EDA365. DesignCon Skew Impact Estimation on High Speed Serial Channels Using Mathematical Analysis and Accurate Lab Measurements

Transcription

1 DesignCon 2010 Skew Impact Estimation on High Speed Serial Channels Using Mathematical Analysis and Accurate Lab Measurements Christopher White, Cray Inc. Andrew Becker, Cray Inc. Jim Fitzke, Cray Inc.

2 Abstract Intra-pair skew in differential signaling has become important in current signal integrity analysis due to its impact on insertion loss and crosstalk in high-speed networks. PCB skew is often the result of design length variation, manufacturing tolerances, and weave effect. Here we have estimated the effects of generic intra-pair skew using transmission line analysis. Our lab measurements from twinaxial cable and PCB test vehicle designs show the relationship between skew and differential signal amplitude, reliably out to 20GHz. We have correlated our analytical estimates to these lab measurements, allowing us a means to predict a maximum tolerable intrapair skew. Author Biographies Christopher White is currently employed as a signal integrity engineer with Cray Inc. and is an IEEE member. He has a Master s Degree in Electrical Engineering from the University of Minnesota and a Bachelor s Degree from Michigan Technological University. He has worked on mixed signal IC design and signal integrity for IBM, JDS Uniphase, Hitachi Global Storage Technology, and Cray Inc. over his career. Andrew Becker currently works for Cray Inc. as a signal integrity engineer where he has been employed for the last five years. Previously he worked on 40Gbps long-haul transceivers for Stratalight Communications in the SF Bay area, and for Lucent Technologies, Bell Laboratories in Murray Hill, NJ. He has a Master's Degree in Electrical Engineering from Stevens Institute of Technology in Hoboken, NJ and a BS degree in Physics from SUNY Binghamton in New York State. Jim Fitzke has been employed at Cray Inc. for the past 16 years, working as a signal integrity lab engineer. Previously he worked at Supercomputer Systems Inc. (SSI) and Control Data Inc. in similar roles.

3 Introduction Any source of skew can be detrimental to the differential signal and can result in the conversion of signal energy between the even and odd modes for coupled signals. The interplay between these modes drains energy out of the differential signal and creates a source for noise injection, derived from the common mode. In PCB designs, skew can be induced through different means, such as length mismatch or material inhomogeneity. Length mismatch can often be minimized by good design methods, but material inhomogeneity is usually a result of PCB weave effects or other manufacturing phenomenon. The goal of our skew analysis is to account for either skew source, within our model framework. For twinaxial cables, the mismatch between the two signal wires can be specified to vary by many picoseconds per meter. Therefore, a long cable of several meters would induce a great amount of skew. Lab measurements have shown, however that little skew is measured at the output of the differential cable, even when 80ps or more of skew is induced at the input. Our modeling shows that this phenomena is a direct result of the skew being cancelled by the heavy attenuation of the common mode signal within the cable. The output differential signal is thereby skewless, but has suffered a significant additional loss, exceeding that predicted by the metal and material attenuation or from simple differential impedance mismatch. Our skew model uses a mathematical formulation built on transmission line theory in the form of ABCD matrices. The mathematics accounts for the skew through a generic delta phase parameter that can implicitly have frequency dependence. A benefit of using ABCD parameters is the inherent ability to calculate the differential and common mode matrices for lossy, uncoupled (or weakly coupled) transmission lines. This calculation results in a more compact estimation of the complex structure of skew, previously shown in other papers. The skew is established through a specification of the delta phase parameter as a relationship between the two transmission lines. The skew parameter can be constant over frequency for either a length (spatial) mismatch or a velocity (temporal) mismatch. Also, the skew can be frequency dependent for material effects that result in permittivity change. Skew Model Theory As a simplified analysis approach, we considered the case of uncoupled differential lines where the True and Complement have two different electrical lengths of transmission line. Each transmission line has a Z-parameter matrix related to it.

