Uncertainty Quantification of Printed Microwave Interconnects by Use of the Sparse Polynomial Chaos Expansion Method

The performance of printed RF interconnect structures for microwave applications is highly dependent on their geometric characteristics as well as manufactured pattern fabrication errors/variations, that can only be insufficiently modeled by current simulation techniques. Here, for the first time, the response of such systems is accurately investigated when random fabrication errors are introduced in the geometric-design variables. To analyze these structures in a computationally efficient way, sparse-basis-polynomial-chaos-expansions (SB-PCE) are used to approximate the quantities of interest using a limited number (sparse) of basis functions. The size of the PCE series is reduced by retaining the most important terms. These are computed using the orthogonal-matching-pursuit algorithms from compressed-sensing (CS). In CS, a relatively small number of deterministic model evaluations is needed and a sparse but reliable PCE is found. The SB-PCE method is proven accurate and much more efficient (roughly two orders of magnitude shorter execution time) compared to alternative methods such as the Monte-Carlo (MC) and least-squares-PCE (LS-PCE) enabling for the first time the accurate modeling of realistic RF structures for specific manufacturing process variations. Numerical results for a monolithic-microwave-integrated circuit (MMIC) verify the effectiveness of the method and describes the structure's performance under uncertainty.