Properties of Triplets with Complex Reflection Zeros

This manuscript investigates intrinsic properties of triplets, as one of the basic blocks to implement a finite transmission zero. Specifically, some phenomena occurring in common synthesis problems are addressed: extreme external coupling, severe detuning of the resonators, mixed signs for cross-coupling. The objective is to study such occurrences, resorting to algebraic analysis of the problem and to specific analyses when the Reduced Chebychev response is invoked with complex reflection zeros. Relevant properties of the polynomials are described and proven when possible, while approximations are introduced otherwise. Synthesized examples support the validity of the approach.