Efficient numerical techniques for extracting parameters of passive elements in RF circuits

Most integral equation-based solvers converge slowly with discretization using first-order collocation or the Galerkin method. While the accuracy improvement achieved by the high-order Nystrom method is severely limited by the singularities in the solution space, in this thesis we describe a high-order Gaussian-Quadrature method for efficient full wave analysis. First, the method discretizes the patch panel on the surface of the conductors according to the Gaussian-node abscissae. Furthermore, the singularities of current are extracted in terms of Gaussian-quadrature schemes, and we only need to solve the smooth parts of the current distribution. The discretization cost is reduced substantially. The new scheme avoids the generation of special position-dependent quadrature rules, and provides a well-behaved matrix that converges rapidly without any pre-conditioning. Numerical results show that this technique can converge much more quickly than the traditional Method of Moments. The Gaussian quadrature scheme together with the high-order weighting functions achieves much higher accuracy than the low-order methods given the same amount of computing time, or it spends much less computing time given the same level of accuracy. The effectiveness of the proposed method has been demonstrated by the agreement between the numerical modeling of the inductors and interdigitated capacitors and the measurement data.; Second, a mixed potential integral equation (MPIE) technique combined with fast multi-layer Green's functions is used to compute the 3-D frequency dependent inductances, resistances, S, Y and Z parameters in lossy multi-layered substrate. Compared to FastHenry, a multipole-accelerated 3-D inductance extraction program, the algorithm presented here is more accurate and faster for lossy multi-layer structures for two reasons: (1) substrate and optional ground plane's loss and the coupling effect are efficiently modeled by multi-layer Green's functions, while the Green's functions are efficiently calculated via window-based acceleration technique; (2) Gaussian Jacobi-based high order techniques are used to capture the singularity of the current distribution at metal edges, leading to significant reduction of problem size and speed-up of computation.; Finally, a fast and efficient Method of Moments (MoM), based on a new subdomain partitioning technique, is presented for rapidly extracting the distributed capacitance and inductance of spiral inductors. By using this approach, the analytical formula of Green's function for multi-layer substrates is obtained through the prioritized wavetracing method. The computing time is much faster than state of the art capacitance and inductance solvers, such as FMMS[37]. Good agreement between numerical results and measurement data is shown to demonstrate the accuracy of the proposed new method.