Variability Analysis of Interconnects Terminated by General Nonlinear Loads

Biondi, Alessandro; Ginste, Dries Vande; Zutter, D. De; Manfredi, Paolo; Canavero, Flavio

doi:10.1109/tcpmt.2013.2259896

Cited by 38 publications

(48 citation statements)

References 26 publications

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“…Additionally, it is worth mentioning that the augmented equations (4) have exactly the same shape as a classical set of Telegrapher's equations for K + 1 lines. From the above PC-representation, statistical information such as the mean and the standard deviation of a voltage waveform v(z, t, β) (2), as well as PDFs and cumulative distribution functions (CDF), are readily computed [5].…”

Section: B Stochastic Galerkin Methods (Sgm)mentioning

confidence: 99%

“…In this contribution, we focus on the inclusion of nonlinear polynomial loads within the SGM framework. An accurate, but numerical, formulation for arbitrary nonlinearities has been proposed in [5]. Consider a deterministic nonlinear load at the far-end z = L of the line, described by a capacitance that is a polynomial function of degree N of the voltage across it :…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Also, in contrast to [5], the BCs are obtained in an analytical way, making them exact. The derivation of the BCs for, e.g, a polynomial conductance can be obtained in a similar way.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Unfortunately, as the technique developed in [3], [4] is in essence a frequency-domain method, only linear loads, connected to the terminals of the interconnects, could be taken into account. Therefore, further steps have been taken and a technique was devised that allows including loads with arbitrary I-V characteristics [5]. In this contribution, we focus on the variability analysis of interconnects that are terminated by nonlinear loads, described by polynomial I-V characteristics, and we show that they can be dealt with via an alternative, closed-form and exact formulation.…”

Section: Introductionmentioning

confidence: 99%

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Variability analysis of interconnects terminated by polynomial nonlinear loads

Biondi

Ginste

Zutter

et al. 2013

2013 IEEE Electrical Design of Advanced Packaging Systems Symposium (EDAPS)

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Abstract-In this paper, a stochastic modeling method is presented for the analysis of variability effects, induced by the manufacturing process, on interconnect structures terminated by polynomial nonlinear loads. The technique is based on the solution of the pertinent stochastic Telegrapher's equations in time domain by means of the so-called stochastic Galerkin method in conjunction with a finite-difference time-domain technique, allowing the inclusion of, e.g., nonlinear capacitors at the terminals of the lines. The proposed technique is validated and illustrated with an example, demonstrating its accuracy and efficiency.

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Section: B Stochastic Galerkin Methods (Sgm)mentioning

confidence: 99%

Section: Boundary Conditionsmentioning

confidence: 99%

“…Also, in contrast to [5], the BCs are obtained in an analytical way, making them exact. The derivation of the BCs for, e.g, a polynomial conductance can be obtained in a similar way.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variability analysis of interconnects terminated by polynomial nonlinear loads

Biondi

Ginste

Zutter

et al. 2013

2013 IEEE Electrical Design of Advanced Packaging Systems Symposium (EDAPS)

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“…The reader is encouraged to consult [3,14,15] and the references therein to gain familiarity with the SGM in the domain of electrical engineering. Here, similarly as in [6], where the SGM was combined with the MoM for small scattering problems, we start from expansions of the stochastic quantities introduced in Eq.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Zubac¹,

Fostier²,

Zutter³

et al. 2015

Opt. Express

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It is well-known that geometrical variations due to manufacturing tolerances can degrade the performance of optical devices. In recent literature, polynomial chaos expansion (PCE) methods were proposed to model this statistical behavior. Nonetheless, traditional PCE solvers require a lot of memory and their computational complexity leads to prohibitively long simulation times, making these methods non-tractable for large optical systems. The uncertainty quantification (UQ) of various types of large, two-dimensional lens systems is presented in this paper, leveraging a novel parallelized Multilevel Fast Multipole Method (MLFMM) based Stochastic Galerkin Method (SGM). It is demonstrated that this technique can handle large optical structures in reasonable time, e.g., a stochastic lens system with more than 10 million unknowns was solved in less than an hour by using 3 compute nodes. The SGM, which is an intrusive PCE method, guarantees the accuracy of the method. By conjunction with MLFMM, usage of a preconditioner and by constructing and implementing a parallelized algorithm, a high efficiency is achieved. This is demonstrated with parallel scalability graphs. The novel approach is illustrated for different types of lens system and numerical results are validated against a collocation method, which relies on reusing a traditional deterministic solver. The last example concerns a Cassegrain system with five random variables, for which a speed-up of more than 12× compared to a collocation method is achieved.

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Sensitivity analysis of crosstalk in transmission lines to geometric uncertainties

Allal,

Ahmed

2024

Electr Eng

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Variability Analysis of Interconnects Terminated by General Nonlinear Loads

Cited by 38 publications

References 26 publications

Variability analysis of interconnects terminated by polynomial nonlinear loads

Variability analysis of interconnects terminated by polynomial nonlinear loads

Efficient uncertainty quantification of large two-dimensional optical systems with a parallelized stochastic Galerkin method

Sensitivity analysis of crosstalk in transmission lines to geometric uncertainties

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