Use S-parameters to describe crosstalk
Once this noise gets on an adjacent transmission line, it will propagate just like any other signal and eventually arrive at the ends of the line. A receiver connected to the end will see this crosstalk eating into its signal’s noise budget. In low-level analog applications, as little as 0.01% crosstalk might be tolerable, while in high speed digital applications, as much as 5% crosstalk may be acceptable.
Unfortunately, in many interconnect systems, signal levels from crosstalk can easily exceed 10% of the wanted signal, which will increase the system’s BER (bit error ratio or bit-error rate). Characterizing the amount of crosstalk from an aggressor line to a victim line can often be an important diagnostic in identifying, and eliminating the possible root cause of bit errors.
S-parameter formalism, developed to describe the microwave properties of interconnects, offers a natural way of describing crosstalk for applications from the audio frequency range to the millimeter-wave frequency range. After all, each S-parameter element is really the ratio of a sine wave coming out of one end of an interconnect compared to a sine wave going into another. In a collection of transmission line structures, many of the S-parameter terms are a direct measure of the line-to-line crosstalk. The same formalism can be extended to differential pairs as well.
A coupled-transmission line test vehicle
To illustrate the use of S-parameters to describe crosstalk, a simple test vehicle was constructed with four coupled transmission lines, as shown in Figure 1. Their ends are labeled with index numbers from 1 to 8. Connected to each end is a port, which can be thought of as a short 50-Ω transmission line terminated in 50 Ω. The recommended port assignment to be used to measure this DUT (device under test) has through connections set up as port 1 to port 2, 3 to 4, 5 to 6 and 7 to 8.
Figure 1. Photo of the four coupled transmission lines used in this example with their ends labeled with the recommended port assignment. Each line is about 11 inches long when unwound.
Each S-parameter matrix element for this DUT is the ratio of the sine wave coming out of a port to the sine wave going into a port. With eight ports, there are 8 x 8 = 64 different combinations of going-ins and coming-outs. The S-parameter matrix formalism is used to keep track of each of the combinations. The index number of each matrix element identifies which is the coming-out port and which is the going-in port.
For example, S21 is the ratio of the wave coming out port 2 compared to the wave going in port 1. This specific term, for historical reasons, is referred to as the insertion loss. It has information about the attenuation of a signal traveling through the interconnect.
As the ratio of two sine waves, each S-parameter matrix element is a complex number, described by either a real and imaginary value or a magnitude and phase. The magnitude is the ratio of the amplitudes of the wave coming out to the wave going into the port, using 50 Ω as the impedance of each port.
Most of the S-parameter terms are a direct measure of the crosstalk between ports. The crosstalk of a sine wave entering port 1 on one transmission line and coming out port 3 of an adjacent line is labeled as S31. The relative crosstalk for a signal entering port 1 and coming out the other end of the adjacent line at port 4 is labeled as the S41 matrix element.
Crosstalk can be subtle
Even at “low” frequency, the crosstalk between two adjacent lines often depends on which end of the victim line we look. Backward propagating crosstalk is the sum of capacitive and inductive coupling while forward propagating crosstalk is the difference between capacitive and inductive coupling. We would expect S31 not to be the same as S41. Figure 2 shows these two S-parameter terms when measured with a LeCroy SPARQ Signal Integrity Network Analyzer. Even at 20 MHz, the near and far end crosstalk are different, with the S31, near end crosstalk, larger than the S41, far end crosstalk.
Figure 2. Crosstalk to an adjacent line measured with a LeCroy SPARQ Signal Integrity Network Analyzer. Left: horizontal scale is 1 GHz full scale. Right: horizontal scale is 20 GHz full scale. Vertical scale is the same: 40 dB full scale with 0 dB at the top of the plot.
This is yet another counter-intuitive property of the behavior of signals on interconnects. Even though S31 and S41 are measuring the crosstalk from the same source on the same interconnect, the noise appearing at each end of the victim line is radically different, especially above about 100 MHz.
It is not enough to specify how much crosstalk occurs between two lines. The direction in which the noise is traveling on the victim line must be specified as well. This is why the two ends of the victim line are labeled differently.
Using the S-parameter notation, S31 is the noise on the victim line on the end near the source and is referred to as the near end noise. Since the signal on the aggressor is propagating in the direction defined as the forward direction, the near end noise is also the noise propagating on the victim line in the backward direction from the signal.
The S41 term is the noise measured on the far end of the victim line, or in the forward direction. With tightly spaced microstrip transmission lines shown in Figure 1, the near-end noise reaches a peak value of only –13 dB, or 22% of the original signal, compared to the far end noise which peaks at about –4 dB which is 63%. These large values are an indication of how tightly coupled are these two transmission lines.
The formalism of S-parameters automatically takes into account which port the signal enters and each port in which it comes out. This makes S-parameters a natural tool to describe crosstalk.
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