Sampling oscilloscope signal jitter analysis method based on TLC improved algorithm

Abstract

The invention discloses a sampling oscilloscope signal jitter analysis method based on a TLC improved algorithm, and the method can better separate periodic jitter from random jitter in total jitter, and comprises the steps: obtaining a jitter TIE data set through the waveform of a tested signal; tLC sample function calculation operation and FFT spectrum analysis operation are carried out on the TIE data set at the same time, frequency points of periodic jitter are screened out according to obtained spectrums, then a to-be-fitted function is constructed, interpolation operation is carried out on a TLC sample function to obtain a fitting sample, least square fitting operation is carried out, periodic jitter amplitude is obtained through fitting, and the periodic jitter amplitude is obtained. And finally, solving the variance of the random jitter so as to finish the jitter decomposition process. According to the method, the TLC jitter decomposition algorithm is improved, and the signal jitter analysis performance of the sampling oscilloscope is obviously improved by using the method provided by the invention.

Description

Technical Field

[0001] This invention relates to the signal quality analysis module of a broadband sampling oscilloscope, and more particularly to a method for decomposing signal jitter. Background Technology

[0002] With the development of electronic technology, the performance of digital circuit systems has improved rapidly. Especially for high-speed serial communication systems, the transmission rate can reach GHz. For such high-speed signals, jitter will have a significant impact on the bit error rate of the system and has become a key factor limiting the upper limit of system performance.

[0003] Jitter is often defined as the deviation between the threshold time of a signal edge and the ideal signal edge time. Total jitter is caused by a combination of factors, and can be initially classified into random jitter (RJ) and deterministic jitter (DJ). DJ can be further divided into periodic jitter (PJ), data-correlated jitter (DDJ), and bounded uncorrelated jitter (BUJ). DDJ can be further subdivided into inter-symbol interference (ISI) and duty cycle distortion (DCD). In practical analysis, engineers can deduce the main factors causing jitter by analyzing the magnitude of each jitter component in the circuit under test, and then take targeted measures to reduce jitter more efficiently, thereby further improving the performance of the circuit system.

[0004] Currently, mainstream jitter decomposition algorithms include Fast Fourier Transform (FFT), Tail-Fit, Empirical Mode Decomposition (EMD), and Time Delay Correlation (TLC). However, these methods all have some shortcomings to varying degrees. For example, the FFT algorithm suffers from spectral leakage; the Tail-Fit algorithm requires a large number of jitter samples, making it difficult to run smoothly with a small sample size; and the smoothing operation can cause information loss in the original probability density function (PDF) statistical histogram, thus introducing errors into the fitting results. Mode aliasing in the EMD algorithm is not conducive to analyzing jitter signals containing transient components and can also affect the accuracy of jitter decomposition.

[0005] The TLC algorithm also has its drawbacks. Because RJ is not an ideal Gaussian distribution in reality, the calculated TLC sample function contains glitches. These glitches can greatly affect the selection of data points, thereby reducing the accuracy and stability of the algorithm. At the same time, the equation solving operation is very time-consuming, which also makes the algorithm inefficient and difficult to apply in practical applications of sampling oscilloscope signal jitter analysis methods. Summary of the Invention

[0006] This invention improves upon the original TLC algorithm, aiming to overcome its shortcomings and provide a higher-performance jitter decomposition algorithm for its application in jitter analysis of sampled oscilloscope signals.

[0007] This invention provides an algorithm based on improved TLC, which effectively separates periodic jitter from random jitter components. The algorithm includes the following steps:

[0008] Step 1: Obtain jitter time interval error (TIE) data samples based on the waveform of the signal under test.

[0009] Step 2: Based on the obtained TIE samples, perform TLC function calculations and FFT calculations.

[0010] Step 3: After preprocessing the obtained TLC sample function, perform cubic spline interpolation to obtain the fitted sample. Simultaneously, select the frequency points of PJ based on the obtained sample spectrum, and then construct the function to be fitted.

