An Indefinite Impedance Matrix Technique for Efficient Analysis of Planar Circuits With Irregular Shapes

An indefinite impedance matrix technique is proposed for efficient analysis of irregular shaped planar microwave and gigabit rate printed circuit board (PCB) circuits. The proposed method combines segmentation and desegmentation algorithms in a single matrix operation. The segmentation algorithm unites multiple planar blocks to make a composite structure by connecting them at their edge ports which become dependent variables of the resulting system. The desegmentation algorithm, on the other hand, removes a planar block or multiple blocks from a structure by delimiting the removed blocks with shared ports which are dependent variables of the overarching system. Both segmentation and desegmentation algorithms require separation of ports into independent and dependent variable groups. The composite system matrix is ill-conditioned due to its dependent entries. The singularity is fixed by casting the matrix into a reduced form with the elimination of dependent entries according to proper terminal conditions. Normally, planar structures with complicated shapes can be characterized with successive application of segmentation and desegmentation methods. The proposed algorithm combines these multiple operations in a single matrix which includes the dependent ports of both added and subtracted blocks. The concomitant ill-conditioning of the augmented matrix is tackled with algebraic operations subject to terminal conditions which result in a reduced size indefinite impedance matrix. The proposed system of equations eliminate the need for successive application of segmentation and desegmentation methods and improve efficiency.