An Introduction to An Introduction to Eye Diagram, Phase Noise and Jitter

1. 1
MOHIEDDIN MORADI
mohieddinmoradi@gmail.com
DREAM
IDEA
PLAN
IMPLEMENTATION

2. Gaussian Distributions
Note: Peak-Peak is dependant on the sample size. Larger samples of the same distribution
will most likely yield a larger peak-peak measurement. Thus, peak-peak must be
discussed in context of the number of samples.
2

3. Gaussian Statistics
Gaussian Distribution with small standard deviation
Gaussian Distribution with large standard deviation
Mean
3

4. • Standard Deviation is used to predict the occurrence of outlying measurements
from the mean.
• The Catch…
– This use of Standard Deviation (1s) is only valid in pure Gaussian
distributions.
– If any deterministic components exist in the distribution, the use of 1s based
on the entire jitter histogram for the estimation of probability of occurrence is
invalid.
-1s-2s
MEAN
Gaussian Statistics
4

5. “Real World” Distributions
• In most cases, time measurement distributions are not entirely Gaussian.
– Typically, some Deterministic/Systematic offset occurs to “mess-up” the distribution to make it
Non-Gaussian
Gaussian Non-Gaussian
Tail regions still appear Gaussian
In non-Gaussian distributions, Gaussian assumptions apply to the tails (left most
and right most regions) if and only if the equivalent 1s of these
tail region can be calculated.
5

6. Non-Gaussian Distributions
Break up distribution into
tail and mid sections.
• Analyze distribution by looking at tail sections separately.
– Allows for probabilistic estimations of out lying measurements
– knowledge of Gaussian component (Random Jitter) on left side of multimodal distribution
enables the calculation of the probability of short cycle measurements
LEFT RIGHT
6

7. Non-Gaussian Distributions
• In order to determine the probability of a measurement occurring at the -3sL
point, it is critical to determine the standard deviation that would correspond to
a Gaussian Distribution with a identical tail region to that of our multimodal
non Gaussian distribution.
-1sL-2sL
MEAN’L
-3sL -1sR -2sR
MEAN’R
-3sR
7

8. Determining Representative Gaussian Distributions
• Tail Fit algorithm enables the user to identify a Gaussian curve with a symmetrical
tail region to that of the non-Gaussian distribution under evaluation.
Keep adjusting 1s
until tails match
8

9. What is Jitter?
9

10. What is Jitter?
Reference
Point Histogram
Period of clock
10

11. What Causes Jitter?
11

12. Phase and amplitude jitter influence
digital systems and can cause bit errors
the significant instants are the exact moments
when the transitioning signal crosses a chosen
amplitude threshold, which may be referred to
as the reference level or decision threshold.
Phase and amplitude jitter
12

13. Noise Voltage in Signal + Threshold = Jitter
Noise added to a signal transitioning through a threshold, adds jitter to the time at which the
signal crosses the threshold.
This is the way jitter is created in nonlinear circuits such as digital circuitry.
The statistics of the jitter can
be computed from the statistics
of the noise at the time of the
threshold crossing and the slew
rate (or time derivative) of the
large signal at the threshold
crossing.
13

14. Jitter in Signal + Sampler = Noise
Jitter, in the time at which a signal is sampled, creates noise in the sampled result if the
signal is changing at the time it is sampled.
The statistics of the noise
can be computed from the
statistics of the jitter at the
time of the sampling and
the slew rate (or time
derivative) of the input
signal at the time of the
sampling. 14

15. Eye-diagram
15

16. Ideal sampling position
Timing skew of Sampling Position Jitter
Ideal reference point
Voltage offset
Jitter
16

17. Jitter
Jitter Frequency 17

18. Main types of Jitter
Deterministic
Jitter (DJ)
Random
Jitter (RJ)
Data Dependent
Jitter (DDJ)
Inter-symbol
Interference (ISI)
Duty Cycle
Distortion (DCD)
Periodic
Jitter PJ
or SJ
Data-Correlated Data-Uncorrelated
Total
Jitter (TJ)
PJ also sometimes called sinusoidal jitter or SJ
DDJ also known as inter-symbol interference or ISI
Echo jitter
(ECJ)
18

