In electronics and telecommunications , jitter is the deviation from true periodicity of a presumably periodic signal , often in relation to a reference clock signal . In clock recovery applications it is called timing jitter . Jitter is a significant, and usually undesired, factor in the design of almost all communications links .
55-402: Jitter can be quantified in the same terms as all time-varying signals, e.g., root mean square (RMS), or peak-to-peak displacement. Also, like other time-varying signals, jitter can be expressed in terms of spectral density . Jitter period is the interval between two times of maximum effect (or minimum effect) of a signal characteristic that varies regularly with time. Jitter frequency ,
110-487: A Gaussian distribution , it is usually quantified using the standard deviation of this distribution. This translates to an RMS measurement for a zero-mean distribution. Often, jitter distribution is significantly non-Gaussian. This can occur if the jitter is caused by external sources such as power supply noise. In these cases, peak-to-peak measurements may be more useful. Many efforts have been made to meaningfully quantify distributions that are neither Gaussian nor have
165-433: A digital-to-analog converter , the time between samples varies and instantaneous signal error arises. The error is proportional to the slew rate of the desired signal and the absolute value of the clock error. The effect of jitter on the signal depends on the nature of the jitter. Random jitter tends to add broadband noise while periodic jitter tends to add errant spectral components, "birdys". In some conditions, less than
220-414: A sinusoidal waveform not to be subject to slew rate limitation, the slew rate capability (in volts per second) at all points in an amplifier must satisfy the following condition: where f is the operating frequency, and V p k {\displaystyle V_{\mathrm {pk} }} is the peak amplitude of the waveform, i.e. half the peak-to-peak swing of a sinusoid. In mechanics
275-401: A burst of traffic at a high rate followed by an interval or period of lower or zero rate transmission may also be seen as a form of jitter, as it represents a deviation from the average transmission rate. However, unlike the jitter caused by variation in latency, transmitting in bursts may be seen as a desirable feature, e.g. in variable bitrate transmissions. Video or image jitter occurs when
330-508: A current of 10 amps used for 12 hours each 24-hour day represents an average current of 5 amps, but an RMS current of 7.07 amps, in the long term. The term RMS power is sometimes erroneously used (e.g., in the audio industry) as a synonym for mean power or average power (it is proportional to the square of the RMS voltage or RMS current in a resistive load). For a discussion of audio power measurements and their shortcomings, see Audio power . In
385-409: A de-jitter buffer is equal to the buffering delay introduced before starting the play-out of the media stream. In the context of packet-switched networks, the term packet delay variation is often preferred over jitter . Some systems use sophisticated delay-optimal de-jitter buffers that are capable of adapting the buffering delay to changing network characteristics. The adaptation logic is based on
440-450: A linearly increasing output. If the second stage has an effective input capacitance C {\displaystyle C} and voltage gain A 2 {\displaystyle A_{2}} , then slew rate in this example can be expressed as: where I s a t {\displaystyle I_{\mathrm {sat} }} is the output current of the first stage in saturation. Slew rate helps us identify
495-427: A load of R ohms, power is given by: However, if the current is a time-varying function, I ( t ), this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. If the function is periodic (such as household AC power), it is still meaningful to discuss the average power dissipated over time, which is calculated by taking the average power dissipation: So,
550-451: A meaningful peak level. All have shortcomings but most tend to be good enough for the purposes of engineering work. In computer networking , jitter can refer to packet delay variation , the variation ( statistical dispersion ) in the delay of the packets . One of the main differences between random and deterministic jitter is that deterministic jitter is bounded and random jitter is unbounded. Random jitter, also called Gaussian jitter,
605-409: A measure of how far on average the error is from 0. The mean of the absolute values of the pairwise differences could be a useful measure of the variability of the differences. However, the RMS of the differences is usually the preferred measure, probably due to mathematical convention and compatibility with other formulae. The RMS can be computed in the frequency domain, using Parseval's theorem . For
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#1732858058909660-423: A nanosecond of jitter can reduce the effective bit resolution of a converter with a Nyquist frequency of 22 kHz to 14 bits. Sampling jitter is an important consideration in high-frequency signal conversion, or where the clock signal is especially prone to interference. In digital antenna arrays ADC and DAC jitters are the important factors determining the direction of arrival estimation accuracy and
715-428: A sampled signal x [ n ] = x ( t = n T ) {\displaystyle x[n]=x(t=nT)} , where T {\displaystyle T} is the sampling period, where X [ m ] = DFT { x [ n ] } {\displaystyle X[m]=\operatorname {DFT} \{x[n]\}} and N is the sample size, that is, the number of observations in
770-442: A slew rate is usually expressed in terms of microseconds (μs) or nanoseconds (ns). Electronic circuits may specify minimum or maximum limits on the slew rates for their inputs or outputs, with these limits only valid under some set of given conditions (e.g. output loading). When given for the output of a circuit, such as an amplifier, the slew rate specification guarantees that the speed of the output signal transition will be at least
