This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. The suggested model is fully general, allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded non-resonating nodes (NRNs), frequency-dependent source-load coupling, multiple frequency-variant cross-couplings, andor multiple dispersive couplings for connecting the source and load to the filter network. 2.2 Coupling matrix for lossy lter synthesis For lossy lter synthesis with MOEA, the size of coupling matrix is a key concern, because there may be a lot of time-consuming complex matrix operations in the optimisation process. Cameron, General coupling matrix synthesis methods for Chebyshev filtering functions, IEEE Trans. We illustrate this by carrying out the synthesis process of two asymmetric filters of 8 th and 10 degree. The engineered formulation is more general than prior-art ones and can be treated as an extension of previous synthesis models, since constant or linear couplings are special cases of arbitrary frequency dependence. coupling matrix synthesis problem appears to be high and offers therefore some flexibility that can be used during the design phase. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary frequency-variant coupling (AFVC) coefficients is proposed. A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this paper.

Coupling matrix synthesis