – Jose Schutt-Aine 123 Phase, Period and CTC Jitter

124. ECE 546 – Jose Schutt-Aine 124 Phase Jitter in Time Domain If the phase varies, the waveform V(t) shifts back and forth along the time axis and this creates phase jitter

125. ECE 546 – Jose Schutt-Aine 125 Phase Jitter in Spectral Domain Phase noise appears as sidebands centered around the carrier frequency

126. ECE 546 – Jose Schutt-Aine 126 Phase Jitter : phase noise power (in watts) : carrier’s power (in watts) : phase noise bandwidth (in hertz) Phase noise magnitude is specified relative to the carrier’s power on a per-hertz basis : PSD of phase noise or

127. ECE 546 – Jose Schutt-Aine 127 Phase Noise to Phase Jitter From the phase noise PSD, random jitter and deterministic jitter can be identified Need: convert phase noise measured in the frequency domain to phase jitter for PLLs, clocks and oscillators

128. ECE 546 – Jose Schutt-Aine 128 Probe Further Course web site http://emlab.uiuc.edu/ece546/appnotes May 09 issue of IEEE Transactions on Advanced Packaging D. Derickson and M. Muller, “Digital Communications Test and Measurement”, Prentice Hall, 2007. Mike Peng Li, “Jitter, Noise and Signal Integrity at High- Speed”, Prentice Hall, 2008.