This paper investigates the efficiency of a perturbative approach for the statistical assessment of differential transmission lines affected by random parameters. Within the polynomial chaos framework, the novel technique reformulates the so-called stochastic Galerkin method in a decoupled and iterative fashion. Instead of solving the classical, augmented and fully coupled transmission line equations, the new approach iteratively solves multiple uncoupled line equations with nominal per-unit-length parameters and suitable equivalent distributed sources accounting for their variability. The methodology is applied to a system of up to four PCB differential pairs. A computational advantage is observed against the classical stochastic Galerkin method for large problems in terms of number of random parameters and/or conductors.

Efficiency of the Perturbative Stochastic Galerkin Method for Multiple Differential PCB Lines / Wu, X.; Grassi, F.; Manfredi, P.; Vande Ginste, D.. - ELETTRONICO. - (2018), pp. 1-3. (Intervento presentato al convegno 2018 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS 2018) tenutosi a Chandigarh (India) nel 2018) [10.1109/EDAPS.2018.8680876].

### Efficiency of the Perturbative Stochastic Galerkin Method for Multiple Differential PCB Lines

#### Abstract

This paper investigates the efficiency of a perturbative approach for the statistical assessment of differential transmission lines affected by random parameters. Within the polynomial chaos framework, the novel technique reformulates the so-called stochastic Galerkin method in a decoupled and iterative fashion. Instead of solving the classical, augmented and fully coupled transmission line equations, the new approach iteratively solves multiple uncoupled line equations with nominal per-unit-length parameters and suitable equivalent distributed sources accounting for their variability. The methodology is applied to a system of up to four PCB differential pairs. A computational advantage is observed against the classical stochastic Galerkin method for large problems in terms of number of random parameters and/or conductors.
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2018
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2759715`
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