Passive Reduced-order Interconnect Macromodeling Algorithm Research Articles

Modelling and analysis of vibration on power electronic module structure and application of model order reduction

Modelling and analysis of vibration of an IGBT power electronic module (PEM) structure were undertaken. PEM structure considered in this study was without molding compound and wirebonds. The most critical resonant frequency was identified by modal analysis. At the critical frequency of 1345 Hz, for the vertical displacement of the base excitation, subsequent stress distribution on the PEM structure was analysed. Concurrent vibration and thermo-mechanical fatigue loads on the reliability of PEM structure solder interconnects were also estimated by widely used linear damage superposition approach. It was concluded that the at critical resonant frequency the vibration induced damage is more severe than the thermo-mechanical fatigue loading. In addition, a quarter car model (QCM) was used to mimic the dynamic interaction between the rough road surface and an electric vehicle (EV) in order to analyse the road surface roughness induced excitation on the PEM structure in the engine compartment. Stress and strain distribution on the PEM structure due to road surface roughness were analysed. Furthermore, three Krylov subspace based model order reduction (MOR) techniques were applied to the resulting dynamic system in vibration analysis. Due to the limits on computing resources, a submodel was utilized for MOR analysis. Within the three MOR techniques, Passive Reduced order Interconnect Macromodeling Algorithm (PRIMA) MOR technique performs better than the other techniques. Computational time ratio between reduced system iteration and the full system iteration is 1: 53.

Model order reduction via eigen decomposition analysis

In this paper, we have proposed a novel model order reduction technique via rational transfer function fitting and eigenmode analysis considering residues. We define a constant as a key in the sorting algorithm as one of correlations in order to sort the order of eigenvalues. It is demonstrated that the accuracy via eigenmode analysis considering residues is improved. The proposed algorithm is a general method to match pole values with frequency domain poles for linear RC and RLC systems. Calculation of pole eigenvalues and eigen vectors can be done with more sophisticated analysis with the same level or smaller cost in the proposed algorithms in comparison to passive reduced order interconnect macromodeling algorithm (PRIMA). The experimental results show that our algorithm reduces up to 90% errors compared to the existing model order reduction algorithm, such as PRIMA, in wide frequency environment with the same number of poles in comparison.

Model Order Reduction of Parameterized Interconnect Networks via a Two-Directional Arnoldi Process

This paper presents a multiparameter moment-matching-based model order reduction technique for parameterized interconnect networks via a novel two-directional Arnoldi process (TAP). It is referred to as a Parameterized Interconnect Macromodeling via a TAP (PIMTAP) algorithm. PIMTAP inherits the advantages of previous multiparameter moment-matching algorithms and avoids their shortfalls. It is numerically stable and adaptive. PIMTAP model yields the same form of the original state equations and preserves the passivity of parameterized RLC networks like the well-known method passive reduced-order interconnect macromodeling algorithm for nonparameterized RLC networks.

Interval-Valued Reduced-Order Statistical Interconnect Modeling

We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in resistance-inductance-capacitance parameters as sets of correlated intervals and show how classical model-order reduction methods - asymptotic waveform evaluation and passive reduced-order interconnect macromodeling algorithm - can be retargeted to compute interval-valued, rather than scalar-valued, reductions. By applying a simple statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show that the technique can predict mean delay and standard deviation with errors between 5% and 10% for correlated parameter variations up to 35%.

Wideband passive multiport model order reduction and realization of RLCM circuits

This paper presents a novel compact passive modeling technique for high-performance RF passive and interconnect circuits modeled as high-order resistor-inductor-capacitor-mutual inductance circuits. The new method is based on a recently proposed general s-domain hierarchical modeling and analysis method and vector potential equivalent circuit model for self and mutual inductances. Theoretically, this paper shows that s-domain hierarchical reduction is equivalent to implicit moment matching at around s=0 and that the existing hierarchical reduction method by one-point expansion is numerically stable for general tree-structured circuits. It is also shown that hierarchical reduction preserves the reciprocity of passive circuit matrices. Practically, a hierarchical multipoint reduction scheme to obtain accurate-order reduced admittance matrices of general passive circuits is proposed. A novel explicit waveform-matching algorithm is proposed for searching dominant poles and residues from different expansion points based on the unique hierarchical reduction framework. To enforce passivity, state-space-based optimization is applied to the model order reduced admittance matrix. Then, a general multiport network realization method to realize the passivity-enforced reduced admittance based on the relaxed one-port network synthesis technique using Foster's canonical form is proposed. The resulting modeling algorithm can generate the multiport passive SPICE-compatible model for any linear passive network with easily controlled model accuracy and complexity. Experimental results on an RF spiral inductor and a number of high-speed transmission line circuits are presented. In comparison with other approaches, the proposed reduction is as accurate as passive reduced-order interconnect macromodeling algorithm in the high-frequency domain due to the enhanced multipoint expansion, but leads to smaller realized circuit models. In addition, under the same reduction ratio, realized models by the new method have less error compared with reduced circuits by time-constant-based reduction techniques in time domain.

Fast interval-valued statistical modeling of interconnect and effective capacitance

Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10/spl times/ faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (C/sub eff/) models for variational interconnect, and show how to extract statistics of C/sub eff/ over 100/spl times/ faster than classical MC simulation, with errors less than 4%.

PRIMA: passive reduced-order interconnect macromodeling algorithm

This paper describes an algorithm for generating provably passive reduced-order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reduced-order macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed.