Statistical Synthesis of Optimal Coupling Matrix for Robotic Automatic Tuning of Microwave Bandpass Filters

This paper presents a new concept of statistical synthesis of coupling matrix (CM) that is optimal in the sense of the least sensitivity and the most tunability for mass production of microwave bandpass filters. Unlike the conventional way to synthesize CM from a filter function with equi-ripple passband return loss, the new statistical synthesis approach is to acquire the optimal CM from the statistical distributions of coupling elements that are extracted from Monte-Carlo optimization against a given design specification. Two criteria are used to demonstrate the superiority of the statistically synthesized optimal CM: 1) the V-curve of each coupling element vs. the error function against the design specification; and 2) Monte-Carlo yield analysis of the CM against the acceptance specification. A large number of case studies reveal that the statistically synthesized optimal CM is least susceptible to the manufacturing error and much easier to tune in mass production as compared to the CM targeting an equi-ripple Chebyshev bandpass response.