New Single-Source Surface Integral Equation for Magneto-Quasi-Static Characterization of Transmission Lines Situated in Multilayered Media

Zheng, Shucheng; Menshov, Anton; Okhmatovski, Vladimir

doi:10.1109/tmtt.2016.2623625

Cited by 15 publications

(7 citation statements)

References 23 publications

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“…To illustrate, we assume we have a top buffer region which is filled with dielectric L so that it is the same as the Lth layer in the region of interest (ROI), and choose [24], [31]…”

Section: An Extension To Unshielded Layered Mediummentioning

confidence: 99%

“…These methods are generally inexpensive for 1D problems, robust, and when formulated in their high-order form, provide exponentially effective error control in the rational function approximation of the Green's function spectrum. Since the resultant pole-residue approximation of the spectral domain solution enables analytic evaluation of the SIs, the proposed adaptive SDEAM produces spatial Green's function approximations that are O(h p ) accurate, when pth order FEM or DGM schemes are implemented using adaptive meshing with element sizes h. In this work, the description of the SDEAM is provided for electro-quasistatic problems; magneto-quasistatic problems can similarly be solved using SDEAM with minor modifications [24].…”

Section: Introductionmentioning

confidence: 99%

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Error-Controlled Static Layered-Medium Green’s Function Computation via hp-Adaptive Spectral Differential Equation Approximation Method

Jeffrey

Al-Qedra

et al. 2021

IEEE Trans. Compon., Packag. Manufact. Technol.

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A numerically robust and computationally efficient approach for evaluating a planar layered substrate's static Green's function is developed based on the adaptive form of the Spectral Differential Equation Approximation Method. The method uses a pth order finite element method solution of the one-dimensional ordinary differential equation governing the spectrum of the layered media Green's function with spatial hadaptive meshing. The resulting pole-residue form of the Green's function spectrum enables analytic evaluation of the pertinent Sommerfeld integrals providing O(h p ) error control of the spatial layered medium Green's function in near, intermediate, and far zones. Detailed error analysis is presented enabling automation of the 1-Dimensional Finite Element Method mesh refinement, which guarantees a prescribed accuracy of the solution depending on the distance between the source and observation locations. The method is well-suited for computing Green's function databases used by method of moments capacitance and inductance extractors.

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“…To illustrate, we assume we have a top buffer region which is filled with dielectric L so that it is the same as the Lth layer in the region of interest (ROI), and choose [24], [31]…”

Section: An Extension To Unshielded Layered Mediummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error-Controlled Static Layered-Medium Green’s Function Computation via hp-Adaptive Spectral Differential Equation Approximation Method

Jeffrey

Al-Qedra

et al. 2021

IEEE Trans. Compon., Packag. Manufact. Technol.

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“…The vector equations ( 28) and ( 32) are tested with n×RWG functions, while the scalar equations ( 29) and ( 33) are tested with h n ( r) /A n . To assemble the final system of equations, the discrete versions of ( 32), ( 28), ( 33), (29), and the KVL equations (35) and (36), are concatenated. The resulting system of equations ( 52) is at the top of the following page.…”

Section: F Final System Of Equationsmentioning

confidence: 99%

“…In (28) (29), and (30), the symbol − ´and dashes through the operators indicate that the associated integrals are computed in a principal value sense [11].…”

mentioning

confidence: 99%

Electromagnetic Modeling of Lossy Interconnects From DC to High Frequencies With a Potential-Based Boundary Element Formulation

Sharma,

Triverio

2021

Preprint

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The accurate electromagnetic modeling of both lowand high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling because it can capture the frequency-dependent variation of skin depth with only a surface-based discretization of the structure. Conventional BEM formulations rely on the mutual coupling of electric and magnetic fields, and can become inaccurate or unstable at low frequencies. We develop a new full-wave BEM formulation based on potentials which can accurately model lossy conductors from exactly DC to very high frequencies. A new set of simple boundary conditions is proposed along with a modified Lorenz gauge to ensure that the proposed formulation has a stable condition number down to DC. Moreover, coupling the potential-based integral equations to a circuit model allows the straightforward extraction of network parameters. Realistic numerical examples at both the chip and package level demonstrate the accuracy and stability of the proposed method from DC to high frequencies, beyond the capabilities of state-of-the-art BEM formulations based on fields.

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“…Often, the proposed methods rely on the (surface-based) boundary integral equation (BIE) approach [1], [5] or resort to the finite element method (FEM) and its volumetric discretization [6]- [9]. Alternative schemes include the volume integral equation (VIE) applied in the partial element equivalent circuit (PEEC) method [10] and the hybrid surface-volumesurface electric field integral equation (SVS-EFIE) approach, involving both contour and volume meshes [11].…”

Section: Introductionmentioning

confidence: 99%

Efficient Characterization of Interconnects with Arbitrary Polygonal Cross-sections using Fokas-derived Dirichlet-to-Neumann Operators

Ginste¹

2023

Preprint

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<p>A novel technique to accurately characterize interconnects with general, piecewise homogeneous material parameters and arbitrary polygonal cross-sections is presented. To compute the per-unit-of-length complex inductance and capacitance matrices of the considered structures, we apply a boundary integral equation framework, invoking a Dirichlet-to-Neumann formalism to recast the problem at hand. The pertinent operators are constructed by means of the numerically fast Fokas method. Numerical examples of various multiconductor transmission lines demonstrate that our proposed scheme is flexible and precise. Since our method is not limited to rectangular cross-sections, manufacturing effects such as etching can also be taken into account. Moreover, the examples are not restricted to RLGC-data as we also consider signal attenuation, slow-wave factors and cross-talk.</p>

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New Single-Source Surface Integral Equation for Magneto-Quasi-Static Characterization of Transmission Lines Situated in Multilayered Media

Cited by 15 publications

References 23 publications

Error-Controlled Static Layered-Medium Green’s Function Computation via hp-Adaptive Spectral Differential Equation Approximation Method

Error-Controlled Static Layered-Medium Green’s Function Computation via hp-Adaptive Spectral Differential Equation Approximation Method

Electromagnetic Modeling of Lossy Interconnects From DC to High Frequencies With a Potential-Based Boundary Element Formulation

Efficient Characterization of Interconnects with Arbitrary Polygonal Cross-sections using Fokas-derived Dirichlet-to-Neumann Operators

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