Full-Wave Model of Frequency-Dispersive Media With Debye Dispersion Relation by Circuit-Oriented FEM

Dispersive materials play an important role in a wide variety of applications (e.g., waveguides, antenna structures, integrated circuits, bioelectromagnetic applications). In this paper, a full-wave finite-element method (FEM-SPICE) technique for modeling dispersive materials is proposed. A finite-element formulation employing Whitney elements capable of analyzing electromagnetic geometries with dispersive media is described, and a Norton equivalent network is developed for each element. The overall network can be analyzed using a circuit simulator based on SPICE, and is suitable for both frequency- and time-domain analysis. This approach exploits the flexibility of finite-element mesh generation and computational efficiency of modern circuit simulators. Simple test configurations are analyzed to validate the proposed formulation.      

PEEC Formulation Based on Dyadic Green's Functions for Layered Media in the Time and Frequency Domains

This paper presents a novel time- and frequency-domain concept of modeling with the partial element equivalent circuit (PEEC) method, which applies the mixed potential integral equation (MPIE) with dyadic Green's functions for layered media (DGFLM-PEEC). On the one hand, it represents an exact full-wave semianalytical solution for an arbitrary configuration of traces and via holes in multilayered printed circuit boards. On the other hand, the DGFLM-PEEC model is represented in a circuit form, and thus, may be included in general-purpose circuit simulators. The paper derives a general DGFLM-PEEC formulation, which may be applied to all types of the MPIE with dyadic Green's functions. Using this concept, a particular type of layered media, namely a lossy dielectric between two grounds (stripline region), is thoroughly investigated and used to set up a particular DGFLM-PEEC model. The closed-form expressions for partial inductances and potential coefficients have been derived for this case. The time- and frequency-domain DGFLM-PEEC models for the stripline region have been validated using the measurements and the simulation by the method of moments.      

Accuracy and stability improvements of integral equation modelsusing the partial element equivalent circuit (PEEC) approach

The partial element equivalent circuit (PEEC) technique is a formulation which transforms an electric field integral equation (EFIE) into a full-wave equivalent circuit solution. In this paper, improvements are made to the PEEC model through the development of a refined method of computing both the partial inductances as well as the coefficients of potential. The method does not increase the number of unknowns. In addition, damping is added to the PEEC model in order to further reduce nonphysical resonances which may occur above the useful frequency range, The observations and solutions presented in this paper are especially important for time domain solvers. The effectiveness of the method is illustrated with several examples     

Nonorthogonal PEEC formulation for time- and frequency-domain EM and circuit modeling

Electromagnetic solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for the solution of combined circuit and EM problems. The inclusion of all types of Spice circuit elements is possible. Due to this, the approach has been used in many different tools. Most of these solvers have been based on a rectangular or Manhattan representation of the geometries. In this paper, we systematically extend the PEEC formulation to nonorthogonal geometries since many practical EM problems require a more general formulation. Importantly, the model given in this paper is consistent with the classical PEEC model for rectangular geometries. Some examples illustrating the application of the approach are given for both the time and frequency domain.     

Synthesis of Reduced Equivalent Circuits for Transmission Lines

This paper presents a method for generating lumped models for symmetrical transmission-line two-ports. These models consist of an ideal transformer and frequency-domain approximations for two physical driving-point impedances. The lumped element values are obtained directly from the distributed parameters or propagation constant and characteristic impedance. The method is applied to dispersive transmission lines, skin effect and waveguides. It is shown that the equivalent circuit is superior in accuracy and number of elements compared to spatial discretizations like ladder approximation.     