4 Z TLINE Z0 coth( γl) = Z0 sinh( γl) Z0 sinh( γl) Z coth( ) 0 γl Equation 1: Z-Parameters for General Transmission Lines One benefit of using the z-parameters for two uncoupled transmission lines is that the differential pair of transmission lines can add z-parameters as a series connection of the pairs. Figure 1: Differential Pair Z-Parameter Structure This configuration allows the overall z-matrix calculation through the summing of each z-parameter (Z11, Z12, etc.). Z DIFF = Z 0 coth( γd ) + coth( γ d ) sinh( γd ) sinh( γ d ) sinh( γd ) sinh( γ d ) coth( γd ) + coth( γ d ) Equation 2: Differential Z-Parameter Matrix The summation is straightforward but difficult when using the hyperbolic trigonometric functions. Also, we do not wish to have to specify two line lengths. Instead, we really want to specify one line length and a skew parameter. Therefore, the resulting z-matrix look is in the following form. Z DIFF Z DIFF Z0 = sinh( γd )sinh( γ d ) cosh( γd )sinh( γ d ) + cosh( γ d )sinh( γd ) sinh( γd ) + sinh( γ d ) sinh( γd ) + sinh( γ d ) cosh( γd )sinh( γ d ) + cosh( γ d )sinh( γd ) Equation 3: Adjusted Differential Z-Parameter Matrix Z sinh(2γd + θδ) 0 = sinh( γd )sinh( γd + θ ) 2γd + θδ θδ 2sinh( ) + cosh( ) 2 2 2γd + θδ θδ 2sinh( ) + cosh( 2 2 Δ sinh(2γd + θδ) )

5 Equation 4: Differential Z-Parameter Matrix with Phase Difference θ ( γ d γd) Δ Equation 5: Phase Difference Definition From this point, the z-matrix can be converted to an ABCD-matrix form. This can be done combined with some hyperbolic trigonometric identities to simplify the form of the ABCD-parameters. The most complicated parameter is the B-parameter, which does not simplify to a short equation as the others do. 2γd + θδ cosh( ) 2 θδ cosh( ) ABCD = Y 0 + sinh( γd) sinh( γd + θδ) 1 2 sinh (2γd + θδ) Z0 sinh( γd)sinh( γd + θ 2 ( sinh( γd) + sinh( γd + θδ) ) )( sinh( γd) + sinh( γd + θ )) Δ 2γd + θδ cosh( ) 2 θδ cosh( ) 2 Equation 6: ABCD Matrix with Phase Difference Term Decomposition of this matrix shows that when θ is zero the matrix collapses to the ABCD-matrix for the traditional transmission line form. Transmission Line Measurements and Modeling Twinaxial Cable Model Creation Several twinaxial cable models were created to assist in the extraction and calculation of γ, the transmission line propagation parameter. This complex parameter contains both the phase and attenuation information of the twinax transmission line and varies with frequency due to finite shield thickness and center wire gauge skin effects. For typical twinaxial cables, the dielectric is a very low loss material such as foam Teflon or polyethylene, in solid or foam form. Δ

6 Figure 2: XT Supercomputer Application - rear view showing extensive twinaxial network cabling The cross-section of the cable was modeled in Q3D to generate the characteristic impedance (Z 0 ), attenuation (α), and propagation (β) values from 100Hz to 25GHz and these transmission line parameters were exported to a text file. This file was then read into another tool to allow the generation of the final skew equation results. Figure 3: Twinaxial Cable Cross-section - 26AWG conductors with center drain wire construction. Low-loss polyethylene foam forms the core, with a very thin aluminized mylar outer shield.

7 The cable was simulated in HFSS as well to first verify that the equations produced the expected solution. Figure 4: HFSS E-Field Plots: Differential and Common Modes in Twinaxial Cable - a lossy shield reduces common mode energy more severely Figure 4 plots the field strength for the differential and common modes contained within the twinaxial cable outer shield. Common mode energy is strongly dissipated in the thin aluminized mylar outer shield, with certain wrap constructions yielding much better highfrequency response. In Figure 5 the insertion loss from HFSS and from the TL equation model is plotted for both 1m and 6m lengths of twinaxial cable showing the two results matching very well up to 25GHz. Figure 6 demonstrates a sweep of cable lengths from 1m to 6m in 1m increments, showing the resultant progression of loss with length. Also, the square root of frequency dependence is still apparent out to 25GHz due to the very low loss dielectric material used in this model. Figure 5: Twinaxial Simulation Comparison for 1m & 6m Cables - HFSS and TL equation differential insertion loss comparison Deleted: Figure 4 Deleted: Figure 5 Deleted: Figure 6

