This paper aims to propose a deterministic framework for the robust synthesis of microstrip filters and multiplexers under manufacturing-induced geometrical uncertainties, ensuring bounded passband ripple and steep out-of-band attenuation under worst-case deviations.
A distortion-aware extremal polynomial framework is developed by reformulating the Chebyshev optimality condition to include bounded root perturbations dictated by manufacturing-yield statistics. Probabilistic tolerances of critical geometrical parameters are mapped to electrical deviations and subsequently to admissible polynomial root variations through a yield-based statistical model. Constrained optimisation reshapes the polynomial response so that all passband extrema remain within prescribed ripple limits while preserving sharp out-of-band attenuation. The optimised polynomials are back-annotated to the physical structures and validated using full-wave finite-element simulations.
Validation on two microwave structures shows that the optimised designs maintain return-loss ripple within specifications under worst-case geometrical deviations while preserving steep out-of-band rejection. Among the proposed schemes, the recursive optimisation method provides the strictly minimax solution.
The proposed framework enables deterministic worst-case robustness under fabrication uncertainties. Unlike Monte Carlo or sensitivity-based approaches, robustness is enforced directly at the synthesis stage with minimal simulation cost, making the method well-suited for yield-driven industrial microwave and electromagnetic compatibility applications.
