ECE 598 JS Lecture 17 Jitter

Transcription

1 ECE 598 JS Lecture 17 Jitter Spring 2009 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois 1

2 Jitter Definition Jitter is difference in time of when something was ideally to occur and when it actually did occur. Some devices specify the amount of marginal jitter and total jitter that it can take to operate correctly. If the cable adds more jitter than the receiver s allowed marginal jitter and total jitter the signal will not be received correctly. In this case the jitter is measured as in the below diagram Timing uncertainties in digital transmission systems Utmost importance because timing uncertainties cause bit errors There are different types of jitter 2

3 Jitter Characteristics 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) 3

4 Types of Jitter Deterministic Jitter (DDJ) Data Dependent Jitter (DDJ) Periodic Jitter (PJ) Bounded Uncorrelated Jitter (BUJ) Random Jitter (RJ) Gaussian Jitter f α Higher Order Jitter 4

5 Jitter Effects 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 Oscillator Phase Noise Present in reference clocks or high-speed clocks In PLL based clocks, phase noise can be amplified

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 6

7 Gaussian Random Jitter Random jitter can be described by a Gaussian distribution with the following probability density function ( x μ ) σ PDFRJ ( x) = e σ 2π x σ μ : 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 Δt approaches infinity 7

8 Gaussian Jitter PDF P( Δ t μ σ) = ( ) P Δ t μ 2σ = ( ) P Δ t μ 3σ = Can be used to estimate the probability when the deviation of the random jitter variable Δt is within a multiple of its σ value. 8

9 Cummulative Density Function Cummulative density function (CDF) is defined as: t CDF() t = PDF( x) dx CDF(t) tells us the probability that the transition occurred earlier than t. For random jitter, we get: 1 1 x CDFRJ ( x) = + erf 2 2 σ 2 erf is the error function 9

10 PDF and CDF of Random Jitter PDF CDF 10

11 Causes of Deterministic Jitter 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 11

12 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 bitd epends on the transition times of the previous bits 12

13 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 13

14 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 14

15 Model for DDJ The generic form for DDJ PDF is: N DDJ DDJ ( Δ ) = i δ Δ i i= 1 ( DDJ ) f t P t D DDJ Pi is the probability for the DDJ value of DDJ D i DDJ P i satisfies the condition N i= 1 P DDJ i = 1 15

16 Periodic Jitter Periodic jitter is a repeating jitter signal at a certain period or frequency. It is described by: Δ t = Acos( ωt+ φ ω : angular frequency o ) φ o : initial phase The PDF for the single PJ is given by 1 fpj ( Δ t) =, A Δt A π 1 Δ / ( t A) 2 Which can be approximated by 1 fpj t t A t A 2 ( Δ ) δ( Δ ) + δ( Δ + ) 16

17 Periodic Jitter PDF for single sinusoidal 1 fpj ( Δ t) =, A Δt A π 1 Δ / ( t A) 2 17

18 Periodic Jitter There are 3 common waveforms for the theoretical analysis of periodic jitter Rectangle Periodic Jitter 1 m 1 m PDFPJ rect ( x) = δ + δ Triangle Periodic Jitter 1 m for x < PDFPJ triang ( x) = m 2 0 otherwise 18

19 Periodic Jitter Sinusoidal Periodic Jitter 1 for x 2 2 PDFPJ line( x) = π m/2 x m 0 otherwise < m 2 19

20 Rectangular Periodic Jitter PDF CDF 20

21 Triangular Periodic Jitter PDF CDF 21

22 Sinusoidal Periodic Jitter PDF CDF 22

23 Phase Noise & Phase Jitter Phase noise in clock oscillators Phase offset term that continually changes timing of signal ( ) St () = Pt+φ() t signal waveform with phase noise undistorted signal phase noise Example: ( 9 P() t = sin π t) 1 ( 9 φ() t = sin π t) St ( ) = sin π t+ 0.25sin( πt) ( ) 23

24 Phase Noise clean signal noisy signal 2 GHz phase noise 24

25 Phase Jitter 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 t n T n φ n For a jittered digital signal tn = Tn φn 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 25

