Michelangelo Bandinu

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

A Parameterization Scheme for Lossy Transmission Line Macromodels With Application to High Speed Interconnects in Mobile Devices

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 permittivity. 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

An automatic algorithm for equivalent circuit extraction from noisy frequency responses

This paper presents a fully automatic algorithm for the extraction of equivalent circuits from noisy frequency responses. The application area involves the generation of SPICE-ready macromodels for critical interconnects for signal integrity characterizations. Direct measurements are often employed to obtain a characterization of a given interconnect structure, leading to its frequency-dependent scattering responses. The proposed technique processes these responses and outputs an equivalent circuit. The algorithm is based on a modification of the well-known vector fitting scheme, which has now become a standard tool in EMC and SI studies. The presented improvements focus on robustness to noise, which is always present in measured data, and on automatic order estimation. These issues are addressed via an automatic detection of any spurious poles due to the noise, which are hard relocated in order to maximize the model accuracy. Several application examples are presented to illustrate the excellent capabilities of the new fitting scheme.

Fast Assessment of Antenna-PCB Coupling in Mobile Devices: a Macromodeling 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.

Fast evaluation of electromagnetic interference between antenna and PCB traces for compact mobile devices

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.

Geometrically Parameterized Circuit Models of Printed Circuit Board Traces Inclusive of Antenna Coupling

This paper presents a systematic methodology for the characterization of mutual couplings between antennas and printed circuit board (PCB) traces in modern mobile devices. The main approach is based on the assumption that the interfering fields produced by the antennas are not perturbed significantly by the PCB traces. The one-way coupling can thus be computed using the theory of field-excited transmission lines. The incident field patterns excited by each antenna are computed via a single preliminary full-wave analysis. We adopt a generalized scattering formulation for the electromagnetic system. Some ports define the terminals of the PCB traces, the other “electromagnetic” ports correspond to the antennas feed points. The main achievement of this paper is a parameterization scheme for this generalized scattering form in terms of the trace-routing path. This parameterization further approximates the frequency dependence of each response in terms of rational functions, enabling the direct synthesis of path-dependent macromodels in an SPICE environment. Fast optimization, what-if, and sensitivity analyses can thus be performed directly via transient SPICE runs, possibly including realistic (transistor-level or behavioral) models for driver and receiver circuits.

An iterative reweighting process for macromodel extraction of power distribution networks

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.

Sensitivity-based weighting for passivity enforcement of linear macromodels in power integrity applications

The electrical performance of Power Distribution Networks (PDNs) is usually assessed by computing frequency responses through quasi-static or full-wave electromagnetic solvers. Such responses, often available in the scattering form, are then fed to suitable macromodeling algorithms for the extraction of compact reduced-order behavioral models that can be seemlessly simulated in the time domain by standard circuit solvers. Such algorithms perform a rational fitting of the raw scattering responses, followed by a passivity check and enforcement step. The resulting macromodel is typically very accurate when compared to the raw scattering responses. It may however happen that the responses of the PDN macromodel exhibit significant deviation from the true system responses under realistic loading conditions, which include appropriate models for active device blocks, decoupling capacitors, voltage regulators, etc. We highlight the source of this accuracy loss, and we propose a sensitivity-based weighting strategy that is able to optimize and tune the macromodel accuracy based on its specific nominal termination network. The particular focus of this paper is the definition and the inclusion of optimal weigths in the passivity enforcement loop, which is recognized as the most challenging step. The result is a reliable macromodeling flow, which is able to produce passive, accurate and efficient reduced-order models of general PDN structures for power integrity analysis and verification.

On Tuning Passive Black-Box Macromodels of LTI Systems via Adaptive Weighting

This paper discusses various approaches for tuning the accuracy of rational macromodels obtained via black-box identification or approximation of sampled frequency responses of some unknown Linear and Time-Invariant system. Main emphasis is on embedding into the model extraction process some information on the nominal terminations that will be connected to the model during normal operation, so that the corresponding accuracy is optimized. This goal is achieved through an optimization based on a suitably defined cost function, which embeds frequency-dependent weights that are adaptively refined during the model construction. A similar procedure is applied in a postprocessing step for enforcing model passivity. The advantages of proposed algorithm are illustrated on a few application examples related to power distribution networks in electronic systems.