# Reflecting on Reflections: An Evaluation of New and Standardized Metrics

by Steve Krooswyk, Richard Mellitz, Adam Gregory, John Riley, **Samtec**; Beomtaek Lee, Stephen Hall, Intel; Hansel Dsilva, Achronix

Today’s high-speed digital interfaces have become more sensitive to signal reflections with the result that there is a greater need to characterize and suppress channel and component discontinuities. There are significant differences between characterization methods in standards such as PCIe, IEEE 802.3 and USB that can be confusing. This article will describe reflection standards such as RL, IMR, ILD, IRL, and ERL, along with new unadopted metrics of RILN and IRL. It will also explain the use of parameters and applications, as well as evaluate their correlation to what matters most: end-to-end channel margins at 32 GB/s NRZ and 112 GB/s PAM4.

Reflections are one of the vital characteristics of any interconnect, especially at higher data rates. Consider the simple metric of performance, signal to noise ratio (SNR)—sensitivity to contributions from reflections increase at higher baud rates and order of modulation. The need to characterize and suppress whole channel or single component reflections has never been higher. The traditional method of characterizing and bounding maximum reflection noise using a frequency domain return loss curve has begun to show its shortcomings.

Often small violations in component frequency domain limits occur, as shown in **Figure 1**. It is difficult to interpret if a violation is really a failure, and if a failure occurs at a high frequency while low frequencies far exceed a requirement, should we expect a failure? How much power was in the reflection? More than half of return loss limit violations are false negatives, as specifications often favor protecting systems from failures. An experienced engineer may know how to reduce the importance of higher frequencies in a quantitative way.

This has led to specifications defining alternative single-point metrics such as Integrated Multi-Reflections (IMR), Integrated Return Loss (IRL_{USB}), Figure of Merit of Insertion Loss Deviation (FOM_{ILD}) and Effective Return Loss (ERL). An overview of the different metrics is covered in this article.

A new variation on IRL_{USB} called IRL_{NEW} is evaluated as well as Figure of Merit Reflectionless Insertion Loss Noise (FOM_{RILN}) previously introduced in [1]. A comprehensive study at varying data rates will be shared by presenting a correlation at various test points to end-to-end channel margin. Channel analysis is to be completed at 32 Gb/s using Seasim and Channel Operating Margin (COM) tools and at 112 Gb/s PAM-4 using COM.

**The Difficulty of Accurate Component Screening**

Screening and qualifying components by themselves such as connectors, packages, cables, and interoperable boards is a common standards practice. Component-only tests are allocated a limited budget to guarantee system function and open interoperability. The most challenging task is relating component test results to system margin, which is especially difficult using frequency domain return loss limit.

An example is illustrated in **Figure 2**. Simulated channel COM is related to connector return loss margin as the minimum difference between connector return loss and a return loss limit for 50 connector models. The graph tries to map ‘pass system’ to ‘pass component’ and vice-versa. The relationship is never ideal and there are miscorrelations. A decision could be made to mitigate the system risk and eliminate false positives, but this may be at the cost of disregarding otherwise good components. The reverse extreme for zero false negatives favors the components.

It is apparent that the use of a reflection metric that correlates well reduces the risk and benefits both system and component suppliers. In the example shown in **Figure 2**, a well-designed return loss limit was used, yielding a linear fit value of 60.2% between COM and RL_{MARGIN}. It is believed this is near the upper limit of return loss capability, and other frequency domain limits may perform worse, especially those flat across frequency. This article will evaluate return loss metrics that may exceed this performance.

**Reflection Metrics**

A number of reflection metrics are used across various standards today and their applications and methodology for characterization are discussed below.

**Power Weighting Filters**

All metrics operating in the frequency domain use a weighting filter to represent the actual power present in the time domain. The weighting filter reduces the importance of higher frequencies that are not transmitted as well as those removed by band limited transceivers. This section reviews weighting filters from IEEE and OIF, which will be referred to as IEEE and that from USB.

The IEEE weighting filter contains three filtering components: a transmitter and a receiver filter, and a sinc function. Transmitting and receiving devices do not have an unlimited bandwidth. In part, limited bandwidth is by design to prevent aliasing and attenuate noise. The transmitter bandwidth is expressed as a filter whose -3 dB roll-off location is defined by the risetime in **Equation 1**. A risetime constant of 23.65% of the UI is used in all cases. The receiver filter is a four-pole Butterworth filter centered at 75% of the baud rate, and defined in **Equation 2**.

