2.1.2 Calculating Peak to Peak Jitter from RMS Jitter Because the period jitter from a clock is random in nature with Gaussian distribution, it can be completely expressed in terms of its Root Mean Square (RMS) value in pico-seconds (pS). However, the peak-to-peak value is more relevant in calculating setup and hold time budgets. To convert the RMS jitter to peak-to-peak (Pk-Pk) jitter for a sample size of 10,000, the reader can use the following equation: Peak-to-peak period jitter = 7.44 x (RMS jitter) Equation 1 For example, if the RMS jitter is 3 pS, the peak to peak jitter is ±11.16 pS. Equation 1 is derived from the Gaussian Probability Density Function (PDF) table. For instance, if the sample size is 100, 99 of those samples will fall within ±2.327σ from the mean value of the distribution, only 1 sample, on average, will fall outside that region. SiTime measures the RMS period jitter over a sample size of 10,000 as specified by the JEDEC standard. Sample Size Sigma (σ) 10 ±1.282 100 ±2.327 1,000 ±3.090 10,000 ±3.719 100,000 ±4.265 1,000,000 ±4.754 10,000,000 ±5.200 100,000,000 ±5.612 1,000,000,000 ±5.998 10,000,000,000 ±6.362 100,000,000,000 ±6.706 1,000,000,000,000 ±7.035 Table 1. Gaussian probability density function (PDF) 2.1.3 Period Jitter Measurement Methodology Period Jitter is defined in JEDEC Standard 65B as the deviation in cycle time of a signal with respect to the ideal period over a number of randomly selected cycles. The JEDEC standard further specified that period jitter should be measured over a sample of 10,000 cycles. SiTime recommends measuring period jitter using the following procedure: 1. Measure the duration (rising edge to rising edge) of one clock cycle 2. Wait a random number of clock cycles 3. Repeat the above steps 10,000 times 4. Compute the mean, standard deviation (σ), and the peak-to-peak values from the 10,000 samples -------------------------------------------------------------------------------------------------------------------------------------------- The Smart Timing Choice™ 4 SiT-AN10007 Rev 1.2 Clock Jitter Definitions and Measurement Methods 5. Repeat the above measurements 25 times. From the 25 sets of results, compute the average peak-to peak value. The standard deviation (σ) or RMS value computed from a measurement of 10,000 random samples (step 4) is quite accurate. The error in the RMS value can be calculated using the following equation: ErrorRMS N n 2 σ = Equation 2 where σn is the RMS (or sigma) of the collected sample and N is the sample size. For a sample size of 10,000, ErrorRMS is 0.0071σn. This error is random and it follows the Gaussian distribution. The worst-case measurement error is typically computed as ±3 ErrorRMS. For example, if the RMS value computed from 10,000 random samples is 10 pS, then the ErrorRMS will be 0.071 pS and virtually all the RMS values of this measurement will still fall within a narrow range of 10 ± 0.213 pS. In practical applications, the RMS errors in a sample set of 10,000 are small enough to be ignored. While an accurate RMS value can be computed from a random 10000-sample set, the peak-topeak value is more difficult to measure. Due to the random nature of period jitter, the larger the sample size, the higher is the probability of picking up data points at the far ends of the distribution curve. In other words, the peak-to-peak value diverges instead of converging as more samples are collected. That is the reason why we added an extra step, step 5 to produce a more consistent and repeatable peak-to-peak measurement. Each measurement of 10,000 random samples (step 4) produces one standard deviation value and one peak-to-peak value. By randomly repeating this process 25 times, we could collect a good set of data points from which we can calculate the average peak-to-peak value with a high degree of accuracy. We can also compute the average RMS value from this data, but it will be very close to the RMS value derived from each individual run. Figure 3 is the period jitter histogram of a 3.3V SiT8102 oscillator running at 125 MHz captured by a Wavecrest SIA-4000C. It represents one set of RMS and peak-to peak values measured from 10,000 samples (step 4)