The Mixed Mode S parameters - Intricacies of SCD21 and SDC21

Introduction to Mixed Mode -S-parameters

Keywords: Single Ended, Differential Ended, Skew, Why SDC21,SCD11 and SCD21 are good to understand from EMI EMC and Signal integrity point of view.

In the last topic, we realized the significance of single ended S-parameter. Please note, we cannot include everything in this series post . I really don't want to make an article sound like an IEEE paper. Most of the times, when I read a paper with more than 10 pages, I feel very sleepy ! I don't want to experience with my own post. Honestly, we can write a paper just based on differential detours and the way it impacts the channel performance :) !

In this topic, we will debug some interesting aspects related to Mixed Mode -S-parameters, which are scattered all around

The advantages and disadvantages of differential signaling is beyond the scope of this post. In a nutshell, in case of differential signaling the two voltage signals are "balanced," meaning that they have equal amplitude and opposite polarity relative to a common-mode voltage. The return currents associated with these voltages are also balanced and thus cancel each other out; for this reason, we can say that differential signals have (ideally) zero current flowing through the ground connection.

If you are a high-speed designer or speaking to a high-speed designer, you will only hear differential signal analysis and nothing else. Single ended signaling discussion should be left in MARS. As shown in Figure 1 above , in single ended world view, we have four ports. The impedance is 50 ohms across the ports and in case of differential world we have only two ports and any wave form that goes through either of the differential ports can be described by a combination of differential and common signals.

Figure 2: Courtesy: Lamsim enterprises-Bert Simonvich

The first quadrant in the upper left of Figure 2 is defined as the four parameters describing the differential stimulus and differential response characteristics of the device under test. This is the actual mode of operation for most high-speed differential interconnects, so it is typically the most useful quadrant that is analyzed first.

The first quadrant includes input differential return loss (SDD11), forward differential insertion loss (SDD21), output differential return loss (SDD22) and reverse differential insertion loss (SDD12). Note the format of the parameter notation SXYab, where S stands for Scattering Parameter or S-Parameter, X is the response type (differential or common), Y is the stimulus type (differential or common), a is the output port and b is the input port. This is typical nomenclature for frequency domain scattering parameters. The matrix representing the four-by-four matrix of time domain parameters have similar notation, except the “S” will be replaced by a “T” (i.e., TDD11).

The fourth quadrant is in the lower right of figure 2 describes the performance characteristics of the common signal propagating through the device under test. If the interconnect is designed with minimal asymmetry to transmit only differential signal, then fourth quadrant data is of little concern. However, if any mode conversion is present due to design flaws, then the fourth quadrant describes how the common signal behaves. The second and third quadrants are in the upper right and lower left of Figure 2. These are also referred to as the mixed mode quadrants. This is because they fully characterize any mode conversion occurring in the device under test, whether it is common-to-differential conversion (EMI susceptibility) or differential-to-common conversion (EMI radiation).

Honestly this is available everywhere with more mathematical derivations. In fact in KEYSIGHT ADS (Easy), SIMBEOR, CST, ANSYS or possibly any 3D tool, we can write down the equations mentioned in Figure 2 and calculate the results accordingly. Also, I would suggest you to read the reference paper mentioned in the article if you intend to really deep dive into the way mixed mode parameters are derived.

I want to emphasize the significance of SCD21 and SDC21 and before I do that, I want you to pause for a second and think ! So, if I drive a differential signal in, either differential or common signal could be the output and vice versa. How come a differential signal is driven in and common signal comes out ? What triggers this asymmetry that makes a differential signal into common mode signal at the end of the output port ! Before we proceed to some examples, Let us discuss in short about the parameter called SKEW

Skew is the deviation of propagation delay from required reference timing. Skew is the time-of-arrival error of a signal with respect to some reference time. It is inherently a time domain parameter, relying on the measurement of propagation delay. Again there is a debate on the reference level chosen hence we measure delay in frequency domain and we can calculate phase delay or group delay as function of frequency. Take a pause here and read what is phase delay/group delay means before proceeding further.

Simple analogy:

Track P : I want to reach from Point A to Point B -Distance 100 km Assume you are driving a car with 100 Kmph. No body obstructs your way. You will reach in 1 hr.

Track N: Everything is same including distance/car/driver. However, I add a small bump in the track (extra copper), pour some sand (change in dielectric), change the track shape like a F1 track with some curvature. Can I reach in an hour ?

Do we measure the same time of arrival/phase delay in both the track P and N ? No right, we are going to see a separate time of arrival in Track N.

Now let us see few parameters which will impact the mode conversion:

Example 1: Asymmetric microstrip transmission line analysis: Width's are different: This example explains beautifully about the importance of S-parameters. Old example but a golden one. If we observe here the Scc21- the ripple pattern , we can clearly understand that there is an issue with the impedance mismatch -common mode propagation. Sdd21- No ripples, less loss , less mismatch in the impedance. However, in contrast if we observe the return loss of SDD11 we see that it is greater than 20 dB ! Where is the loss coming from ? It is coming from the mode conversion due to the asymmetric microstrip width. Differential energy is converted to both common mode transmission SCD21 and common mode reflection SCD11. In this way mixed more parameters are quite helpful to realize the losses.

Example 2: Did the manufacturing team pour extra solder on the trace causing any change in the way signal arrives at the other end?

Point 3: Did we match the length of the differential signals? I recently understood in one of the webinars that now Altium gives PCB designers to match the traces based on timing rather than on length! That’s a great news. We will see further the impact of this by studying some skew length’s and how the SCD21 results get impacted due to the change in skew. If you see, in this simulation, we tried to compensate the skew but the length of the traces was little longer in Model 2 in comparison to Model 1. What happens can be visualized in SCD21 and SCD11. Check the TDR impedance plotted in the results and see whether anything can be understood from the plot ! Reference impedance is 95 ohms !

Point 4: Is the stack up that has been used in the board development symmetrical in nature? Weave effect – We will discuss this topic little later in another blog post. But for now remember that fiber weave effect causes significant issue in terms of mode conversion.

Point 5: Unbalanced via loading effect. This is a case where we cannot place symmetrical vias due to routing feasibilities.

Point 6: Via back drill depth. This can really be disastrous from the fab house if the via drill on the P side is done well but on N side went for a toss. This is a rare phenomenon but can happen too.

If you observe in the above quoted examples, understanding the mode conversion results are really important in realizing the product. Any asymmetry can be easily dealt using mixed mode parameters. Understanding the magnitude and location of mode conversion is very helpful when trying to optimize the design of interconnects for gigabit data throughput.

Points to Ponder: We spoke about SCD21 and SCD11 but nothing related to SDC21. The first two parameters are important to understand when we are working on stand alone models. First, we don't want our product to create any emissions. We will discuss again about mixed mode parameters in the next EMI EMC topic. Until then Good Bye ! Thanks for reading !

Sorry one last second, In case you feel something is missed or should have been discussed, comment in the article, it helps me to realize things which I have never heard or didn't write in the article due to the sake of brevity. I want to collect all comments and add the text after the end of series. Please dont except maths ;)

Reference Papers:

1.Bockelman D. E. and Eisenstadt W. R., Combined Differential and Common-Mode Scattering Parameters: Theory and Simulation. IEEE transactions on microwave theory and techniques, Vol. 43, No. 7, pp.1530-1539, July 1995