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Three different shielding structures for noise coupling suppression between through silicon vias (TSVs) are proposed in this manuscript. These structures are modeled using the 3-dimensional transmission line matrix (3D-TLM) method, and the model is verified using EM-simulation. The shielding structures are analyzed with regard to consumption area, manufacturing process compatibility, and noise isolation...
The thin, high-contrast, fine layers with dielectric and conductive properties, such as ground planes, are feature structures in IC packagings. Their responses to the pulsed electromagnetic field is important both theoretically and practically. In this paper, a new semi-analytical method is proposed to model the interaction of the layer with an incident electromagnetic field via a boundary condition...
An efficient approach based on adjoint sensitivity is presented for time-domain sensitivity analysis of linear and networks containing lossy transmission lines. The sensitivity of an output with respect to all parameters of interest can be calculated by simulating the original and adjoint circuits simultaneously. The proposed approach provides a significant decrease in the computational expense for...
This paper focuses on the derivation of an enhanced transmission-line model allowing to describe a realistic high-speed interconnect with the inclusion of external uncertainties, like tolerances or process variations. The proposed method, that is based on the expansion of the well-known telegraph equations in terms of Hermite polynomials, turns out to be accurate and more efficient than alternative...
This paper describes a straightforward mathematical method to approximate the signal at the die pad using a time-domain convolution method and the measured signal at the pin. The paper shows how a step-response of the pin and pad signal, either measured or simulated, can be converted into a time-domain convolution filter. Then, using this filter with MATLAB or other mathematical software, captured...
Bottom Surface Metals (BSM) pin assignment for high frequency signals on a package device is a tedious manual job. Recently, [3] proposed a network flow based method to assign BSM automatically for one layer without routing blockages. In this paper, we extend the work of [3] to do BSM pin assignment on multiple layers with routing blockages. [3] also considers BSM differential pairing constraints,...
Existing delay-based convolution macromodels for S-parameters of electrical interconnects can compromise accuracy. This paper solves this problem by extending the recently-proposed convolution-based macromodeling method called least-squares convolution (LSC) to model propagation delays. The new method is referred to as the delayed LSC (DLSC) method.
This paper proposes a closed-form empirical equation to account for the eddy-current loss due to metal fill. For a given average magnetic field the formula estimates the loss due to in-plane fills. The formula was developed over a wide range of dimensions and frequencies up to 50 GHz, and was found to be accurate to within 8% over this range. We also verify the formula using an example microstrip.
This paper presents an evolutionary algorithm for symbolic macromodeling of parameterized frequency responses. The method does not require an a priori specification of the multivariate functional form or complexity of the model. Numerical results are shown to illustrate the performance of the technique.
This paper discusses the challenges in system level timing closure of a high speed DDR interface. The different aspects of the DDR controller, I/O buffer, package and board to be modeled for ensuring stable operation at the targeted speed are described.
With increasing demand on higher performance for I/O links, equalization in transmitters and receivers has been identified as a critical contributor that can improve the opening of the eye. This paper describes a method to optimize the equalization using zeroforcing to maximize I/O performance and its application to a realistic high-speed functioning system. Both hardware characterization and simulation...
This paper presents the electrical characterization of annular TSV technology for full wafer applications. A possible utilization of this technology is the WaferBoard™, a reconfigurable circuit board for rapid system prototyping. Electrical resistance and capacitance of a single 2-4µm thick annular TSV with a diameter of 110µm and a height of 350µm are measured to be about 10mΩ and 0.27 pF, respectively...
A causality checker is developed and used to validate and improve S-parameter data computed with a commercial 3D electromagnetic simulator. Improved data quality as shown by the causality checker is demonstrated to fix a flawed SerDes link simulation and an impedance extraction based on a TDR simulation. It is demonstrated that simple examination of the S-parameters cannot differentiate between good...
An efficient clustering scheme for macromodeling of massively coupled interconnect structures is presented. The proposed method addresses the issue of dense reduced models through a novel reduction algorithm that leads to sparse block-diagonal system matrices. It also overcomes the accuracy degradation, normally associated with the existing port-reduction techniques.
It has been observed that a finite-element based solution of full-wave Maxwell's equations breaks down at low frequencies. Existing approaches have not rigorously solved the problem yet since they rely on low-frequency approximations. Moreover, little work has been reported for overcoming the low-frequency breakdown for realistic circuit problems in which dielectrics and non-ideal conductors coexist...
A novel defected ground structure (DGS) with mushroom structures is proposed. This structure is a three-layer structure composed of a patterned metal plane on the top layer and mushroom structures occupying the second and the third layer. It can be applied to a multilayer structure with lower radiation compared with conventional DGS due to its well shielding. Based on slow wave characteristic, this...
We describe the inclusion of parametric behavioral macromodels within the Transmission-Line Modelling (TLM) method. The macromodels reproduce the input/output port nonlinear behavior of digital integrated circuit (IC). They are integrated in the 3D electromagnetic full-field code Minisolve either through a current source or conductance of the medium. The numerical results are compared to experimental...
We address the problem of parametric model order reduction given measurements of the response of a device performed with respect to frequency, and also with respect to a design parameter, which could relate to its geometry or material properties. The proposed approach is based on a generalization of the Loewner matrix [12] to the case when data depend on two variables, namely frequency and a design...
Causality of tabulated data is detected by checking for Hilbert-consistency between data's real and imaginary parts. This consistency can be robustly checked if the generalized Hilbert transform is used. Existing algorithms evaluate an integral in this transform numerically. In this paper, a new algorithm for checking causality that involves only analytical integration is presented.
An I/O design framework is presented which combines statistical link analysis with circuit power models to predict the power-optimum equalization architecture, circuit style, and transmit swing at a given data rate, channel, and process node.
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