Coupling Matrix Reconfiguration Based on Matrix Completion

This article proposes a general and efficient filter topology reconfiguration method based on matrix completion theory, which allows for frequency-dependent couplings (FDCs) and nonresonating nodes (NRNs). The projected gradient of the objective function on the manifold of constraints is determined analytically, expressed as the stiff ordinary differential equation (ODE). This constructs the descent flow that can be numerically followed to solve the ODE with integration. Since all the gradient calculations are performed with advanced matrix operations instead of elementwise computation, the proposed synthesis algorithm is significantly efficient. Moreover, to cover more varied filter networks, the ODE expressions of the projected gradient are extended to the topologies incorporating FDCs and NRNs. Multiple synthesis examples are presented to demonstrate the efficiency of the approach. In particular, one experimental example is used to exhibit the parameter extraction application of the proposed method for post-production tuning.