Eliminating DC Resistively Coupled Noise: A Signal and Power Integrity Tutorial

Figure 8. The measured voltage noise on the victim
trace, on the other side of the ground plane gap,
showing no resistively coupled cross talk on the
order of 10 uV, the noise floor of the measurement.

The following is excerpted from Professor Eric Bogatin's article in the Signal Integrity Journal, The Case for Split Ground Planes. Reprinted by permission of Signal Integrity Journal.

This section continues from the discussion on Inductively Coupled Noise and Resistively Coupled Noise.

. . .

When we cut a gap in the return plane, there will be no DC current flow across the gap. There will be magnetic field coupling across the gap which is why we still see significant mutual inductance coupling between the aggressor and victim across the gap. The gap has only a small impact on this noise.

However, we would expect there would be no resistively coupled noise on the victim trace on the other side of the ground plane gap. In Figure 8, the resistively coupled noise is measured with the same scale and averaging as the noise on the victim line with no gap. The noise floor of this measurement is about 10 uV. To this level, there is no measurable resistively coupled noise, a significant reduction. 

Mode Conversion

Figure 1: The lower-left and upper-right quadrants of this
matrix show the S-parameters that represent mode conversion
from differential to common signal, and vice versa.

As said earlier, mixed-mode S-parameters describe the general case of combinations of differential and common signals. When we speak of mode conversion in mixed-mode S-parameters, we are referring to the change of a differential signal into a common signal, or a common signal into a differential signal, as it travels the transmission line. If we look at the matrix of mixed-mode S-parameters in Figure 1, we see that those mixed mode S-parameters affected by such a mode conversion—with a different type of signal going out than what went in—are in the lower-left and upper-right quadrants.  

Let’s take the S-parameters SCD11 and SCD21 to see how the combination of single-ended S-parameters they represent reveal the source of mode conversion. If we look at SCD11, the reflected mode conversion, as a function of its single-ended S-parameters, we see:

Converting Single to Mixed-Mode S-Parameters

Figure 1: Model of two transmission lines with crosstalk
showing the transmission and crosstalk related S-parameters.

We have introduced mixed mode S-parameters and developed a formal structure for handling them. It is now time to discuss converting single-ended S-parameters into mixed-mode S-parameters. This is important because every instrument manufacturer obtains mixed mode S-parameters by first measuring single-ended S-parameters, then converting them mathematically to mixed-mode. This assumes that the interconnects being measured are passive, linear and time invariant.  Let’s begin with our model of two transmission lines with crosstalk shown in Figure 1.

Introduction to Mixed-Mode S-parameters

Figure 1: Single-ended vs. differential signal
"world views" of S-parameters

We’ve treated single-ended S-parameters quite extensively in this blog. Links to several entries are listed at the bottom of this post. Now, we’re going to look at how we go from single-ended to mixed-mode S-parameters and what new information we can find in them. This will come in handy when we start looking at some of the MDI S-parameter tests that are performed for Automotive Ethernet compliance a bit down the road.

With single-ended S-parameters, we look at every combination of ‘going in signals’ and ‘coming out signals’. For example, two single-ended transmission lines and their return paths would yield a four-port S-parameter file. We take the complex ratios of each port combination to obtain the S-parameter value in the form of:

S_(OUT,IN) =  V_OUT/V_IN 

The bold typeface indicates complex quantities. 

But what happens if we drive two transmission lines with a differential source? Figure 1 compares the single-ended and differential signal world views.