19. 19

20. 20

21. Types of Jitter
Jitter can be random or deterministic. In most cases, both types occur.
RJ: Random Jitter
Random changes in the phase. It is often assumed to be of Gaussian distribution.
Causes: Thermal Noise, Shot Noise
PJ: Periodic Jitter (deterministic).
Is a periodic variation in the phase. Causes: External coupling into the circuit, power
supply noise, PLL comparator frequency feed-through
DCD: Duty Cycle Distortion (deterministic).
Is the difference in the mean pulse width between positive and negative pulses in a
clock. Causes: Amplitude offset, turn-on delay, saturation.
ISI: Inter-Symbol Interference (deterministic)
Previous signals have not rang down, before new data arrives. Causes: Impulse response
is longer than a data bit.
21

22. Types of Jitter (1)
Random (Gaussian) Jitter (RJ)
•Originates from external and internal random noise sources
•This component best modeled by a Gaussian function.
•Random Jitter is unbounded and therefore directly effects long term reliability.
•Stochastic in nature (probability-based)
•Measured in RMS units
•Observed as Gaussian histogram around zero-crossing
Histogram measurement at zero crossing
exhibiting Gaussian probability distribution
22

23. • Where does Random Jitter Come from?
– Thermal vibrations of semiconductor crystal structure causes mobility to vary
depending instantaneous temperature of material
– Material boundaries have less than perfect valence electron mapping.
• Imperfections due to semi-regular doping density through semiconductor
substrate, well and transistor elements,
• Imperfections due to process anomalies
– Thermal effects of conductor material. Thermal vibration of conductor atoms
effect electron mobility
– And many more minor contributors such as:
• cosmic radiation, etc...
Types of Jitter (1)
23

24. σ
24

25. Types of Jitter (2)
Deterministic Jitter (DJ):
 Originates from circuit non-idealities (e.g., finite bandwidth, offset, etc.)
 Amount of DJ at any given transition is predictable
 Measured in peak-to-peak units
 Jitter with non-Gaussian probability density function.
 Deterministic jitter is always bounded in amplitude and has specific causes.
• Different types of DJ:
• Inter Symbol Interference (ISI) (Data correlated)
• Duty-Cycle Distortion (DCD) (Data correlated)
• Sinusoidal (SJ) or Periodic Jitter (PJ)
Deterministic
Jitter (DJ)
Random
Jitter (RJ)
Data
Dependent
Jitter (DDJ)
Inter-symbol
Interference (ISI)
Duty Cycle
Distortion (DCD)
Periodic
Jitter PJ
or SJ
Total
Jitter (TJ)
Echo jitter
(ECJ)
25

26. 26

27. DJ Measurement Method I: From Jitter PDF or BER
• Measure overall jitter PDF with a scope or TIA, or BER CDF with a BERT
• Fit Gaussian for jitter PDF, or integrated Gaussian for BER CDF at tails to obtain RJ, σ
• Obtain DJ PDF via deconvolution (directly from jitter PDF, or derivative of BER CDF)
• Note that fitting needs to start from the probability level where DJ pk-pk levels-off and
downward to warrant accuracy
OJ: Overall Jitter
27

28. DJ Measurement II :From Jitter Spectrum
• Measure jitter spectrum as shown with a Real-Time Scope or TIA and subtract RJ
background spectrum
• Do FFT-1to the residue DJ spectrum and find its pk-pk (e.g., max-min) in time-domain
Deterministic
Jitter (DJ)
Random
Jitter (RJ)
Data Dependent
Jitter (DDJ)
Inter-symbol
Interference (ISI)
Duty Cycle
Distortion (DCD)
Periodic
Jitter PJ
or SJ
Total
Jitter (TJ)
Echo jitter
(ECJ)
28

29. Caused by channel loss, dispersion, and reflections
•Equalization can improve ISI jitter
Types of Deterministic Jitter
a) Inter Symbol interference (ISI)
29

30. Consider a 1 UI output pulse applied to a buffer:
If rise/fall time << 1 UI, then the output pulse is attenuated and the pulse width decreases.