[0011] Step 4: Perform a least squares-based fitting operation to obtain the amplitude of PJ.

[0012] Step 5: Substitute the frequency and amplitude of each PJ and the zero of the TLC sample function into the TLC function to solve for the variance of RJ.

[0013] The main advantages of this invention are as follows: The existing approach of combining the TLC algorithm with the FFT algorithm can quickly and accurately obtain the frequency values ​​of each PJ (Pulse Jet), while reducing the unknowns in the equations and improving the algorithm's timeliness. Building upon this, this invention incorporates least squares fitting to extract effective information from the TLC sample function with glitches by fitting the amplitude of the PJ, thereby improving the accuracy and stability of the original algorithm. It also completely avoids solving the equations, significantly reducing the algorithm's running time and further improving its timeliness. In summary, this invention improves the performance of the TLC algorithm in the jitter analysis module of a sampling oscilloscope. Attached Figure Description

[0014] Figure 1 The flowchart below illustrates the overall concept of the improved TLC algorithm of this invention.

[0015] Figure 2 This is a flowchart illustrating the least squares fitting approach used in this invention.

[0016] Figure 3 This is a diagram showing the final result of the fitting operation in this invention. Detailed Implementation

[0017] The concept and principle of the present invention will be further explained below with reference to the accompanying drawings.

[0018] like Figure 1 The flowchart shown represents the overall idea of ​​the improved algorithm. This algorithm mainly includes three operations: TLC function calculation, FFT spectrum calculation, and least squares fitting. The following example uses a circuit system containing only one RJ and two PJs to effectively explain the detailed principles.

[0019] Step 1: The first step is to generate TIE samples. TIE data is the time interval between the ideal signal edge and the actual signal edge. By acquiring a signal waveform, determining the edge of the signal under test, and subtracting it from the position of the ideal signal edge, a TIE sample can be obtained. Acquiring 3000 cycles of signal waveforms will generate 3000 TIE data points.

[0020] Step 2: The core of calculating the TLC sample function is the autocorrelation function. To ensure that the function has no decay at the tail and facilitates subsequent fitting operations, this invention uses the unbiased autocorrelation function:

[0021]

[0022] For the RJ component, its autocorrelation function is expressed as:

[0023]

[0024] For the PJ component, its autocorrelation function is expressed as:

[0025]

[0026] For a system containing a single RJ and two PJs as described above, its TLC function is:

[0027]

[0028] In a circuit system, there is only one RJ, which generates one unknown σ. Each additional PJ will add two unknowns, P and ω. For the circuit system described above, there are a total of five unknowns.

[0029] Meanwhile, the spectrum of the TIE samples can be obtained by FFT spectrum calculation based on the generated TIE sample set.

[0030] Step 3: Calculate the TLC function on the TIE samples to obtain a TLC sample function with spikes. The generation of fitted samples is based on these TLC sample functions with spikes.

[0031] Because of the use of an unbiased autocorrelation function, the tail of the TLC sample function will have significant distortion. Therefore, the tail cannot reflect the information of the real signal and cannot be used as a fitting sample. It should be removed. In fact, only the first half of the TLC sample function points are taken as fitting samples.

[0032] In addition, because the zeros of the TLC sample function contain the variance term of RJ, they are significantly higher than those of other points. This is redundant for the function to be fitted after removing the RJ variance term, and should be removed. However, removing the zeros will cause a change in the phase of the TLC sample function, which is very important for fitting. To ensure phase alignment, the zeros of the TLC sample function are changed to the function value of the next point.

[0033] Furthermore, since too few TLC sample points are not conducive to fitting operations, this invention uses a cubic spline interpolation algorithm to supplement more information points to the TLC sample function after preprocessing. Ten points are inserted between two adjacent TLC sample points to obtain the final fitted sample.

[0034] Meanwhile, based on the spectrum generated by the FFT algorithm, the spike pulses can be separated, and then the frequency points ω1 and ω2 of the two PJs can be obtained. Thus, the TLC equation is left with only three unknowns.

