Review on jitter terminology and definitions

Measurement 145 (2019) 264–273

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Review on jitter terminology and definitions E. Balestrieri ⇑, F. Picariello, S. Rapuano, I. Tudosa Department of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy

a r t i c l e

i n f o

Article history: Received 8 January 2019 Received in revised form 9 April 2019 Accepted 13 May 2019 Available online 21 May 2019 Keywords: Jitter Wander Phase noise Definitions Terminology

a b s t r a c t Jitter is a crucial parameter in digital and analog electronics and particularly in RF communication systems as it can seriously affect their proper performances. Unfortunately, several different approaches for defining jitter and methods for measuring it have been developed depending on the particular system and application. This can lead to misconceptions and setup dependent results. In the paper a classification scheme concerning jitter terminology is proposed to provide an overview of the different existing jitter terms that can help in the perspective of finding a way to carry out a harmonized standardization of the jitter measurements. Ó 2019 Elsevier Ltd. All rights reserved.

Contents 1. 2. 3. 4.

5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jitter Standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jitter classification from literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Jitter signal based terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Jitter types from signal parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. Jitter types from source models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3. Phase and amplitude jitter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4. Jitter and wander . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5. Jitter and phase noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Jitter system based terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Jitter terminology for systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Jitter terminology for components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction In digital or analog electronic systems, as well as in RF communication systems, jitter can seriously affect signal integrity leading to, for example, a reduced signal-to-noise ratio (SNR) or effective ⇑ Corresponding author. E-mail addresses: [email protected] (E. Balestrieri), fpicariello@unisannio. it (F. Picariello), [email protected] (S. Rapuano), [email protected] (I. Tudosa). https://doi.org/10.1016/j.measurement.2019.05.047 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

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number of bits (ENOB) in analog-to-digital converters (ADCs), or an increased bit error rate (BER) in digital electrical and optical communication channels [1]. Jitter occurs in many different parts of digital systems as for example the jitter of data with respect to clock in synchronous protocols or the jitter of the clock signal in clock data recovery (CDR) applications [2]. Every circuit element generating, conveying and receiving signals can introduce jitter. As a result, jitter can affect the whole system and understanding how much jitter is introduced by each element of a system is essential to foresee the overall system performance [3].

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This article has started introducing jitter without defining it, because of there are many misconceptions about what exactly jitter is, and there is often a strictly dependence of jitter definition by the specific application. This situation is not the best possible prerequisite for a correct measurement. It is well known, in fact, that a clear and objective definition minimizes the intrinsic uncertainty, also called definition uncertainty [4], that is the basic component of any measurement uncertainty. That is the reason for long debates about terminology in the metrology field. An unambiguous definition of a quantity is also the first step to design reference standards to create a calibration chain to the main measurement units. Currently a universal accepted definition of jitter, suitable for all applications is missing [5–7]. For this reason, the first aim of this paper is to depict the current situation of the jitter terminology discussing its current issues in order to highlight the needs for a standardized terminology. Most often, the term jitter expresses the deviation from the ideal timing of an event. The exact meaning of ideal timing, as well as the meaning of actual timing, and the type of event may change depending on the application. The event could be referred to a signal, for example, the rising or falling edge of a clock waveform, the optimum sampling of an non return to zero (NRZ) encoded waveform, the differential zero crossing, or something else [8]. Jitter can be caused by a great variety of processes, as for example noise (thermal noise, shot noise, dispersion), system non idealities (spurious of the reference signals, crosstalk, duty cycle distortion, radiated or conducted signals), and data transmission (impedance mismatch, receiver detector characteristics, inter symbol interference (ISI), CDR design, pseudo random binary sequence generation). Jitter can be classified as random and deterministic, bounded and unbounded, correlated and uncorrelated, periodic and nonperiodic, data-dependent or not, etc. [9]. Furthermore, different terms related to jitter are used by different application engineers, as for example phase noise and wander. Since a standard technique able to cover every measurement case is missing, multiple measurement methods have been developed to measure the specific jitter aspect of interest. Consequently, measuring jitter with different setups by different test suppliers can lead to different results, even operating on the same system [10]. Except for some cases related to specific technical fields, knowing how accurate jitter measurement are, is very hard, as a unique well-established cross-field reference standard does not exist yet, as well as a comprehensive guide able to address in the right standard choice and to carry out compatible results [10,11] as reported in [4]. Issues can arise in the design of systems that include several components very different from each other, due to the jitter definitions and measurement methods strictly related to the specific application and well established in a given field. Finally, the comparison of improvements in the measurement methods can be a very difficult task too, due to the lack of a universally accepted comprehensive guide to jitter measurement [10]. For such reasons, the second aim of this paper is to present a potential classification of the existent jitter terminology looking at the definition similarities to cluster them in small groups that are as much application independent as possible, in order to ease the future standardization efforts. According to the previously stated aims, this paper introduces general aspects about jitter related terminology. In particular, a brief review of jitter units of measurement and the existing standards is first presented. Then, a classification scheme concerning jitter terminology is proposed to provide an overview of the different existing jitter terms.