8 Figure 6: Twinax Differential Insertion Loss Model for Multiple Twinax Lengths The model can then be used to sweep the amount of inherent, distributed skew. In the following example the 2m twinaxial cable skew was swept up to 40ps and the insertion loss plotted below shows the moving resonance that results from the skew. The insertion loss degrades by 2.95dB by adding 40ps of inherent skew. However, with 20ps of skew the insertion loss degrades by only 0.68dB, showing a steep loss impact as skew increases beyond a certain threshold. Figure 7: 2m Twinax Skew Sweep Insertion Loss Impact

9 Twinaxial Cable Measurement Correlation To further verify the mathematical model, several twinaxial cables were fixtured and measured using a 40GHz Agilent PLTS 4-port VNA and the resultant data was plotted along with the modeled results. Figure 8 shows the measurement methodology employed in characterizing the twinaxial cable samples detailed in this paper. Connectorized semirigid uniform tubing (0.047" OD) was cut and skew-matched to provide a precise launching mechanism into the fine interior of the stripped twinaxial cable ends. Using a TDR, the launch ends were tuned using a small ball of excess solder near the 26AWG twinax center conductor attach point, to help compensate for the parasitic inductance resulting from the absence of the (short) stripped-back shield. Finally, the uniform tubing and SMA connectors are attached to a backing plate for rigidity and support. By carefully employing these techniques we are able to create a launch capable of reliable operation up to 30GHz in frequency, with return loss values consistently below 10dB out to this extreme. The RL to 10GHz remains below -20dB typically. Figure 8: Twinaxial Cable Measurements: using direct coax-attach launch fixturing The measured cable showed an inherent skew of roughly 12ps (2ps/m) and an identical ideal skew was inserted into the model for comparison. The insertion loss in Figure 9 shows very strong correlation between the model and measurement up to 25GHz. The lab measurement shown is a T-matrix de-embedded file created from two separate twinax data files, produced from measured 1m and 7m sections of wire. The resultant 6 meter de-embedded modal S-parameters were then created in Simbeor using their new generalized S-parameter extraction algorithm. These results were comparable to a simple IL subtraction between the two lengths, but also provided accurate phase information for the extracted 6m length. Deleted: Figure 8 Deleted: Figure 9

10 Figure 9: Twinax Insertion Loss Comparison of Equation Model and Measurement Twinaxial Cable Shield Effects - Common-Mode Variation While the differential response of twinaxial cable is well-behaved out beyond 20GHz, we have noted enormous variation in the common-mode response between various cable construction types. Due to the high-volume, low-cost nature of twinaxial cable wire, it is not trivial to produce a cable which exhibits resonance-free, low-loss response out beyond 5GHz. The primary cause of problems seems to arise from the construction of the outer shield, which is typically made from very thin aluminized mylar film. As such, it suffers from high insertion loss, due to metal losses in the thin sputtered Al film. Cable constructions which reduce the H-fields on the shield have been shown to exhibit less db/m insertion loss, but this often requires an oversized cable or higher target characteristic impedance. Another difficulty with the wrapped mylar shield is that it invariably creates periodic discontinuities along the length of the cable which manifest themselves as resonances, seriously impacting the channel performance. Manufacturers have made good progress producing new longitudinal wrapping techniques which can reduce these periodic discontinuities in the shield, resulting in resonance-free performance beyond 20GHz. Figure 10 shows the dramatic impact a standard spiral wrapped shield can have on the insertion loss of a cable operating at frequencies above 10GHz. The 7m spiral-wound twinax exhibits a deep resonance at 15GHz, whereas the longitudinally-wrapped cable shows no significant dips in IL until 26GHz, and even there this effect is muted in comparison. When considering the effects of skew on twinaxial cable performance however, we find that even at frequencies below 1GHz, there are enormous differences between these two Deleted: Figure 10

