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.

How to Use Memory Properly

In a recent post, we addressed setting sample rate for serial data acquisition, but let’s look again at how time per division (time/div), memory length and sample rate all interact, and what you can do to optimize your use of oscilloscope capture memory when setting up your timebase.

Figure 1: Sample rate as a function of time/div for three different memory lengths.
Longer memory extends the range of time/div settings that support the highest sample rate.

Debugging Automotive Ethernet Transmitter Output Droop

Everyone manufacturing devices used for Automotive Ethernet knows what compliance limits they must meet, based on the electrical test specification, but it is not always obvious where to look for the source of the problem when a compliance test fails. We'll provide more Automotive Ethernet debugging tips in future posts, but here is one that arose from a reader's question: namely, why the 45% limit on output droop for 100Base-T1, and what might cause the problem?

Figure 1: Automotive Ethernet electrical testing is performed at the transmitter connector and is largely governed by channel/connector recommendations.  Between the transmitter and the connector is a Low-Pass Filter and a Common Mode Choke both affecting signal droop.

How to Use Measurement Statistics to Set Up Triggers

Figure 1.  Histogram of the different pulse widths occurring
in a pulse-width modulated rectangular pulse train.

Triggering is an essential element in all modern digital oscilloscopes.  The trigger synchronizes the oscilloscope’s data acquisition with a user-specified event on the signal, be that an edge, threshold crossing or a specific signal characteristic. Teledyne LeCroy Smart Triggers can trigger oscilloscope acquisitions based on properties such as a period, width, low signal amplitude, slew rate or signal loss. These trigger types are ideal for capturing transient events like glitches, but they require knowing at least a range of possible values for the trigger to detect.

Intermittent transient events and glitches are among the most frustrating problems to detect and solve. This is especially true if you have no idea about the nature of the transient. However, you can use the oscilloscope’s measurement tools to help locate these bothersome transients, then use that information to set up your trigger to capture them when they occur. Here’s how.

How to Test the CMRR of Differential Probes

Figure 1: CMRR plots for two attenuation
settings of an HVD3106A differential probe.

While recently we told you not to connect two probes to the same place at the same time, there is a case where connecting two tips of a differential probe to the same place at the same time is useful, and that is when testing the probe’s common mode rejection ratio (CMRR). CMRR is frequency dependent, so part of developing “situational awareness” of your test environment is to know how your probe behaves with different signals at different frequencies. 

Although CMRR as a function of frequency is a principal specification for differential probes, manufacturer's CMRR plots are the result of testing with a narrowband source under strictly controlled laboratory conditions. In real-world applications of probes to broadband sources, you can expect a different result. This quick test will inform you how different.