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2. Measurement units Reflecting the different approaches to jitter, a number of different measurement units can be found in literature to quantify it. Since it most frequently refers to a time variability, time units or phase angle units are mostly used as reported below. Absolute time: jitter can be expressed in units of time ‘‘describes the magnitude of the jitter” [12]. Unit intervals (UIs): ‘‘one UI is one cycle of the clock frequency, which is the normalized clock period. Jitter expressed in UIs represents the magnitude of the jitter as one UI decimal fraction” [12]. Degrees: jitter can be expressed in degrees ‘‘describes the magnitude of the jitter in units of degree for which one cycle equals 360” [12]. Relative time: jitter can be expressed ‘‘in units of radians or unit intervals squared, which is often expressed in decibels relative to one cycle squared” [12]. In the telecommunication field, the unit used for jitter is usually the UI. It is possible, in fact, in this way, the jitter amplitude comparison at different hierarchical levels in a digital transmission system, being jitter normalized to the clock period and therefore independent of bit rate [13]. In microprocessor applications, instead, absolute units as for example picoseconds are preferred [14]. A peak-to-peak value defined as ‘‘the maximum to minimum time deviation amount” is the jitter describing how much a clock edge varies in time in [15]. If the sources of noise are characterized by a Gaussian distribution peak-to-peak values cannot be determined [16], therefore the standard deviation of the jitter distribution has to be considered in the calculation of the amount of jitter, or the root-mean-square (rms) value [17]. To identify an rms value, usually the measurement unit symbols are marked with a subscript rms: psrms or UIrms. The symbols of units for peak-to-peak jitter measurements, instead, are usually marked with the subscript p-p: psp-p or UIp-p [8].

3. Jitter Standards There are many Standards dealing with both components and systems and including jitter published by different organizations: the International Electrotechnical Commission (IEC), the Institute of Electrical and Electronics Engineers (IEEE), the American National Standards Institute (ANSI), the International Telecommunication Union (ITU), the Joint Electron Device Engineering Council (JEDEC). It is possible to find documents with general use, as the International Electrotechnical Vocabulary (IEC 60050) [18], the IEC Standard for Transitions, pulses and related waveforms Terms, definitions and algorithms (IEC 60469) [19] and the IEEE Standard for Transitions, Pulses, and Related Waveforms (IEEE 181) [20], or documents focused on a more specific field, as the Standard for Radar Definitions (IEEE 686) [21], the Standard for a High-Performance Serial Bus (IEEE 1394) [22] or the Standard for Terminology and Test Methods for Analog-to- Digital Converters (IEEE 1241) [23]. The efforts of the single standardizing entities to harmonize definitions in one application field often contributed to raise the confusion in fields where more Standards are pertinent. The existence of different terms and meanings of jitter depending on the application is well shown in the IEC 60050 ‘‘International electrotechnical standard” [18]. Instead of providing a comprehensive definition, this Standard relates the jitter definitions to the particular application area. In the ‘‘broadcasting: sound, television, data” area, the term frame bounce is the ‘‘jitter affecting a television picture in a vertical direction”, while the term jitter is ‘‘short-term non-cumulative variations in the significant instants of a digital signal from their ideal positions in time”. In the fields concerning electrical and electronic measurement, the

