Neural Networks to create Causal and Passive S-Parameters

H. M. Torun, A. C. Durgun, K. Aygün and M. Swaminathan, "Causal and Passive Parameterization of S-Parameters Using Neural Networks," in IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 10, pp. 4290-4304, Oct. 2020

Maximum crosstalk estimation and modeling of electromagnetic radiation from PCB/high-density connector interfaces

Doctoral Dissertation: Summer 2014 by Matthew Scott Halligan

Maximum crosstalk estimation and modeling of electromagnetic radiation from PCB/high-density connector interfaces

• "Despite an ample supply of literature devoted to the study of crosstalk, little research has been performed to formulate maximum crosstalk estimates when signal lines are electrically long."
• "the resulting information from these studies often do not provide the necessary insight into the exact causes or solution strategies to mitigate crosstalk.
• "Most literature has focused on exact crosstalk formulations that capture every peak and valley in the crosstalk over frequency. While these exact formulations are necessary, design decisions are often better formulated from a maximum, worst case crosstalk envelope rather than an exact response because the transmission line parameters are never fully known
• Maximum Crosstalk Estimation in Weakly Coupled Transmission Lines - Paper
• Use the mutual terms in the transmission line per-unit-length parameters to predict the maximum crosstalk for electrically long systems.
• The maximum crosstalk expressions are dependent on 1) the total electrical length of the aggressor circuit and 2) the electrical length of the coupling region.
• results show that the maximum crosstalk envelope can be found within a few dB.
• "Although exact formulations for crosstalk are beneficial, the most useful tool for many designers is the maximum, worst case crosstalk over frequency [22]-[24]. Designers are often interested in a worst case performance limit because passing this limit obviates the need for further design analysis and modifications. This type of analysis is also preferred over exact crosstalk calculations in many cases because the system parameters are not perfectly known. Small shifts in resonant frequencies in this case can significantly change a crosstalk estimate. If the maximum crosstalk is found using a closed-form estimate, this technique may also give a better understanding of what causes crosstalk problems and how these problems might be solved.
• Excellent insights
• "When the signal lines are electrically large, resonances in the crosstalk response occur due to the electrical length of the signal lines and, in many cases, due to load impedance resonances.
• "The purpose of this paper is to develop a mathematically rigorous, worst-case, high-frequency crosstalk estimate that includes transmission line losses.

Signal Integrity Paper Reads

B. Ravelo and O. Maurice, “Kron-Branin Modeling of Y-Y-Tree Interconnects for the PCB Signal Integrity Analysis”, IEEE Transactions on Electromagnetic Compatibility, Vol. 59, No. 2, Apr. 2017, pp. 411-419.

•  "proposes an innovative circuit theory of the PCB electrical interconnects modeling based on the tensorial analysis of network (TAN).
• "for the complex asymmetrical Y-Y shape tree interconnects, as can be identified in various PCB designs shown in Fig. [fly by topology], the ABCD matrix modeling becomes practically difficult. This modeling method [RJA, i.e. cascading of S-parameters] requires complex procedures via successive calculations and combinations of Z- andY-matrices. Therefore, different steps of complex matrix transform must be fulfilled to determine the global system S-parameter. In this case, the analytical calculation is unrealizable without simplified numerical approximations, which can generate significant computation errors.
• "To overcome this difficulty, it is preferable to proceed with simpler systemic modeling as the tensorial analysis of network (TAN). This modeling methodology was initially inspired from the Kron’s method which offers unfamiliar flexibility to model complex systems asY-Y-tree [34]–[36]. The Kron’s graph topology enables to perform outstanding analytical interaction between different vector spaces (node, mesh, and branch spaces) [34].Associated with Branin’smethod, theKron’s formalism allows fast computation from abstract model [36], but the Branin’s models available in the literature are limited to elementary single TLs.
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• "The tensorial matrix equation solutions enable to determine the frequency-dependent currents propagating along the different branches of the topology presented in Fig. 4.
• How this relates to my Reflection budget paper based on Mason's rule and CSLT.  1) My paper only addresses point to point and defers branched and Y topologies to future work.  Maybe this is where I can reference this paper as it is an interesting approach. 2) The use of cascaded ABCD parameters has some problems which this paper addresses.  I can perhaps nod to some of these limitations of cascading. [29] and [30] in this paper (which are also by B. Ravelo). 3) My method is agnostic as to where the S-parameters come from, they can be measured, calculated, simulated, etc.

T. Eudes, B. Ravelo and A. Louis, “Experimental Validations of a Simple PCB Interconnect Model for High-Rate Signal Integrity”, IEEE Tran. EMC, Vol. 54, No. 2, Apr. 2012, pp. 397-404.

• I reviewed this paper for my PhD Proposal.  Ah, good memories.
• This paper describes a method for determining the electrical characteristics of a transmission line.  As how it relates to my Reflection budget paper, it could be a source of where S-parameter comes from.

T. Eudes, B. Ravelo and A. Louis, “Transient response characterization of the high-speed interconnection RLCG-model for the signal integrity analysis”, Progress In Electromagnetics Research (PIER), Vol. 112, 2011, pp. 183–197.

• Mentions that NGD (negative group delay) circuits as an alternative to repeaters.
• This paper describes an equation based approach to determining the RLGC parameters of a transmission line.  This particular approach is nice for Ripple Analysis since the model bandwidth (i.e. the max frequency of the S-parameters) can be arbitrarily set.  So using equation based approaches is nice.

B. Ravelo, S. Lalléchère, A. Thakur, A. Saini and P. Thakur, “Theory and circuit modelling of baseband and modulated signal delay compensations with low- and band-pass NGD effects”, Int. J. Electron. Commun. (AEÜ), Ed. Elsevier, Vol. 70, No. 9, Sept. 2016, pp. 1122–1127.

• NGD - negative group delay
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• Their objective is to have a unity gain transfer function |H(0)|=1 and negative group delay to compensate for the delay of the interconnect?
• Very sensitive to impedance mismatch, as seen in figure 6b where the conductivity of the transmission line.
• The time domain results show that the signal is negatively delayed but I'm having trouble understanding the utility of such a circuit.  Maybe to align signals?  Any SerDes application would have a PLLs and DLLs that can be used to compensate for delay mismatch.  As an equalization technique for SerDes, I don't really see the need for reducing latency by a sensitive circuit.