[0035] Furthermore, by removing the variance term of RJ, we can construct an equation containing only the unknown magnitudes of PJ, P1 and P2:

[0036]

[0037] Use this equation as the function to be fitted.

[0038] Step 4: After preparing the fitting samples and the function to be fitted, the least squares fitting operation can be performed, such as... Figure 2 The diagram shows the flowchart of the least squares fitting method. For the sake of overall algorithm timeliness, the fitting operation is divided into two orders. The first and second order fitting are based on the same idea, differing only in the step size and range selection. The first order fitting range is from 0 to the maximum value in the fitted sample, with a step size of 5% of the fitting range. The second order fitting range is the left and right 20% of the first order fitting result, with a step size of 2% of the fitting range. The specific fitting operation involves calculating the square of the difference between the fitted sample point value and the value of the function to be fitted, and summing these differences as the final fitting effect criterion; a smaller sum indicates a better fitting effect. Figure 3 The image shows a comparison between the final fitting result and the fitted sample. It can be seen that the fitted curve fits the sample very well, and can effectively recover the PJ amplitude information from the TLC fitted sample with spikes. After the fitting operation, the PJ amplitudes P1 and P2 that best fit the fitted sample can be determined. At this point, only the RJ variance remains as an unknown.

[0039] Step 5: Since the zeros of the TLC sample function contain information about the RJ variance term:

[0040]

[0041] Therefore, by substituting its zero point and the fitted PJ amplitude into the TLC theoretical equation, the variance of RJ can be directly solved, thus completing the jitter decomposition process.

Claims

1. A method for analyzing jitter in a sampled oscilloscope signal based on an improved TLC algorithm, characterized in that, Includes the following steps: Step 1: Obtain the TIE dataset based on the waveform sample being tested. Step 2: Perform TLC function calculation and FFT spectrum generation operations simultaneously. Step 3: Process the TLC sample function to obtain the fitted sample and filter the spectrum to construct the function to be fitted. Step 4: Perform least squares fitting operation Step 5: Calculate the variance of random jitter.

2. The TLC function calculation operation according to step 2 of claim 1, characterized in that: When calculating the TLC function, an unbiased autocorrelation function is used.

3. The method for processing the TLC sample function to obtain fitted samples according to step 3 of claim 1, characterized in that: The processing is divided into preprocessing operations and interpolation operations: The preprocessing operations include:

1. Extracting only the first half of the TLC sample function as the initial fitting sample.

2. Modifying the zero point of the TLC sample function to the value of the first function point thereafter; The interpolation algorithm used in the interpolation operation specifically refers to the cubic spline interpolation algorithm.

4. The method for constructing the function to be fitted according to step 3 of claim 1, characterized in that: The function to be fitted is a TLC function with the random jitter variance term removed and the periodic jitter frequency value substituted, as shown below: The number of PJs selected from the spectrum obtained by FFT is the specific number of terms in the function to be fitted.

5. The least squares fitting operation described in step 4 of claim 1, characterized in that: The specific operation of fitting is to sum the squares of the differences between the fitted sample and the function to be fitted, and use this sum as the evaluation criterion for the fitting effect. The smaller the value, the better the fitting effect. For the sake of timeliness, fitting is divided into first-order fitting and second-order fitting. The fitting range of first-order fitting is from 0 to the maximum value of the fitted sample, and the fitting step size is 5% of the fitting range. The fitting range of second-order fitting is 20% to the left and right of the first-order fitting result, and the fitting step size is 2% of the fitting range.

6. The method for calculating the random jitter variance according to step 5 of claim 1, characterized in that: The theoretical TLC function model is as follows: The zeros of the theoretical TLC function contain the variance information of RJ. By substituting the PJ amplitude obtained by least squares fitting and the zeros of the TLC sample function into the TLC function, the variance term of RJ can be solved.

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