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time base jitter is an ‘‘unwanted fluctuation of the position of the display, or a part of it, in a direction parallel to the sweep”. Jitter is defined as a ‘‘perceptible instability of the time base of a reproduced video signal” in the ‘‘recording and reproduction of audio and video” area. Finally, jitter is a ‘‘sudden, small, irregular departures from the ideal value of a characteristic of a signal, such as the phase, pulse duration or magnitude” in the area devoted to the oscillations, signals and related devices. It is clear that those definitions have not been designed to reduce the definition uncertainty, basic source of measurement uncertainty. It is also possible to find the same figure of merit with different meanings, referring to different physical quantities related to each other. For example, in [18] the transit-time jitter for a photo-multiplier is ‘‘the variation in the times of occurrence of a stated point on the output current pulses arising from the application to the photocathode of delta light pulses, each giving rise to not more than a single photoelectron”. In the same Standard the transit time jitter for a photomultiplier tube, instead is the ‘‘variation in the transit times corresponding to different photoelectrons”. Jitter definitions can also differ if they are mainly concerned with the effects of a phenomenon, like the deviation from the sampling instants in the IEEE 1057 [24] and the IEEE 1241 [23], or if they are mainly concerned with the characteristics of the signal as for the IEEE 181 [20], where jitter is ‘‘the variation (dispersion) of a time parameter between successive cycles of a repetitive signal and/or between successively acquired waveforms of a repetitive signal for a given reference level instant or duration”. To deal with the vast availability of different meanings of jitter in different applications the IEEE Instrumentation and Measurement Society TC-10 ‘‘Waveform generation, measurement and analysis” is developing the IEEE Standard Project P2414 on Jitter, Wander and Phase Noise. The main aim of the Standard under development is to provide general models for jitter that can be used as reference for several applications without ambiguity. Along with the ambiguity of jitter terminology another issue arises when the Standards provide measurable jitter limits without providing at the same time satisfactory information to orientate in the proper choice of the jitter type most crucial for the specific application [25]. Finally, unlike many other measurements, there is no certified, traceable ‘‘jitter” standard [11]. It is well known, however, that the existence of an uninterrupted traceability chain is a prerequisite for the compatibility of measurement results taken in reproducibility conditions. Finally, without a traceable standard for jitter, it is impossible to determine the accuracy of a jitter measurement unless an alternative measurement method is adopted [11].

4. Jitter classification from literature The literature proposals dealing with jitter terminology include much more than the Standard sources. Several papers and application notes coming from researchers or equipment manufacturers are focused on jitter measurement and/or mitigation. When they do not refer to definitions coming from Standards, they introduce their own ones. Since before designing measurement methods it is necessary to focus on objective definitions based on well identified physical quantities this paper proposes a general classification of jitter definitions that supersedes that proposed in [26]. Since most of jitter definitions from literature depend on a signal characteristic, as for example clock and data signals, the proposed jitter terminology classification include a jitter signal based branch, as shown in Fig. 1. The classification of definitions can rely on an approach based on (i) the direct influence of jitter on the signal model, where the different types of jitter lead to differently distorted signal models; or on (ii) the influence of jitter on the system

Fig. 1. Jitter terminology classification scheme.

model, where a system can be seen as a source of jitter or can modify the quantity of jitter on signals. The signal based approach includes both jitter terminology related to specific parameters of the signal, as the period and cycle to cycle jitter, and to jitter source model, as for example random and deterministic jitter. Moreover, jitter can be measured also in the time as well as in the amplitude and frequency domains [26]. The system based approach does not refer to the measurement of jitter but on its relation with electronic systems or their components as data converters, PLL, oscillators, seen as sources, targets or transmitting media for jitter. According to those two points of view the proposals can be grouped as described in the next three sub-Sections. 4.1. Jitter signal based terminology To clarify jitter terminology, it can be useful to differentiate between jitter types oriented to model the jitter effects on given signal parameters or characteristics and those oriented to the detection and separation of jitter sources, often called components. Hence, the next two subsections are focused on the most used jitter types and components. Provided that a figure of merit definition has been chosen, jitter analysis can be carried out in time domain as well as in the frequency domain, each domain providing useful information about jitter. In the following sub-section, jitter parameters in the time domain as phase and amplitude jitter will be first presented. Then two parameters coming from frequency domain analysis and related to jitter, will be discussed in separate sub-sections: wander and phase noise. The first one is the jitter arising at low frequency, the second one concerns a class of signals for which the phase can be defined, representing the same mechanism of noise the jitter comes from in the time domain, but by means of a different representation or manifestation. 4.1.1. Jitter types from signal parameters Period jitter, cycle to cycle jitter and the time interval error are examples of types of jitter coming from signal parameters. In order to better clarify the differences, consider the example in Fig. 2. The effect of jitter on the clock signal in figure is the variability of the actual time instants of the rising and/or falling edges in the waveform compared to their ideal counterparts. The period jitter, obtained by comparing the intervals P1, P2 and P3 in Fig. 2, consists in the variability of the clock cycle period on several periods in the waveform, referring to the rising or falling edges. The cycle to cycle jitter, pointed out by C2 and C3, derives from the comparison of any two contiguous cycle durations. The time interval error (TIE), that can be seen in Fig. 2 by TIE1 through TIE4, represents how much each active edge of the clock departs from its ideal position [27]. Period jitter is object of analysis mainly for the clock

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Fig. 2. Period (P1, P2, P3), cycle to cycle (C2, C3) and time interval error (TIE1, TIE2, TIE3, TIE4).

