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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
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Noise shaping Asynchronous SAR ADC based time to digital converter
Time-to-digital converters (TDCs) are key elements for the digitization of timing information in modern mixed-signal circuits such as digital PLLs, DLLs, ADCs, and on-chip jitter-monitoring circuits. Especially, high-resolution TDCs are increasingly employed in on-chip timing tests, such as jitter and clock skew measurements, as advanced fabrication technologies allow fine on-chip time resolutions. Its main purpose is to quantize the time interval of a pulse signal or the time interval between the rising edges of two clock signals. Similarly to ADCs, the performance of TDCs are also primarily characterized by Resolution, Sampling Rate, FOM, SNDR, Dynamic Range and DNL/INL. This work proposes and demonstrates 2nd order noise shaping Asynchronous SAR ADC based TDC architecture with highest resolution of 0.25 ps among current state of art designs with respect to post-layout simulation results. This circuit is a combination of low power/High Resolution 2nd Order Noise Shaped Asynchronous SAR ADC backend with simple Time to Amplitude converter (TAC) front-end and is implemented in 40nm CMOS technology. Additionally, special emphasis is given on the discussion on various current state of art TDC architectures.Electrical and Computer Engineerin
Uncertainty Quantification for Electromagnetic Systems Using ASGC and DGTD Method
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