## Twisted Crosstalk

My recent EDN article, "Visualizing Differential Crosstalk" (Dec. 5, 2008) displayed some beautiful E&M field patterns associated with edge-coupled differential stripline pairs. From those field patterns, the article explained how to estimate crosstalk.

After reading that article, several people asked for similar information regarding broadside-coupled pairs. That information has now been added to the web version of the article archived here: VisualizeDiffCrosstalk.htm .

Today's article extends the field analysis to twisted-pair cables. The geometry of a twisted-pair cable varies with its twisting pattern along the length of the cable. To show the changing field patterns that result from twisting, I've prepared a little movie.

## Twisted Crosstalk

Pull two long, straight wires across your lab bench. Tape them in place about an inch apart. At one end connect a differential source and at the other a differential receiver. You have just made a balanced, differential link.

Experiment #1: Place a cell phone adjacent to one of the wires so that it affects the nearby wire much more strongly than the other. The differential receiver, which is programmed to detect any difference between the signals on the two wires, clearly picks up the cell phone signal.

Differential links have a good reputation for rejecting external noise. Unfortunately, that good reputation extends only to noise that affects both wires equally.

Experiment #2: Place cell phone above the two wires, centered between them, the situation changes. Make sure you orient the phone so it radiates the same field towards each wire. When you hold it just right, the wires respond equally.  E&M field theorists call that a common-mode signal. In this purely common-mode situation the differential receiver reports zero difference between the two wires, that is, it receives zero interference.  That is the principle of noise rejection in a differential system.

Experiment #3: Rip up everything we just did and start again. This time press the wires close together, with only their insulation holding them apart, as you tape them in place. Because the wires are held so close, and the cell phone is so much physically larger than the wire spacing, you will find that the phone induces less interference that in the first experiment.

Interference goes down because differential pickup has to do with how close the phone lies to the first wire and how close to the second. The ratio of those two distances pretty much determines the ratio of noise pickup on the two wires. In experiment #1, with the wires widely separated and the antenna held very close to one wire, you get a big ratio of distances and therefore a big difference in pickup. In experiment #3, given the same distance to the first wire, the change in wire separation brings the second wire much closer to the antenna, making it respond much more like the first wire. In the terminology of field theory, "Pressing the wires closer together reduces the exposed loop area between them thus reducing their magnetic pickup."

If you could force both wires to have the same relation to the antenna they would respond identically, nulling interference to zero. That is accomplished in experiment #2, but only for an interfering source held in one particular location, with one particular orientation.

Experiment #4: Rip up everything one last time. Twist the wires tightly together and tape them back down. As the wires pass by your cell phone the twist first brings one wire closest to the phone, then the other, then the first wire again, and so on. No matter where you place the phone, as the twisted wires pass by they each maintain the same average distance from the cell phone so they both pick up the same signal. Crosstalk in this setup should be significantly less than any of the previous experiments.

A tight twist improves the symmetry of the system, dramatically so if the rate of twist is small compared to the wavelength of the signals involved.

## Multi-conductor twisted-pair cables

Most multi-conductor twisted-pair cables twist the individual pairs at different rates. The usual explanation for this practice is that it ensures, on average, equal probability of the plus (+) and (-) wires from one pair being near either the (+) or (-) wire of any interfering signals, thus preventing crosstalk. In this case the crosstalk averages to zero over a length commensurate with the difference in rates of twist between the aggressor and victim.

For example, in an Ethernet category-5 UTP cable if one pair twists at 5 TPI (twists per inch) and the next at 7 TPI, the difference in twist rates is 2 TPI.  I must therefore proceed down the cable 1/2 an inch before I see one complete additional revolution of the second wire pair relative to the first.  The "coherence length" of the twist pattern is 1/2 in. This twist pattern effectively nulls out crosstalk for any signals having a rise/fall time greatly exceeding 1/2 in. The usual rise/fall time used on category-5 UTP is 4 ns, corresponding at 124 ps/in to a signal length of some 31 in.

