Jitter's faces: Random, periodic, and ISI
In The many faces of jitter, I described how jitter can be represented in different fashions, each with a unique and distinctive perspective. Now, I explore this concept and apply it to several common jitter components.
A thorough description of jitter in time, frequency, and statistical domains can, however, be very verbose. But, it is said that a picture is worth a thousand words. Therefore, by extension, a video with a thousand frames must be worth a million words, right? So, I exploited Matlab’s animation capabilities to create some videos that can help us develop an intuitive feel of the properties of jitter components.
Let's start with random jitter (RJ), which is often described as being white, Gaussian noise. That is to say, the PSD (power spectral density) is flat across all relevant frequencies and the PDF (probability density function) is a bell curve. The PDF has "tails" that extend very far, but are difficult to observe because they occur with very low probability such that it requires a very long observation time to capture them.
In the video below, I simulate the measurement of RJ with four different perspectives:
- The upper left plot shows the waveform around a data transition edge with persistence (in grey) similar to most oscilloscopes. The threshold of the transition is denoted by the dashed line.
- The upper right plot shows a normalized histogram (or PDF) with the number of samples accumulated.
- The lower left plot is the jitter spectrum (or PSD) with a frequency resolution that improves with observation time.
- The lower right plot is the bathtub curve (or cumulative density function, CDF) showing the eye closure due to RJ.
Initially, the shape of the histogram doesn't look Gaussian. It takes a fair number of samples before we can make out its shape. As expected, events in the tail region far from the mean occur less frequently and only show up after a substantial number of samples have been collected.
The jitter spectrum ripples as it accumulates data, but is overall generally flat without any dominant spikes or spurs rising above the noise, thus approximating white noise.
The bathtub curve doesn't initially reach very far down. As more data accumulates, the bathtub curve reaches lower and lower, indicating that low probability events are being observed. After many samples have been accumulated, the bathtub curve takes on the familiar shape of the error function. We can also see that the eye opening is reduced with long observation times.
To me, the benefit of this video is that is shows how outlier events in the waveform transition captured in the histogram subsequently affect the eye opening in the bathtub curve. Tying all these perspectives together in one video gives me a very intuitive view of how jitter behaves in each domain.
I hope you find this type of data visualization helpful in your understanding of jitter. In the upcoming blog posts, I will explore other jitter components such as periodic jitter, intersymbol interference (ISI), duty cycle distortion (DCD), and others.