Signal and power integrity co-simulation using the multi-layer finite difference method

Mixed signal system-on-package (SoP) technology is a key enabler for increasing functional integration, especially in mobile and wireless systems. SoP allows the integration of high speed digital, RF and passive components at a package level, thereby preserving performance at a lower cost compared to system-on-chip based solutions. Due to the presence of multiple dissimilar modules, each having unique power supply requirements, the design of the power distribution network (PDN) becomes critical.;The goal for the simulation of multi-layer power/ground planes, is the following: Given a stack-up and other geometrical information, it is required to find the network parameters (S/Y/Z) between port locations. For simple structures, it is possible to use existing commercially available methods (full-wave EM solvers) to obtain the response of the PDN. However, commercial packages have extremely complicated stack-ups, and the trend to increasing integration at the package level only points to increasing complexity. It is computationally intractable to solve these problems using these existing methods.;The approach proposed in this thesis for obtaining the response of the PDN is the multi-layer finite difference method (M-FDM). A surface mesh / finite difference based approach is developed, which leads to a system matrix that is sparse and banded, and can be solved efficiently. The approach relies on approximating the electric field distribution in power/ground planes. Certain geometrical features may invalidate these approximations, which may lead to significant inaccuracy in simulation results.;Thus, methods to update the system matrix to restore accuracy to M-FDM, while not adding significant computational overhead, have been considered. These methods are called the fringe augmentation (FA) and plane gap augmentation (PGA) methods.;While discussing the simulation of multi-layer packages, it is not possible to isolate the PDN from the signal traces routed between them. With increasing frequency, these signal traces behave as transmission lines, and hence, their distributed properties such as delay and phase become important. Also, signal traces use the PDN as their reference planes, and hence their characteristics cannot be decoupled from the PDN. Discontinuities in the PDN can manifest as signal integrity problems such as reduction in eye height or increased jitter.;Finally, an application of M-FDM for the optimization of a PDN design using Genetic Algorithms (GA) is considered. From a design perspective, the requirement on the PDN is that it should represent a low impedance at all frequencies at which current transients exist. Traditionally, the solution to providing a low impedance power supply as seen by the device has been to place decoupling capacitors (decaps) across the power supply pins.;The impedance profile of the PDN can be optimized by carefully choosing the values and placement locations of the decaps. This is critical since the anti-resonances (or parallel-resonances) that occur between decaps and between the decap and the PDN can lead to an impedance maximum. If this impedance maximum occurs at a frequency at which current transients exist, the severity of the SSN can be exacerbated. This choice and placement of decoupling capacitors can be accomplished using an optimization engine based on a genetic algorithm (GA).;To summarize, the contributions of this research are the following: (1) The development of a PDN modeler for multi-layer packages and boards called the the multi-layer finite difference method. (2) The enhancement of M-FDM using multi-port connection networks to include the effect of fringe fields and gap coupling. (3) An adaptive triangular mesh based scheme called the multi-layer finite element method (MFEM) to address the limitations of M-FDM. (4) The use of modal decomposition for the co-simulation of signal nets with the PDN. (5) The use of a robust GA-based optimizer for the selection and placement of decoupling capacitors in multi-layer geometries. (6) The implementation of these methods in a tool called MSDT 1. (Abstract shortened by UMI.)...