Eq. (1)

Eq. (2)

Where,

f_{t} is 0.2635/risetime (7 ps)

f_{r} is 0.75 of baud rate (32 GHz)

The data pattern has limited power spectral content related to its switching rate. This limited band is represented for random data patterns by the square of the sinc function. The pi-normalized sinc function is used in:

Eq. (3)

Where,

f_{b} is baud rate (32 GHz)

sinc(x)=sin(x*pi)/(x*pi)

A constant A is provided in front of the final weighting function in **Equation 4 **to represent transmitted peak voltage. In crosstalk applications, this constant has been known to represent mean-peak (IEEE) or peak-to-peak (OIF). For the purpose of evaluations, the constant is excluded.

Eq.(4)

**Figure 3** represents the role of each individual filtering component and the final weighting filter. For ease of viewing the relative rate of change across frequencies, the final PWF is normalized to 1. Together, about 40% of power is present at Nyquist and has been reduced to 4% at 1.5x Nyquist. This view is highly informative to understanding the relevance of different frequencies. The relevant importance between frequencies of interest can now be quantified. It should be apparent why many frequency domain limit standards terminate at Nyquist or 1.5x Nyquist.

The USB filter performs all its weighting through a trapezoidal transmitter filter with a finite risetime as shown in **Equation 5**. This is in contrast to the IEEE filter, which uses multiple terms of an instantaneous risetime (**Equation 3**) and further filtering in **Equations 1 **and **2**. In **Equation 5** the first term defines the rise time and the second the signaling rate power.

Eq. (5)

Where,

T_{b} = 1/fb (32 GHz)

T_{r} = 0.4*T_{b} (12.5ps )

**Figure 4** compares the IEEE and USB weighting filters for the same data rate of 32 Gb/s. This article makes no judgement of whether IEEE or USB weighting filter design have any advantage and only highlights the differences. However, the USB filter yields less filtering than IEEE.

**Figure of Merit of Insertion Loss Deviation**

Introduced in IEEE 802.3 [2], FOM_{ILD} evaluates reflections for connectors on a compliance test fixture in a single value. FOM_{ILD} measurements are taken for a pair of PCBs mated to a connector, the Host Compliance Board (HCB) and Main Compliance Board (MCB). The fixtures are not de-embedded, and the form factor performs well, leading to relatively low measured reflection levels.

ILD is a measure of the ripple on the insertion loss. Ripple is caused when reflections on the component occur, taking power away from the through path. As defined in **Equation 6**, deviations are determined by subtracting the insertion loss from an insertion loss fit line. A set of parameters exists in **Equation 2** to tune depending on the application conditions, such as the ratio of interconnect conductor to dielectric loss.

ILD(f)= IL(f)- IL_{fit} (f) Eq. (6)

A connector component IL, IL_{fit}, and resulting ILD are shown in **Figure 5**. The low frequency fit response of IL_{fit }below 500 MHz is poor conforming, leading to higher ILD(f). Accuracy of the IL_{fit} is paramount to useful ILD data. New applications can vary in conductor and dielectric losses, which affects the ability of a successful fit; therefore, tuning parameters available defined in [2] should be diligently reviewed.

FOM_{ILD} is then created by multiplying ILD with an IEEE weighting filter and integrating the result as shown in **Equation 7**. The effect of the filters prior to integration is illustrated in **Figure 6** for a signaling rate of 32 Gb/s. In this example, low frequencies show little reflection, are near zero, and will contribute little to the integral. Larger reflections at 18 GHz and higher will contribute most to the FOM_ILD value.

Eq. (7)

**Integrated Multi Reflection (IMR)**

Integrated Mutli Reflection (IMR) is used to evaluate cable assemblies in USB Type C Revision 1.4 for USB 3.2 Gen2 and USB4 Gen2 found in **Equation 3**. Like FOM_{ILD}, IMR performs an integration of ILD defined in **Equation 6**. However, the IMR **Equation 8** differs from FOM_{ILD} in the weighting filter and the integrated units. IMR exchanges the IEEE for USB weighting filters. In **Equation 8 **the magnitude of ILD is performed before squaring.