11 cable types. Because skew manifests itself as common-mode energy in these TEM transmission line structures, excessive attenuation of the common mode will tend to remove the skew at the cable output, and thereby reduce the resultant differential signal energy in the process. While the longitudinally-wrapped cable exhibits a suck-out in common-mode IL at 2GHz, as shown in Figure 10, we still retain a significant amount of common mode signal up to 10GHz. The spiral wrap shield cable in comparison possesses almost no common mode energy beyond a few hundred MHz in frequency. Deleted: Figure 10 Figure 10: Twinaxial Cable Measurements - differential and common-mode comparison between spiral and longitudinal shield wrap construction A twinaxial cable (or other transmission line) which does not support the common mode transforms the skewed signal entering the cable and quickly attenuates the skew, and effectively converts this input skew into additional insertion loss. This affect hinders the ability to recover energy through skew compensation. We have demonstrated this skew reduction effect in Figure 11, for three different measured wire types samples, each driven with input skew values ranging from -50pS to +50pS. The laboratory-grade coax shows a near perfect correlation between input and output skew, as one would expect for a perfect pair of test & measurement grade cables. The 7m longitudinally wrapped twinax cable shows a dramatic reduction in output skew and the 1m twinax proportionally less. The output skew for the spiral wrap 7m twinax cable shows almost no remaining skew due to the extreme common-mode loss experienced in the shield. These measurements were performed using a simple low-frequency toggle pattern to better illustrate this effect. At higher data rates this effect becomes even more pronounced, depending on the common mode loss response of the transmission line under test. The loss of the common mode signal in such structures requires the designer to perform any skew compensation necessary in the channel design before the signal enters the lossy structure. Since the output signal will be nearly skew-free at his point, adding additional compensation would only be counterproductive. Being aware of which Deleted: Figure 11

12 structures in the channel exhibit this common mode loss effect can help the designer determine how to set running skew requirements throughout the design. Figure 11: Measured Skew Response - ideal coax and twinax (spiral & continuous wrap shield) Stripline Model Creation The stripline model was created using the same methodology as described previously for the twinaxial cable. The propagation parameter, γ, was calculated using a Q3D extraction of the physical PCB stripline geometry shown in Figure 12. The γ parameter is sensitive to dielectric material and to the trace width and thickness because of internal inductance affects, up to ~300MHz. The stripline dielectric also has more loss than the twinaxial cable and is not constant across the range of frequencies under consideration. Accurate modeling of this structure requires an accounting for dielectric variation over frequency (e.g. multi-pole analysis) and a mechanism to account for metal roughness. Deleted: Figure 12

13 Figure 12: Stripline Test Structure Cross Section As with the twinax, the cross-section of the stripline was modeled in Q3D to generate the characteristic impedance (Z 0 ), attenuation (α), and propagation (β) values from 1kHz to 25GHz. The dielectric parameters had frequency dependent relative permittivity and loss tangent. The resulting transmission line parameters were exported to a text file. This file was then read into another tool to allow the generation of the initial stripline model. The model s propagation parameter was then optimized at high frequencies to account for metal roughness. The final stripline model was generated for the long 20in section of stripline and the inherent skew was swept from 0 to 32.5ps. Across that range of skew, the insertion loss saw a degradation of 1.95dB, and the degradation decreased to only 0.67dB for 20ps of skew. Figure 13: 20in Stripline Skew Sweep Insertion Loss

14 Stripline Measurement Correlation The stripline model was also compared to our PCB measured traces to produce additional confirmation of the model's validity. Figure 14 details our 4-port measurement setup using an Agilent 40GHz Physical Layer Test System and GGB Industries 250um pitch GS microwave probes. Our surface probe launch structure is also detailed in Figure 14 which was modeled in HFSS for de-embedding purposes. SOLT wafer calibration of the PLTS VNA allowed us to produce accurate probed data out beyond 30GHz in frequency, at the reference plane of the probes. The HFSS solid model of the PCB probe launch structure allowed us to account for the non-ideal impact of the surface structure and associated vias. Future designs have been improved to remove the unwanted parasitic capacitance experienced in this original design. This has been accomplished through a tuning of the antipad region in the PCB along with an adjustment to the width of the stripline escape traces, using the Optimetrics feature in HFSS. Two PCB test structures were measured here: 8in and 20in striplines along with the associated probe launches. One errant test board was found to have roughly 0.6ps/in of skew for both these lengths of stripline. upon further investigation, an identical duplicate board was found to posses no skew for either of the two stripline lengths. We have attributed this difference to fiber weave effect, or some other defect in the manufacture of the dielectric stackup. Due to this observed difference, models for both boards were created and compared in Figure 15. The insertion loss graph shows strong correlation between measured and model data out to 17GHz. Figure 14: PLTS VNA Measurement Setup and HFSS Microwave Probe Launch Model VNA measurements of these probed structures provided valuable insight into the subtle impact of skew on IL which would have been much more difficult to discern using more conventional SMA launch structures. While SMA launching techniques can be used at Deleted: Figure 14 Deleted: Figure 14 Deleted: Figure 15