circuitry design, to provide the most accurate, predictable frequency and overall stability. Short clock periods lead to instantaneous frequency increases, and data errors can arise due to violation of the allowed parameter values as for example setup and hold time. Therefore, it is crucial, in this case, measuring and minimizing both the period jitter and the cycle to cycle jitter [25]. In the case it is important to analyze the transmitted data stream behavior when a phase-locked-loop (PLL) is used to recover the reference clock from the data signal, TIE measurements are convenient. If the data stream bit rate changes to fast respect the PLL response time, the TIE will accumulate during all the cycles spent by the PLL to catch up the data stream again [25]. In order to give an idea of how complicated can be to assign a practical meaning to a term, it can be observed that period jitter can be defined as ‘‘the variation of the instantaneous period from the constant mean period” [28] or ‘‘the difference between the longest period and the shortest period” [29], (also known as peak-to-peak period jitter [30]), or ‘‘between measured clock periods”, as well as, ‘‘the difference between half-cycle threshold crossings of a single half-cycle over a random sample of half cycles” (in this case named half period jitter) [31,32]. In addition, period jitter can be defined as ‘‘the maximum deviation of each single period of the jittered clock from that of the ideal clock”, but the ideal period in real world applications is very hard to be quantified, therefore the average period is considered in some definition in the place of the ideal period [33]. In particular, JEDEC standard JESD65B [31] defines period jitter as ‘‘the deviation in cycle time of a signal with respect to the ideal period over a random number of cycles”. It is easy to observe that those definitions would provide different results when applied to the same example waveform in Fig. 2. The number of cycles selected for this measurement ‘‘should be significant (1000 to 10,000) to have sufficient confidence in the measurement” [32,34]. However, measuring each period of the jittered waveform is not always practicable, therefore, some definitions limit the period jitter determination over ‘‘all measured clock cycles” [35] that can be ‘‘randomly selected” [33] as indicated in the JEDEC definition. Cycle to cycle jitter, sometimes called adjacent cycle jitter [35], can be defined as simply the difference between adjacent clock periods [36], without specifying which and how many clock periods must be considered, as well as the maximum difference [37], sometimes also called peak cycle to cycle jitter [30]. As in the case of the period jitter also for the cycle to cycle jitter the number of the cycles considered for its calculation should be significant and the cycle pairs can be randomly selected [31–33]. N cycle to cycle jitter and half period cycle to cycle jitter are other terms used to indicate respectively ‘‘the variation between the output clocks’s first and Nth rising edges” where the value N depends on the particular application, or ‘‘the variation in time of a signal between adjacent intervals, where each interval is N cycles (i.e., periods) long, over a random sample of adjacent interval pairs”, and ‘‘the

variation in time of a signal between matching half-periods between adjacent periods over a random sample of adjacent matching half-period pairs”[32]. Time interval error is sometimes called accumulated or phase jitter [30], even if the term phase should be used only for specific type of signals, and can be expressed as the time difference, at a given frequency, between the measured clock rising or falling edge and its ideal position in time. The same term is used also to indicate the maximum deviation [37], raising some possible confusion. Accumulated jitter and the long term jitter, defined quite similarly to the TIE as ‘‘the variation in the time difference between the edge of a reference clock and the same edge of the delayed n clock cycles”, are often used interchangeably [38]. As it can be seen from above that the previous type-based classification of jitter doesn’t take in account the source of the signal distortion, thus the random or deterministic nature of the deviations of the significant instants of interest in the signals is not considered. Nevertheless, there are so many terminology variations that it’s difficult to identify a parameter of the signal starting from the term used only. 4.1.2. Jitter types from source models Jitter decomposition aims at identifying and separating the phenomena that generate the jitter by using a type-based classification referring to elementary jitter models called components. Each component is modeled from one source considering the others negligible. Results are important to find out a jitter budget and it sources in order to discover, for example how much jitter is coming from a device under test, how much jitter is being coupled from the power supply, etc. [39]. Regarding the components, the total jitter can be divided in: random and deterministic jitter (RJ and DJ) as in Fig. 3. Unbounded and bounded jitter sources are related to respectively RJ and DJ [40]. Bounded jitter sources arise from mechanisms due to systematic and data-dependent jitter source, as for example crosstalk, systematic modulation, reflections, electromagnetic interference, etc., reaching maximum and minimum time instant or interval deviations within an identifiable time interval of analysis [40,41]. In the case of unbounded jitter sources, on the contrary, a maximum or minimum deviation are not achieved within any analysis interval, since the maximum jitter amplitude theoretically approaches infinity. Unbounded jitter arises from several sources of random noise [36], as for example random modulation, flicker, shot and thermal noise, etc. [35,41,42]. Although RJ is generally broken into Gaussian and non-Gaussian distributions, since most unbounded noise sources have a Gaussian distribution, this kind of jitter is in most cases modeled using this last distribution [43]. DJ can be separated into subcategories according to the different source that has originated it [26], as shown in Fig. 3. Time deviations depending on the used data pattern are regarded as data dependent jitter (DDJ), an uppermost form of DJ [44], also recognized as pattern dependent jitter [14]. DDJ can be