射频高损耗硅基双互连线建模

针对高损耗硅衬底,采用部分元等效电路法和准静磁积分公式,将衬底涡流等效为衬底镜像电流,建立射频硅基双互连线等效电路模型。该模型考虑了趋肤效应、邻近效应和衬底损耗对互连线串联电感Ls和串联电阻Rs频率特性的制约。通过与全波分析方法对比,验证了在20 GHz范围内由该模型导出的互连线等效电感L、等效电阻R误差均在8%以内。该模型可望应用于硅基射频集成电路设计。     

等效电路模型方法在滤波器设计中的应用

针对传统耦合系数方法在设计包含NRN元件滤波器中的缺点,通过引入广义耦合系数的概念并结合等效电路模型,分析了NRN元件的阻抗缩放特性,提出了一种基于等效电路模型的设计方法,以分析包含非谐振节点(NRN)的滤波器响应特性。电路软件仿真结果验证了该等效电路模型设计方法的有效性。     

Generating compact, guaranteed passive reduced-order models of 3-D RLC interconnects

As very large scale integration (VLSI) circuit speeds and density continue to increase, the need to accurately model the effects of three-dimensional (3-D) interconnects has become essential for reliable chip and system design and verification. Since such models are commonly used inside standard circuit simulators for time or frequency domain computations, it is imperative that they be kept compact without compromising accuracy, and also retain relevant physical properties of the original system, such as passivity. In this paper, we describe an approach to generate accurate, compact, and guaranteed passive models of RLC interconnects and packaging structures. The procedure is based on a partial element equivalent circuit (PEEC)-like approach to modeling the impedance of interconnect structures accounting for both the charge accumulation on the surface of conductors and the current traveling in their interior. The resulting formulation, based on nodal or mixed nodal and mesh analysis, enables the application of existing model order reduction techniques. Compactness and passivity of the model are then ensured with a two-step reduction procedure where Krylov-subspace moment-matching methods are followed by a recently proposed, nearly optimal, passive truncated balanced realization-like algorithm. The proposed approach was used for extracting passive models for several industrial examples, whose accuracy was validated both in the frequency domain as well as against measured time-domain data.     

分数阶记忆元件通用等效电路的设计

根据分数阶记忆元件之间的转换关系,设计了一种分数阶记忆元件通用等效电路。该等效电路在不改变电路拓扑结构的情况下,通过选择五个阻抗元件的类型,可以将任意一种接地型分数阶记忆元件转换为任意一种浮地型分数阶记忆元件。在仿真实验中,根据提出的通用等效电路,分别实现了三种分数阶记忆元件。对三种分数阶记忆元件的特性进行了分析,验证了该等效电路的正确性。     

Analysis of 3-D interconnect structures with PEEC using SPICE

This paper discusses the possibilities of using the circuit simulation program, simulation program with integrated circuit emphasis (SPICE) for the simulation of partial element equivalent circuit (PEEC) models. After an introduction into the PEEC method, the simulation of quasi-stationary models is considered. An enhancement of SPICE is described, allowing the simulation of retarded PEEC models. This enables the computation of electric fields radiated from an interconnection structure. With the modified SPICE simulator it is possible to use existing SPICE models and combine them with full wave PEEC models     

An efficient PEEC algorithm for modeling of LTCC RF circuits with finite metal strip thickness

In this letter, a simple but effective method is introduced to facilitate the partial element equivalent circuit (PEEC) algorithm to model multilayered low-temperature co-fired ceramics (LTCC) embedded RF circuits with finite metal thickness. The method makes use of the quasistatic assumption that charges only reside on the surfaces of a conductor. In the calculation of the coefficient of potential matrix, one thick conductor plate is treated as two inter-connected zero-thickness plates. Recombining the two plates analytically can correctly account for the increase of plate-to-plate capacitance without adding extra elements to the resultant equivalent circuit model. Experimental results have verified the validation of the proposed method.     

Broadband Macromodels for Retarded Partial Element Equivalent Circuit (rPEEC) Method

The partial element equivalent circuit (PEEC) method is, nowadays, widely used in electromagnetic compatibility and signal integrity problems in both the time and frequency domains. Similar to other integral-equation-based techniques, its time domain implementation may suffer from late time instabilities, especially when considering delays [(Lp,P,R,tau)PEEC] (rPEEC). The cause of the instabilities may be either the numerical technique used for the time integration or problems created by the discrete representation of the electromagnetic continuous problem. In this paper, we concentrate on the latter and show that frequency dispersion plays an important role and must be taken into account in order to preserve accuracy and mitigate instabilities issues. An enhanced formulation of the PEEC method is presented that is based on a more accurate computation of partial elements describing the electric and magnetic field couplings; broadband macromodels are generated incorporating the frequency dependence of such elements, thus, allowing us to obtain better stability properties of the resulting (Lp,P,R,tau)PEEC model. The proposed equivalent circuits resemble those of the standard PEEC formulation but are able to capture the dispersion that, when neglected, might contribute to inaccuracies and late time instabilities     