825-412: Is and the RMS for a function over all time is The RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a sample consisting of equally spaced observations. Additionally, the RMS value of various waveforms can also be determined without calculus , as shown by Cartwright. In
880-458: Is about 340 volts. A similar calculation indicates that the peak mains voltage in Europe is about 325 volts, and the peak-to-peak mains voltage, about 650 volts. RMS quantities such as electric current are usually calculated over one cycle. However, for some purposes the RMS current over a longer period is required when calculating transmission power losses. The same principle applies, and (for example)
935-418: Is denoted f R M S {\displaystyle f_{\mathrm {RMS} }} and can be defined in terms of an integral of the square of the function. In estimation theory , the root-mean-square deviation of an estimator measures how far the estimator strays from the data. The RMS value of a set of values (or a continuous-time waveform ) is the square root of the arithmetic mean of
990-402: Is denoted as either x R M S {\displaystyle x_{\mathrm {RMS} }} or R M S x {\displaystyle \mathrm {RMS} _{x}} . The RMS is also known as the quadratic mean (denoted M 2 {\displaystyle M_{2}} ), a special case of the generalized mean . The RMS of a continuous function
1045-584: Is extremely small compared to parallel bus architectures with equivalent performance, which may have eye openings on the order of 1000 picoseconds . Jitter is measured and evaluated in various ways depending on the type of circuit under test. In all cases, the goal of jitter measurement is to verify that the jitter will not disrupt normal operation of the circuit. Testing of device performance for jitter tolerance may involve injection of jitter into electronic components with specialized test equipment. A less direct approach—in which analog waveforms are digitized and
1100-453: Is the RMS deviation of x {\displaystyle x} from its arithmetic mean x ¯ {\displaystyle {\bar {x}}} . They are related to the RMS value of x {\displaystyle x} by From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the squared deviation (error) as well. Physical scientists often use
1155-478: Is unpredictable electronic timing noise. Random jitter typically follows a normal distribution due to being caused by thermal noise in an electrical circuit . Deterministic jitter is a type of clock or data signal jitter that is predictable and reproducible. The peak-to-peak value of this jitter is bounded, and the bounds can easily be observed and predicted. Deterministic jitter has a known non-normal distribution. Deterministic jitter can either be correlated to
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#17328580589091210-481: Is usually expressed in units of V / μs . where v o u t ( t ) {\displaystyle v_{\mathrm {out} }(t)} is the output produced by the amplifier as a function of time t . The slew rate can be measured using a function generator (usually square wave) and an oscilloscope (CRO). The slew rate is the same, regardless of whether feedback is considered. There are slight differences between different amplifier designs in how
1265-501: The DC component is removed (that is, RMS(signal) = stdev(signal) if the mean signal is 0). Slew rate In electronics and electromagnetics , slew rate is defined as the change of voltage or current, or any other electrical or electromagnetic quantity, per unit of time. Expressed in SI units , the unit of measurement is given as the change per second, but in the context of electronic circuits
1320-421: The analog-to-digital converter and digital-to-analog converter . Examples of anti-jitter circuits include phase-locked loop and delay-locked loop . Jitter buffers or de-jitter buffers are buffers used to counter jitter introduced by queuing in packet-switched networks to ensure continuous playout of an audio or video media stream transmitted over the network. The maximum jitter that can be countered by
1375-414: The direct current (or average) component of the signal, and RMS AC {\displaystyle {\text{RMS}}_{\text{AC}}} is the alternating current component of the signal. Electrical engineers often need to know the power , P , dissipated by an electrical resistance , R . It is easy to do the calculation when there is a constant current , I , through the resistance. For
1430-405: The physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: where R represents the gas constant , 8.314 J/(mol·K), T is the temperature of the gas in kelvins , and M is the molar mass of the gas in kilograms per mole. In physics, speed is defined as
1485-404: The slew rate is the change in position over time of an object which orbits around the observer, measured in radians , degrees or turns per unit of time. It has dimension T − 1 . {\displaystyle {\mathsf {T}}^{{-}1}.} The slew rate of an electronic circuit is defined as the rate of change of the voltage per unit time. Slew rate
1540-446: The RMS value, I RMS , of the function I ( t ) is the constant current that yields the same power dissipation as the time-averaged power dissipation of the current I ( t ). Average power can also be found using the same method that in the case of a time-varying voltage , V ( t ), with RMS value V RMS , This equation can be used for any periodic waveform , such as a sinusoidal or sawtooth waveform , allowing us to calculate
1595-574: The US, or 230 V in Europe) are almost always quoted in RMS values, and not peak values. Peak values can be calculated from RMS values from the above formula, which implies V P = V RMS × √ 2 , assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 × √ 2 , or about 170 volts. The peak-to-peak voltage, being double this,
