Abstract
A novel statistical method, referred to as the maximum entropy (MaxEnt) method is proposed in this paper for effective probabilistic modeling of crosstalk in multi-conductor transmission lines (MTLs). The principle of the MaxEnt method states that for the given information constraints, the probability distribution that has the MaxEnt is considered to be the most unbiased and reasonable one. As for low- and high-dimensional spaces composed of the input random variables in MTL, the statistical moments of crosstalk required by the MaxEnt method as its information constraints are obtained through full-factorial numerical integration and sparse grid numerical integration, respectively. Then, a probability distribution model of crosstalk in MTL is established based on the MaxEnt method. Compared with the conventional Monte Carlo method, the proposed method can not only accurately predict the probability distribution and statistics of crosstalk in MTL but also considerably increases the computational efficiency. Therefore, the MaxEnt method is effective in modeling the probability distribution of crosstalk in MTL.
Highlights
In recent years, much attention has been devoted to the availability of simulation techniques that allow for the analysis of multi-conductor transmission lines (MTL), such as interconnects or cables, with the inclusion of the effects of the variability of geometrical or electrical parameters of the structures
In Part II, the maximum entropy (MaxEnt) method for the probability distribution modeling of crosstalk in MTL is introduced, and the statistical moment calculation method of crosstalk is studied when the input random variables belong to low- and highdimensional spaces
The probability distribution of crosstalk and the related statistical information of crosstalk are discussed through the MaxEnt method combined with full factorial numerical integration (FFNI) and sparse grid numerical integration (SGNI) when H, d, L, VS, R, and r serve as the random variables in low- and high-dimensional input spaces
Summary
Much attention has been devoted to the availability of simulation techniques that allow for the analysis of multi-conductor transmission lines (MTL), such as interconnects or cables, with the inclusion of the effects of the variability of geometrical or electrical parameters of the structures. Given that FFNI is based on the idea of the Gaussian quadrature formula, the statistical moments of the performance function can be obtained with relative accuracy, and FFNI shows strong robustness for different distribution types of the input random variables. In the statistical moment calculation method based on SGNI, the nodes and weights of d-dimensional quadrature points are obtained from the 1D quadrature points with the highest probability and by using the special tensor product rule unique to SGNI, which conducts the statistical moment calculation of the performance function when the input random variables belong to high-dimensional space [33]. In Part II, the MaxEnt method for the probability distribution modeling of crosstalk in MTL is introduced, and the statistical moment calculation method of crosstalk is studied when the input random variables belong to low- and highdimensional spaces.
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