Power consumption modelling of integrated circuit micropoweroperational amplifiers

A modification to macromodels for integrated circuit micropower operational amplifiers is presented which involves the addition of an identical power section to each amplifier. The resulting macromodels account for influences of the input signal and load resistance on currents taken from the supply sources. The modelling accuracy of the integrated circuit power consumption is sufficient for typical macromodel applications     

Parametric macromodels of digital I/O ports

Addresses the development of macromodels for input and output ports of a digital device. The proposed macromodels consist of parametric representations that can be obtained from port transient waveforms at the device ports via a well established procedure. The models are implementable as SPICE subcircuits and their accuracy and efficiency are verified by applying the approach to the characterization of transistor-level models of commercial devices.     

Efficient Generation of FDTD Subcells Using Krylov Subspace Technique to the Wave Equation

This letter describes an efficient method for generating finite difference time domain (FDTD) subcells directly from the wave equation. An efficient macromodel technique is employed to reduce the number of internal state variables for a region functioning as a subcell in the FDTD method. Using a system of second-order state space equations to generate macromodels for objects with fine structural details, the macromodels are constructed with fewer internal state variables. The proposed method is tested against a couple of scattering examples to show the accuracy and efficiency     

Methods of accelerated characterization of VLSI cell libraries with prescribed accuracy control

The problems of simulation and characterization of VLSI standard cell libraries designed on the basis of semiconducting CMOS-technologies of the deep submicron and nanometer level are considered. The acceleration methods of the characterization process resulted in the identification of parameters of logic cell macromodels under the multiple simulation of cells on a circuit level for different versions of input actions and under the values of process-dependent parameters and modes of circuit operation. The algorithms of constructing the circuit characterization are directed at decreasing computational expenditures and ensuring the required accuracy of the macromodels. The results of the comparative analysis of different versions of the proposed algorithms are given.     

Construction of broadband passive macromodels from frequency data for simulation of distributed interconnect networks

This paper discusses a method for the construction of multiport broadband passive macromodels using frequency data obtained from an electromagnetic simulation or measurements. This data could represent the frequency response of a distributed interconnect system. The macromodels are generated using rational functions by solving an eigenvalue problem. For numerical computation, the macromodels are represented as a summation of rational functions consisting of low-pass, band-pass, high-pass, and all-pass filters. The stability and passivity of the macromodels are enforced through constraints on the poles and residues of rational functions. To enable the construction of broadband macromodels, methods based on band division, selector, subband reordering, subband dilation, and pole replacement have been used. Two test cases that describe the performance of the proposed algorithm, and three test cases that are representative of distributed systems have been analyzed to verify the efficiency of the method.     

基于特征线方法的无源传输线模型

基于特征线方法的传输线模型只能保证模型的因果性,但是不能保证模型的无源性。针对上述问题,该文提出了一种无源性补偿方法来实现传输线宏模型的无源性。该方法扩展了现有的用于集总模型的无源性补偿算法,以等式约束的二次规划方法为基础,采用拉格朗日乘数法进行优化。数值例子表明该方法在有限的仿真时间内产生了精确的无源宏模型。     

开关电源控制芯片宏模型的自动生成

开关电源控制苍片宏模型是开关电源CAD中一个重要组成部分。本文讨论了开关电源控制芯片宏模型的自动生成方法，分两类构造了控制芯片的整体拓扑和各功能单元宏模型，并详细介绍了宏模型的生成步骤，实现了自动生成软件，最后给出了测试结果。     

Passivity verification in delay-based macromodels of electrical interconnects

This paper presents a new theory that addresses the issue of passivity in macromodels of electrical interconnects constructed based on the method of characteristics (MoC). The proposed approach develops a new algebraic test to check for passivity in macromodels generated using MoC. The theory behind the developed test is based on deriving the necessary and sufficient conditions for the loss of positive-realness in the admittance matrix of the developed macromodel. An algorithmic procedure is proposed to verify passivity of general macromodels derived from the MoC. The results presented in this paper can be employed to test for positive-realness in dynamical systems described by algebraic delay-differential equations with discrete commensurate delays.     

一种快速的混合参数宏模型无源性补偿方法

针对高速数字系统的混合参数宏建模,采用模态矢量拟合算法具有模型拟合精度高,易于电路仿真集成的优点,但是初始生成的宏模型可能会在局部频带内不满足系统无源性。该文提出一种基于特征值模态的混合参数宏模型无源性补偿方法。首先构建了包含宏模型特征对的无源性目标函数,利用特征对加权的形式来控制参数扰动带来的模型精度变化,然后结合相应的无源性约束条件,将无源性补偿过程等效为可以解析求解的最小二乘优化问题。该方法在补偿混合参数宏模型无源性的同时,兼顾模型在任意端接激励源条件下的应用要求。结合实例并与留数扰动、模态扰动等无源性补偿方法进行比较,结果表明该方法在精度或效率方面均具有一定的优势。     

Macromodels in the frequency domain analysis of microwave resonators

We present a new technique of incorporating macromodels into the frequency domain formulation of grid based methods. Unlike previous methods, the new scheme does not introduce any frequency dependent elements into the system matrix and thus can be used in the analysis of resonator problems. Numerical results show an increase in accuracy of computations in a wide frequency range while convergence properties of the underlying matrix eigenvalue solver are not affected.     