  UI

  UI

  UI
1UI
< 1UI
ISI (cont.)
Types of Deterministic Jitter
30

31. 0 0 1
1 0 1
ISI (cont.)
Consider 2 different bit sequences:
t = ISISteady-state not reached
at end of 2nd bit
2 output sequences
superimposed
ISI is characterized by a double edge
in the eye diagram.Double-edge (DJ) combined with RJ
Types of Deterministic Jitter
31

32. • Occurs when rising and falling edges exhibit different delays
• Caused by circuit mismatches
b) Duty cycle distortion (DCD)
Eye diagram with DCD
Crossing offset from
nominal threshold
Nominal data sequence
Data sequence with late falling edges
& early rising edges due to threshold shift
t = DCD
Tb 2Tb
Types of Deterministic Jitter
32

33. c) Periodic Jitter (PJ) or SJ
Timing variation caused by periodic sources unrelated to the data pattern.
Can be correlated or uncorrelated with data rate.
Clock source with
duty cycle ≠50%
Synchronized data
exhibiting correlated PJ
Δt1 Δt0

PJ  t1  t0
Uncorrelated jitter (e.g., sub-rate PJ due to supply ripple) affects the eye
diagram in a similar way as RJ.
Types of Deterministic Jitter
33

34. Can be decomposed into a Fourier series of sinusoids
The jitter produced by an individual sinusoid is
c) Periodic Jitter (PJ)
Types of Deterministic Jitter
34

35. • Deterministic Jitter from Cross talk
– Victim line is affected by magnetic field from Driver line.
– Incremental inductance of victim conductor converts induced magnetic
field into induced current.
– Induced Current adds (positively or negatively) to Victim Line current
increasing or decreasing potential and thus causing jitter on Victim Line
Driver Line
Current
Victim Line
Current
Were dose deterministic jitter come from?
35

36. Switching
Power Supply
• EMI Radiation (Ampere’s Law)
– Victim line is affected by magnetic field from EMI Source. This could be
a power supply, AC Power line, RF signal source, etc.
– As in cross talk induced jitter, the magnetic field induces a current that is
added (positively and negatively) to the victim line current thereby
effecting the timing of the signal on the victim line.
Victim Line
Current
Were dose deterministic jitter come from?
36

37. • Noisy reference plane
– Noise in power planes can result in reference shifts in threshold voltages
for downstream logic gates.
– Resultant timing shift is proportional to slew rate of input signal.
– The output transistor will switch when VT is exceeded at the gate.
• A change in ground reference at VT will result in a shift in the
required voltage to switch the gate thereby delaying or advancing the
switch
– VCO in PLL is sensitive to GND level variance.
Vout
Vout
VCC
VT
ROUT Edge Transition on the input to the
transistor
T
V
Were dose deterministic jitter come from?
37

38. • Simultaneous Switching Outputs
– If all output pins switch to same state, spike currents will be induced on
VCC and on GND.
– Spike Currents on Reference Plane can cause Threshold Voltage sense
point to shift
– Due to the pattern sensitivity and the bounded max. amplitude of edge
jitter due to SSO, this is considered deterministic jitter.
Vout1
Vout2
VCC
VT
ROUT
ILOAD
Vout2
Vout3
Vout1
VCC
VT
ROUT
ILOAD
Vout3
VCC
VT
ROUT
ILOAD
Were dose deterministic jitter come from?
38

39. Deterministic
Jitter (DJ)
Random
Jitter (RJ)
Data
Dependent
Jitter (DDJ)
Inter-symbol
Interference (ISI)
Duty Cycle
Distortion (DCD)
Periodic
Jitter PJ
or SJ
Total
Jitter (TJ)
Echo jitter
(ECJ)
39

40. 40

41. Measurements from eye diagram
41

42. Unterminated eye display
Measurements from eye diagram
42

43. Jitter within the SDI signal will change the time when a transition occurs and
cause a widening of the overall transition point. This jitter can cause a
narrowing or closing of the eye display and make the determination of the
decision threshold more difficult.
Measurements from eye diagram
43

