Computationally-efficient statistical design and yield optimization of resonator-based notch filters using feature-based surrogates

Modern microwave devices are designed to fulfill stringent requirements pertaining to electrical performance, which requires, among others, a meticulous tuning of their geometry parameters. When moving up in frequency, physical dimensions of passive microwave circuits become smaller, making the system performance increasingly susceptible to manufacturing tolerances. In particular, inherent inaccuracy of fabrication processes affect the fundamental operating parameters, such as center frequency or bandwidth, which is especially troublesome for narrow-band structures, including notch filters. The ability to quantify the effects of tolerances, and—even more—to account for these in the design process, are instrumental in making the designs more reliable, and to increase the likelihood that adequate operation is ensured despite manufacturing errors. This paper proposes a simple yet computationally efficient and reliable procedure for statistical analysis and yield optimization of resonator-based notch filters. Our methodology involves feature-based surrogate models that can be established using a handful of training data points, and employed for rapid evaluation of the circuit fabrication yield. Furthermore, a yield optimization procedure is developed, which iteratively sets up a sequence of feature-based models, constructed within local domains relocated along the optimization path, and uses them as predictors to find a robust (maximum yield) design at a low computational cost. The presented approach has been demonstrated using two complementary split ring resonator (CSRR)-based notch filters. The cost of statistical design is about a hundred of EM simulations of the respective filter, with yield evaluation reliability corroborated through EM-based Monte Carlo analysis.