A new element-saving equivalent circuit for the analysis of generalcoupled n-wire transmission lines

A novel efficient method for modeling the general coupled n -wire transmission line is proposed. The equivalent circuit presented has the following advantages: (1) no balanced lines are needed; (2) all element values are positive; and (3) the number of elements required by the equivalent circuit is at most equal to the number of nonzero couplings plus one. A simple method for deriving the equivalent circuit is outlined. Examples are supplied to show the application of the method     

VLSI局部电源网络的宏模型研究

针对大规模VLSI电源网络分析效率问题,提出一种局部电源网络宏模型求解方法,根据其结构特点,结合电路等效变换与电路合并,对电路模型进行简化,并建立其宏模型.在全局电源网络分析中,利用各局部电源网络宏模型替代其完整电路模型,以降低分析问题的规模与复杂度.实验结果表明,在电源网络分析中应用宏模型技术,可以将分析效率提高1.7倍,且性能随电源网络规模的增大而提高.     

Small signal equivalent circuit modeling of resonant converters

A general analytical procedure is presented for the equivalent circuit modeling of resonant converters, using the series and parallel resonant converters as examples. The switched tank elements of a resonant converter are modeled by a lumped parameter equivalent circuit. The tank element circuit model consists, in general, of discrete energy states, but may be approximated by a low-frequency continuous time model. These equivalent circuit models completely characterize the terminal behavior of the converters and are solvable for any transfer function or impedance of interest. With the approximate model it is possible to predict the lumped parameter poles and zeros, and to quickly determine the relevant DC gains of the output impedance and the control to output transfer function. Closed-form solutions are given for the equivalent circuit models of both converter examples. Experimental verification is presented for the control-to-output transfer functions of both series and parallel resonant converters, and good agreement between theoretical prediction and experimental measurement is obtained     

Unstructured PEEC formulation by dual discretization

This letter presents a new lumped parameter approach for the solution of the electromagnetic problem of a system of conductors lying in a homogeneous region. By exploiting duality relations between two systems of meshes, an equivalent network of lumped parameters is obtained. This approach is conceptually equivalent to the partial element equivalent circuit formulation but it can overcome the limits imposed by a regular discretization present in its original version. Details about computation of lumped parameters and definition of equivalent network are given. Results obtained on two configurations referenced in the literature are finally discussed.     

Circuit models for three-dimensional geometries includingdielectrics

The partial element equivalent circuit (PEEC) approach has proved useful for modeling many different electromagnetic problems. The technique can be viewed as an approach for the electrical circuit modeling for arbitrary 3-D geometries. Recently, the authors extended the method to include retardation with the rPEEC models. So far the dielectrics have been taken into account only in an approximate way. In this work, they generalize the technique to include arbitrary homogeneous dielectric regions. The new circuit models are applied in the frequency as well as the time domain. The time solution allows the modeling of VLSI systems which involve interconnects as well as nonlinear transistor circuits     

Impact of partial element accuracy on PEEC model stability

This paper details the impact of partial element accuracy on quasi-static partial element equivalent circuit (PEEC) model stability in the time domain. The potential sources of inaccurate partial element values are found to be poor geometrical meshing and the use of unsuitable partial element calculation routines. The impact on PEEC model stability of erroneous partial element values, and the coefficients of potential and partial inductances, are shown as theoretical constraints and practical results. Projection meshing, which is a discretization strategy suitable for the PEEC method, is shown to improve calculated partial element values for the same number of unknowns, thus improving model stability.     

高速双面共面结构印刷电路板电特性仿真

为了适应高速双面共面印刷电路板的不规则布线结构,本文采用三维电磁参数提取的部分元等效电路方法对任意形状接地/馈电板进行自动分割及单元建模,然后对包括I/O缓冲器在内的非线性电路进行时域信号响应分析.高速双面共面结构印刷电路板电特性的仿真与实际测试结果吻合较好,表明了方法的有效性.