Eq. (8)

**Figure 7** shows the IMR processing of ILD into magnitude, its square, and the weighting filter effect at 32 Gb/s. Compared to ILD processing in **Figure 6 **on the same connector response, notable differences can be observed in the noise at 20 and 25 GHz on the pre-integration curve ILD*Wf. In IMR, both frequencies carry similar weight, whereas in ILD 25 GHz is quite attenuated relative to 20 GHz. This is attributed to the weighting filter differences in **Figure 4**.

**Reflectionless Insertion Loss Noise**

Reflectionless Insertion Loss Noise (RILN) was introduced at Designcon 2019 as a new metric for reflection characterization. Rather than subtracting IL_{FIT}(f) from IL(f)as in ILD and IMR, a Reflectionless Insertion Loss (RIL(f)) is determined and used as in **Equation 9**.

RILN(f)=IL(f)-RIL(f) Eq. (9)

RIL(f) is found by zeroing out the reflections on each port. Removal of reflections observed at the network ports in RIL(f) leads to a smooth curve. As demonstrated in **Equation 1**, this method improves on the use of IL_{FIT}(f) in ILD and IMR measurements.

RIL(f) represents the reflections caused by effects outside of the network as observed by a chosen reference impedance. It is possible that RIL(f) is not entirely smooth. In the case of reflections within the network that are not observed at the port, these will remain on the RIL(f) response. However, this is acceptable because these reflections did not continue outward into the system and will be removed when subtracted (**Equation 9**). Loss and resonances appearing on IL(f) due to crosstalk will also remain on IRL(f), which represents the reflections.

Like other metrics, the figure of merit FOM_{RILN} is found through integration after the use of a weighting function, given in **Equation 10**.

Eq. (10)

W(f) follows the IEEE definition in **Equation 4**. **Figure 8** shows the components of FOM_{RILN} leading to integration and using the same connector as in **Figure 6** and **Figure 7.** The location of power across frequencies is notably different in RILN^{2}(f) (yellow) compared to ILD. Like ILD and IMR, strong reflection power content exists at 20 GHz. However, the 15 and 25 GHz content is eliminated. There may be an advantage of RILN(f), determining 15 and 25 GHz to effects do not leave the network. As seen on ILD and due to the IEEE weighting function, content is severely attenuated by 25 GHz.

**Integrated Return Loss (USB)**

Integrated Return Loss (IRL_{USB}) is a compliance metric for USB 3.2 Gen2 and USB4 Gen4 cable assemblies. In contrast to IMR, IRL_{USB} characterizes the reflections between the cable assembly and the rest of the system. IRL_{USB} is the integration of the worst case RL power multiplied with the component insertion loss and the USB weighting function (5) and is given in **Equation 11**.

Eq. (11)

The previously discussed metrics have represented reflections traveling the entire through path, while IRL_{USB }characterizes noise returned by the network. Before this reflection can be realized at a receiver, a re-reflection on another component must occur. The reflection coefficient of this component and its distance from a discontinuity is never known but IRL_{USB} suggests that at least the cable loss must be traveled and the reflection must be attenuated. SDD_{21}(f) is included in **Equation 11**.

A cable assembly with meaningful SDD_{21}(f) magnitude is used to illustrate the progression of IRL_{USB} in **Figure 9**. Strong return loss near 10, 20 and 30 GHz are attenuated. As observed in this figure, it is possible for the artificial worst case return loss |SDD_{11}(f)|^{2}+|SDD_{22}(f)|^{2} to become greater than zero. W(f) continues the high-frequency attenuation and ends at f_{b}. Integration is performed on the final response (orange).

**Integrated Return Loss (New)**

A new metric, Integrated Return Loss (IRL_{NEW}), is not used in any standards. In contrast to IRL_{USB}, IRL_{NEW} uses the IEEE weighting filter, does not include the component insertion loss term, and operates on one side (either SDD_{11} or SDD_{22}) as given in **Equation 12**.

