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Presented by Fang Gong

Fast, Non-Monte-Carlo Transient Noise Analysis for High-Precision Analog/RF Circuits by Stochastic Orthogonal Polynomials. Fang Gong 1 , Hao Yu 2 and Lei He 1. 1 University of California, Los Angeles, Los Angeles, USA 2 Nanyang Technological University, Singapore. Presented by Fang Gong.

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Presented by Fang Gong

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  1. Fast, Non-Monte-Carlo Transient Noise Analysis for High-Precision Analog/RF Circuits by Stochastic Orthogonal Polynomials Fang Gong1, Hao Yu2 and Lei He1 1University of California, Los Angeles, Los Angeles, USA 2Nanyang Technological University, Singapore Presented by Fang Gong

  2. Motivation • Device noise can not be neglected for high-precision analog circuit anymore! • Signal-to-noise ratio (SNR) is reduced; • Has large impact on noise-sensitive circuits: PLLs (phase noise and jitter), ADCs (BER) … • Device Noise Sources: • Thermal Noise: random thermal motion of the charge carriers in a conductor; • Flicker Noise (1/f Noise): random trapping and de-trapping of charge carriers in the traps located at the gate oxide interface.

  3. Existing Work • Monte Carlo method • Model the thermal noises as stochastic current sources attached to noise-free device components. • Sample the stochastic current sources to generate many traces. • Non-Monte-Carlo method: [A. Demir, 1994] • Decouple the noisy system into a stochastic differential equation (SDE) and an algebraic constraint. • Use perturbation analysis and covariance matrix to solve for variance of transient noise in time domain. • Examples of Commercial tools: • Transient noise analysis in HSPICE (Synopsys) • AFS transient noise analysis (Berkeley Design Automation), …

  4. stationary process with constant power spectral density (PSD) • Stochastic differential algebra equation (SDAE) Stochastic component noise intensities deterministic component Standard noise sources (White noise) • Integrate it to build Itô-Integral based SDAE Wiener process SDAE based Noise Analysis- primer slide • Modeling of Thermal Noise

  5. Transient noise Nominal response Existing Solution to Itô-Integral based SDAE • Stochastic Integral scheme for SDAE (e.g. backward differentiation formula (BDF) with fixed time-step) • With piecewise linearization along nominal transient trajectory: Sampled with Monte Carlo at each time step

  6. New SOP based Solution • Stochastic Orthogonal Polynomials without Monte Carlo • Expand random variables with SoP SoP expansions 3σ boundary in time domain nominal response

  7. CMOS comparator Experimental Results • Experiment Settings • Consider both thermal and flicker noise for all MOSFETs. • Resistors only have thermal noise. • Accuracy and efficiency validity • SoP expansion method can achieve up to 488X speedup with 0.5% error in time domain, when compared with MC. Runtime Comparison on Different Circuits

  8. Conclusion • A fast non-Monte-Carlo transient noise analysis using Itô-Integral based SDAE and stochastic orthogonal polynomials (SoPs) • The first solution of SDAE by SoPs • Expand all random variables with SoPs • Apply inner-product with SoPs to expansions (orthogonal property) • Obtain the SoP expansion of transient noise at each time-step • To learn more come to poster session!

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