26 Phase Jitter clean signal noisy signal 26

27 Cycle-to-Cycle Jitter Phase jitter causes bit periods to contract and expand Actual bit periods are given by the time difference between 2 consecutive transitions ( φ ) ( φ ) P = t t = T T Ideal bit period: Period jitter: n n+ 1 n n+ 1 n+ 1 n n TB = T T n n+ 1 n PerJ n = TBn Pn ( ) ( ) PerJ = T T T T + φ φ = φ φ n n+ 1 n n+ 1 n n n+ 1 n+ 1 n 27

28 Cycle-to-cycle jitter: CCJit = P P n n+ 1 n Cycle-to-Cycle Jitter CCJit = PerJ PerJ n n+ 1 n 28

29 Bounded Uncorrelated Jitter BUJ is primarily due to crosstalk The PDF for BUJ is given by f PJ 2 pbuj Δ = 2πσBUJ 0 for Δt A ( t) t 2 2σ BUJ e for Δt ABUJ BUJ 29

30 Mix of Random and Periodic Jitters Gaussian RJ and Rectangle PJ Obtain convolution of 2 PDFs + m m RJ* PJrect = RJ( t τ ) δ + δ dτ = e + e 2σ 2π ( t m/2 ) ( t+ m/2) σ 2σ 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 30

31 Jitter Mixing 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 31

32 Total Jitter Time Waveform TJ(t) = PJ(t) + RJ(t) The total jitter waveform is the sum of individual components 32

33 Jitter Statistics TJ(x) = PJ(x) * RJ(x) The total jitter PDF is the convolution of individual components 33

34 Jitter Mechanisms 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 prsent in reference clocks especially in systems based on PLL 34

35 Jitter Mechanisms Jitter Mechanisms Transfer of noise into time domain Bandwidth limitation in channels Oscillator phase noise V NJ = t Noise pk pk t V V H L t t V Noise V H V L rise time pk-pk noise amplitude Hi signal level Lo signal level 35

36 Jitter Mechanisms Transfer of voltage noise into time domain Linear model Random noise caused by thermal effects 36

37 Jitter Mechanisms Transfer of voltage noise into time domain First order model Periodic noise: switching power, crosstalk, etc 37

38 Jitter Mechanisms Multiple threshold crossing of a signal with high-frequency level noise 38

39 Bandwidth Limitations data pattern 39

40 Bandwidth Limitations data pattern 40

41 Q-Scale Transformation Q-scale is defined such that the Gaussian distribution mapped onto the Q-scale is a straight line Use CDF CDF( x) 1 1 x = + erf 2 2 σ 2 Qx ( ) = 2erf 2 CDFx ( ) 1 = 1 ( ) x σ A Gaussian CDF is a straight line in the Q scale with slope 1/σ. DJ is given by distance d 41

42 Q-Scale Transformation Gaussian RJ σ = 0.5 PDF CDF 42

43 Q-Scale Transformation Gaussian RJ σ = 0.25 PDF CDF 43

44 Q-Scale - Generalization Qx ( ) = 2erf 2 CDFx ( ) 1 = 1 ( ) x σ Mixed Gaussian RJ and PJ σ = 0.1 PDF CDF 44

45 Q-Scale - Generalization Qx ( ) = 2erf 2 CDFx ( ) 1 = 1 ( ) x σ Mixed Gaussian RJ and PJ σ = 0.25 PDF CDF 45

46 Dual Dirac Model Mixed Gaussian RJ and Triangular PJ 46

47 Jitter Classification 47

48 Measuring Jitter 48

49 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

50 Eye Diagram

51 High-Speed Oscilloscope 8-bit flash ADCs provide 256 discrete levels along vertical axis 51

52 Interleaving Architecture 52

53 High-Speed Scope Digitizers SiGe Based Technologies Fastest ADCs run at Gsamples/s Typically 8 16 digitizers CMOS Designs ADCs sample at lower rate 80 digitizers or more 53

54 Timing Diagram 54

55 Sampling Procedure 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 55

56 Frequency Interleaving 56

57 Nyquist Criterion A signal of bandwidth B that has been sampled at regular intervals T can be exactly recovered if the sampling rate satisfies FN 1 = > T 2* B F N : Nyquist rate T B : sampling interval : bandwidth 57

58 High-Speed Oscilloscopes Oscilloscopes use DSP techniques to: Extend their analog bandwidth Flatten their amplitude Practice has benefits However, limitations should be understood 58