Eq. (12)

This form, using the input or the output, does require calculation to be performed twice for a complete characterization. Evaluation of return loss at only one port may assist in correlation improvement if one side is dominant, e.g., facing a receiver. The exclusion of SDD_{21} enables the use on end-to-end channels and connectors. An example of a connector return loss and return loss with the weighting filter is shown in **Figure 10**.

**Adding PCB Loss to Reflection Metrics**

**Figure 11** shows how re-reflections may travel segments of the PCB multiple times before reaching a receiver. It is possible that higher-frequency reflections must be further attenuated to promote correlation to system margins. IRL_{USB} may represent the re-reflection path by the use of SDD_{21} in **Equation 11 **if the S-parameter contains significant loss (from cables, etc). In this case little-to-no additional loss would be included.

A review of additional loss included on all frequency domain metrics is achieved by repurposing an existing method used for crosstalk characterization where an analytical loss component is given as

Eq. (13)

Where

f_{b} is baud rate

K_{xa} is loss in dB

The loss factor input is an insertion loss in dB. The loss filter is a simple monotonic curve. An example is shown in **Figure 12** when K_{xa}=2.5 dB. This curve is meant as an approximation of PCB loss and does not capture the physics of the real PCB. This may be an area for future improvement.

This opportunity to include actual PCB losses may increase the relevancy of a return loss metric if assumptions about the system are made. An example of the updated equation for IRL_{NEW} is given as

Eq. (14)

The new progression of filtering for IRL_{NEW} with a 9 or 35 dB PCB loss filter is shown in **Figure 13**. In the same way, the PCB loss term will be evaluated on all other frequency domain metrics.

**Effective Return Loss**

Effective Return Loss (ERL) was introduced to control reflections in IEEE 802.3 and OIF CEI standards for channel and package compliance for some data rates 50 Gb/s PAM4 and higher. Values for ERL specification limits were derived from COM end-to-end performance correlations in the IEEE 802.3 and OIF CEI. Operating in the time domain and including equalization if needed, ERL better represents actual reflections at a given data rate.

A simple way to think of ERL is like an echo pinging into a port. The injected pulse is representative of a single symbol. The histogram of pinged responses can be thought of as a model of the collection of reflections. Combining this histogram with a histogram for random symbols produces a histogram of random symbol reflections.

ERL reported in dB is a single valued statistical property of that histogram of reflections. The IEEE and OIF standards convert the histogram to a cumulative distribution function (CDF) and compute the amount of reflection at a defined symbol error rate. ERL_{RMS} and ERL from CDF are well correlated when there are many reflections of similar magnitude. ERL from the CDF may apply better if reflections are concentrated in time.

The “pinged echo” response is a pulse time domain reflection (PDTR) waveform as shown in **Figure 14**. The associated TDR is also shown. For this article, the RMS of the histogram of the red dots convolved with random symbols and reported as dB will be used for ERL. In many specifications, ERL is defined at all ports looking in both directions but in this case ERL for the channel is measured at the receive port looking back towards the transmit port through the channel. The component ERL is performed on the component without the channel attached. For purposes of this explanation, ERL for the component is only measured into the receive side of the component.

Accommodation for the presence of a decision feedback equalizer (DFE) in a victim receiver may be included in ERL calculations. The idea is that, for a package connected to a channel, there is essentially a DFE shadow around the BGA ball area; the shadow could be associated with a small collection of the red dots in the PTDR. Many connector specifications include the connection to a PCB, making DFE accommodation less useful. The accommodation for DFE canceling is included in many standards but it is not utilized in the reported data here.

**Simulation Channel**

A channel achieving near 32 dB of loss at 16 GHz is represented in **Figure 15**. Packages compose each end of the link and a variable connector is placed in the channel to alter reflections. The connector is placed near the receiver but outside of the DFE equalization range to represent worst case reflection conditions for the least amount of loss. Positions further away from the receiver at 2.5 and 4 in. were also evaluated with the same total 16-in. length. In those cases, the correlation coefficients in the results are slightly reduced but the overall conclusions are unchanged; no crosstalk is included.

Full channel margins shown in this article are computed in the Channel Operating Margin (COM) tool at Test Point 4 (TP4). The simulator is configured for a BER of 1 to 12 and representative 32 Gb/s TXLE, CTLE, and 3-tap DFE. To check for consistency, simulations were also executed using the Seasim tool. However, as Seasim correlation results were consistent with the COM tool, the numeric results will be reported only for COM. Reflection metrics are computed for both end-to-end (TP1 to TP4) and component by itself (TP2 to TP3).

