# Jitter Analysis Functions

This chapter describes the jitter analysis concepts and functions in detail. These are not generalized functions, they are provided specifically to support jitter analysis.

## Working with Jitter Analysis Data

Jitter Analysis is used to decompose aggregate total jitter of serial data into the individual jitter components, random jitter (RJ), and deterministic jitter (DJ) as shown in Jitter Components. ADS jitter analysis leverages the techniques from the DCA-J, equivalent-time sampling, and the Infiniium DSO80000 real-time oscilloscopes.

###### Jitter Components

### Definitions

BER |
Bit Error Rate |

DCD |
Duty Cycle Distortion. Derived from the Composite DDJ Histogram graph. It is the absolute value of the difference between the mean of the histogram of the rising edge positions and the mean of the histogram of the falling edge positions. |

DDJ |
Data Dependent Jitter. DDJ is the difference in the position of the earliest edge (rising or falling) and the latest (rising or falling) edge. If DCD = zero, DDJ = ISI. If ISI = zero, DDJ = DCD. |

DDJ _{pp} |
Data dependent jitter, peak-to-peak value of the jitter that is correlated to the data pattern. It is the difference in the position of the earliest edge (rising or falling) and the latest (rising or falling) edge. If DCD=0, DDJ is just ISI. If ISI=0, then DDJ is just DCD. |

DJ |
Deterministic Jitter. DJ is bounded by a finite magnitude. It can be broken into jitter which is correlated to the data sequence and jitter that occurs independent of data. |

DJ( δδ ) |
Delta-Delta Deterministic Jitter of the bimodal equivalent model used to represent all aggregate deterministic jitter as defined in the dual-Dirac model for total jitter. Deterministic jitter is defined by the dual-Dirac jitter model as all those components of total jitter that do not fit a Gaussian probability density function. It is given by the time delay separation of the two delta functions. |

ISI _{pp} |
Inter-Symbol Interference peak-to-peak (p-p) range of the jitter that is correlated to rising edges or the jitter that is correlated to falling edges (whichever is greater). ISI is the largest of the difference between the earliest falling/rising and latest falling/rising edges, determined from measuring the average position of each bit in the pattern. When doing a jitter analysis if the rising or falling edge modes are selected, then only the specified edges are used in the calculation of ISIpp. |

MinSeqDDJ |
Minimum number of sequences needed for a successful DDJ separation. |

MinNTIEs |
Minimum number of TIEs that are needed if the corresponding number of Nbps is used. |

MinNSeqs |
Minimum number of sequences that can be used for given NTIEs. |

MaxNSeqs |
Maximum number of sequences that can be used for given MinSeqsDDJ. |

Nbps |
Number of bits per sequence |

Nbpp |
Number of bits per pattern |

NTIEs |
Number of TIEs |

NumSeqs |
Number of sequences |

Nwpps |
Number of whole patterns per sequence |

PJ |
Periodic Jitter. PJ represents all of the periodic jitter that is uncorrelated from the data pattern. There are 2 types: |

PJ( δδ ) |
Periodic Jitter delta-delta, is the jittered magnitude required to make RJ PDFs match the Dual-Dirac model with the measured or simulated RJ and PJ. |

PJ _{rms} |
The root-mean-square value of the uncorrelated periodic jitter. |

RJ |
Random Jitter. RJ follows a Gaussian distribution and is represented by the rms value of the RJ distribution, RJ _{rms} . RJ is the baseline noise floor of the aliased power spectrum. Peaks (anything above a particular threshold) are identified and removed. |

RJ _{rms} |
Random Jitter follows a Gaussian distribution. RJ is the baseline noise floor of the aliased power spectrum. Anything above it is periodic jitter and is removed in calculating RJ. |

TJ |
Total Jitter. TJ is interpreted as total eye closure at a specified BER (10-12 default). If the closure threshold is the default and TJ=50ps, the likelihood that and edge will be 25ps late or 25ps early is 1 in a billion. |

TJ _{pp} |
The peak-to-peak value of the total jitter calculated at a specific bit error rate (BER). The BER level specified as one of the arguments during jitter analysis identifies the specified BER for which the TJ value was calculated. This TJpp value is calculated as an estimate of the true total jitter, as defined by the dual-Dirac jitter model. |

## Jitter Analysis Process

This section describes steps involved in jitter analysis.

### Time Interval Error

The first step in the jitter analysis/decomposition process is finding the time interval error (TIE), which is the time difference between the serial data signal relative to a reference signal (usually a clock signal) as shown in Time Interval Error. TIE is then used in the jitter decomposition.

###### Time Interval Error

### Sub-Sampled Decimation for DDJ Separation

After the TIE data has been calculated, the next step is DDJ separation. Jitter analysis can be done on periodic or arbitrary data. Currently, only periodic data is supported. In order to decompose jitter, the TIE calculated is associated with the specific bit in the source signal's logical bit sequence. The TIE data is decimated into sub-sampled TIE data, where the value in the sub-sampled sequence corresponds to a specific bit within the pattern. The number of original samples skipped during decimation is a function of the RJ bandwidth. The narrow-band mode maximizes the decimation ratio, and the wide-band minimizes the decimation. The next step is to perform a FFT on the sub-sampled data. The first value of each jitter spectrum (DC component) is the DDJ for the particular bit of the repeating pattern.

### RJ PJ Separation

Once the DDJ component has been subtracted from TJ, the remaining jitter spectrum is comprised of RJ and PJ. The power spectrum density (PSD) of the RJ/PJ spectrum is calculated. All of the individual RJ/PJ spectrums are averaged together (as well as averaged with spectrums from previous sequences) to form the averaged PSD (APSD). All APSD's frequency components that have a value above a threshold are removed as PJ. The remaining APSD are then combined to obtain RJrms. Refer to Reference 1 in References for more details.