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Fig. 3. Jitter component classification.

further divided in: duty cycle distortion (DCD), arising from the rising and falling edge timing differences or single ended system ground shifts, and inter-symbol interference (ISI), arising from limitations of component and system bandwidth. DJ components are also periodic jitter (PJ), sometimes called sinusoidal jitter [34], and bounded uncorrelated jitter (BUJ). Periodic variations of signal edge positions over time are expressed by the first parameter, while the second one is typically caused by on-chip random logic switching or coupling from adjacent data-carrying links [43]. PJ and BUJ are data uncorrelated, differently from DDJ and its subcomponents that are correlated with the data pattern [35]. In general, two random variables are correlated if changing one of them, makes the other change too. Jitter is data correlated if the transmitted data signal or the data rate influence its amplitude [45]. Signals from a switching power supply coupling into the data or system clock signals can be a good example of uncorrelated PJ, since it is not time-correlated with either the clock or data signal if based on a different clock source. But, coupling from an adjacent data signal based on the same clock or a clock at the same frequency is, instead, an example of correlated PJ [40]. Therefore, PJ can be either correlated or uncorrelated to the data signal, but most PJ is uncorrelated to the data carrying signal therefore it is mainly considered in this way in jitter component classification. As quoted above, RJ has a Gaussian probability density function (PDF) which is unbounded and can be completely defined by means of its mean and standard deviation. RJ peak-to-peak measurements can be ambiguous in case of additional boundary conditions are not considered [8]. DJ is measured in terms of peak-to-peak values since it has been defined

to have upper and lower bounds. The computation of the worst case overall peak-to-peak jitter can be simply carried out as an addition of all the peak-to-peak jitter components [8]. In order to compute TJ (total jitter), resulting from the combination of all RJ and DJ components, in [8] it is proposed to convert all rms jitter (RJ) numbers to peak-to-peak values. In this way all of the peak-to-peak jitter components can then be added together to carry out a peak-to-peak TJ. Converting rms jitter to peak-topeak jitter can be done by defining arbitrary limits on the RJ Gaussian PDF, depending, for example, on the BER required by the system [8]. Since the RJ and DJ have different statistic nature it would be more appropriate to combine distributions or standard deviations, by following the approach described in [46], for example. 4.1.3. Phase and amplitude jitter Jitter can come from both time deviations respect to the ideal zero-transition time instant, known as phase jitter, and digital system signal level variations, often called amplitude jitter [47] even if this can be seen simply as additive noise (Fig. 4). Phase and amplitude jitter are visible singularly [47] and joined [48] in Fig. 4. IEEE std 743 [49] includes the phase jitter definition similar to the jitter definition reported in IEEE std 181, but referred to holding tone or combination of tones. According to the IEEE standard the amplitude jitter focuses on the cause of jitter as the incidental amplitude modulation, interference and noise [49]. 4.1.4. Jitter and wander Wander is a parameter mostly adopted in the telecommunications field. It can be defined as ‘‘long term variations in the

Fig. 4. Amplitude and phase jitter (on the left); phase and amplitude jitter together (on the right).

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significant instants” [50]. ITU-T G.810 [51] provides the limit at 10 Hz between jitter and wander. This distinction comes from the fact that unlike higher frequency jitter, the edge position variations due to wander do not lead to bit errors. The recovered clock can, in fact, easily follow the slow changes in the edges caused by wander. However, over longer time intervals wander amplitudes can gather together producing very large amounts of deviation from the ideal edge [52]. In case of daisy-chains of time digitally clocked devices, wander can arise. Due to the random nature of the jitter patterns in separate devices, small errors can add up as the clock is passed on, and propagate through the device belonging to the chain, leading in short time to large errors, as shown in Fig. 5 [53]. In Table 1 a comparison between jitter and wander is shown including consequences for test equipment [52]. In particular, wander test equipment requires an external reference clock source of high precision [52], a clock extracted from the data signal, instead, is the reference used in the case of jitter measurement [13]. The absolute magnitude in ns is the measurement unit of wander amplitude, differently from the case of jitter, for which the UI unit is typically adopted. In addition, long wander test times (millihertz range) are required due to the extremely low frequency components [52]. Table 1 Jitter and wander comparison [52].