15 frequencies approaching 20GHz, they work best for single-ended applications where there is no uncoupled to coupled transition region as is the case for differential stripline. Small microprobe structures such as the one shown in Figure 14 (or more improved designs) allow the engineer to create a much smaller footprint and differential stripline transition region. Wafer calibration techniques also allow for an extremely high level of accuracy and placement of the reference plane very close to the DUT. This technique does have the drawback of being more time-consuming and labor-intensive, however. Deleted: Figure 14 Figure 15: Stripline Insertion Loss Model vs. Measurement For the stripline geometry investigated here, we do not observe a great difference between the common mode and differential mode insertion loss, compared to a challenging structure such as twinax. As such, the inherent stripline skew observed in our test board appears nearly identical to a discrete skew added before or after the channel DUT. Figure 16: Measured Stripline Group Delay - PCB #6 showing 14pS of intra-pair skew

16 Figure 16 shows the group delay of our two 20" stripline structures under investigation; with PCB #4 yielding a nominal skew of <1ps between the true and compliment stripline traces, and PCB #6 showing a 14ps skew, possibly due to fiber weave effect or other material defect. We can see the resultant impact on insertion loss in the skewed stripline sample in Figure 17, where the increased loss becomes particularly important above 10GHz. By adding back the inherent 14ps of ideal skew in simulation we can see that nearly all of the common mode signal energy is restored, resulting in identical differential IL to the un-skewed PCB trace. This 20" stripline trace was a typical meander line and so no significant barriers would prevent this technique from working when compensating for running skew between channel components. Figure 17: Measured differential IL on 20" PCB Stripline - PCB #6 showing additional loss due to intrapair skew. Additional loss is effectively removed by adding 14ps of ideal delay, yielding identical loss to PCB #4 Channel Simulations and Measurements The primary goal in modeling skew is to accurately account for it within a channel simulation, as excessive skew will degrade insertion loss if it becomes too large. Much effort is put into mitigating even the smallest sources of skew during the design and layout phase of high-speed designs. For lumped skew sources such as bends and escape structures, the skew impact is not an inherent part of the transmission line. Therefore, these sources often result in discontinuities that have insertion and return loss affects. However, for inherent, distributed skew, the return loss impact is much smaller so the main issue is to mitigate the degradation of the insertion loss. The following channel setup includes a driver and receiver with some parasitic models to represent the connection to the skew impacted stripline or twinaxial cable. The driver used an edge rate of 30ps, and the channel was simulated at a data rate of 12.5Gbps. Deleted: Figure 16 Deleted: Figure 17

17 Twinaxial Cable Simulations The twinaxial cable simulations inject skew up to 40ps into a 2m cable. The 6m cable was unable to pass an open eye at this data rate and was not included in the proceeding channel analysis. A typical twinaxial cable would not have 40ps of skew for a short 2m section, but we have simulated it here to show how much this skew degrades the eye opening. The eye diagrams in Figure 18 show the gradual eye closure resulting from inherent skew in the twinaxial cable. As the skew reaches 20ps, or 0.25UI, the eye diagram has discernibly changed, but does not impact the eye significantly. The eye height at 0.25UI is reduced by only 4.6%, and the width has shrunk by 3.5%. It is above 20ps of skew that the eye quickly deteriorates. The steep degradation of eye height indicates that the skew s affect is largely an edge rate issue and that the signal s edge rate has slowed but with a small jitter impact for large additions of skew. The slower edges are a result of the energy loss to the common mode signal. In Table 1, the rise time increases as the amplitude decreases showing the significant degradation in the slew rate at the output of the cable. Deleted: Figure 18: 2m Twinax Cable Skew Sweep Eye Diagrams The five eye diagrams are for 0ps (upper left) through 40ps (bottom right) of skew in 10ps increments. Deleted: Figure 18 Table 1

