Elektronik devre simülasyonunda durağan olmayan alçak frekanslı gürültünün modellenmesi ve analizi

Modeling and analysis of low-frequency noise, such as 1/f and burst noise, under time-varying bias conditions is a long-standing open problem in circuit simulation. It has been shown, both in theory and experimentally, that analyses based on simplistic noise models with stationary or modulated stationary statistics produce erroneous results. We offer a solution to this problem and present a new computational modeling and analysis framework for low-frequency noise. This framework is based on a mathematical description of the random activity that is caused by the defects located in the atomic lattice structures of semiconductors. The merits of our noise model are two-fold: First, it is fully nonstationary. It can represent noise processes with time-varying statistics that are tightly coupled to the circuit variables in a stochastically correct manner. Second, its mathematical structure allows the utilization of well-established, non Monte Carlo noise analysis techniques which are orders of magnitude faster than their Monte Carlo counterparts. We develop our low-frequency noise modeling and analysis techniques by building on a mathematical foundation based on the theory of Markov chains and the theory of stochastic differential equations aided by the extensive literature on modeling and simulation of stochastic chemical kinetics. We present a detailed explication of our modeling method with regard to its stochastic properties and develop carefully crafted circuit simulation algorithms that are stochastically correct. We implement these algorithms in a new circuit simulation tool and establish the correctness of our methods via rigorous simulations. We examine circuits and operating conditions where the legacy noise model mispredicts the effects of low-frequency noise and demonstrate how these effects can be correctly simulated using the new noise modeling and analysis framework we propose.