44. Jitter and Wander
– Jitter > 10Hz (difficult for receiver to adjust , so can be a problem)
– Wander <= 10Hz (receiver can adjust , so normally not a problem)
44

45. Timing Jitter
• The variation in time of the significant instants (such as zero crossings) of a
digital signal relative to a clock with no jitter above 10Hz
 Measurement based on very stable clock in test device
 Used to determine general health of system
f1=10Hz, f3=1KHz for SDTV
f4=PLL Upper limit
45

46. Alignment Jitter
 Jitter that the receiver PLL cannot track it.
Measured based on clock recovered from the signal itself
 Indicates jitter that can cause system problems
46

47. 47

48. 48

49. Logic-Based Measurement
● E.g., BERT
● Bit errors caused by jitter
● Data measured at sampling point has
BER
● Sweeping the sampling point creates
bathtub curve
0 1
Sampling Point
BER
The bit error ratio, sometimes referred to as the
bit error rate, is defined as the number of bits
received in error divided by the total number of
bits transmitted in a specified time interval.
Within the specified interval, it is numerically
equal to the bit error probability.
49

50. Time
BER
Time
BER Bit error curve as a function of
sampling moment
How long would it take if we like to get down to 10e-12 Bit Error Rate?
Logic-Based Measurement
50

51. Jitter applications
Jitter tolerance: How much
jitter, as a function of the jitter
frequency, can be tolerated by
a system
Jitter transfer: How strong, as a
function of the jitter frequency, a
jitter at an input is transmitted to an
output in e.g., by a clock recovery
circuit
51

52. Jitter Tolerance of ADCs at Nyquist frequency
(ps rms)
52

53. 53
Jitter generation is defined as intrinsic jitter present at the output port of a device in the
absence of applied input jitter.
Jitter generation

54. Jitter Tolerance Testing
• Sweep through frequency range for modulation sensitivity testing.
– Many internal circuits feature an embedded PLL
– Since all PLL devices have a bandwidth, it is important to sweep the
modulation frequency through several different frequencies to determine
specific sensitivities.
• Use several different Jitter combinations.
– Increase psuedo random jitter to test for Random Jitter,
– Sweep Periodic Jitter through several frequencies and amplitudes.
– Check Power sensitivities to jitter tolerance.
– Check thermal sensitivities to jitter tolerance.
54

55. Jitter Visualization
Graphical views of jitter provide great insight into jitter behavior
Histogram:
–Frequency of Occurrence versus Jitter Amplitude
–To a practiced eye, allows quick assessment of RJ vs. DJ, and how the DJ is
distributed
Time Trend:
–Jitter Amplitude versus Time
–Reveals PLL transient behavior
–Allows quick diagnosis of clock recovery failures
Spectrum:
–Jitter Amplitude versus Frequency
–Deterministic jitter that is not discernable in other domains is easily seen
–Root cause can be traced back due to spectral signature
55

56. Jitter Visualization
56

57. Jitter measurements
57

58. Jitter measurements
Period Jitter (JPER)
• Time difference between measured period and ideal period (rising edge to next
adjacent rising edge)
Cycle to Cycle Jitter (JCC)
• Time difference between two adjacent clock periods
• Important for budgeting on-chip digital circuits cycle time
• it shows the instantaneous dynamics a clock recovery PLL might be subjected to.
Time Interval Error (TIE) (or Accumulated Jitter (JAC) )
• Time difference between measured clock and ideal trigger clock
• Jitter measurement most relative to high-speed link systems
There are several ways in which jitter may be measured on a single waveform.
It is important to understand how these measurements relate to each other and what
they reveal.
58

59. The period jitter (P1, P2 and P3) measures the period of each clock cycle.
The cycle-cycle jitter (C2 and C3) measures how much the clock period changes between
any two adjacent cycles.
It can be found by applying a first-order difference operation to the period jitter.
(The ideal edge locations of the reference clock was not required for above measurements)
The TIE measures how far each active edge of the clock varies from its ideal position.
(The ideal edges must be known or estimated)
59