59 Scope Channel Equalization 59

60 Edge Triggering T OFF is recorded with high resolution but is subject to noise 60

61 Trigger Jitter Trigger jitter is the amount of effective timing instability between the trigger path and the signal capture path 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 61

62 Trigger Jitter 62

63 Sample Jitter 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 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 63

64 Oscillator Phase Noise 64

65 Sample Jitter Gaussian Errors Phase noise Aperture jitter in track and hold circuits Deterministic Errors Interleaving mismatches Can be calibrated out 65

66 Eye Diagram An eye diagram is a time-folded representation of a signal that carries digital information Eye is horizontally centered on the ideal sampling instant 66

67 Eye Diagram 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 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. 67

68 Eye Diagram Construction Eye diagram construction in real-time oscilloscope is based on hardware clock recovery and trigger circuitry 68

69 Eye Diagram Construction 69

70 Eye Diagram Construction 1. Capture of the Waveform Record 2. Determine the Edge Times 70

71 Eye Diagram Construction 3. Determine the Bit Labels 71

72 Eye Diagram Construction 4. Clock Recovery 72

73 Eye Diagram Construction 5. Slice Overlay 6. Display 73

74 Eye Diagram Measurements 74

75 Eye Diagram Measurements 75

76 Reference Levels 76

77 Eye Height Eye Height is the measuremnt of the eye height in volts ( 3 ) ( 3 ) PTop PTop PBase PBase Eye Height = μ σ μ + σ μ PTop : mean value of eye top σ PTop μ PBase σ PBase : standard deviation of eye top : mean value of eye base : standard deviation of eye base 77

78 Eye Width Eye Width is the measuremnt of the eye width in seconds Eye Width = μ 3σ μ + 3σ ( ) ( ) TCross2 TCross2 TCross1 TCross1 Crossing percent measurement is the eye crossing point expressed as a percentage of the eye height ( μ μ ) PCross1 PBase Crossing Percent = 100% ( μ μ ) PTop PBase 78

79 Jitter Measurements Jitter peak-to-peak is the peak-to-peak value for the edge jitter in the current horizontal units ( TCross ) ( TCross ) Jitter pp = max 1 min 1 Jitter root mean square is the RMS value of the edge jitter in the current horizontal units Jitter RMS = σ TCross1 Jitter 6σ represents the same measurement reporting the 6σ TCross1 value 79

80 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 pp ( ) ( ) max PTop min PTop, or = max ( PBase) min ( PBase) Noise root mean square is the RMS value of the noise at the top or base of the signal Noise RMS = σ σ PTop or PBase 80

81 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 S/N Ratio = ( μ μ ) PTop PBase ( σ σ ) PTop PBase 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 TDCD DCD = p-p 100% ( μ μ ) TCross2 TCross1 81

82 Eye Quality Factor Quality factor is the ratio of the eye size to noise Quality Factor = ( μ μ ) PTop PBase ( σ + σ ) PTop PBase 82

83 Eye Diagram Specifications PCI Express 2.0 eye diagram specification for full and deemphasized signals 83

84 Margin Testing Eye diagram with low margin 84

85 Eye Pattern Analysis Fiber Pseudorandom sequence generator Data Transmitter Receiver Clk Scope Trig Vert 85

86 Eye Diagram Typical Eye Diagrams

87 Jitter Mixing 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 87

88 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 88 88

89 Extracting Random Jitter Time domain Statistical domain Spectral domain Total jitter Random jitter 89

90 Jitter Spectrum Time record: 10N Time record: N A longer FFT yields a spectrum with greater frequency resolution and lower noise floor. 90

91 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 91

92 Dual Dirac Model Unknowns - gap between 2 impulses - σ for Gaussian distribution Equal Amplitudes Two unknown variables Linear Problem Explicit solution 92

93 Dual Dirac Model Unknowns - gap between 2 impulses - σ for Gaussian distribution - ratio of 2 impulse amplitudes Unequal Amplitudes Three unknown variables Nonlinear Problem No explicit solution 93

94 Dual Dirac Model Assume Gaussian RJ and Rectangle PJ Obtain convolution of 2 PDFs + m m RJ* PJrect = RJ( t τ ) δ + δ dτ = e + e 2σ 2π ( t m/2 ) ( t+ m/2) σ 2σ 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 94

95 DDJ and DC D DDJ and DCD are correlated to the data pattern F R = Gbits/s N=40 bits 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 95

