Estimated reading time: 8 minutes

Crosstalk, Part 3: More On Shapes and Amplitudes

In Part 1 of this series (Note 1), I pointed out that people seemed to find the concept of crosstalk difficult to get their arms around. I pointed out that this might be because of the following reasons:

1:  It has two different fundamental causes

2:  These causes generate two different signals

3: These two signals flow in opposite directions

4:  These signals can interact with each other

5:  These two signals have significantly different shapes

6:  These shapes behave differently as a function of coupled length, and

7:  Neither shape resembles the “aggressor” signal that caused the crosstalk in the first place!

Part 1 of the series dealt with the first 4 items above. Crosstalk is caused by electromagnetic coupling, which has two components: an electric (capacitive) coupling and magnetic (inductive) coupling. These components result in two independent crosstalk components, forward and backward crosstalk. The two coupling components tend to cancel in the forward direction and to reinforce each other in the backward direction. And the two components, forward and backward crosstalk, have decidedly different characteristics.

In Part 2 of the series (see again Note 1) I showed that a step-function change in the aggressor signal results in two crosstalk components, neither one of which resembles the aggressor signal. The forward crosstalk component is a sharp pulse, which grows increasingly larger in amplitude as the coupled region increases but whose pulse width is only the rise time of the aggressor signal. The backward crosstalk component is a trapezoid whose amplitude does not change as the coupled region increases (except at the very beginning) but whose width (from zero to zero) is equal to two times the length of the coupled region plus one rise time.

In this column, Part 3 of the series, we will explore the shapes of these components and their amplitudes a little more fully.

First, a quiz. Look at Figure 1. Assume you saw this waveform somewhere in one of your circuits. Could you identify what is causing it?

Figure 1. What is causing this waveform?

Shape of the Backward Crosstalk Component

Figure 2 is an animated GIF showing how the backward crosstalk signal grows as the aggressor signal starts down the coupled region. The backward crosstalk component starts as a small trapezoid and grows in both amplitude and pulse width until a point. At that point, the amplitude stops increasing, and only the pulse width continues to increase.

The point at which the amplitude stops growing is a very precise point known as the “critical length.” It is the same critical length we refer to in transmission line situations – the length where the round-trip signal propagation time (through the coupled region) equals the rise time of the aggressor signal.

Figure 2. Animation showing how the backward crosstalk signal grows to a maximum amplitude and then stops growing.

This critical point can be easily demonstrated using a HyperLynx simulation. Consider two parallel coupled traces. An aggressor signal propagates down the aggressor trace (see Figure 3). It is a step-function signal with a two ns rise time (a). Assuming an Er of 4.0, a 2 ns rise-time signal will have a critical length of 1 ns or approximately 6 inches. Traces (b), (c), and (d) represent three different simulations with coupled regions equal to 0.5 ns (3.0”), 1.0 ns (6.0”), and 2.0 ns (12”) respectively. The figure shows that the shape of the signal for a coupled region shorter than the critical length (b) is a trapezoid whose amplitude has not yet reached its maximum. For a coupled region longer than the critical length (d), the shape of the backward crosstalk signal is a trapezoid whose amplitude has reached its maximum and will not grow any larger. For a coupled region exactly equal to the critical length (c) the shape of the backward crosstalk signal is a triangle whose amplitude has just reached the maximum and will not grow any larger.

Figure 3. Backward crosstalk components for coupled regions less than (b), equal to (c) and greater than (d) the critical length.

It is clearly seen from this simulation that the backward crosstalk pulse width is (in every case) two times the length of the coupled region plus one rise time.

Technical Note: For those of you with eyes sharp enough to see that the backward crosstalk component in Figure 2 never becomes a triangle, the explanation is straightforward. In Figure 2, the coupled length is longer than the critical length and the animation shows how the signal grows as the aggressor signal propagates. In Figure 3, trace (c), the coupled region is exactly equal to the critical length. This is the condition necessary for the backward crosstalk component to become a triangle.

Amplitude of the Crosstalk Components

The amplitude of the backward crosstalk component is not particularly easy to estimate. Howard Johnson estimates the crosstalk coupling coefficient as shown in Equation 1 (Note 2):

Equation 1

where H is the height of the traces above the plane and D is the centerline spacing between them. One item of note is that the trace width and thickness do not appear in this equation. It is not that they do not matter; it is just that they are secondary effects and are (mostly) captured with these terms. I have found this equation to be reasonably close in microstrip environments. But, if anything, it tends to overstate the crosstalk coupling coefficient in stripline environments. In any event, this equation is just an approximation. More accuracy requires field solver simulation techniques.

