Efficient calculation technique for the impedance matrix equation in the MPIE technique for microstrip and slotline planar structures of arbitrary shape

A mixed-potential integral equation (MPIE) technique is used to simulate the circuit parameters of arbitrary shaped microstrip and slotline circuits embedded in a multilayered medium. The well-known rooftop functions defined over a mixed grid of rectangular and triangular cells are used to model the electric and magnetic currents on the microstrip and slot circuits. Galerkin's method is applied to reduce the integral equation to a linear system of equations Z.I = V. Special approximations of the Green's functions make the analytical calculation of the cell-cell interactions possible. An efficient calculation technique for the elements of the impedance matrix Z is presented. Simulation results for a microstrip bandpass filter and a microstrip-slot coupler are presented.<>