1650-619: The affected application. For clock jitter, there are three commonly used metrics: In telecommunications , the unit used for the above types of jitter is usually the unit interval (UI) which quantifies the jitter in terms of a fraction of the transmission unit period. This unit is useful because it scales with clock frequency and thus allows relatively slow interconnects such as T1 to be compared to higher-speed internet backbone links such as OC-192 . Absolute units such as picoseconds are more common in microprocessor applications. Units of degrees and radians are also used. If jitter has
1705-401: The case of the RMS statistic of a random process , the expected value is used instead of the mean. If the waveform is a pure sine wave , the relationships between amplitudes (peak-to-peak, peak) and RMS are fixed and known, as they are for any continuous periodic wave. However, this is not true for an arbitrary waveform, which may not be periodic or continuous. For a zero-mean sine wave,
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1760-416: The common case of alternating current when I ( t ) is a sinusoidal current, as is approximately true for mains power, the RMS value is easy to calculate from the continuous case equation above. If I p is defined to be the peak current, then: where t is time and ω is the angular frequency ( ω = 2 π / T , where T is the period of the wave). Since I p is a positive constant and
1815-409: The data stream ( data-dependent jitter ) or uncorrelated to the data stream (bounded uncorrelated jitter). Examples of data-dependent jitter are duty-cycle dependent jitter (also known as duty-cycle distortion) and intersymbol interference . Total jitter ( T ) is the combination of random jitter ( R ) and deterministic jitter ( D ) and is computed in the context to a required bit error rate (BER) for
1870-473: The depth of jammers suppression. In the context of computer networks, packet jitter or packet delay variation (PDV) is the variation in latency as measured in the variability over time of the end-to-end delay across a network. A network with constant delay has no packet jitter. Packet jitter is expressed as an average of the deviation from the network mean delay. PDV is an important quality of service factor in assessment of network performance. Transmitting
1925-408: The digital input value registered by the circuit may oscillate between 0 and 1 during the signal transition. In other cases, a maximum slew rate is specified in order to limit the high frequency content present in the signal, thereby preventing such undesirable effects as ringing or radiated interference . In amplifiers, limitations in slew rate capability can give rise to non-linear effects. For
1980-426: The effect of sampling jitter. A jitter signal can be decomposed into intrinsic mode functions (IMFs), which can be further applied for filtering or dejittering. Root mean square In mathematics , the root mean square (abbrev. RMS , RMS or rms ) of a set of numbers is the square root of the set's mean square . Given a set x i {\displaystyle x_{i}} , its RMS
2035-414: The given minimum, or at most the given maximum. When applied to the input of a circuit, it instead indicates that the external driving circuitry needs to meet those limits in order to guarantee the correct operation of the receiving device. If these limits are violated, some error might occur and correct operation is no longer guaranteed. For example, when the input to a digital circuit is driven too slowly,
2090-530: The horizontal lines of video image frames are randomly displaced due to the corruption of synchronization signals or electromagnetic interference during video transmission. Model-based dejittering study has been carried out under the framework of digital image and video restoration. Jitter in serial bus architectures is measured by means of eye patterns . There are standards for jitter measurement in serial bus architectures. The standards cover jitter tolerance , jitter transfer function and jitter generation , with
2145-428: The jitter estimates computed from the arrival characteristics of the media packets. Adjustments associated with adaptive de-jittering involves introducing discontinuities in the media play-out which may be noticeable to the listener or viewer. Adaptive de-jittering is usually carried out for audio play-outs that include voice activity detection that allows the lengths of the silence periods to be adjusted, thus minimizing
2200-460: The large open loop gain of the amplifier is generated. This also means that a fairly small input voltage can cause the input stage to saturate . In saturation , the stage produces a nearly constant output current. The second stage of modern power amplifiers is, among other things, where frequency compensation is accomplished. The low pass characteristic of this stage approximates an integrator . A constant current input will therefore produce
2255-464: The maximum input frequency and amplitude applicable to the amplifier such that the output is not significantly distorted. Thus it becomes imperative to check the datasheet for the device's slew rate before using it for high-frequency applications. Slew rate can be deliberately limited using two op amps , a capacitor, and two resistors. In electronic musical instruments, slew circuitry or software-generated slew functions are used deliberately to provide
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2310-414: The mean power delivered into a specified load. By taking the square root of both these equations and multiplying them together, the power is found to be: Both derivations depend on voltage and current being proportional (that is, the load, R , is purely resistive). Reactive loads (that is, loads capable of not just dissipating energy but also storing it) are discussed under the topic of AC power . In
