Guaranteed passive parameterized model order reduction of the partial element equivalent circuit (PEEC) method

The decrease of IC feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the system under study as a function of design parameters, such as geometrical and substrate features, in addition to frequency (or time). Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters. We propose an innovative PMOR technique applicable to PEEC analysis, which combines traditional passivity-preserving model order reduction methods and positive interpolation schemes. It is able to provide parametric reduced-order models, stable, and passive by construction over a user-defined range of design parameter values. Numerical examples validate the proposed approach

Compact and accurate models of large single-wall carbon-nanotube interconnects

Single-wall carbon nanotubes (SWCNTs) have been proposed for very large scale integration interconnect applications and their modeling is carried out using the multiconductor transmission line (MTL) formulation. Their time-domain analysis has some simulation issues related to the high number of SWCNTs within each bundle, which results in a highly complex model and loss of accuracy in the case of long interconnects. In recent years, several techniques have been proposed to reduce the complexity of the model whose accuracy decreases as the interconnection length increases. This paper presents a rigorous new technique to generate accurate reduced-order models of large SWCNT interconnects. The frequency response of the MTL is computed by using the spectral form of the dyadic Green's function of the 1-D propagation problem and the model complexity is reduced using rational-model identification techniques. The proposed approach is validated by numerical results involving hundreds of SWCNTs, which confirm its capability of reducing the complexity of the model, while preserving accuracy over a wide frequency range

Efficient design optimization of complex electromagnetic systems using parametric macromodeling techniques

We propose a new parametric macromodeling technique for complex electromagnetic systems described by scattering parameters, which are parameterized by multiple design variables such as layout or substrate feature. The proposed technique is based on an efficient and reliable combination of rational identification, a procedure to find scaling and frequency shifting system coefficients, and positive interpolation schemes. Parametric macromodels can be used for efficient and accurate design space exploration and optimization. A design optimization example for a complex electromagnetic system is used to validate the proposed parametric macromodeling technique in a practical design process flow

Model order reduction for delay systems by iterative interpolation

AbstractAdaptive algorithms for computing the reduced‐order model of time‐delay systems (TDSs) are proposed in this work. The algorithms are based on interpolating the transfer function at multiple expansion points and greedy iterations for selecting the expansion points. The ‐error of the reduced transfer function is used as the criterion for choosing the next new expansion point. One heuristic greedy algorithm and one algorithm based on the error system and adaptive sub‐interval selection are developed. Results on four TDSs with tens of delays from electromagnetic applications are presented and show the efficiency of the proposed algorithms

Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis

The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach

Time-domain analysis of RF and microwave autonomous circuits by vector fitting-based approach

This work presents a new method for the analysis of RF and microwave autonomous circuits directly in the time-domain, which is the most effective approach at simulation level to evaluate nonlinear phenomena. For RF and microwave autonomous circuits, time-domain simulations usually experiment convergence problems or numerical inaccuracies due to the presence of distributed elements, preventing de-facto their use. The proposed solution is based on the Vector Fitting algorithm applied directly at circuit level. A case study relative to a RF hybrid oscillator is presented for practical demonstration and evaluation of performance reliability of the proposed method

Partial element equivalent circuit models in the solution of the electric field integral equation

3-D electromagnetic methods are fundamental design tools for complex high-speed systems. Among the integral equation-based techniques, the Partial Element Equivalent Circuit (PEEC) method has received a special attention in interconnect modeling, where mixed electromagnetic/circuit problems need to be solved. Retardation effects and the resulting delays must be taken into account and included in the modeling, when signal waveform rise times decrease and the corresponding frequency content increases or the geometric dimensions become electrically long. In this case, the enforcement of the Kirchhoff laws to PEEC delayed models leads to a set of delayed differential equations in a neutral form. The aim of this contribution is to present an overview of the PEEC method with special focus on the analysis of electrically long structures that require taking delays into account

On the Flux Linkage between Pancake Coils in Resonance-Type Wireless Power Transfer Systems

This work presents a series representation for the mutual inductance of two coaxial pancake coils which remains accurate in non-quasi-static regime under the hypothesis that the current in the source coil is uniformly distributed. Making use of Gegenbauer's addition theorem and a term-by-term analytical integration, the mutual inductance between two generic turns belonging to distinct coils is expressed as a sum of spherical Hankel functions with algebraic coefficients. The accuracy and efficiency of the resulting expression is proved through pertinent numerical examples

Reduced order modeling of delayed PEEC circuits

We propose a novel model order reduction technique that is able to accurately reduce electrically large systems with delay elements, which can be described by means of neutral delayed differential equations. It is based on an adaptive multipoint expansion and model order reduction of equivalent first order systems. The neutral delayed differential formulation is preserved in the reduced model. Pertinent numerical results validate the proposed model order reduction approach

Time-domain green's function-based parametric sensitivity analysis of multiconductor transmission lines

We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines. This technique can handle multiple design parameters, such as substrate or geometrical layout features, and provide time-domain sensitivity information for voltages and currents at the ports of the lines. It is derived from the dyadic Green's function of the 1-D wave propagation problem. The rational nature of the Green's function permits the generation of a time-domain macromodel for the computation of transient voltage and current sensitivities with respect to both electrical and physical parameters, completely avoiding similarity transformation, and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels that provide sensitivity information are well suited for design space exploration, design optimization, and crosstalk analysis. Two numerical examples validate the proposed approach in both frequency and time-domain