**Variable Connector Model**

A small set of five HFSS models of similar but varying geometry are available for simulation and include PCB breakout details. To increase the rigor of this analysis, a variable synthetic connector model is designed to allow a greater number of simulations. The model follows a low-high-low impedance profile that is similar to a connector and PCB attachments.

Synthetic models cascade a capacitive load for the low impedance regions and a mathematical transmission line representing the higher impedance connector contact. The transmission line region includes the delay and loss necessary to represent connector performance. The transmission line and each of the loads are uniformly randomized within the ranges noted in **Figure 16**. It is difficult to represent an entire connector in a synthetic way and modeling may have unintended side effects.

The charted return loss for both model types considered is shown in **Figure 17**. Return loss ranges at 16 and 28 GHz are diverse, leading to return loss above -10 dB.

**Reflection Metric Results at 32 Gb\s**

Reflection metrics are calculated for each connector by itself, TP2 to TP3, and then related to end-to-end channel COM performance. **Figure 18** and **19** chart this relationship for the HFSS and synthetic models, respectively. For each, an R-Squared is obtained from a linear fit as an evaluation metric and is shown in the figures.

Reflection metrics are calculated for the end-to-end channel (TP1 to TP4) and compared to channel COM from the same test points. The results and those from **Figure 18** and **Figure 19** are summarized in **Table 1**.

An acceptable threshold is suggested to be near or exceeding that of a well-designed return loss limit. Discussed earlier in **Figure 2**, an Rsq of 60.2% is the minimum margin to a return loss limit measured TP2 to TP3 on synthetic models. Results exceeding this mark are shown in green in **Table 1**.

HFSS model sample size is small, and conclusions should be cautious. HFSS models introduce a high geometric variability with physical meaning and give an initial headwind into a metrics ability (or inability) to relate to channel margin. Often standards teams are limited to similar sample size. Synthetic models promote more testing but may have acted as a T-resonator or other unexpected behavior that is difficult to characterize.

FOM_{ILD} and IMR are challenged on the HFSS models and show improvement on the synthetic. This can be explained by the IL_{FIT}(f) coefficients that were designed to fit transmission line behavior. Evaluation and adjustment for these coefficients is likely necessary for optimal results.

FOM_{RILN} offers high correlation marks on all tests. Notably reaching 90% for the channel metric, this metric along with FOM_{ILD} and IMR, effectively describes the magnitude of reflections that have reached TP4 when measured from TP1 to TP4.

IRL_{USB} is effective for components (TP2-TP3) and was not intended for use on full-link channel (TP1-TP4). In a full link, the channel loss IL(f) likely far exceeds the attenuation of re-reflections near the receiver. The IL(f) term could be removed or IRL_{NEW} may be considered.

IRL_{NEW} demonstrates modest correlation for connectors by themselves at both TP2 and TP3. At these test points Rsq scores are near identical. This does not necessarily suggest both sides are equal in importance, but may be an artificact of both sides having similar performance. Re-reflections at TP2 must travel a long path and this Rsq result may be artificial. When IRL_{NEW} is evaluated on the channel only TP4 (receive location) shows relevancy. This could suggest initial reflections near TP1 are less relevant than re-reflections occurring near TP4. It may also be that component placement near TP4 has created the strongest reflections.

ERL_{RMS} offers sufficient correlations on TP3 and TP4 evaluations. The cause of lower margins for the synthetic models is uncertain. Standards adoption has moved to a CDF-based method that could have a different outcome than that shown here.

**Reflection Metric Results with Additional PCB Loss at 32 Gb\s**

Additional loss terms from **Figure 11** and **Equation 13** were considered for all frequency domain metrics. Two choices, 9 dB and 35 dB, were selected to represent possible shorter and longer re-reflection paths such as triple transit, 5x transit, etc. Calculations with additional loss are only performed at TP2 and TP3; results are shown in** Table 2**.

