## Jitter Tracking

Imagine a serial-data clock recovery system based on a phase-locked loop (PLL) circuit. Presented with a sudden change in input timing the PLL responds sluggishly, taking many cycles to track the new incoming phase. That is part of its function. A sluggish response prevents small deviations in received timing from jolting the recovered clock out of kilter.

The response time of the PLL partitions the world of all possible input timing variations into two categories:  those variations so slow that the PLL easily tracks them, and other, faster variations that the PLL cannot track. The slow variations we call wander, the fast ones jitter. Note that this definition of wander and jitter depends entirely upon the characteristics of the PLL at hand. Another circuit might perceive wander and jitter differently.

Being a time-oriented thinker, I describe the dividing line between wander and jitter as something that depends on the rise or fall time of the incoming variations. If you like the frequency domain, then you may imagine that the dividing line depends on the frequency of the incoming variations. Either way works—these are interchangeable ideas.

A deep grasp of jitter, wander, and how a PLL reacts to them will help refine your understanding of serial data communications. It will also help you debug jittery reference clock problems and design systems that work reliably in the face of noise.

If you already know about phase tracks then you may step out for a cup of tea while I run through the next part of this discussion. Of course, I can't promise that I won't say something important….

##### Phase track

We are all used to seeing plots of voltage versus time. The concept of jitter analysis requires that you master a new skill: you must imagine a new track of information running parallel to the voltage track. The new track encodes nothing but pure timing information.

The new track is a series of impulses. At the location of every zero-crossing position in the original voltage track, the new timing track records an impulse whose height indicates whether that edge appears early or late compared to a theoretically ideal signal.

Figure 1 shows the new timing track running alongside the original voltage plot. The timing track extends sideways into a third dimension representing the "early or lateness" of each edge. This new vector of timing information is called a "phase track".

Figure 1—A phase track represents the complete range of all timing variations in the signal.

Moving from left to right in the figure, the first nine edges all arrive early. The next three are late. The degree of earliness or lateness is difficult to discern in the voltage plots, which is precisely why it helps to show the phase track. If you look very carefully at the points where the purple voltage track touches or leaves the bottom axis you will see that the first nine transitions precede their respective phase track impulses. The next three fall slightly behind. The phase track impulses are drawn on a grid of ideal timing locations.

Whenever you encounter a synchronous digital signal, think about the phase track.

If you work with RF circuits, you may be more comfortable thinking of the phase track as the output of an ideal phase detector, or perhaps the demodulated Q-channel output of a phase modulated receiver. These are similar concepts.

### A PLL is a filter

A phase-locked loop (PLL) circuit responds not to a voltage waveform, but a phase track. A PLL transforms the incoming phase track into a new signal with a different phase track.

A PLL phase-track transformation has two important properties: it is linear, and it is time-invariant. The linear property implies that, within its tracking limits, the PLL responds linearly to timing variations in the incoming phase track. The time invariant property means that it responds the same way at all moments; the circuit has no internal memory that modifies its behavior versus calendar time.

Any circuit that responds in a linear and time-invariant fashion to its inputs constitutes a type of linear filter. Those of you steeped in DSP theory may recognize the PLL is a discrete-time filter, meaning that it accepts inputs and modifies it outputs only at discrete times (signal edges).

A PLL circuit forms a specific type of filter called a low-pass filter. That happens because, by design, a PLL tracks slow changes in timing that occur over spans of time longer than its characteristic response time. The same PLL cruises through short, quick changes without reacting. Any filter that passes slow changes while filtering out quick ones must be a type of low-pass filter.

### Mechanical Low-Pass Filter

If you are going to work with PLL circuits it is important that you fix in your mind a concrete image of how a low-pass filter interacts with a signal. Towards that end, I shall build a simple mechanical tracking device that emulates the low-pass filtering action of a PLL.

The body of my tracking device is made of wood. It holds a felt-tip pen so positioned that the tip drags on a sheet of paper. When you pull the string, the pen follows, leaving a mark. Figure 2 illustrates the device in action. In plan view, the wooden body appears triangular (Figure 3).

Figure 2—(Side view) A string drags the tracking device across a sheet of paper.

On a clean sheet of paper I draw a waveform to serve as input to the system. Call it the "source track". The source track could represent any signal, including possibly the phase track of an incoming serial-data channel.

To operate the tracking device, I place my marker on the source track. The marker is just a piece of cardboard with crosshairs that helps me center the string precisely on the waveform. The string connects the source marker to the tracking device, dragging it along.

Figure 3—By hand, carefully advance the source marker along the source waveform, dragging the pen behind.

As I advance the marker, the pen creates a new waveform (dotted red line in Figure 4). The new waveform is a filtered version of the source track. The filter appears much like a first-order, linear, time-invariant low-pass filter; similar to the response of a simple PLL circuit. The longer you make the string, the more sluggish the response. If you can mentally imagine the pen dragging behind the marker, you've got yourself a good mental model of PLL behavior.

Figure 4—The pen traces a low-pass filtered version of the source waveform.

• The wooden triangle does not need wheels, it just drags.
• Use a felt-tipped pen.
• You do not need an elaborate source marker. A pencil with a string tied near its tip will do.
• The pen trails the source by the length of the string. I draw the source waveform on white paper first and then cover it with an overlay of transparent film. Let the pen draw on the film. When you are done, slide the film horizontally to align the output timing with the input drawn on the white paper.
• Keep the vertical displacement small compared to the length of the string and use a long strip of paper.
• Don't go too fast.

The animation 0377-LPF-Animation illustrates the operation of my tracking system. The animation depicts step response, jitter filtering, and wander-tracking behavior.

### Bob Pease—Analog by Design show

If you would like to see a tracking a machine in action, I made a quick version out of a wooden clothes pin and a felt-tip marker on one of my appearances at the Analog by Design show over at National Semiconductor. It worked beautifully. Here's the link. You may need to register to see the show:

Now, whenever I think about serial data, I imagine the phase track laid out sideways, as in Figure 1, the little tracking device from Figure 3 scurrying along beside, and Bob Pease, smiling.

Best Regards,
Dr. Howard Johnson