60. 60

61. Period Jitter (JPER)
Its peak-to-peak value may be estimated by adjusting an oscilloscope to display a little
more than one complete clock cycle with the display set for infinite persistence. If the
scope triggers on the first edge, the period jitter can be seen on the second edge.
61

62. (Cycle-to-Cycle) Adjacent Cycle Jitter (Rambus Jitter)
• Adjacent Cycle Jitter
– Referred to as “Cycle-to-Cycle”
• Since this is inconsistent with established definitions from Tektronix, Intel,
Hewlett Packard (Agilent), Wavecrest and many others, we will simply refer
to this jitter phenomena as “Adjacent Cycle Jitter”
– Adjacent Cycle Jitter is the worst case period deviation from one period to the
next adjacent cycle.
– Measurement must be taken at exactly the same voltage for stop as well as start.
Dtn
Dtn+1
Dtn+1
Dtn
62

63.  For this measurement to be
performed, the ideal edges must
be known or estimated.
 For this reason, it is difficult to
observe directly with an
oscilloscope, unless some means
of clock recovery or post-
processing is available.
 The TIE may also be obtained by
integrating the period jitter, after
first subtracting the nominal
(ideal) clock period from each
measured period.
 TIE is important because it
shows the cumulative effect that
even a small amount of period
jitter can have over time.
TIE: Time Interval Error
An eye diagram for a signal with only
Gaussian jitter, together with the
associated TIE histogram
63

64. Mathematical Connection between Jitter Types
64

65. What is Accumulated Time Analysis?
• The key to Periodic Jitter Detection.
– Accumulated Time Analysis (ATA) is a technique that uses
accumulated jitter to determine the presence of periodic jitter.
– Using ATA, the user can quickly and simply measure the cumulative
amplitude and frequency of modulation for all Periodic Jitter elements
riding on the clock.
– Using a patented normalization technique, the user can also see the
worst case period deviation due to each of the PJ components.
• What is Cumulative Jitter (long term jitter)?
– Periodic Jitter has the effect of increasing the period and decreasing the
period of a clock over time.
– Accumulated jitter is observed as variation in signal waveforms across
multiple consecutive cycles, not just one cycle.
65

66. Period DecreasingPeriod IncreasingPeriod DecreasingPeriod Increasing
The effect of a Periodic
• Period Increasing
– In this section the period of the modulated clock is increased from the ideal.
Notice how much longer the elapsed time for 5 periods.
• Period Decreasing
– In this section the period of the modulated clock decreases from the ideal. The
net effect of the shorter periods results in a canceling out of the increased periods
from the prior section. Note that the same number of clocks is completed after
both sections.
Ideal Clock
Real Clock
Period Jitter
Amplitude
66

67. Accumulated Time Analysis
Clock
1
2
3
4
5
n
For Cycle Count = 1
For Cycle Count = 2
For Cycle Count = 3
For CycleCount = 4
For Cycle Count= 5
For CycleCount = n
11 12
13
14
15
1n
Frequency (in Hz)
Fn/2 Fn
FFT of Accumulated Jitter Data
0dB
-5dB
-10dB
-15dB
-20dB
-25dB
-30dB
3Fn/4Fn/40Hz
Fn = Apparent Nyquest Frequency
Most Significant Jitter
Modulation Contributor
Less Significant Modulation Contributors
Distribution of Time Measurements
Measurement Schedule
2 4
Number of Cycles
6 8 10 12 14
Jitter Analysis Graph with Period as Function
AccumulatedJitter
67

68. 
Tosc 
1
fosc
Free-running
oscillator output
Histogram plots
Experiment:
Observe N cycles of a free-running VCO on an oscilloscope over a long measurement
interval using infinite persistence.
NT
1 2 3 4
trigger 
1

2

3

4
Accumulated Time Analysis
68

69. Observation:
As  increases, rms jitter increases.




2
proportional
to 2
proportional
to 

Accumulated Time Analysis
69

70. Jitter Statistical Parameters
Mean Value:
• FCan be interpreted as a fixed timing offset or “skew”
• Generally not important, as usually can corrected for
RMS Jitter:
• Useful for characterizing random component of jitter
Peak-to-Peak Jitter:
• Function of both deterministic (bounded) and random (unbounded) jitter
components
• Must be quoted at a given BER to account for random (unbounded) jitter
70