IRL_{USB} and IRL_{NEW} are the only metrics offering improvement each time more loss is added. IRL_{USB} with additional loss outperformed any other metric evaluating TP2 to TP3, receiving 89%. These are also the only two metrics operating single-sided as SDD11 or SDD22, where the characterized port must be still be re-reflected to impact margins and may explain the correlation improvement.

All other frequency domain metrics characterize already re-reflected noise entering the system at TP3 and additional loss may over-attenuate the 5x transit reflections and not represent system behavior. Improvement only occurred for HFSS connector models. Synthetic models performed worse with added loss and the reason is not certain.

**Reflection Metric Results at 112 Gb\s PAM-4**

Simulation results were performed in the COM tool with preliminary 112G-PAM4 mid-reach transmit and receive Rx assumptions. The channel selection shown in **Figure 20** places a connector between 4 in. of the low-loss PCB trace. Reflection metrics are calculated for connector alone at TP2 to TP3. The synthetic connector models from the 32 Gb/s analysis are also used at 112 Gb/s PAM4 and have higher noise levels near 28 GHz as seen in **Figure 17**.

Two metrics of IRL_{NEW} and FOM_{RILN} are evaluated for these initial studies at 112 Gb/s PAM4. Correlation to channel COM is very high (>90%), showing promise for use of these metrics at higher data rates under PAM4 modulation. Higher Rsq than 32 Gb/s results may be attributed to amplified return loss sensitivity due to the models behavior at 28 GHz or PAM4 modulation sensitivity.

**Conclusion**

Reflection metrics that have been used for channels, packages, or cables have been reviewed and evaluated for their effectiveness against a new use: characterizing a connector. Reflection metrics differed in methodologies including frequency or time domain, weighting filters, and additional loss factors, but all are effective in at least one application. In most cases, evaluated metrics outperformed the best-case return loss frequency limit performance of 60.2%. The inclusion of additional losses for re-reflections adds an interesting prospect for metrics operating on return loss where Rsq values are the top performers, but due to inconsistency with synthetic connector models the results are not decisive.

Correlations were not perfect and should not be expected. In some experiments, the metric was used in a case for which it was never intended, such as IRL_{USB} for channel characterization. “Good but not great” results should not discourage metric use but instead demonstrate the importance of the test environment and application. A different channel or connector behavior could re-focus a behavior, such as a near re-reflection, in a new way. The simulators themselves can also introduce noise due to variations in the adaptive equalization and reflection alignment at the receiver, creating a Rsq ceiling.

There really is no one-size-fits-all metric. A summary provided in **Table 3 **highlights the takeaways. Overall ranking by Rsq value is taken from the connector only (TP2 to TP3) analysis on synthetic connector models. The ranking changes whether models are HFSS or synthetic from **Table 1**, so caution should be taken as previously discussed. Recommended applications are given based on the results of this article and existing standards applications. The applications include characterizing end-to-end channel or components (package, cable, connector). If a metric is successful for a connector, the package and cable are also recommended.

Further work beyond this paper may include inclusion of more than five HFSS models, a more complex and varying synthetic connector model, pulse response and TDR analysis to root cause poor correlations or outliers, ERL by CDF and results at TP1 and TP2, a correlation to system variance and reflection metric, a correlation against channels of short and medium lengths, and evaluations at other data rates requiring return loss metrics such as 64 Gb/s PAM4, 112 Gb/s PAM4, or 128 Gb/s PAM4.

**References**

1 H. Dsilva, J. Sasikala, A. Jain, A. Kumar, R. Mellitz, A. Gregory, and B. Lee. “Finding Reflective Insertion Loss Noise and Reflectionless Insertion Loss,” Designcon 2020

2 “IEEE Standard for Ethernet,” in IEEE Std 802.3-2015 (Revision of

IEEE Std 802.3-2012), vol., no., pp.1-4017, 4 March 2016.

3 Universal Serial Bus Type-C Cable and Connector Specification, Release 2.1 May 2021

4 C. Kao, B. Rothermel and J. Stephens, “Methodology for Calculating Component Level Crosstalk Contribution”, DesignCon 2019

5 Clause 93A.5, IEEE Std 802.3™-2015

6 R. Mellitz and E. Sayer. “Effective Return Loss for 112G and 56G PAM 4”, DesignCon 2018

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