## Viewing Results

ADS provides a Jitter Analysis FrontPanel as part of the Data Display. For information on viewing Jitter Analysis simulation results, see "Jitter Analysis FrontPanel" in the *Data Display* documentation.

BER Bathtub Graph

###### Bathtub

The BER Bathtub graph plots the sampling time (in UI) of a serial data signal on the X-axis versus bit error rate on the Y-axis. The trace in red represents BER values that are calculated directly from the TIE data, and the trace in blue represents BER values that are extrapolated using the calculated values of RJ and DJ.

The BER value for the TIE data is calculated by integrating the TJ Histogram. The extrapolated values are obtained from the Dual-Dirac model of the way RJ and DJ combine into a CDF. RJ is modeled as a Gaussian distribution with standard deviation RJ, and DJ is modeled as two Dirac-Delta functions, separated by distance DJ. This function is basically the integral of the function defined by Dual-Dirac PDF model, except that because this is intended to model BER curves, this CDF has been modified to peak at the transition density rather than 1.0, for a maximum BER equivalent to the transition density.

The Q of BER bathtub graph plots the sampling time (in UI) versus the Q of BER.

###### Q of BER Bathtub

#### Jitter Histograms

##### TJ Histogram

###### Total Jitter (TJ) Histogram

The Total Jitter (TJ) Histogram shows the combined Random Jitter (RJ), Periodic Jitter (PJ) and Data Dependent Jitter (DDJ) probability density functions. The TJ histogram is calculated by cross-correlating the RJ, PJ histogram with the DDJ histogram. It is the a histogram of all of the measured jitter, both correlated to the data pattern and uncorrelated to the data pattern, combined in a single histogram. The graph's horizontal axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected.

##### RJ PJ Histogram

###### Random Jitter, Periodic Jitter (RJ, PJ) Histogram

The RJ, PJ Jitter Histogram shows the histogram of all uncorrelated jitter. The graph's horizontal axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected.

##### Composite TJ Histogram

###### Composite TJ Histogram

The Composite TJ Histogram shows separate graphs of Total Jitter (TJ), Data-Dependent Jitter (DDJ), and the combined histogram of uncorrelated Random Jitter (RJ) and uncorrelated Periodic Jitter (PJ). The graph's horizontal axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected.

##### Data Dependent Jitter Histogram

###### Data Dependent Jitter (DDJ) Histogram

The Data Dependent Jitter (DDJ) histogram displays the jitter that is correlated to the data pattern. The graph's horizontal axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected. For data-type source waveform signal, the mean of the histogram of DDJ from all edges is always equal to zero.

##### Composite DDJ Histogram

###### Composite Data Dependent Jitter (DDJ) Histogram

The Composite Data Dependent Jitter (DDJ) Histogram shows three histograms of correlated jitter based on data from all edges, rising edges, and falling edges. The peak-to-peak spread of the all-edges histogram represents the DDJ. The peak-to-peak spread of the rising-edges histogram or the falling-edges histogram, whichever is greater, represents Inter-Symbol Interference (ISI). The difference between the mean of the rising edge positions and the mean of the falling edge positions represents the Duty Cycle Distortion (DCD). The graph's horizontal axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected.

#### DDJ versus Bits Graph

###### Data Dependent Jitter (DDJ) versus Relative Bit Position

The graph of Data-Dependant Jitter (DDJ) versus Relative Bit Position shows relative bit position on the horizontal axis. The vertical axis indicates negative time for samples that occur earlier than expected and positive time for samples that occur later than expected.

The bit numbers displayed on the horizontal axis are relative values only and may change each time the logical bit pattern of the source waveform is recalculated.

#### RJ PJ Spectrum

###### RJ, PJ Spectrum Graph

The RJ, PJ (Random Jitter, Periodic Jitter) Spectrum graph shows the discrete Fourier transform of the combined RJ and PJ. The vertical axis represents the magnitude of each spectral jitter component and the horizontal axis identifies the frequency. The displayed magnitude spectrum is calculated independently for each sequenced waveform and then averaged with magnitude spectrums from previous sequences.

The frequency resolution of the RJ, PJ Spectrum is improved by increasing Nbps, sequence record length. However, increasing the Nbps can significantly affect calculation time. Overall calculation time can be improved by not displaying the RJ, PJ Spectrum graph (not using MeasType equal 4).

### References

*Precision Jitter Analysis Using the Agilent 86100C DCA-J*- Agilent Literature Number 5989-1146EN*Jitter Analysis: The dual-Dirac Model, RJ/DJ, and Q-Scale*- Agilent White Paper 5989-3206EN*MJSQ - Methodologies for Jitter and Signal Quality Specification*- T11.2/Project 1316-DT*Analyzing Jitter Using Agilent EZJIT Plus Software*- Application Note 1563*Selecting RJ Bandwidth in EZJIT Plus Software*- Application Note 1577*EZJIT and EZJIT Plus Jitter Analysis Software for Infiniium Serial Oscilloscopes*- Data Sheet 5989-0109EN- U
*nderstanding Jitter and Wander Measurements and Standards*- 5988-6254EN *Jitter Separation - 50 Mb/s to Over 40 Gb/s Using the Agilent 86100C Infiniium DCA-J,*whitepaper, Agilent Technologies, Inc. http://www.eeplace.com/dm/2802/tw/DCAjwhitepaper3.pdf

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