Frequency range of edge variations Primary disruption Reference clock source for measurement Unit for amplitude Test times

Jitter

Wander

>10 Hz

0–10 Hz

Cause bit errors Not required

Synchronization problems Absolutely necessary

UI (Unit Interval) Minutes

Ns Long-term measurement (hours, days)

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4.1.5. Jitter and phase noise Jitter can be analyzed in the time domain but most real world applications operate within a certain band of frequencies and therefore the jitter effect only needs to be measured in that band. Measuring jitter over a particular frequency band, requires to carry out a frequency domain changeover [54] providing a figure of merit known as phase noise. For example, while jitter is required in digital systems, phase noise is favored in radio frequency (RF) communications [55]. Fig. 6 shows the phase noise dependence on the noise power spectrum, P, around the fundamental frequency. A Dirac-delta function at the fundamental output frequency, f0 represents the spectrum in the ideal case of a noiseless sine wave. In presence of phase noise, the output spectrum spread around the fundamental frequency as shown in Fig. 6 [56]. Phase noise is specified ‘‘in dBc/Hz at a given offset from the fundamental frequency (dBc is the level in dB with respect to the carrier)” [57] and it is defined from ‘‘the ratio of the power in a 1 Hz bandwidth at the offset frequency to the total power of the carrier” [57]. The phase noise values in dBc are obtained for a continuous moving 1 Hz band over a frequency offset range of interest, as shown in Fig. 7, generating a phase noise plot [58]. The time domain is usually associated to the term jitter, while the frequency domain is generally related to phase noise [59]. However, sometimes the two terms are used interchangeably [59,60]. Although jitter and phase noise are related, closed-form mathematical expressions do not exist for describing the conversion between them. Anyway, in analytic environments as for example the design software, good approximations are used [61]. In theory, with faultless measuring instruments, the integration from the carrier out to an infinite offset of the phase noise, on the same signal and measurement conditions, equal numeric amounts should be obtained for both the jitter and the phase noise. Unfortunately,

Fig. 5. Wander resulting from small variations in the clock frequency (jitter) that can add up as the clock is retransmitted from one device to the next.

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Fig. 7. Phase noise plot generation [58].

due to the existing practical test equipment limitations, a difference between the two parameter measurements will always arise [59]. Moreover, the conversion between phase noise and jitter by integration cannot be applied when jitter presents a time varying behavior, as in the case of oscillators. In this case, in fact, the variance and the standard deviation defined in classical statistics diverge and jitter is not correctly characterized by the classic variance [62–64]. Anyway, such phenomena have been modeled successfully in terms of Allan deviation or variance, and specifically by its modified version [62-64]. The Allan variance is defined as:

1 2







r2y ðsÞ ¼ E y2  y1

2 

ð1Þ

where y is the frequency deviation normalized to the nominal fre



quency, y1 e y2 are the average values of y over consecutive periods s. Allan deviation is the square root of the Allan variance, r2y ðsÞ. It has been shown that the Allan deviation can be used for characterizing the behavior in the frequency domain of the phase noise affecting oscillators [65–67]. 4.2. Jitter system based terminology Measuring the equipment response to jitter is no less important than the characterization of jitter itself, when concerned about systems. For this reason, jitter specifications for systems are presented in subsection A, while the subsection B is focused on jitter specifications for components. This class of jitter terms, therefore, is focused on the effects of systems or components on input signals. 4.2.1. Jitter terminology for systems In order to assess the response to jitter of a system, a calibrated stimulus to the system input is considered the essential element on which the definitions included in this subsection are built [48]. When looking at systems the term jitter corresponds to a definition taken from the previously presented types or even an application