18 Figure 19: Twinax Contours The five contours show the BER contour for 0ps, 10ps, 20ps, 30ps, and 40ps of skew. Skew Height at Width at Amplitude Rise Time ps UI mv Delta (%) ps Delta (%) mv ps Table 1: 2m Twinax Skew Sweep Results Stripline Simulations The stripline channel simulations address the added affect of skew on a 20in section of differential PCB stripline. We also have VNA measured data for this structure to allow comparison to the model results, accurately out to 20GHz. This allows a validation of the model in the channel analysis at two data points: no skew, and 13ps of skew, inherent in one of the measured PCB samples. In Figure 20, the eye diagrams for the measured data and model data are presented. Both the 8in and 20in traces are shown for comparison. This is useful since both trace lengths have a skewless data set and an inherent skew data set with which to compare. The figure clearly shows very similar eye diagrams for the model and the measured data. Deleted: Figure 20

19 Figure 20: Comparative 8in and 20in Stripline Channel Simulations Four pairs of eye diagrams are shown: left set is for 8in traces and right set is for 20in traces. Each eye diagram pair consists of the measured S-Parameter eye and the modeled stripline eye. The 20in stripline model was then simulated for the different amounts of skew. The skew was swept up to 32.5ps in 6.5ps steps to show the degradation of the eye as the skew is increased. The eye contours shown in Figure 22 are taken from the eye diagrams in Figure 21 at a BER of Deleted: Figure 22 Deleted: Figure 21

20 Figure 21: 20in Stripline Skew Sweep Eye Diagrams The six eye diagrams are for 0ps through 32.5ps of skew in 6.5ps increments. Figure 22: Stripline Contours The eye contours are shown for a BER of at each incremental skew step. Skew Height at Width at Amplitude Rise Time ps UI mv Delta (%) ps Delta (%) mv Ps Table 2: Stripline Skew Sweep Results Again, the stripline eye diagrams show that the skew impacts the eye height more than the eye width. The net effect of this skew is on the slew rate of the differential signal at

21 the output of the transmission line. The edges are significantly slower but the jitter component increase is not as significant. Conclusions The distributed skew affect has been accurately modeled using hyperbolic trigonometric functions; the resultant model represents the distributed skew by using an electrical length delta parameter. By restructuring these matrix equations, a transmission line can use the typical γ transmission line parameter along with an associated θ phase offset skew parameter. The skew parameter can then be manipulated to generate arbitrary amounts of skew within a model. By sweeping the skew in simulation, a set of models can be quickly simulated within the channel to assess the impact on eye diagram metrics. We have taken very accurate lab measurements of twinaxial cable and stripline out to 40GHz. This data demonstrates the impact that skew has on differential insertion loss. And, the data shows clearly that skew causes energy to be lost to the common mode signal. We have fit transmission line models to this data very closely out to 25GHz and implemented the models within channel simulations. Thus, as our models and measured data have shown, a substantial amount of skew relative to the bit width can be tolerated. The eye closure from twinaxial cable simulations shows that 0.22UI of skew is only an eye height degradation of 10% and an eye width reduction of 3.8mUI. And the stripline analysis shows that a 0.12UI of skew results in the same percentage of eye height reduction, 10%, with an eye width decrease of 3.2mUI. Therefore, a 12.5Gbps channel loss budget that allows for 10% vertical closure due to skew could have an intrapair skew specification of 8.8ps/m for twinaxial cable or an intrapair skew specification of 0.48ps/in for stripline. References [1] Blando, Gustavo et al., Losses Induced by Asymmetry in Differential Transmission Lines. Proc. of DesignCon 2007, pp [2] Matthaei, G. Young, L. & Jones, E.M.T., Microwave Filters, Impedance- Matching Networks, and Coupling Structures. Norwood, MA: Artech House. [3] Pozar, David M., Microwave Engineering. 2 nd ed. John Wiley & Sons, Inc. [4] Ramo, S. Whinnery, J. R. Van Duzer, T., Fields and Waves in Communication Electronics. 3 rd ed. John Wiley & Sons, Inc. [5] Smith, Stephen B.et al., Theory and Measurement of Unbalanced Differential- Mode Transmission Lines. Proc. of DesignCon 2006, pp.1-23.