It may surprise you to know that you can get an even better effect using precisely the same rate of twist on each pair. To realize this benefit you must hold the central axis around which each pair rotates in a fixed position. In a multi-pair cable that is difficult to achieve. As the pairs rotate, they tend to mush against one another, perturbing the perfect geometric conditions necessary for ideal crosstalk cancellation. That's why most multi-conductor cables use staggered rates of twist on the various pairs. Nevertheless, I'd like to show you the exact cancellation that would occur if you held everything in perfect alignment. Some twisted ribbon cables actually do that, using the ribbon membrane to hold the wires in exact alignment.

To see how the cancellation works I'm going to show you an animation.  The animation displays magnetic field patterns. From the patterns you can estimate crosstalk.  If that process is not familiar to you, read the following article. It explains how to interpret crosstalk from the magnetic-field diagrams:
"Visualizing Differential Crosstalk", VisualizeDiffCrosstalk.htm

The two pairs are set side-by-side, as in Figure 1. The aggressor pair appears on the left. The positive (+) wire is surrounded by red field lines. The minus (-) wire is surrounded by blue lines.  The victim pair appears on the right (again, red and blue).  As the animation proceeds, both pairs will rotate counterclockwise. As the pairs rotate, crosstalk will alternate between (+) and (-), averaging to zero. A small graph at the bottom of the animation records the crosstalk amplitude versus rotational position.

The rules for computing the polarity of crosstalk in the animation are simple. The following notes apply to Figure 1.

• Start with the two pairs laid out "heads up", the positive wire of each pair pointing up at 12 o'clock. This is called a "broadside" configuration. Crosstalk is positive. A magnetic-field expert deduces that fact by drawing arrows on the magnetic field lines circulating counter-clockwise around the red aggressor wire and noting that the arrows circulate the same direction around the red victim wire. You can deduce the polarity by simply noting that if you were to slide the victim pair to the left it would pick up a more intense field, but would not change polarity. In the limit when the wires touch (red to red and blue to blue) the crosstalk has got to be positive. Ergo, it must be positive as drawn in Figure 1-1.
• After 45 degrees of counterclockwise rotation the victim wires align with the magnetic field pattern. Both victim wires experience the same B-field effect, producing no differential crosstalk.
• The heel-to-toe orientation places the blue source nearest the red victim. Crosstalk being an extremely strong function of distance, the contributions of the other wires cannot cancel the resulting negative crosstalk.
• 135 degrees. The B-field lines in this picture represent crosstalk voltages. Both victim wires lie on the same line, so they pick up the same voltage. Some common-mode noise enters the victim circuit, but zero differential crosstalk.
• This is the broadside configuration, with red facing red and blue facing blue. Crosstalk is positive.
• 225 degrees. Aligning the victim wires parallel to the magnetic field pattern nulls differential crosstalk to zero.
• A heel-to-toe orientation again much like (3). If the two red wires were innermost you would get positive crosstalk, but in this case it's positive source to negative victim, making crosstalk negative.
• At 315 degrees the magnetic field lines pass parallel to the orientation of the two victim wires. Crosstalk varies as the number of magnetic field lines falling between the victim wires, in this case zero.
• Back to start.

The animation is large (6.8 MB). I provide a more highly compressed version (2.3 MB), but really encourage you to watch the big one as the field lines show up better. As you watch the film, keep your finger poised over the pause button. Every time the field pattern advances, pause to read and absorb the comments listed at the bottom of the screen.

UTP-big.wmv 6.8MB; no sound; please right-click to "Save Target As..."

UTP-small.wmv 2.3MB: highly compressed, no sound;

I discuss this same effect in my book, "High-Speed Digital Design", page 332, and again with a little more detail in "High-Speed Signal Propagation", page 423.

<click figure to enlarge>

Now, for your homework assignment. Re-draw the patterns in Figure 1 assuming one pair rotates clockwise and the other counterclockwise.  Do you think the crosstalk still cancels?

Best Regards,
Dr. Howard Johnson