It is clear from this expression that if we want to minimize crosstalk effects we want to minimize H (i.e., place the traces as close as practical to the underlying plane) and maximize D (i.e., place the traces as far apart as possible).

I know of no practical way to credibly estimate the forward crosstalk component short of a field-solver-based simulation.

Why Troubleshooting Can be so Difficult

The simulation shown in Figures 4 and 5 illustrate why troubleshooting crosstalk problems can be so difficult. We have a pair of microstrip traces driven by a ramp (identified as TDR1nsec) whose rise time is one ns. A sharply defined ramp is useful in simulations because it provides sharply defined edges in the crosstalk signal that would otherwise be somewhat obscured by the slower round-on and round-off portions of the aggressor waveform. But a ramp aggressor does not change the magnitude of the crosstalk signal nor any rise times associated with the crosstalk signals.

The traces are 8.0 mil wide with 5 mil separation, 5 mils above the plane – a very poor stackup configuration from a crosstalk standpoint!

Figure 4. Simulation showing why troubleshooting can be difficult.

The aggressor signal is the top trace, and the victim is the bottom trace. Behind the victim-coupled region is a short (500 ps) section of an uncoupled transmission line. That is, the victim trace is 500 ps longer than the aggressor trace and is only partly coupled to the aggressor.

The purpose of including this uncoupled region is to separate the forward crosstalk component from the backward crosstalk component at the far end of the victim trace. That is, the backward crosstalk component travels an extra 1.0 ns – 500 ps back before it reflects off the near end, and an additional 500 ps on its way back to the far end. Therefore, the backward crosstalk component arrives at the far end of the victim trace 1.0 ns after the forward crosstalk component does.

The aggressor signal is a 50 MHz waveform with a 30% duty cycle.

Figure 5. Results of the simulation.

The results of the simulation are shown in Figure 5. The green waveform is the aggressor signal. The orange waveform is the combined forward and backward crosstalk components at the far end of the victim trace. The forward crosstalk component associated with the rising edge of the aggressor signal is a negative-going pulse whose pulse width is the same as the rise time of the aggressor: 1.0 ns. It arrives at the far end of the victim trace 1.77 ns after the aggressor signal starts (i.e., the length of the coupled region). The backward crosstalk component is a trapezoid that arrives 1.0 ns later (i.e., the trip through the uncoupled region and back again, 500 ps each way). It has a pulse width of 4.5 ns (two times the length of the coupled region plus one rise time). The falling edge of the aggressor signal generates exactly the same type of forward and backward crosstalk components, this time with an opposite sign (because the aggressor edge is falling rather than rising).

Recognize that the crosstalk signal in Figure 5 is the same signal I showed in Figure 1. After the explanation of the simulation, it begins to make a little sense. But Figure 1, without any explanation, could be very difficult to decipher. And even in Figure 5 I have been careful to structure the simulation so that the components are somewhat separated from each other. Consider how messy this might look if the duty cycle were 50%, or were variable (as in a data signal) and the frequencies higher and the coupled and uncoupled regions less structured. The resulting crosstalk signals would be confused and messy, indeed.

That is why it takes some experience to be able to work through crosstalk problems in the real world. Or better yet – design the boards so they just don’t happen!

Notes

1. See Parts 1 and 2 of the series here http://www.pcbdesign007.com/pages/columns.cgi?clmid=55&artid=81280 and http://www.pcbdesign007.com/pages/columns.cgi?clmid=55&artid=81772 .
2. Johnson, Howard, High Speed Digital Design, A Handbook of Black Magic, Prentice Hall, 1993, p 192. Note that this equation applies to coupled regions longer than the critical length.

Douglas Brooks has an MS/EE from Stanford University and a Ph.D. from the University of Washington. He has spent most of his career in the electronics industry in positions of engineering, marketing, general management, and as CEO of several companies. He has owned UltraCAD Design Inc. since 1992. He is the author of numerous articles in several disciplines, and has written articles and given seminars all over the world on Signal Integrity issues since founding UltraCAD. His book, Printed Circuit Board Design and Signal Integrity Issues was published by Prentice Hall in 2003. Visit his website at www.ultracad.com.