Clock jitter and phase noise and their measurement methods

　　Jitter measurement has always been called the highest realm of oscilloscope test measurement. The most intuitive traditional jitter measurement method is to use afterglow to view the changes in the waveform. Later, it evolved into a difficult problem in advanced mathematical probability statistics, and the question of whether the jitter measurement result is accurate or not became more complicated.

　　The characteristics of a clock can be measured by using a frequency meter to measure frequency stability, a spectrum analyzer to measure phase noise, and an oscilloscope to measure TIE jitter, period jitter, and cycle-cycle jitter. But what are the principles of the time domain measurement method and the frequency domain measurement method? How is the relationship between TIE jitter and phase noise jitter derived?

　　Jitter is an important indicator for measuring clock performance. Jitter is generally defined as the short-term deviation of a signal from its ideal position at a specific moment. This short-term deviation is manifested as jitter in the time domain (hereinafter referred to as time domain jitter) and as phase noise in the frequency domain. This article mainly discusses clock jitter and phase noise, their measurement methods, and the relationship between the two.

　　1 Introduction to Jitter

　　Jitter is the measurement result of the time domain signal, reflecting how much the signal edge deviates from its ideal position. There are two main components of jitter: deterministic jitter and random jitter. Deterministic jitter is repeatable and predictable, and its peak-to-peak value is bounded. DJ in the usual sense refers to its pk-pk value; random jitter is unpredictable timing noise. When analyzing, it is generally approximated by Gaussian distribution. In theory, it can deviate infinitely from the middle value, so random jitter has no peak-to-peak boundary. The RJ index in the usual sense refers to its RMS value, and its value at a certain bit error rate can be inferred based on its RMS value. The most commonly used analysis method at present is to use the dual Dirac model. This model assumes that the tails on both sides of the probability density function obey the Gaussian distribution. The Gaussian distribution is easy to simulate and can be inferred downward to a lower probability distribution. The total jitter is the convolution of the RJ and DJ probability density functions.

　　However, there is still controversy in the industry as to whether the Gaussian distribution can accurately describe the tail of the random jitter histogram. The real random jitter follows the Gaussian distribution, but in actual measurements, multiple low-amplitude DJs will be convolved into a distribution function, which causes the center of the measured probability density distribution to be close to the Gaussian distribution, while the tail is mixed with some DJs. Therefore, the real RJ may only account for a part of the jitter of the Gaussian model, and the RJ may be amplified in the measurement, and the total jitter will also be amplified.

　　2 Jitter Measurement

　　There are usually three ways to measure clock jitter, corresponding to the three jitter indicators of TIE (TIme Interval Error), period (period jitter) and Cycle-Cycle (adjacent cycle jitter).

　　TIE jitter (Time Interval Error) takes the time difference between the measured clock edge and the ideal clock edge as the sample, that is, TIEn in the figure as the sample. By performing statistical analysis on many samples, the change and distribution of the deviation value between the clock edge and the ideal clock edge are characterized, as shown in the following figure:

　　Period Jitter uses the period of the clock signal as a sample, that is, Pn in the figure as a sample. By performing statistical analysis on many samples, the change and distribution of the clock signal period Pn are characterized, which is very meaningful for ensuring the establishment and hold time specifications in the digital system. As shown in the following figure:

　　Cycle-Cycle Jitter uses the difference between adjacent cycles of the clock signal as a sample, that is, Cn in the figure as a sample. By performing statistical analysis on many samples (1K~10K), it characterizes the change and distribution of the adjacent cycle change value of the clock signal. It is generally used in situations where frequency mutation needs to be limited. As shown in the following figure:

　　The relationship between the three jitter indicators TIE, Jperiod and Jcycle-cycle is as follows:

　　The differentiation of TIE can obtain the period jitter.

　　Among them, Δtpn is the period jitter, tn is the actual period, T0 is the ideal period, and ΔtIEn is the TIE jitter.

　　The differentiation of period jitter gives cycle-cycle jitter.

　　Among them, Δtcn is the period jitter, tn is the actual period, and Δtpn is the period jitter.

　　The relationship between the three can be represented by the following figure:

　　3 Phase Noise Introduction

　　Phase noise reflects the spectral purity of a single-carrier signal. If there is no phase noise, all the power of the signal should be concentrated at its oscillation frequency f0 (Carrier on the left in the figure below). This ideal signal is represented by Asin (ωt). Due to the existence of phase noise (Noise on the left in the figure below), it is equivalent to modulating a Φ (t) phase signal on the ideal signal. At this time, the entire signal is represented by Asin (ωt + Φ (t)). In the spectrum, it is reflected as a part of the power extending to the adjacent frequency to form a sideband (right in the figure below). Phase noise is defined as the logarithm of the ratio of the power Pn within a 1Hz bandwidth at a given offset frequency fn of the single sideband to the total signal power Ps, that is, 10lg (Pn/Ps). Phase noise is expressed in dBc/Hz@fn. Here, dBc means the ratio of the power at a certain frequency point to the total signal power (right in the figure below), which corresponds to the ratio of the clock phase offset to the clock period.