Partial Element Equivalent Circuit Technique Research Articles

Frequency response and transient analysis of through glass packaging vias using matrix-rational approximation (MRA) technique for three-dimensional ICs

In this paper, a computationally efficient matrix rational approximation (MRA) technique is developed to analyze the electrical behaviour of through packaging vias in glass interposer (TGVs). Using MRA technique, the electrical behaviour of TGVs utilizing differential multi-bit configuration, filled with composite copper-mixed carbon nanotube bundle (Cu-mCNTB), is investigated. A temperature-dependent π-type equivalent circuit of such differential multi-bit (DM) composite TGVs is developed using partial-element equivalent-circuit technique. The effective complex conductivity of Cu-mCNTB is also derived by appropriately considering the effects of temperature-dependent mean free path in CNTs. The frequency dependent differential- and common-mode impedances are obtained up to 100 GHz through PEEC technique. It is analyzed that composite DM-TGVs outperform silicon via counterparts in terms of reduced insertion loss using proposed MRA technique and verified through high-frequency structure simulator (HFSS). The transient analysis including crosstalk-induced propagation delay, peak crosstalk, and peak timing of coupled Cu-mCNTB/composite DM-TGVs is determined through the proposed MRA model, which exhibits error within 1% compared to the SPICE. The robustness of proposed model is examined under a wide variety of test cases including the proposed 5-Cu-mCNTB composite TGV array. For the transient analysis, the CPU runtime using the MRA model is 18.57 × faster than the SPICE. To the best of the authors’ knowledge, it is for the first time that temperature-dependent modeling and crosstalk analysis of coupled TGV structures is reported using MRA technique.

Partial-inductance retarded partial coefficients: Their exact computation based on the Cagniard–DeHoop technique

The Partial Element Equivalent Circuit (PEEC) method is a well recognized integral-equation (IE) technique to solve Maxwell’s equations. Similarly to the method of moments (MoM), the electromagnetic (EM) interactions between currents and between charges are described in terms of integrals. In contrast to the standard MoM, the PEEC method keeps the electric and magnetic coupling phenomena separate, which leads to different interaction integrals to be computed. These integrals admit simplified solutions for the case of the static free-space Green’s function and orthogonal geometries but their applicability is limited to electrically small problems only. When the full-wave free-space Green’s function is considered, the integrals are typically computed in the frequency domain (FD) by resorting to Gaussian quadrature schemes. The accuracy and efficiency of such schemes is a delicate issue. Therefore, recent works have investigated the possibility of applying the Cagniard–DeHoop (CdH) technique to calculate the interaction integrals for zero-thickness elementary domains. In this paper, we close the loop and shall apply the CdH technique to calculate the partial-inductance between two elementary bricks as prescribed by the PEEC technique exactly in the time domain (TD). The analytical approach is demonstrated on the interaction between two bricks as it occurs in the modeling of the magnetic field coupling between volumetric currents. The accuracy of the proposed approach is (successfully) tested for two representative cases.

Research on Calculation of Rail Self-Impedance of Track Circuit Based on Partial Element Equivalent Circuit

The self-impedance of the steel rail, as the signal transmission medium in the electrified railway track circuit, has a direct impact on the track circuit’s transmission performance. The finite element method is the most common method for calculating rail impedance, although it has a number of drawbacks, including a complicated model, a long computation time, and poor accuracy. The partial element equivalent circuit (PEEC) approach is used in this paper to provide a method for determining rail self-impedance. Firstly, the rail equivalent method is determined by analyzing the physical model of the rail. Considering the skin effect, the PEEC model of the rail is established. The internal impedance of the rail can be obtained by solving the equivalent circuit. The external impedance considering the influence of the earth is calculated by the Carson impedance calculation formula, which is processed by the segmented linear approximation method. The rail’s self-impedance is determined using the two procedures together. Finally, the actual measurement data verified the PEEC method to calculate the rail impedance. Compared with the finite element method (FEM), the calculation accuracy of the PEEC method is higher. The current frequency, the height of the rail from the ground, and the earth’s conductivity impact on the rail’s self-impedance are analyzed. The results show that the PEEC technique can be used to calculate the rail’s self-impedance and that the impact of current frequency, rail height above the ground, and ground conductivity on the rail’s self-impedance may be accurately represented. The self-impedance computation of the track circuit provides a theoretical basis.