71. Peak-to-Peak Jitter:
71

72. RMS Jitter:
σ
72

73. Jitter Calculation Examples
JPER = time difference between measured period and ideal period
JCC = time difference between two adjacent clock periods
JAC = time difference between measured clock and ideal trigger clock
73
Deterministic
Jitter (DJ)
Random
Jitter (RJ)
Data Dependent
Jitter (DDJ)
Inter-symbol
Interference (ISI)
Duty Cycle
Distortion (DCD)
Periodic
Jitter PJ
or SJ
Total
Jitter (TJ)
Echo jitter
(ECJ)

74. The relationship between oscillator output and jitter
Other frequencies in the vicinity of the fundamental frequency.
This is produced by phase modulation due to random signals; that is, the noise source modulates
the oscillator.
Commonly called phase noise:
where E(t) is amplitude fluctuation (AM noise), φ(t) is phase fluctuation (PM noise). φ(t)is phase
noise.
Phase noise is usually stated as a ratio between carrier power and noise power at an offset
frequency from the carrier. All phase noise is jitter.
74

75. SSB (single sideband) phase noise L(f) is usually used to express phase noise.
L(f) is a function of offset frequency f
It is the total power of an electrical signal in the 1 Hz bandwidth at a frequency f HZ away from
the carrier.
Phase noise C is expressed using the following equation:
Since L(f) is noise, it must be converted to units of 1 Hz for comparison purposes.
If A is the measurement bandwidth when phase noise is measured, then the measured phase noise
is calculated by dividing it by A.
75

76. Phase jitter
Phase noise and jitter both indicate the stability of a signal, and are interrelated.
PHASE NOISE is the instability of a frequency expressed in the frequency domain.
JITTER is fluctuation of the signal waveform in the time domain.
The part that corresponds to the integral value of this phase noise (the shaded area) is
phase jitter and corresponds to RMS jitter.
As for PHASE JITTER, you can obtain a value for jitter that has components within a
specific frequency range by calculating the integral value of a specific offset
frequency range.
76

77. PHASE NOISE
It is defined as the ratio of the noise in a 1-Hz bandwidth at a specified frequency
offset, fm, to the oscillator signal amplitude at frequency fO.
77

78. 78

79. Effect of Sampling Clock Phase Noise
Ideal Digitized Sine wave
The "broadband" phase noise will cause a degradation in the overall SNR as
predicted by
79

80. It is customary to characterize an oscillator in terms of its single-sideband phase
noise.
In order to relate phase noise to ADC performance, the
phase noise must be converted into jitter.
80

81. Calculating Jitter from Phase Noise
A graph relevant to modern ADC applications
The oscillator frequency (sampling frequency) =100 MHz
81

82. 82

83. 83

84. f

1
Tb

2
Tb

3
Tb
P(f)
Binary Data Representations in Frequency Domain (1)

x(t)  bk  p t  kTb 
k

A random data signal x(t) can be represented as:
t
p(t)
Tb
1
0
where is the bit sequence and p(t) is a unit-interval pulse::

bk  1,1 
Sx f
1
Tb
P f
2
Tb 
sin fTb 
fTb








2
If there is equal probability of low or high logic levels (i.e., dc level is 0), the
power spectral density of x(t) is given by:

P fTb 
sin(fTb )
fTb
84

85. 
Sx f
1
Tb
P f
2
Tb 
sin fTb 
fTb








2
f (GHz)

Sx f
5 10 15 20 25 30repeating 0101
Example: 10 Gb/s data signals
random data
100 ps
Binary Data Representations in Frequency Domain (2)
f

1
Tb

2
Tb

3
Tb

Sx f
85

86. 86

87. 87

88. 88

89. 89

90. 90

91. Phase Noise vs. Amplitude Noise (1)

Vosc(t)  Vc v(t) exp j osct (t)  
osct

v
v Spectrum of Vosc would include
effects of both amplitude noise v(t)
and phase noise (t).
How are the single-sideband noise spectrum Ltotal() and phase spectral
density S() related?
91

