This paper proposes a design and fine-tuning method for mixed electric and magnetic coupling filters. It derives the quantitative relationship between the coupling coefficients (electric and magnetic coupling, i.e., E_C and M_C) and the linear coefficients of frequency-dependent coupling for the first time. Different from the parameter extraction technique using the bandpass circuit model, the proposed approach explicitly relatesE_C and M_C to the coupling matrix model. This paper provides a general theoretic framework for computer-aided design and tuning of a mixed electric and magnetic coupling filter based on coupling matrices. An example of a 7th-order coaxial combline filter design is given in the paper, verifying the practical value of the approach.

A new optimization method is proposed to realize the synthesis of duplexers. The traditional optimization method takes all the variables of the duplexer into account, resulting in too many variables to be optimized when the order of the duplexer is too high, so it is not easy to fall into the local solution. In order to solve this problem, a new optimization strategy is proposed in this paper, that is, two-channel filters are optimized separately, which can reduce the number of optimization variables and greatly reduce the probability of results falling into local solutions. The optimization method combines the self-adaptive differential evolution algorithm (SADE) with the Levenberg-Marquardt (LM) algorithm to get a global solution more easily and accelerate the optimization speed. To verify its practical value, we design a 5G duplexer based on the proposed method. The duplexer has a large external coupling, and how to achieve a feed structure with a large coupling bandwidth at the source is also discussed. The experimental results show that the proposed optimization method can realize the synthesis of higher- order duplexers compared with the traditional methods.