Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Equalization of multi-Gb/s chip-to-chip interconnects affected by manufacturing tolerances

Electrical chip-to-chip interconnects suffer from considerable intersymbol interference at multi-Gb/s data rates, due to the frequency-dependent attenuation. Hence, reliable communication at high data rates requires equalization, to compensate for the channel response. As these interconnects are prone to manufacturing tolerances, the equalizer must be adjusted to each specific channel realization to perform optimally. We adopt a reduced-complexity equalization scheme where (part of) the equalizer is fixed, by involving the channel statistics into the equalizer derivation. For a 10 cm on-board microstrip interconnect with a 10% tolerance on its parameters, we point out that 2-PAM transmission using a fixed prefilter and an adjustable feedback filter, both with few taps, yields only a moderate bit error rate degradation, compared to the all-adjustable equalizer; at a bit error rate of 1e-12 these degradations are about 1.1  dB and 3  dB, when operating at 20 Gb/s and 80 Gb/s, respectively

An Approach to Assess Solder Interconnect Degradation Using Digital Signal

Department of Human and Systems EngineeringDigital signals used in electronic systems require reliable data communication. It is necessary to monitor the system health continuously to prevent system failure in advance. Solder joints in electronic assemblies are one of the major failure sites under thermal, mechanical and chemical stress conditions during their operation. Solder joint degradation usually starts from the surface where high speed signals are concentrated due to the phenomenon referred to as the skin effect. Due to the skin effect, high speed signals are sensitive when detecting the early stages of solder joint degradation. The objective of the thesis is to assess solder joint degradation in a non-destructive way based on digital signal characterization. For accelerated life testing the stress conditions were designed in order to generate gradual degradation of solder joints. The signal generated by a digital signal transceiver was travelling through the solder joints to continuously monitor the signal integrity under the stress conditions. The signal properities were obtained by eye parameters and jitter, which represented the characteristics of the digital signal in terms of noise and timing error. The eye parameters and jitter exhibited significant increase after the exposure of the solder joints to the stress conditions. The test results indicated the deterioration of the signal integrity resulted from the solder joint degradation, and proved that high speed digital signals could serve as a non-destructive tool for sensing physical degradation. Since this approach is based on the digital signals used in electronic systems, it can be implemented without requiring additional sensing devices. Furthermore, this approach can serve as a proactive prognostic tool, which provides real-time health monitoring of electronic systems and triggers early warning for impending failure.ope