specific one. Not always, the application specific definition is provided within the same document including the system specifications, therefore this approach adds potential confusion to the definition and the measurement of the figure of merit. The output jitter is ‘‘a measurement of the jitter present on a system output, generated within a single piece of equipment (jitter generation or intrinsic jitter), or built up as the signal traversed a large network (network jitter)” [13]. Output jitter is mainly provided when analyzing transmitting subsystems, as, for example, line drivers, limiting amplifiers, regenerator CDR circuits, serializers and laser drivers [8]. The jitter tolerance can quantify ‘‘the resilience of an equipment to input jitter” [13], defined as ‘‘how much input jitter a system or a device can handle before bit errors occur” [68]. In this way, it is possible to compare results arising from different systems and to write system specifications usually by means of a jitter tolerance mask or template [13,50]. An example of jitter tolerance template is shown in Fig. 8. The template identifies the region over which the equipment must operate without exceeding the allowed degradation in error performance. The pass/fail status is determined by the difference between the template and actual equipment tolerance curve representing the operating jitter margin [50]. Receiving subsystems performance, as, for example, CDR circuits and deserializer performance can be specified by using jitter tolerance [8]. Jitter transfer, often referred to as jitter attenuation [68], determines the amount of jitter in the input signal transferred to the output [8]. Taking into account that excessive jitter attenuation can cause problems with frame slippage and synchronization, jitter attenuation specifications are useful to define an acceptable range of values for a given jitter frequency [68]. Regeneration components performance, including, for example, CDR circuit and data retimers performance can be specified in terms of jitter transfer [8]. 4.2.2. Jitter terminology for components In system design, much attention must be paid in the selection of timing components to meet system performance requirements and providing, at the same time, the lowest jitter and highest system noise margin possible, taking into account that jitter can be added and accumulated by each component of a system [59]. Connectors for electronic equipment, PLLs and oscillators, analog to digital converters (ADCs) and digital to analog converters (DACs) are examples of components aimed at the implementation of several timing functions, and the performance of the system they belong to are compromised by any jitter in their output. Jitter issues related to ADCs and oscillators will be briefly reported as example. Jitter aspects related to other components can be discussed in a similar way but referring to the specific function they are aimed to. High-speed ADC systems strongly depend on the sampling clock performance. Any noise, distortion, or timing jitter on the clock, in fact, can degrade the desired signal at the ADC output [69] resulting in an error voltage dependent from the magnitude of the jitter and the input-signal slew rate [70]. Therefore, the greater the input frequency and amplitude, the more susceptible the ADC is to jitter on the clock source [68]. ADC jitter can be associated to various terms such as aperture jitter, aperture uncertainty, timing phase noise, timing jitter that are used interchangeably. It is ‘‘the standard deviation of the apparent sampling time”, as well as ‘‘the standard deviation of the aperture delay”, being the aperture delay the ‘‘delay from a threshold crossing of the analog-to-digital converter clock which causes a sample of the analog input to be taken to the center of the aperture (the interval during which the input to the ADC affects the output or the weighting function that determines the sampled output from the input signal) for that sample” [23].

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Fig. 8. Jitter tolerance template [50].

Jitter requirements must be taken into account before choosing the clock oscillator for a specific application. Many factors, in fact, can contribute to oscillator jitter as for example device noise, power supply variations, thermal noise, interference coupled from nearby circuits and loading conditions [71]. However, it is often difficult to specify jitter oscillator performance since they can vary according to the frequency and load conditions [72]. Oscillator noise performance is both characterized in the time domain, referring in this case to the term jitter, and in the frequency domain, referring to the term phase noise, since depending on the particular application the first domain can reveal more than the second one and vice versa [73]. For example, in digital systems, oscillator performance is mostly represented by jitter, in RF communications by the phase noise [73]. Due to the number of existing jitter types, selecting and measuring the relevant jitter specification for a given application is critical [74]. As mentioned above, for example, if a clock oscillator is feeding a PLL, the cycle-to-cycle jitter becomes a relevant specification since if it reaches a large value, the PLL may not be able to keep lock [72]. When dealing with setup and hold times, instead, the period jitter becomes critical. Long-term jitter is important for graphics applications since it can lead to picture instability and long-range telemetry applications such as range finders [72]. It is worth to note that, in the case of oscillators, a term phase jitter [75] or RMS phase jitter [58,74] is often used. However, it is not a time domain measurement as it depends on the phase noise. In particular, first a phase noise plot has to be built starting

