In a previous blog, I discussed how channel quality is quantified by eye patterns [1]. There, it is explained how eye patterns are created from the thru S-parameters only. So, if you are using the thru S-parameters alone, do reflections even matter? Intuitively, it would seem like they don’t matter since they are not directly used to calculate the eye pattern.

But, of course reflections matter! Reflections cause signal integrity problems, and I’d like to start explaining how, by showing the relationship between the transmission parameter, insertion loss (IL), the reflection parameter, and return loss (RL). Simply put, RL takes away power from IL. For example, here is the behavior of plane waves at a boundary[2].

T is the transmission coefficient (how much power is transmitted) and Γ is the reflection coefficient (how much power is reflected).

This equation is expressed in terms of power and coefficients for other equations, and when the equation is converted to voltage and S-parameters, it looks like this.

This equation is much more useful since it can be directly applied to the S-parameters we get from measurements or simulations. Here is that equation plotted.

The takeaway here is reflections reduce the thru signal.

Before I continue, I’d like to talk a little about the nomenclature of insertion loss (IL) and return loss (RL). Since these terms include the word “loss”, when the values are negative, that means they are adding power to the system. In other words if there is negative loss, the result is gain. However, plots of transmission parameters are typically called insertion loss, and thus show negative numbers. This has become the standard way the industry communicates. So in this article, I’m going to follow suit: insertion loss and return loss will be negative values.

With that out of the way, the IL is significantly decreased once RL rises above -10 dB, and this is something that can easily be seen in S-parameters. I am using QUCS to easily get some reflective S-parameters by modeling a lossless Beatty structure [3]. A Beatty structure is a serial resonator created by a large discontinuity. Here, the discontinuity is a transmission line between two other transmission lines that has a different impedance.

As was observed in the RL vs. IL chart, you can see that at frequencies where the RL crosses -10 dB, the IL is noticeably lower. So perhaps we can determine how reflections impact the system by observing these dips. The industry calls these dips Insertion Loss Deviation (ILD), and it was first proposed by Adam Healey in 2009 [4]. He observed that the move insertion loss moves away from nominal the more the system pulse response deviates from nominal.

To calculate ILD, use the set of equations below to fit the insertion loss.

Each of the frequency coefficients has physical meaning. DC loss is assumed to be zero, the square root coefficient (a1) represent skin-effect, and the power one and square coefficients (a2 and a4) represent the dielectric losses. In addition, skin-effect has been shown to affect all the terms besides DC [5]. So using these terms, you can get coefficients that fit the insertion loss quite well using the following equation.

Finally, ILD is the difference between the measured IL and the fit.

When there are no reflections ILD is small, the IL is well matched, and ILD is as you would expect, small

When there are reflections, the plots looks much worse.

This ILD plot can have limits or a mask, and that gives us SI engineers quantity to target when reducing reflections. Further, we can use FOM ILD to quantify the reflections with one number [6].

It looks like our job here is finished, right? We now have a way to quantify reflections with insertion loss alone, and we can describe them with one number. Well, perhaps we can call it a day right now, but then again, we didn’t check if FOM ILD correlates to COM.

In COM, the noise related to reflections is determined in time at the sampling point and the error rate we are interested in. This metric is referred to as ISI noise, and here is the original proposal on how to calculate COM which includes ISI noise.

ISI noise is the sum of all the slices within a thru after the sampling point. A slice is a point nUI(s) away from the sampling point of the pulse response. Where ‘n’ is 1 to infinity and UI is the bit width, or Unit Interval, in seconds. The pulse response is the time-domain response of the system after injecting a single bit of data. The image below helps clarify these statements.

The red line is the pulse response before equalization—for our purposes, it’s meaningless, so ignore it. The blue line is the pulse response after equalization, and this is the dataset used to quantify the channel quality. The green circle at the top of the blue equalized pulse response is the sampling point. In COM, there is an equation that defines where this point is. Other tools, like Seasim just pick the peak. Personally, I’m a fan of just picking the peak, but that’s neither here nor there. The circles are the slices. If there is a circle at a non-zero level, it adds noise to the system. The pinkish circles (please excuse my engineering knowledge of colors) are the noise contributors that are zero’ed out by the DFE. The rest of the black circles are what adds to ISI noise. In the above plot, it looks like the DFE took care of almost everything, but in the next plot you can see there is still a large quantity of noise added from reflections.