Passivity Compensation Algorithm for Method-of-Characteristics-Based Multiconductor Transmission Line Interconnect Macromodels

Computation of passive and compact macromodels of distributed interconnects has gained considerable importance during the recent years. Method of characteristics (MoC) is widely used for macromodeling of transmission lines, however, it may not be guaranteed passive. This paper presents a new algorithm for passivity enforcement of MoC-based macromodels of multiconductor transmission lines. The algorithm is based on the first-order perturbation of the related delay differential equations and can handle single as well as coupled interconnects. Necessary theoretical foundations and validating numerical results are presented.      

Hybrid algorithm for compact and stable macromodelling of parameterised frequency responses

A novel hybrid technique for the macromodelling of parameterised frequency responses is presented. A more compact model representation is proposed that guarantees stability of the poles by construction. It is shown that accurate parametric macromodels can be calculated using a reduced amount of model coefficients and data samples. The obtained macromodels can be used for efficient real-time design space exploration, design optimisation and sensitivity analysis.     

Efficient Algorithm for Passivity Enforcement of $S$-Parameter-Based Macromodels

This paper presents an efficient and robust algorithm for passivity enforcement of $S$ -parameter-based macromodels. The method computes updated values of the model residues by least squares fitting of nonpassive residuals of the scattering matrix. Several examples show that the proposed method yields accurate passive macromodels at a limited computational cost.      

Multilevel model order reduction

We present a multilevel Model Order Reduction scheme for enhancing numerical analysis of electromagnetic fields by means of grid based techniques. The scheme allows one to create nested macromodels and combine macromodels with the Fast Frequency Sweep. The implementation of the method is illustrated on the Finite Difference Frequency Domain technique and efficient nodal order reduction algorithm (ENOR) but the concept can easily be applied also for other mesh based methods and other order reduction schemes.     

The Chip. A methodology for fast SPICE simulation of frequencysynthesizers

Welcome to the Chip! Last year in the January issue of this magazine, the problem of simulating a sigma-delta modulator at the transistor level using SPICE was discussed and a simulation flow presented that could speed up simulation time significantly while keeping the accuracy almost intact. Transistor-level simulation is a must for optimizing the design at the final stages. In this column, we discuss a flow for the fast simulation of phase-lock loops, another widely used mixed-signal feedback system where transistor-level simulation is prohibitive. in the article, we discuss a mixed-mode methodology that uses macromodels for the digital parts while keeping the critical analog parts at the transistor level. We show that the method is effective and maintains very high accuracy     

多层梁机电耦合系统的等效电路宏模型

实现MEMS器件系统级模拟的关键是建立其宏模型。由单层梁构成的机电耦合系统的等效电路宏模型 ,已做过深入的研究 ,但实际的MEMS器件通常都是多层的 .本文提出了一种基于力 电压 (F V)类比的、适用于由多层梁构成的机电耦合系统的等效电路宏模型 ,该模型可进行小信号时域和频域分析 ,能为多层梁机电耦合系统的设计带来很大的方便。模拟结果表明 ,该模型具有较高的精度     

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     

Perturbation Schemes for Passivity Enforcement of Delay-Based Transmission Line Macromodels

This paper introduces two different algorithms for passivity enforcement of transmission-line macromodels based on the generalized method of characteristics (MoC). The first scheme corrects passivity violations via perturbation of purely imaginary solutions of a nonlinear Hamiltonian eigenvalue problem. The second scheme is based on a linearly constrained quadratic optimization formulated at carefully selected frequency samples. Both schemes can be viewed as extensions to the case of MoC-based macromodels of existing techniques that were only available for lumped macromodels. The resulting passive delay-based macromodels can be safely employed in system-level signal integrity simulations, due to their inability to produce any spurious energy gain. Several numerical examples illustrate the behavior of both schemes on transmission line structures of practical interest, highlighting their main differences and the open problems deserving further research work.      

Passivity Verification in Delay-Based Macromodels of Multiconductor Electrical Interconnects

This paper presents a generalized theory of passivity verification in delay-based macromodels for multiconductor transmission line networks generated using the method of characteristics (MoCs). We demonstrate that the passivity in an MoC macro-model is equivalent to the nonnegative definiteness in the admittance matrices of two submodels. We then provide the necessary and sufficient conditions for each submodel to have a nonnegative definite admittance matrix. The presented theory develops an algebraic test to verify the passivity in MoC macromodels. Numerical results demonstrate the validity of the proposed theory.     

On the generation of large passive macromodels for complex interconnect structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed techniques.