Yield optimization can be a crucial step in highvolume passive microwave component design, however it is typically a very expensive process, as a multitude of full-wave electromagnetic analyses are required for statistical analysis at each step of the optimization process. Metamodeling techniques have been shown to be useful solutions to this problem. In this paper yield optimization of a 43-variable passive 100 GHz ridged waveguide filter is done using the novel combination of a performance-guided random walk and Non-Linear Partial Least Squares based Polynomial Chaos Expansion (NLPLS-based PCE). It is shown that a substantial improvement of the yield is achieved with reduced model evaluations using this method.

This paper presents a global sensitivity analysis of a high-Q partially air-filled pedestal resonator integrated in a printed circuit board. Nonlinear partial-least-squares-based polynomial chaos expansion (NLPLS-based PCE) approach is used for the global sensitivity analysis. Using NLPLS-based PCE a surrogate model is constructed with a reduced dimensionality, which enhances the performance of the algorithm. A standard PCE surrogate model, with all the system parameters, is created from the reduced NLPLS-based PCE surrogate model. The statistical information needed to perform the sensitivity analysis, i.e., variance, is extracted from the standard PCE surrogate model. A variance-based global sensitivity analysis is performed on the PCE model, each system parameter's sensitivity is quantified as the partial influence on the total variance of the performance variable S11. The chosen manufacturing technology involves a three-stage process: micromachining of the cavity, metallization, and thermos-diffusion stacking. During the three stages several problems may occur that can have an influence on the performance of the resonator, such as shape and size variation, and misalignment. The system parameters are set up according to these most common problems. The results show that, of the 8 system parameters chosen to evaluate, the height of the cavity and pedestal are the most sensitive parameters.

Non-linear Partial Least-Squares based Polynomial Chaos Expansions (NLPLS-based PCE) has recently been shown to allow yield analysis for high-dimensional problems. A com-parison of coefficient calculation techniques in the PCE step of the algorithm is done to determine the appropriate technique for generalized antenna problems. An NLPLS-based PCE surrogate of an 8-variable dual-band patch antenna and a 37-variable diplexer is constructed using Ordinary Least-Squares (OLS), Least Angle Regression (LAR), and Orthogonal Matching Pursuit (OMP). LAR and OMP provided a more stable solution when compared to OLS for both the dual-band patch antenna and diplexer, with OMP outperforming LAR for the 8-variable dual-band patch solution. The choice of an appropriate coefficient calculation method is thus determined to have a significant influence on the effectiveness of NLPLS-based PCE.

For high-volume manufacturing, yield estimation is an important design step to determine the effects of uncertainties in the fabrication process. The tolerances associated with the fabrication process are applied to the statistically significant system parameters, and a Monte Carlo (MC) simulation is historically done to accurately estimate the yield. This process becomes computationally very expensive when the number of statistically significant system parameters are either too difficult to intuitively determine or are too high. A nonlinear partial-least-squares-based polynomial chaos expansion (NLPLSs-based PCE) is proposed as a solution for complex antenna yield analysis. NLPLS-based PCE effectively reduces the system dimensionality using NLPLS and simultaneously extracts the statistical information on the same sample set, that is, yield, using PCE. It is also possible to perform a global sensitivity analysis using NLPLS-based PCE surrogates, providing an additional advantage. This method is illustrated using an eight-variable single-frequency patch antenna, an eight-variable dual-band patch antenna, and a 37-variable diplexer requiring 30, 10, and 30 analysis points, respectively, to obtain converged yield estimates.

This paper presents a Non-Linear Partial-Least-Squares-based Polynomial Chaos Expansion (NLPLS-based PCE) approach for high dimensional global sensitivity analysis. NLPLS-based PCE effectively reduces the system dimensionality using NLPLS and simultaneously extracts the statistical information on the same sample set, i.e. variance, using PCE. A post-processing step is applied to transform the NLPLS-based PCE surrogate to a standard PCE surrogate, described by the full set of system parameters. A variance-based global sensitivity analysis is then applied, quantifying each system parameter’s sensitivity as the partial influence on the total variance of the performance variable. This method is illustrated using a high-dimensional problem, namely, a 37-variable passive diplexer structure, requiring 30 analysis points to obtain a converged global sensitivity analysis. The diplexer is optimized for manufacturing and the fabricated diplexer performs as expected. Another 37-variable global sensitivity analysis is performed and compared to the original diplexer.

Polynomial Chaos Expansion (PCE) based yield analysis of a conical Quad-Mode Antenna (QMA) is performed, as an alternative to computationally very expensive Monte-Carlo based methods. A PCE surrogate is constructed using the most appropriate coefficient calculation technique and sub-sampling method based on structure limitations and computational cost. The QMA is shown to be well-behaved in terms of yield. Possible design improvements are discussed.

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross-polarization of an inset-fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high-volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem-specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte-Carlo analysis.