Methods for checking and enforcing physical quality of linear electrical network models

Most CAD tools allow system-level simulation for signal integrity by computing and connecting models together for the various sub-parts. The success of this model derivation depends on the quality of the network parameters. Different errors may seriously affect the quality of the frequency characterization: frequency-dependent measurement errors, errors due to the numerical simulation and/or discretization, etc. When these errors are large, model assembly and simulation becomes difficult and may even fail. This thesis gives an overview of the most significant properties of physically valid network parameters, describes existing methods for checking and enforcing these properties, and presents several new methodologies for checking and enforcing causality. A time domain methodology based on the vector fitting approximation as well as the frequency domain methodologies based on the Kramers-Kronig relations enforcement by numerical integration and Fast Fourier Transform are presented. A new algorithm is developed for a stable recursive convolution after time domain causality enforcement. In addition, global qualities of data for system simulations are discussed: a study of an accurate causal frequency domain interpolation as well as a robust technique for extrapolation to DC is included --Abstract, page iii