Stochastic steady-state and AC analyses of mixed-signal systems

Authors:
Jaeha Kim;Jihong Ren;Mark A. Horowitz
Affiliations:
Stanford University, Stanford, CA and Kenosys Research, Inc., Los Altos, CA;Rambus, Inc., Los Altos, CA;Stanford University, Stanford, CA
Venue:
Proceedings of the 46th Annual Design Automation Conference
Year:
2009

Citing 5
Cited 1

Sensitivity of the Stationary Distribution of a Markov Chain

SIAM Journal on Matrix Analysis and Applications
Analysis and Design of Integrated Circuits

Analysis and Design of Integrated Circuits
Modeling and analysis of communication circuit performance using Markov chains and efficient graph representations

Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Digitally Assisted Analog Circuits

IEEE Micro
Electronic Circuit & System Simulation Methods (SRE)

Electronic Circuit & System Simulation Methods (SRE)

Fortifying analog models with equivalence checking and coverage analysis

Proceedings of the 47th Design Automation Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper demonstrates that the steady-state and adjoint sensitivity analyses can be extended to stochastic mixed-signal systems based on Markov chain models. The examples of such systems include digital phase-locked loops and delta-sigma data converters, of which steady-state response is statistical in nature, consisting of an ensemble of waveforms with probability distribution. For efficient Markov-chain analysis, the paper describes three methods that can limit the number of states: a state discretization scheme based on Gaussian decomposition, a state exploration algorithm that discovers the recurrent states, and a state truncation algorithm that eliminates the states with negligible stationary probabilities. The stochastic AC analysis is performed by deriving a first-order ordinary differential equation governing the perturbations in the stationary probabilities and solving it via phasor analysis. In the digital PLL and first-order ΔΣ ADC examples, the number of states was reduced by a factor of 35 and the frequency-domain phase and noise transfer functions were simulated with a 57~22,000x speed-up compared to using transient, Monte-Carlo simulations.