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from the noise power spectrum plot as described in Sec.4.1E. Then, phase jitter or RMS phase jitter can be extrapolated from the plot as ‘‘an integral function (i.e. area under the phase noise plot)” [58] or ‘‘the integration of phase noise over a certain spectrum and is expressed in picoseconds or femtoseconds” [75]. The integration range, also referred to as the mask, for this type of jitter is an essential qualifier representing the jitter frequency filter specific to the application [74]. The jitter mask specifies the oscillator performance specifically for the system in which it is included, also avoiding its over-specification and providing different weighting at different frequencies [58]. Several jitter masks have been predetermined by industry protocols and can have band-pass, low-pass or high-pass filter profile with roll offs that vary in dB/decade. An example is shown in Fig. 9. The quantification of jitter in the frequency domain makes the phase jitter specification relevant also for serializer-deserializer applications like several baseband digital communications [74]. Timing jitter is an important parameter also for mode-locked fiber lasers. Many emerging applications, in fact, such as photonic ADCs, synchronization of next-generation light sources (such as xray free-electron lasers) and ultrafast electron sources, timing distribution, photonic radars, optical communications and interconnections or low-noise microwave generation rely on ultralow timing jitter optical pulse trains from mode-locked fiber lasers [76–78]. Moreover, due to the correlation between timing jitter and optical comb-line frequency noise, low timing jitter is relevant to construct low-noise optical frequency combs in the frequency domain, too [76]. Gordon–Haus jitter [76,77], quantum jitter [77,79] and pulse-to-pulse jitter [80] are terms related to jitter for this kind of applications. The first, specifically referred to optical fiber communications systems, is ‘‘a timing jitter originating from fluctuations of the center frequency” [81] caused by ‘‘the spontaneous emission noise injected by each optical amplifier into the signal” [82]. Quantum jitter, specifically referred in singlephoton detection, is ‘‘based on the observation of a finite rise time in the quantum probabilistic signal transduction (absorption)” [79]. Pulse-to-pulse jitter, is similar to the general definition of jitter since it is defined as arising from the ‘‘variation in the time delay between successive pulses” [68]. 5. Discussion It is well known that, in order to design correct measurement methods for a given measurand, it should be clearly and unambiguously defined. The definition uncertainty, often called intrinsic uncertainty, in fact, can never be mitigated, unless changing the definition. This basic approach to terminology seems less followed

Fig. 9. Filtered jitter mask [58].

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Fig. 10. Jitter terminology list.

when the measurand is called jitter. As described in the previous Sections, the current situation concerning jitter terminology and definitions suffers from the lack of a universal accepted definition of jitter, as one could expect when talking of a quantity to be measured, that is the ‘‘property of a phenomenon, body, or substance” [83]. Instead there are different jitters for different technical fields. The word jitter is sometimes used to describe a phaenomenon, sometimes it is used to describe the effects of one or more phaenomena on a signal or a system, sometimes it is used to describe a parameter of a signal. As a result, jitter is a broad term to which different meanings can be attributed, different parameters can be referred, different units can be associated. To give an idea of the magnitude of the existing jitter term set, in Fig. 10 a list of parameters taken from the references quoted in this paper is shown. Although, jitter terminology and definition ambiguity could seem a false problem when looking within a specific technical field or even at a specific application, the lack of agreement among international standards observed and presented in the previous Sections surely represents a relevant problem for assuring equipment, system and network interoperability. As a consequence, an effort to harmonize standard jitter definitions is critical in system specifications, product assessment as well as in component requirements. From the presented review of jitter terminology and definitions, that has highlighted the existing analogies, dissimilarities and lacks, some observations can be done about the first steps to be taken to reach the harmonization in the field as described below. Currently, the same parameter can be defined in different ways or addressed with different names as well as not univocally defined, requiring additional assumptions on the parameter that can led to different results even if applied on the same signal or system or component under test. Moreover, the coexistence of different unit of measurement for jitter can make challenging the performance comparison of different timing product datasheets using different units [84]. Therefore, useful information can be derived by ordering the list of definitions and figures of merit, along with their suggested measurement units, referring to the same physical quantity. In this way, connections and similarities among the list elements can be highlighted as the starting point to extrapolate a univocal definition to describe the same measurand. It can be also evaluated the appropriate use of direct or indirect figures of merit. The analysis starting from specific definitions and terms has to be directed at introducing a general framework of definitions and related models. Afterwards, the dependence of jitter terminology and definitions on the specific context and application suggests the need to

map the current list of application-related definitions to the new general ones. Considerations about the choice to focus on the effects of jitter or to generally refer on the signal characteristics have to be done, too. Another open question can deal with the opportunity of including specific procedures rather than general guidance to the uncertainty estimation and statement as well as the choice to focus on the harmonization among the existing standards or a new approach to the matter need to be thoroughly addressed, too. Apart from the current efforts of the TC-10 working group developing the P2414 standard and in spite of the already existing mass of literature proposals there is still space for a lot more research in the field of jitter metrology.

6. Conclusions The proper design, operation, and proof of operation of any digital equipment can be seriously affected by jitter. Nevertheless, a universally accepted specification defining jitter for all applications is still missing. The impact of jitter can vary widely from one application to another. Therefore, several jitter definitions and measurement methods have been developed making difficult to compare jitter measurement or combination of measurement results as well as to assign them appropriate measurement accuracy. This is a serious problem for all devices, systems and networks affected by jitter both in the case they operate singularly and together. In the paper jitter definitions have been presented by means of a classification scheme to put in evidence analogies and dissimilarities as a first step towards of jitter definition and measurement harmonization.

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