92. Phase Noise vs. Amplitude Noise (2)
t t
i(t) i(t)
Vc(t) Vc(t)
0t
osc
q
t



Recall that an input current impulse causes an enduring phase perturbation and a
momentary change in amplitude:
Amplitude impulse response
exhibits an exponential decay due
to the natural amplitude limiting
of an oscillator ...
92

93. Vosc(t)  Vc v(t) cos osct (t) 
 Vc v(t)  cos(osct) (t) sin(osct) 
 Vc cos(osct) (t) Vc sin(osct) v(t) cos(osct)
Phase & amplitude noise
can’t be distinguished in a signal.
Phase Noise vs. Amplitude Noise
noiseless
oscillation
waveform
phase noise
component
amplitude
noise
component
Amplitude limiting will decrease amplitude noise
but will not affect phase noise.
osc
Sv()
phase
noise
amplitud
e noise

93

94. Sideband Noise/Phase Spectral Density

Vosc(t)  Vc cos osct (t) 
 Vc  cos(osct) (t) sin(osct) 

Vc cos(osct)Vc (t)sin(osct)

Pphase noise
Psignal

1
2
Vc
2
2
1
2
Vc
2
2

Lphase  
1
2
S  
noiseless
oscillation
waveform
phase noise
component
94

95. Jitter/Phase Noise Relationship (1)


2

1
osc
2
E (t ) (t) 
2







1
osc
2
 E 2
(t ) E 2
(t) 2E (t) (t )  

R () 
1
2
S () ej ( )
d()



Recall Rf and S() are a Fourier transform pair:


2

2
osc
2
 R (0) R () 

Tosc 
1
fosc
NT
1 2 3 4

1

R (0)

R (0)

2R ()autocorrelation functions

2

3

4
95

96. 
R (0) 
1
2
S ()d()



R () 
1
2
S () ej ( )
d()



Jitter/Phase Noise Relationship (2)


2

1
osc
2
 S () 1ej ( )
 


 d()

1
osc
2
 S () 1cos()  j sin() 


 d()

4
osc
2
 S () sin2 
2






0

 d()
96

97. Let

S () 
a
()2

2

4
osc
2

a
()2
sin2 ()
2






0

 d()

4
osc
2

a
4


a
osc
2

Consistent with jitter accumulation measurements!
Jitter/Phase Noise Relationship (3)
Jitter from 1/( noise:
2
Let

S () 
b
()3


2

4
osc
2

b
()3
sin2 ()
2








 d()

 2
Jitter from 1/( noise:
3
^
^
^
^


a
fosc
2
 wherea  (2)2
a^
97

98. Jitter/Phase Noise Relationship (4)
f
S f  (dBc/Hz)
-100
-20dBc/Hz
per decade
• Let fosc = 10 GHz
• Assume phase noise dominated by 1/()2

S f 
a
(f)2

S 2106
 
a
2106
 
2
1010
 a  400
Setting f = 2 X 106
and S =10-10
:
Let  = 100 ps (cycle-to-cycle jitter):
  = 0.02ps rms (0.2 mUI rms)

2

a
fc
2
 
400
10 109
 
2
  41018
 
Accumulated jitter:

  2109
  
2 MHz
98

99. More generally:
f

S f  (dBc/Hz)
fm
Nm
-20 dBc/Hz
per decade

 
fm
fosc





 10Nm 20
  ps 


Tosc
 fm  10Nm 20
  UI 


2

a
fosc
2
  
fm
fosc






2
 10Nm 10
 

S f 
a
(f)2

(fm )2
10Nm 10
(f )2
Jitter/Phase Noise Relationship (5)


Tosc
fm  10
Nm 10  20
   fm  10Nm 20
   100.5
 rms jitter increases by a factor of 3.2
Let phase noise increase by 10 dBc/Hz:
99

100. 100

101. 101

102. 102
An Introduction to 3D TV

103. Questions??
Discussion!!
Suggestions!!
Criticism!!
103