Fast Distributed Simulation of “Defect-Irrelevant” Behaviors of No-Insulation HTS Coil

This paper proposes a new equivalent circuit model to calculate current distribution in an NI (no-insulation) high temperature superconductor (HTS) coil that contains a defect. When the well-known defect irrelevant behaviors of an NI HTS coil are analyzed, the so-called partial element equivalent circuit (PEEC) technique has been commonly adopted. However, the PEEC technique often takes an extremely long time, days or even weeks, for just a single simulation depending on the number of internal elements within the target NI coil. Here we propose an alternative method that may substantially reduce computation time and load in distributed simulation of the defect-irrelevant behaviors of an NI HTS coil. We showed that the current sharing region of an NI coil containing a defect could be divided into 5 segments, and an equivalent circuit, which is named “B model” as the equivalent circuit resembles the alphabet “B,” could be constructed using circuit parameters in each segment. Using the proposed method that significantly simplifies the existing PEEC model, we successfully simulated the defect-irrelevant behaviors of an NI HTS single pancake coil, essentially the local current sharing between the defect spot and its healthy neighboring turns.

Investigation of low‐frequency behaviour of two surface integral full‐Maxwell formulations

PurposeTo apply two different integral formulations of full‐Maxwell's equations to the numerical study of interconnects in a low‐frequency range and compare the results.Design/methodology/approachThe first approach consists of a surface formulation of the full‐Maxwell's equations in terms of potentials, giving rise to a surface electric field integral equation. The equation, given in a weak form, is solved by using a finite element technique. The solenoidal and non‐solenoidal components of the electric current density are separated using the null‐pinv decomposition to avoid the low‐frequency breakdown. The second model is an extension of partial element equivalent circuit technique to unstructured meshes allowing the use of triangular meshes. Two systems of meshes tied by duality relations are defined on multiconductor systems. The key point in the definition of the equivalent network is to associate the pair primal edge/dual face to a circuit branch. Solution of the resulting electrical network is performed by a modified nodal analysis method and regularization of the outcoming matrix is accomplished by standard techniques based on the addition of suitable resistors.FindingsBoth the formulation have a regular behaviour at very low frequency. This is automatically achieved in the first approach by using the null‐pinv decomposition.Research limitations/implicationsSurface sources of fields.Originality/valueTwo different integral formulations of full‐Maxwell's equations for the numerical study of interconnects are compared in terms of low‐frequency behaviour.

A fast PEEC technique for full-wave parameters extraction of distributed elements

In this paper, a full wave partial element equivalent circuit (PEEC) technique using exact Green's function is introduced for the parameter extraction of a passive device in a homogeneous media over a wide frequency range from de to a frequency of interest. This technique makes use of some analytical techniques and cartesian multipole expansion to derive simple closed form expressions for each individual element of the coupling matrices that commonly arise in integral equation algorithms, in terms of the wave number alone. Hence, these matrices can be reused each time a new frequency is selected. As simple closed form expressions are used, very fast computation is possible.

A prediction model for electromagnetic interferences radiated by an industrial power drive system

Power conversion systems and in particular power drives are now present in a large number of applications and environments. The switching operations of power drive systems (PDS) are sources of radiated and conducted electromagnetic interferences that give rise to problems of electromagnetic compatibility with other systems. This work proposes an efficient numerical technique to evaluate the radiated emissions due to a PDS, taking into account the radiation from intentional apertures (i.e. those for ventilation). The power section of the PDS is simulated by a combination of radiating dipoles in which the current is known. The radiated EM field induces currents on the PDS metallic cage surface that in turn radiate outside the cage. These currents are computed by an efficient numerical method known as partial element equivalent circuit technique. Finally an equivalent EM model for the apertures needed for the air cooling and ventilation of the device is given. The proposed prediction model is hence able to predict the total radiated emission from a PDS in its design stage in order to fulfil the electromagnetic compatibility requirements called by the international standards.

Modeling of multiconductor systems for packaging and interconnecting high-speed digital IC's

In the design of high-speed circuits, it is important to consider the adverse effects of packaging and interconnections on signal integrity. A review of quasi-TEM capacitance and inductance analysis of multiconductor transmission line systems is presented. The development of three general modeling techniques is discussed, namely, the boundary element method, the finite element method, and the partial element equivalent circuit technique. The application of each method to practical systems is outlined, with particular reference to the literature. A complete formulation for the boundary element, which is applicable to multiconductor systems of arbitrary geometry in nonhomogeneous media, is provided. The analysis of a seven-line buried microstrip structure illustrates the main differences between the finite element and boundary element approaches.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>