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.

We introduce a novel parameterization scheme based on the generalized method of characteristics (MoC) for macromodels of transmission-line structures having a cross section depending on several free geometrical and material parameters. This situation is common in early design stages, when the physical structures still have to be finalized and optimized under signal integrity and electromagnetic compatibility constraints. The topology of the adopted line macromodels has been demonstrated to guarantee excellent accuracy and efficiency. The key factors are propagation delay extraction and rational approximations, which intrinsically lead to a SPICE-compatible macromodel stamp. We introduce a scheme that parameterizes this stamp as a function of geometrical and material parameters such as conductor-width and separation, dielectric thickness, and permettivity. The parameterization is performed via multidimensional interpolation of the residue matrices in the rational approximation of characteristic admittance and propagation operators. A significant advantage of this approach consists of the possibility of efficiently utilizing the MoC methodology in an optimization scheme and eventually helping the design of interconnects. We apply the proposed scheme to flexible printed interconnects that are typically found in portable devices having moving parts. Several validations demonstrate the effectiveness of the approach.

This paper presents a fast procedure for the evaluation of electromagnetic coupling between antennas and Printed Circuit Board (PCB) traces on mobile devices. Starting from the geometrical description of the device, a single full-wave simulation is used to compute the electric fields at selected PCB locations. Then, the theory of field-excited transmission lines is used to compute the antenna-induced EMI coupling coefficients at the terminations of an arbitrarily routed PCB trace. The results are finally fed to a rational fitting algorithm for the generation of a broadband SPICE-compatible netlist. This netlist can be used in system-level circuit-based simulations for signal integrity assessments including antenna-induced EMI.

This paper proposes a technique for the fast evaluation of antenna-induced noise at the terminations of PCB traces on compact mobile phones platforms. The main approach is based on the classical theory of transmission lines with external field excitation. We show that a single full-wave electromagnetic simulation is needed to compute the coupling coefficients for an arbitrary location of the trace on the phone PCB. Therefore, the approach is ideally suited for the automated incorporation of EMI constraints within routing and placement algorithms and for parametric and what-if analyses.

This paper introduces a new algorithm for the generation of optimal time-domain macromodels of power distribution networks, starting from a set of tabulated scattering responses and given a nominal termination scheme for active blocks, decoupling capacitors, and voltage regulator module. The new concept being introduced is a modified metric to characterize and optimize the accuracy of the macromodel, which takes into account the operation conditions that will be applied to run transient simulations for power integrity assessment. This metric is applied through an iterative frequency-dependent reweighting scheme in a fully automated flow. Two examples illustrate the performance of the proposed algorithm.