Ugh. Even if we only consider the variance used for the FOM, this is MUCH more difficult than ILD! Therefore, it’s important to determine if the juice is worth the squeeze. The first thing to recognize is the publicly available COM code gives you this number, and the COM code is free-ish and easy to use. Second, COM is determined in the context of data rate and technology. The data rate is just how fast you’re sending the bits, and the technology is related to the quality of the SERDES.

For this experiment, I used the latest COM script from IEEE 802.3bj and used the 100GBASE-CR4 spreadsheet. Since I implemented lossless transmission lines in QUCS, I took advantage of the fact that COM adds transmission line loss in the CR4 setups.

COM considers several sources of signal degradation. First is the SERDES package. The SERDES package has loss and two reflections: one for the die (Cd) and one for the pad (Cp). Secondly, COM implements inherent noise related to the technology of the SERDES. These sources include package crosstalk and how well the transmitter can maintain a voltage level. That being said, it is easy to see that COM will have an upper limit even if you consider a lossless transmission line without reflections (which is the first dataset).

I remove the reflections caused by the pad by simply using the first COM scenario. In this scenario, the package is considered 12mm. The second scenario, which wasn’t used, is 30mm in length. The reflections from the 12mm package can be completely negated by the ideal DFE implemented within the COM script, and in the second the DFE isn’t long enough to mitigate the package reflections. In short, package reflections are not a variable in this analysis. The amount of signal is held constant by using a lossless transmission line. Finally, the system noise is a constant since I am using the same COM script for all calculations. The only thing that is changing is the reflective transmission line impedance. So, this setup is isolating reflections fairly well.

My impression of the plot above is that COM isn’t trending well with ILD. It isn't horrible, but it it’s not at a level where I’d be willing to bet my career on it. So you need to ask yourself, is ILD really working? I talk to many OEMs about their internal metrics and ILD comes up fairly often. In fact, I would say the majority of the field still highly relies on ILD as a metric of transmission line quality. But should they and is it enough? I think in the context of 100GBASE-CR4 (and KR4 for that matter), it probably is. However, there is likely a breaking point where ILD isn’t enough. Further, I certainly would not trust an ILD specification limiting a component since COM is meant to be used with an entire channel and not a part of a channel. If ILD is used to quantify components only, I believe false passing and failing results are achievable once the components are placed into a link.

So, what’s the verdict: ISI or ILD? In my opinion, ILD is a great sniff test. It is super easy to calculate, it can be done in excel or free coding languages easily, and it gives a decent view of what the reflections are doing. ISI noise gives the real view of what is going on, and in that regard it will always be better than ILD. With that said, I don’t think it’s enough to rely solely on the ISI given from the COM script. Remember, I said the sampling point is chosen by an equation. That doesn’t mean all SERDES will pick that point. I think to get a complete idea of what is happening, you would need to sweep several of these sampling points to see if you do indeed always have a passing figure. If you were going to rely on one, I recommend ISI. If you’re doing sweeps or need quick checks before digging into the time-domain, ILD is fine.

As a side note, I mentioned above that COM is free-ish, and I’m referencing the need for MATLAB. While MATLAB isn’t expensive for commercial use for a multi-million dollar company. However, it is quite an investment for an individual trying to make any money that isn’t from “the man” (Trust me, I know). If COM gets ported to say Python or Octave in the near future, things will be a lot better for us freelancers. Until then, we gotta put-up or shut-up when it comes to the cost of doing business.

Would you like to find out more about how Altium can help you with your next PCB design? Talk to an expert at Altium. You can also read an overview of everything you need to know, including transmission lines, terminations, and controlling backward crosstalk in high-speed PCB Design.

## References:

[1] Jason Ellison, Channel Operating Margin Isn’t so Bad, https://resources.altium.com/pcb-design-blog/what-is-channel-operating-margin

[2] D. Pozar, “Electromagnetic Theory”, in Microwave Engineering, 3rd ed, New York, Wiley

[3] QUCS: http://qucs.sourceforge.net/

[4] Adam Healey, Noise considerations for 40/100GBASE-CR4/10, http://www.ieee802.org/3/ba/public/jul09/healey_02_0709.pdf

[6] A. Koul, M. Y. Koledintseva, S. Hinaga, and J. L. Drewniak, “Differential extrapolation method for separating dielectric and rough conductor losses in printed circuit boards,” IEEE Trans. Electromagn. Compat., vol. 54, no. 2, pp. 421–433, Apr. 2012

[6] OIF-CEI-04.0, December 29, 2017

## About the Author

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