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Enter the matrix: get used to differential S parameters. They're the new standard for interconnect characterization.

A DIFFERENTIAL PAIR, universally used to transport all high-speed serial links and many other high-frequency busses, is really composed of two independent transmission lines. We can describe these two lines as either two single-ended transmission lines with crosstalk, or separately, but equally, as one single differential pair.

Though any two single-ended transmission lines can make up a differential pair, two specific qualities make them particularly effective for high-speed digital communications. The first quality is symmetry between the two lines. Line widths, dielectric thicknesses and all other geometrical features should be the same. This will assure that there is minimal conversion of differential signals into common signals.

The second quality is that the time delay down each line should be the same. Most high-speed serial links have a spec for the maximum allowable timing skew between the two lines that make up a pair, which ranges from 25 psec to 100 psec.

Everything we ever wanted to know about how a single-ended signal interacts with these two single-ended lines is contained in the four-port S parameters. The diagonal elements have information about the impedance distribution of each line. The S21 and S43 terms provide the timing and attenuation information about each line independently. And the S31 and S41 terms have information about the near- and far-end crosstalk between the two lines.

But these two lines are also simultaneously a single differential pair with a port 1 on one side and a port 2 on the other side of the pair (FIGURE 1). We can describe this one pair with a new set of S parameters, called the differential, balanced or mixed-mode S parameters, which describe how a differential or common signal would interact with the differential pair through the ports on the ends.


In a single-ended S parameter matrix, there are 16 elements arrayed in a 4 x 4 matrix (FIGURE 2). A mixed-mode S parameter matrix is also a 4 x 4 matrix with 16 elements, but they have a much different meaning than in a single-ended matrix.


The 16 elements are divided into four quadrants. The upper left quadrant describes how a differential signal goes into one port and a differential signal comes out a port. We label these elements Sdd.

The lower right quadrant describes how a common signal enters the pair and a common signal comes out the pair at a port. We label these elements Scc.

The upper right quadrant describes how a common signal enters the differential pair and a differential signal comes out. This can only happen if there is conversion of some of the pure differential signal into common signal. This is called mode conversion.

The lower left quadrant describes how a differential signal enters the differential pair and a common signal comes out. This will only happen if there is mode conversion.

For differential signals, the most important terms are Sdd11, which tells about the uniformity of the differential impedance profile of the channel, and Sdd21, which tells of the transmitted differential signal quality, bandwidth and time delay. The Scd21 tells of the mode conversion--how much common signal comes out port 2 after being created somewhere along the line from the pure differential signal going in on port 1.

If any of this common signal gets out on an unshielded twisted pair, it will contribute to radiated emissions. By looking at Scd11, it is sometimes possible to determine where along the differential channel this conversion happened, and where to focus attention to prevent it.

The mixed-mode S parameter matrix is becoming the de facto standard for describing the performance of all high-speed differential channels.

Get comfortable with them.

DR. ERIC BOGATIN is the CTO at IDI and president of Bogatin Enterprises. Many of his papers are available at www.BeThe He can be reached at
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Title Annotation:NO MYTHS ALLOWED
Author:Bogatin, Eric
Publication:Printed Circuit Design & Manufacture
Date:Oct 1, 2005
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