Multi-objective optimisation technique for coupling matrix synthesis of lossy filters

Coupling matrix synthesis technique based on multi-objective evolutionary algorithm (MOEA) is proposed for pseudoelliptic low-pass filter prototypes with lossy resonators and arbitrary topology. MOEA-based synthesis can deal with multi-objective functions so that different filter characteristics of high-performance lossy filter, such as return loss, out of band rejection and passband flatness, can be optimised simultaneously. In the proposed MOEA-based lossy filter synthesis, a chromosome pair coding model is defined to treat real and imaginary parts of complex coupling matrix of a lossy filter, and additional constraints on Q-factor to characterise lossy resonator in the filter are applied. For demonstration, non-dominated sorting genetic algorithm II with extended arithmetic crossover and adaptive mutation operator are used to synthesise three symmetric/asymmetric lossy filters. The results indicate that the proposed MOEA-based synthesis technique can provide perfect passband ripple as required in high-performance microwave filters.