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Tolerances in component values will affect a product manufacturing yield. The yield can be maximized by selecting component nominal values judiciously. Several yield optimization routines have been developed. A simple algorithm known as the center of gravity (CoG) method makes use of a simple Monte Carlo sampling to estimate the yield and to generate a search direction for the optimal nominal values. This technique is known to be able to identify the region of high yield in a small number of iterations. The use of the importance sampling technique is investigated. The objective is to reduce the number of samples needed to reach the optimal region. A uniform distribution centered at the mean is studied as the importance sampling density. The results show that a savings of about 40% as compared to Monte Carlo sampling can be achieved using importance sampling when the starting yield is low. The importance sampling density also helped the search process to identify the high yield region quickly and the region identified is generally better than that of Monte Carlo sampling.

System design centering process searches for nominal values of system designable parameters which maximize the probability of satisfying the design specifications (yield function). Statistical design centering implements a statistical analysis method such as Latin hypercube sampling (LHS) for yield function estimation, and explicitly optimizes it. In this chapter, we introduce a new statistical design centering technique for microwave system design. The technique combines a modified surrogate-based derivative-free trust region (TR) optimization algorithm, and the generalized space mapping (GSM) technique. The modified TR algorithm is a derivative-free optimization algorithm that employs quadratic surrogate models to replace the computationally expensive yield function in the optimization process. The modified TR algorithm allows the shape of the TR to be dynamically adapted to a hyper-elliptic shape accompanied with the quadratic model. This improves the accuracy and convergence properties of the algorithm. Generally, TR algorithms exhibit global convergence features irrespective of the starting point setting. The new design centering approach utilizes the GSM technique to approximate the feasible region in the design parameter space with a sequence of iteratively updated space mapping (SM) surrogates. At each SM iteration, the modified TR algorithm optimizes the yield function for the current SM region approximation to get a better center. Two microwave circuit examples are used to show the effectiveness of the new design centering technique to obtain an optimal design in few SM iterations. In the design process, we employ Sonnet em for the bandstop microstrip filter design and CST Studio Suite for the ultra-wideband (UWB) multiple-input–multiple–output (MIMO) antenna.

Uncertainty quantification is an important aspect of engineering design, also pertaining to the development and performance evaluation of high-frequency structures systems. Manufacturing tolerances as well as other types of uncertainties, related to material parameters (e.g., substrate permittivity) or operating conditions (e.g., bending) may affect the characteristics of antennas or microwave devices. For example, in the case of narrow- or multi-band antennas, this usually leads to frequency shifts of the operating bands. Quantifying these effects is imperative to adequately assess the design quality, either in terms of the statistical moments of the performance parameters or the yield. Reducing the system sensitivity to parameter deviations is even more essential when increasing the probability of the system satisfying the prescribed requirements is of concern. The prerequisite of such procedures is statistical analysis, normally carried out at the level of full-wave electromagnetic (EM) analysis. Although necessary to ensure reliability, it entails considerable computational expenses, often prohibitive. Following the recently fostered concept of constrained modeling, this chapter discusses a simple technique for rapid surrogate-assisted yield optimization of high-frequency structures. The keystone of the approach is an appropriate definition of the optimization domain. This is realized by considering a few pre-optimized designs that represent the directions featuring maximum variability of the circuit responses (particularly the parts thereof that affect the yield value in the most significant way) with respect to its geometry parameters. Due to a small volume of such a domain, an accurate replacement model can be established therein using a small number of training samples, and employed to improve the yield. The implementation details are tailored to a particular type of device. Verification results obtained for several antenna structures and a miniaturized rat-race coupler indicate that the optimization process can be accomplished at low cost of a few dozen of EM simulations. The result reliability is validated through comparisons with EM-based Monte Carlo simulations.