Package Macromodeling via Time-Domain Vector Fitting

Abstract—This paper addresses the construction of lumped macromodels for package structures. A technique named Time-Domain Vector Fitting (TD-VF) is introduced for the identification of the dominant poles of the structure. This method uses as raw data transient excitations and responses at the ports of the struc-ture. These responses are easily obtained from transient full-wave electromagnetic solvers based, e.g., on Finite Differences. The rational approximation can be easily synthesized into a SPICE-compatible subcircuit providing a broadband approximation to the input-output behavior of the package. Index Terms—Circuit extraction, macromodeling, time-domain vector fitting, vector fitting

Robust macromodeling of frequency responses with outliers

This paper introduces a robust Vector Fitting algorithm for macromodeling of measured of simulated frequency responses with outliers. The use of a new frequency-dependent weighting scheme ensures that the complex fitting error is minimized in the L1 sense, rather than the L2 sense. Numerical results indicate that this approach leads to more accurate results

A Bayesian approach to adaptive frequency sampling

This paper introduces an adaptive frequency sampling scheme, based on a Bayesian approach to the well-known vector fitting algorithm. This Bayesian treatment results in a data-driven measure of intrinsic model uncertainty. This uncertainty measure can in turn be leveraged to sample sequentially in an efficient and robust way. A realistic example is used to visualize the proposed scheme, and to confirm its proficiency

Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses

The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise.We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise.We denote the resulting algorithm as vector fitting with adding and skimming (VF-AS). A thorough validation of the VF-AS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VF-AS algorithm to measured scattering responses of interconnect structures and networks typical of high-speed digital systems

Generation of passive macromodels from transient port responses

Abstract: This paper presents a new technique for the generation of linear lumped macromodels from input-output port characterization. A complete set of transient port responses is processed by a new time-domain formulation of the well-known Vector Fitting algorithm. The data processing involves a combination of digital filtering and least squares fitting. Passivity of the obtained macromodel is enforced a posteriori by applying an iterative perturbation technique to the associated Hamiltonian matrix.