96 Pattern-Correlation-Based Approaches Most of the DDJ and DCD on a given data edge is caused by prior waveform edges. The number of relevant prior edges is determined by the speed of the system s response. If response to an edge fully settles within M unit intervals, only M preceding edges need to be analyzed to characterize DJ This analysis method is uniquely possible with realtime instruments For M bits, there are 2 M bit patterns 96

97 Pattern Correlation 97

98 Pattern Correlation The phase errors from all occurrences of each M-bit pattern are averaged together to estimate the phase error due to that M-bit pattern 98

99 Extracting DDJ DDJ Dominant DDJ & RJ RJ Dominant Spectral domain Eye 99

100 Periodic Jitter Time domain Statistical domain Spectral domain PJ PJ subcomponent 100

101 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 Clock jitter is the single most important degrader of clock performance 101

102 Definition Most of the definitions of data jitter (DJ, Rj, ) apply to clock jitter ISI does not apply to clock jitter 102

103 Clock Jitter 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. 103

104 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 104

105 Timing Parameters 105

106 Timing Conditions The minimum conditions are that both setup time and hold time margin should be larger than 0 T T + T + T + T 0 c _ jitt c _ skew d _ pd su T T + T T hd d _ pd c _ skew c _ jitt 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 106

107 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) 107

108 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 108

109 System Performance 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 109

110 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. 110

111 Clock Types 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 111

112 Asysnchronized Link DJ = DJ + DJ clk _ tot clk _ tx clk _ rx σ = σ + σ clk _ tot clk _ tx clk _ rx 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. 112

113 t n Phase Jitter : timing for nth edge for jittery clock T n : timing for nth edge for ideal clock T o : ideal clock period Δ t = t T T n n n n = nt o 113

114 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 φ n = t n T o 2π 114

115 Period Jitter Period jitter is defined as the period deviation from the ideal period. ( ) Δ t = t t T pn n n 1 o using previous relations Δ =Δ Δ tpn tn tn 1 in terms of phase units φ = Φ Φ ' n n n 1 Period jitter and phase jitter are not independent we can derive one from the other. 115

116 Phase, Period and CTC Jitter 116

117 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 117

118 Phase Jitter in Spectral Domain Phase noise appears as sidebands centered around the carrier frequency 118

119 Phase Jitter Phase noise magnitude is specified relative to the carrier s power on a per-hertz basis P ( ) n f P o Δf Pn ( ) ( f L f = ) PΔf o : phase noise power (in watts) : carrier s power (in watts) : phase noise bandwidth (in hertz) 1 L( f) = SΦ ( f) or 2 S Φ ( f) : PSD of phase noise Φ = 10 L( f) 10log S ( f) 2 119

120 Phase Noise to Phase Jitter Need: convert phase noise measured in the frequency domain to phase jitter for PLLs, clocks and oscillators From the phase noise PSD, random jitter and deterministic jitter can be identified 120

121 Phase Lock Loop Phase noise or jitter is the key metric for evaluating the performance of a PLL system 121

122 Jitter in PLLs External Source Reference clock input Internal Source Voltage controlled oscillator (VCO) 122

123 Time Domain PLL Analysis When PLL is a first order system, it can be modeled by a closed form solution It is not straightforward to model jitter/noise process with loop components in the time domain 123

124 Frequency- Domain PLL Analysis H The error transfer function is: o θo() s KdKoF() s () s = = θ () s s + K K F() s i d o θe() s He() s = = 1 Ho() s θ () s i 124

125 PLL Transfer Function 125

126 PLL Frequency Response Large peaking causes PLL to be unstable Larger 3dB frequency faster PLL tracking Larger peaking jitter amplification bit error For PLL stability, Barkhausen condition must be satisfied KK d o Fs () s = 1 Fs () Arg KdKo = 180 s 126

127 PLL Frequency Response 127

128 Pole and Zero Location 128

129 Tracking Time and Frequencies 129

130 Transmitter Architecture 130

131 Receiver Architecture 131

132 Channel or Medium 132

133 Probe Further Course web site May 09 issue of IEEE Transactions on Advanced Packaging D. Derickson and M. Muller, Digital Communications Test and Measurement, Prentice Hall, M. P. Li, Jitter, Noise and Signal Integrity at High Speed, Prentice Hall,