2365-567: The more commonly quoted figure, is its inverse. ITU-T G.810 classifies deviation lower frequencies below 10 Hz as wander and higher frequencies at or above 10 Hz as jitter . Jitter may be caused by electromagnetic interference and crosstalk with carriers of other signals. Jitter can cause a display monitor to flicker, affect the performance of processors in personal computers, introduce clicks or other undesired effects in audio signals, and cause loss of transmitted data between network devices. The amount of tolerable jitter depends on
2420-410: The perceptual impact of the adaptation. A dejitterizer is a device that reduces jitter in a digital signal . A dejitterizer usually consists of an elastic buffer in which the signal is temporarily stored and then retransmitted at a rate based on the average rate of the incoming signal. A dejitterizer may not be effective in removing low-frequency jitter (wander). A filter can be designed to minimize
2475-552: The product of one simple waveform with another is zero for all pairs other than a waveform times itself). Alternatively, for waveforms that are perfectly positively correlated, or "in phase" with each other, their RMS values sum directly. The RMS of an alternating electric current equals the value of constant direct current that would dissipate the same power in a resistive load . A special case of RMS of waveform combinations is: where V DC {\displaystyle {\text{V}}_{\text{DC}}} refers to
2530-411: The relationship between RMS and peak-to-peak amplitude is: For other waveforms, the relationships are not the same as they are for sine waves. For example, for either a triangular or sawtooth wave: Waveforms made by summing known simple waveforms have an RMS value that is the root of the sum of squares of the component RMS values, if the component waveforms are orthogonal (that is, if the average of
2585-598: The required values for these attributes varying among different applications. Where applicable, compliant systems are required to conform to these standards. Testing for jitter and its measurement is of growing importance to electronics engineers because of increased clock frequencies in digital electronic circuitry to achieve higher device performance. Higher clock frequencies have commensurately smaller eye openings, and thus impose tighter tolerances on jitter. For example, modern computer motherboards have serial bus architectures with eye openings of 160 picoseconds or less. This
2640-445: The resulting data stream analyzed—is employed when measuring pixel jitter in frame grabbers . Anti-jitter circuits (AJCs) are a class of electronic circuits designed to reduce the level of jitter in a clock signal. AJCs operate by re-timing the output pulses so they align more closely to an idealized clock. They are widely used in clock and data recovery circuits in digital communications , as well as for data sampling systems such as
2695-407: The sample and DFT coefficients. In this case, the RMS computed in the time domain is the same as in the frequency domain: The standard deviation σ x = ( x − x ¯ ) rms {\displaystyle \sigma _{x}=(x-{\overline {x}})_{\text{rms}}} of a population or a waveform x {\displaystyle x}
2750-414: The scalar magnitude of velocity. For a stationary gas, the average speed of its molecules can be in the order of thousands of km/h, even though the average velocity of its molecules is zero. When two data sets — one set from theoretical prediction and the other from actual measurement of some physical variable, for instance — are compared, the RMS of the pairwise differences of the two data sets can serve as
2805-403: The slewing phenomenon occurs. However, the general principles are the same as in this illustration. The input stage of modern amplifiers is usually a differential amplifier with a transconductance characteristic. This means the input stage takes a differential input voltage and produces an output current into the second stage. The transconductance is typically very high — this is where
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#17328580589092860-527: The squares of the values, or the square of the function that defines the continuous waveform. In the case of a set of n values { x 1 , x 2 , … , x n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}} , the RMS is The corresponding formula for a continuous function (or waveform) f ( t ) defined over the interval T 1 ≤ t ≤ T 2 {\displaystyle T_{1}\leq t\leq T_{2}}
2915-471: The system: in which the value of n is based on the BER required of the link. A common BER used in communication standards such as Ethernet is 10. In analog-to-digital and digital-to-analog conversion of signals, the sampling is normally assumed to be periodic with a fixed period—the time between every two samples is the same. If there is jitter present on the clock signal to the analog-to-digital converter or
2970-412: The term root mean square as a synonym for standard deviation when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. This is useful for electrical engineers in calculating the "AC only" RMS of a signal. Standard deviation being the RMS of a signal's variation about the mean, rather than about 0,
3025-537: Was to be squared within the integral: Using a trigonometric identity to eliminate squaring of trig function: but since the interval is a whole number of complete cycles (per definition of RMS), the sine terms will cancel out, leaving: A similar analysis leads to the analogous equation for sinusoidal voltage: where I P represents the peak current and V P represents the peak voltage. Because of their usefulness in carrying out power calculations, listed voltages for power outlets (for example, 120 V in
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